id	sid	tid	token	lemma	pos
ejpam-1535	1	1	2_hollings.dvi	2_hollings.dvi	NUM
ejpam-1535	1	2	european	european	ADJ
ejpam-1535	1	3	journal	journal	NOUN
ejpam-1535	1	4	of	of	ADP
ejpam-1535	1	5	pure	pure	ADJ
ejpam-1535	1	6	and	and	CCONJ
ejpam-1535	1	7	applied	apply	VERB
ejpam-1535	1	8	mathematics	mathematic	NOUN
ejpam-1535	1	9	vol	vol	NOUN
ejpam-1535	1	10	.	.	PROPN
ejpam-1535	1	11	5	5	NUM
ejpam-1535	1	12	,	,	PUNCT
ejpam-1535	1	13	no	no	INTJ
ejpam-1535	1	14	.	.	NOUN
ejpam-1535	1	15	4	4	NUM
ejpam-1535	1	16	,	,	PUNCT
ejpam-1535	1	17	2012	2012	NUM
ejpam-1535	1	18	,	,	PUNCT
ejpam-1535	1	19	414	414	NUM
ejpam-1535	1	20	-	-	SYM
ejpam-1535	1	21	450	450	NUM
ejpam-1535	1	22	issn	issn	PROPN
ejpam-1535	1	23	1307	1307	NUM
ejpam-1535	1	24	-	-	SYM
ejpam-1535	1	25	5543	5543	NUM
ejpam-1535	1	26	–	–	PUNCT
ejpam-1535	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1535	1	28	the	the	DET
ejpam-1535	1	29	ehresmann	ehresmann	PROPN
ejpam-1535	1	30	–	–	PUNCT
ejpam-1535	1	31	schein	schein	PROPN
ejpam-1535	1	32	–	–	PUNCT
ejpam-1535	1	33	nambooripad	nambooripad	NOUN
ejpam-1535	1	34	theorem	theorem	NOUN
ejpam-1535	1	35	and	and	CCONJ
ejpam-1535	1	36	its	its	PRON
ejpam-1535	1	37	successors	successor	NOUN
ejpam-1535	1	38	christopher	christopher	PROPN
ejpam-1535	1	39	hollings	holling	VERB
ejpam-1535	1	40	the	the	DET
ejpam-1535	1	41	queen	queen	PROPN
ejpam-1535	1	42	’s	’s	PART
ejpam-1535	1	43	college	college	NOUN
ejpam-1535	1	44	,	,	PUNCT
ejpam-1535	1	45	oxford	oxford	PROPN
ejpam-1535	1	46	,	,	PUNCT
ejpam-1535	1	47	ox1	ox1	PROPN
ejpam-1535	1	48	4aw	4aw	NOUN
ejpam-1535	1	49	,	,	PUNCT
ejpam-1535	1	50	uk	uk	PROPN
ejpam-1535	1	51	abstract	abstract	NOUN
ejpam-1535	1	52	.	.	PUNCT
ejpam-1535	2	1	the	the	DET
ejpam-1535	2	2	ehremann	ehremann	PROPN
ejpam-1535	2	3	–	–	PUNCT
ejpam-1535	2	4	schein	schein	PROPN
ejpam-1535	2	5	–	–	PUNCT
ejpam-1535	2	6	nambooripad	nambooripad	PROPN
ejpam-1535	2	7	theorem	theorem	NOUN
ejpam-1535	2	8	expresses	express	VERB
ejpam-1535	2	9	the	the	DET
ejpam-1535	2	10	fundamental	fundamental	ADJ
ejpam-1535	2	11	connection	connection	NOUN
ejpam-1535	2	12	between	between	ADP
ejpam-1535	2	13	the	the	DET
ejpam-1535	2	14	notions	notion	NOUN
ejpam-1535	2	15	of	of	ADP
ejpam-1535	2	16	inverse	inverse	NOUN
ejpam-1535	2	17	semigroups	semigroup	NOUN
ejpam-1535	2	18	and	and	CCONJ
ejpam-1535	2	19	inductive	inductive	ADJ
ejpam-1535	2	20	groupoids	groupoid	NOUN
ejpam-1535	2	21	,	,	PUNCT
ejpam-1535	2	22	which	which	PRON
ejpam-1535	2	23	exists	exist	VERB
ejpam-1535	2	24	because	because	SCONJ
ejpam-1535	2	25	these	these	DET
ejpam-1535	2	26	concepts	concept	NOUN
ejpam-1535	2	27	provide	provide	VERB
ejpam-1535	2	28	two	two	NUM
ejpam-1535	2	29	distinct	distinct	ADJ
ejpam-1535	2	30	approaches	approach	NOUN
ejpam-1535	2	31	to	to	ADP
ejpam-1535	2	32	the	the	DET
ejpam-1535	2	33	study	study	NOUN
ejpam-1535	2	34	of	of	ADP
ejpam-1535	2	35	one	one	NUM
ejpam-1535	2	36	-	-	PUNCT
ejpam-1535	2	37	one	one	NUM
ejpam-1535	2	38	partial	partial	ADJ
ejpam-1535	2	39	transformations	transformation	NOUN
ejpam-1535	2	40	.	.	PUNCT
ejpam-1535	3	1	in	in	ADP
ejpam-1535	3	2	the	the	DET
ejpam-1535	3	3	case	case	NOUN
ejpam-1535	3	4	of	of	ADP
ejpam-1535	3	5	arbitrary	arbitrary	ADJ
ejpam-1535	3	6	partial	partial	ADJ
ejpam-1535	3	7	transformations	transformation	NOUN
ejpam-1535	3	8	,	,	PUNCT
ejpam-1535	3	9	the	the	DET
ejpam-1535	3	10	analogous	analogous	ADJ
ejpam-1535	3	11	two	two	NUM
ejpam-1535	3	12	approaches	approach	NOUN
ejpam-1535	3	13	are	be	AUX
ejpam-1535	3	14	provided	provide	VERB
ejpam-1535	3	15	by	by	ADP
ejpam-1535	3	16	restriction	restriction	NOUN
ejpam-1535	3	17	semigroups	semigroup	NOUN
ejpam-1535	3	18	and	and	CCONJ
ejpam-1535	3	19	inductive	inductive	ADJ
ejpam-1535	3	20	categories	category	NOUN
ejpam-1535	3	21	,	,	PUNCT
ejpam-1535	3	22	the	the	DET
ejpam-1535	3	23	former	former	ADJ
ejpam-1535	3	24	being	being	NOUN
ejpam-1535	3	25	generalisations	generalisation	NOUN
ejpam-1535	3	26	of	of	ADP
ejpam-1535	3	27	inverse	inverse	NOUN
ejpam-1535	3	28	semigroups	semigroup	NOUN
ejpam-1535	3	29	,	,	PUNCT
ejpam-1535	3	30	and	and	CCONJ
ejpam-1535	3	31	the	the	DET
ejpam-1535	3	32	latter	latter	ADJ
ejpam-1535	3	33	of	of	ADP
ejpam-1535	3	34	inductive	inductive	ADJ
ejpam-1535	3	35	groupoids	groupoid	NOUN
ejpam-1535	3	36	.	.	PUNCT
ejpam-1535	4	1	there	there	PRON
ejpam-1535	4	2	is	be	VERB
ejpam-1535	4	3	indeed	indeed	ADV
ejpam-1535	4	4	also	also	ADV
ejpam-1535	4	5	a	a	DET
ejpam-1535	4	6	generalisation	generalisation	NOUN
ejpam-1535	4	7	of	of	ADP
ejpam-1535	4	8	the	the	DET
ejpam-1535	4	9	ehremann	ehremann	PROPN
ejpam-1535	4	10	–	–	PUNCT
ejpam-1535	4	11	schein	schein	PROPN
ejpam-1535	4	12	–	–	PUNCT
ejpam-1535	4	13	nambooripad	nambooripad	NOUN
ejpam-1535	4	14	theorem	theorem	NOUN
ejpam-1535	4	15	which	which	PRON
ejpam-1535	4	16	encapsulates	encapsulate	VERB
ejpam-1535	4	17	the	the	DET
ejpam-1535	4	18	connection	connection	NOUN
ejpam-1535	4	19	between	between	ADP
ejpam-1535	4	20	these	these	DET
ejpam-1535	4	21	two	two	NUM
ejpam-1535	4	22	more	more	ADV
ejpam-1535	4	23	general	general	ADJ
ejpam-1535	4	24	objects	object	NOUN
ejpam-1535	4	25	.	.	PUNCT
ejpam-1535	5	1	in	in	ADP
ejpam-1535	5	2	this	this	DET
ejpam-1535	5	3	article	article	NOUN
ejpam-1535	5	4	,	,	PUNCT
ejpam-1535	5	5	we	we	PRON
ejpam-1535	5	6	will	will	AUX
ejpam-1535	5	7	explore	explore	VERB
ejpam-1535	5	8	the	the	DET
ejpam-1535	5	9	origins	origin	NOUN
ejpam-1535	5	10	of	of	ADP
ejpam-1535	5	11	these	these	DET
ejpam-1535	5	12	theorems	theorem	NOUN
ejpam-1535	5	13	,	,	PUNCT
ejpam-1535	5	14	and	and	CCONJ
ejpam-1535	5	15	survey	survey	VERB
ejpam-1535	5	16	the	the	DET
ejpam-1535	5	17	basic	basic	ADJ
ejpam-1535	5	18	theory	theory	NOUN
ejpam-1535	5	19	surrounding	surround	VERB
ejpam-1535	5	20	them	they	PRON
ejpam-1535	5	21	.	.	PUNCT
ejpam-1535	6	1	2010	2010	NUM
ejpam-1535	6	2	mathematics	mathematic	NOUN
ejpam-1535	6	3	subject	subject	NOUN
ejpam-1535	6	4	classifications	classification	NOUN
ejpam-1535	6	5	:	:	PUNCT
ejpam-1535	6	6	20m18	20m18	NUM
ejpam-1535	6	7	,	,	PUNCT
ejpam-1535	6	8	20l05	20l05	NUM
ejpam-1535	6	9	key	key	ADJ
ejpam-1535	6	10	words	word	NOUN
ejpam-1535	6	11	and	and	CCONJ
ejpam-1535	6	12	phrases	phrase	NOUN
ejpam-1535	6	13	:	:	PUNCT
ejpam-1535	6	14	restriction	restriction	NOUN
ejpam-1535	6	15	semigroup	semigroup	PROPN
ejpam-1535	6	16	,	,	PUNCT
ejpam-1535	6	17	inductive	inductive	ADJ
ejpam-1535	6	18	category	category	NOUN
ejpam-1535	6	19	,	,	PUNCT
ejpam-1535	6	20	inverse	inverse	NOUN
ejpam-1535	6	21	semigroup	semigroup	PROPN
ejpam-1535	6	22	,	,	PUNCT
ejpam-1535	6	23	inductive	inductive	ADJ
ejpam-1535	6	24	groupoid	groupoid	PROPN
ejpam-1535	6	25	1	1	X
ejpam-1535	6	26	.	.	PUNCT
ejpam-1535	7	1	introduction	introduction	NOUN
ejpam-1535	7	2	the	the	DET
ejpam-1535	7	3	ehresmann	ehresmann	PROPN
ejpam-1535	7	4	–	–	PUNCT
ejpam-1535	7	5	schein	schein	PROPN
ejpam-1535	7	6	–	–	PUNCT
ejpam-1535	7	7	nambooripad	nambooripad	PROPN
ejpam-1535	7	8	theorem	theorem	NOUN
ejpam-1535	7	9	(	(	PUNCT
ejpam-1535	7	10	hereafter	hereafter	ADV
ejpam-1535	7	11	,	,	PUNCT
ejpam-1535	7	12	“	"	PUNCT
ejpam-1535	7	13	esn	esn	PROPN
ejpam-1535	7	14	theorem	theorem	PROPN
ejpam-1535	7	15	”	"	PUNCT
ejpam-1535	7	16	)	)	PUNCT
ejpam-1535	7	17	was	be	AUX
ejpam-1535	7	18	first	first	ADV
ejpam-1535	7	19	formulated	formulate	VERB
ejpam-1535	7	20	explicitly	explicitly	ADV
ejpam-1535	7	21	by	by	ADP
ejpam-1535	7	22	lawson	lawson	PROPN
ejpam-1535	7	23	[	[	X
ejpam-1535	7	24	29	29	NUM
ejpam-1535	7	25	,	,	PUNCT
ejpam-1535	7	26	theorem	theorem	VERB
ejpam-1535	7	27	4.1.8	4.1.8	NUM
ejpam-1535	7	28	]	]	PUNCT
ejpam-1535	7	29	,	,	PUNCT
ejpam-1535	7	30	bringing	bring	VERB
ejpam-1535	7	31	together	together	ADV
ejpam-1535	7	32	the	the	DET
ejpam-1535	7	33	work	work	NOUN
ejpam-1535	7	34	of	of	ADP
ejpam-1535	7	35	the	the	DET
ejpam-1535	7	36	three	three	NUM
ejpam-1535	7	37	named	name	VERB
ejpam-1535	7	38	authors	author	NOUN
ejpam-1535	7	39	.	.	PUNCT
ejpam-1535	8	1	this	this	DET
ejpam-1535	8	2	theorem	theorem	NOUN
ejpam-1535	8	3	(	(	PUNCT
ejpam-1535	8	4	presented	present	VERB
ejpam-1535	8	5	below	below	ADV
ejpam-1535	8	6	as	as	ADP
ejpam-1535	8	7	our	our	PRON
ejpam-1535	8	8	theorem	theorem	NOUN
ejpam-1535	8	9	1	1	NUM
ejpam-1535	8	10	)	)	PUNCT
ejpam-1535	8	11	expresses	express	VERB
ejpam-1535	8	12	the	the	DET
ejpam-1535	8	13	important	important	ADJ
ejpam-1535	8	14	connection	connection	NOUN
ejpam-1535	8	15	between	between	ADP
ejpam-1535	8	16	the	the	DET
ejpam-1535	8	17	class	class	NOUN
ejpam-1535	8	18	of	of	ADP
ejpam-1535	8	19	inverse	inverse	NOUN
ejpam-1535	8	20	semigroups∗	semigroups∗	NOUN
ejpam-1535	8	21	and	and	CCONJ
ejpam-1535	8	22	that	that	PRON
ejpam-1535	8	23	of	of	ADP
ejpam-1535	8	24	inductive	inductive	ADJ
ejpam-1535	8	25	groupoids	groupoid	NOUN
ejpam-1535	8	26	,	,	PUNCT
ejpam-1535	8	27	where	where	SCONJ
ejpam-1535	8	28	an	an	DET
ejpam-1535	8	29	inductive	inductive	ADJ
ejpam-1535	8	30	groupoid	groupoid	NOUN
ejpam-1535	8	31	is	be	AUX
ejpam-1535	8	32	a	a	DET
ejpam-1535	8	33	small	small	ADJ
ejpam-1535	8	34	ordered	order	VERB
ejpam-1535	8	35	category	category	NOUN
ejpam-1535	8	36	,	,	PUNCT
ejpam-1535	8	37	subject	subject	ADJ
ejpam-1535	8	38	to	to	ADP
ejpam-1535	8	39	certain	certain	ADJ
ejpam-1535	8	40	conditions	condition	NOUN
ejpam-1535	8	41	on	on	ADP
ejpam-1535	8	42	its	its	PRON
ejpam-1535	8	43	ordering	ordering	NOUN
ejpam-1535	8	44	,	,	PUNCT
ejpam-1535	8	45	in	in	ADP
ejpam-1535	8	46	which	which	PRON
ejpam-1535	8	47	all	all	DET
ejpam-1535	8	48	arrows	arrow	NOUN
ejpam-1535	8	49	are	be	AUX
ejpam-1535	8	50	invertible	invertible	ADJ
ejpam-1535	8	51	(	(	PUNCT
ejpam-1535	8	52	note	note	VERB
ejpam-1535	8	53	that	that	SCONJ
ejpam-1535	8	54	a	a	DET
ejpam-1535	8	55	“	"	PUNCT
ejpam-1535	8	56	small	small	ADJ
ejpam-1535	8	57	textquotedblright	textquotedblright	NOUN
ejpam-1535	8	58	category	category	NOUN
ejpam-1535	8	59	is	be	AUX
ejpam-1535	8	60	one	one	NUM
ejpam-1535	8	61	which	which	PRON
ejpam-1535	8	62	is	be	AUX
ejpam-1535	8	63	based	base	VERB
ejpam-1535	8	64	upon	upon	SCONJ
ejpam-1535	8	65	a	a	DET
ejpam-1535	8	66	set	set	NOUN
ejpam-1535	8	67	,	,	PUNCT
ejpam-1535	8	68	rather	rather	ADV
ejpam-1535	8	69	than	than	ADP
ejpam-1535	8	70	a	a	DET
ejpam-1535	8	71	class	class	NOUN
ejpam-1535	8	72	)	)	PUNCT
ejpam-1535	8	73	.	.	PUNCT
ejpam-1535	9	1	it	it	PRON
ejpam-1535	9	2	should	should	AUX
ejpam-1535	9	3	in	in	ADP
ejpam-1535	9	4	fact	fact	NOUN
ejpam-1535	9	5	be	be	AUX
ejpam-1535	9	6	no	no	DET
ejpam-1535	9	7	surprise	surprise	NOUN
ejpam-1535	9	8	that	that	SCONJ
ejpam-1535	9	9	these	these	DET
ejpam-1535	9	10	two	two	NUM
ejpam-1535	9	11	notions	notion	NOUN
ejpam-1535	9	12	are	be	AUX
ejpam-1535	9	13	so	so	ADV
ejpam-1535	9	14	closely	closely	ADV
ejpam-1535	9	15	related	relate	VERB
ejpam-1535	9	16	,	,	PUNCT
ejpam-1535	9	17	for	for	SCONJ
ejpam-1535	9	18	they	they	PRON
ejpam-1535	9	19	are	be	AUX
ejpam-1535	9	20	,	,	PUNCT
ejpam-1535	9	21	in	in	ADP
ejpam-1535	9	22	essence	essence	NOUN
ejpam-1535	9	23	,	,	PUNCT
ejpam-1535	9	24	two	two	NUM
ejpam-1535	9	25	distinct	distinct	ADJ
ejpam-1535	9	26	solutions	solution	NOUN
ejpam-1535	9	27	to	to	ADP
ejpam-1535	9	28	the	the	DET
ejpam-1535	9	29	same	same	ADJ
ejpam-1535	9	30	problem	problem	NOUN
ejpam-1535	9	31	:	:	PUNCT
ejpam-1535	9	32	that	that	PRON
ejpam-1535	9	33	of	of	ADP
ejpam-1535	9	34	axiomatising	axiomatise	VERB
ejpam-1535	9	35	systems	system	NOUN
ejpam-1535	9	36	of	of	ADP
ejpam-1535	9	37	one	one	NUM
ejpam-1535	9	38	-	-	PUNCT
ejpam-1535	9	39	one	one	NUM
ejpam-1535	9	40	partial	partial	ADJ
ejpam-1535	9	41	transformations	transformation	NOUN
ejpam-1535	9	42	.	.	PUNCT
ejpam-1535	10	1	if	if	SCONJ
ejpam-1535	10	2	we	we	PRON
ejpam-1535	10	3	are	be	AUX
ejpam-1535	10	4	content	content	ADJ
ejpam-1535	10	5	to	to	PART
ejpam-1535	10	6	work	work	VERB
ejpam-1535	10	7	email	email	NOUN
ejpam-1535	10	8	address	address	NOUN
ejpam-1535	10	9	:	:	PUNCT
ejpam-1535	10	10	hristopher.hollings	hristopher.hollings	PROPN
ejpam-1535	10	11	�	�	NOUN
ejpam-1535	10	12	maths.ox.a	maths.ox.a	NOUN
ejpam-1535	10	13	.uk	.uk	PUNCT
ejpam-1535	10	14	∗defined	∗define	VERB
ejpam-1535	10	15	abstractly	abstractly	ADV
ejpam-1535	10	16	as	as	ADP
ejpam-1535	10	17	a	a	DET
ejpam-1535	10	18	semigroup	semigroup	NOUN
ejpam-1535	10	19	s	s	X
ejpam-1535	10	20	in	in	ADP
ejpam-1535	10	21	which	which	PRON
ejpam-1535	10	22	every	every	DET
ejpam-1535	10	23	element	element	NOUN
ejpam-1535	10	24	s	s	PART
ejpam-1535	10	25	has	have	VERB
ejpam-1535	10	26	a	a	DET
ejpam-1535	10	27	unique	unique	ADJ
ejpam-1535	10	28	generalised	generalised	ADJ
ejpam-1535	10	29	inverse	inverse	NOUN
ejpam-1535	10	30	s′	s′	NOUN
ejpam-1535	10	31	:	:	PUNCT
ejpam-1535	10	32	ss′s	ss′s	NOUN
ejpam-1535	10	33	=	=	SYM
ejpam-1535	10	34	s	s	PROPN
ejpam-1535	10	35	and	and	CCONJ
ejpam-1535	10	36	s′ss′	s′ss′	PROPN
ejpam-1535	10	37	=	=	PUNCT
ejpam-1535	10	38	s′.	s′.	PROPN
ejpam-1535	10	39	equivalently	equivalently	ADV
ejpam-1535	10	40	(	(	PUNCT
ejpam-1535	10	41	and	and	CCONJ
ejpam-1535	10	42	often	often	ADV
ejpam-1535	10	43	easier	easy	ADJ
ejpam-1535	10	44	to	to	PART
ejpam-1535	10	45	prove	prove	VERB
ejpam-1535	10	46	)	)	PUNCT
ejpam-1535	10	47	,	,	PUNCT
ejpam-1535	10	48	an	an	DET
ejpam-1535	10	49	inverse	inverse	NOUN
ejpam-1535	10	50	semigroup	semigroup	NOUN
ejpam-1535	10	51	is	be	AUX
ejpam-1535	10	52	a	a	DET
ejpam-1535	10	53	semigroup	semigroup	NOUN
ejpam-1535	10	54	in	in	ADP
ejpam-1535	10	55	which	which	PRON
ejpam-1535	10	56	every	every	DET
ejpam-1535	10	57	element	element	NOUN
ejpam-1535	10	58	has	have	VERB
ejpam-1535	10	59	at	at	ADV
ejpam-1535	10	60	least	least	ADJ
ejpam-1535	10	61	one	one	NUM
ejpam-1535	10	62	generalised	generalised	ADJ
ejpam-1535	10	63	inverse	inverse	NOUN
ejpam-1535	10	64	,	,	PUNCT
ejpam-1535	10	65	and	and	CCONJ
ejpam-1535	10	66	in	in	ADP
ejpam-1535	10	67	which	which	PRON
ejpam-1535	10	68	idempotents	idempotent	NOUN
ejpam-1535	10	69	commute	commute	VERB
ejpam-1535	10	70	with	with	ADP
ejpam-1535	10	71	each	each	DET
ejpam-1535	10	72	other	other	ADJ
ejpam-1535	10	73	.	.	PUNCT
ejpam-1535	11	1	we	we	PRON
ejpam-1535	11	2	will	will	AUX
ejpam-1535	11	3	assume	assume	VERB
ejpam-1535	11	4	that	that	SCONJ
ejpam-1535	11	5	the	the	DET
ejpam-1535	11	6	reader	reader	NOUN
ejpam-1535	11	7	has	have	VERB
ejpam-1535	11	8	a	a	DET
ejpam-1535	11	9	passing	pass	VERB
ejpam-1535	11	10	familiarity	familiarity	NOUN
ejpam-1535	11	11	with	with	ADP
ejpam-1535	11	12	the	the	DET
ejpam-1535	11	13	theory	theory	NOUN
ejpam-1535	11	14	of	of	ADP
ejpam-1535	11	15	inverse	inverse	NOUN
ejpam-1535	11	16	semigroups	semigroup	NOUN
ejpam-1535	11	17	.	.	PUNCT
ejpam-1535	12	1	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1535	13	1	414	414	NUM
ejpam-1535	14	1	c	c	NOUN
ejpam-1535	14	2	©	©	PROPN
ejpam-1535	14	3	2012	2012	NUM
ejpam-1535	14	4	ejpam	ejpam	VERB
ejpam-1535	14	5	all	all	DET
ejpam-1535	14	6	rights	right	NOUN
ejpam-1535	14	7	reserved	reserve	VERB
ejpam-1535	14	8	.	.	PUNCT
ejpam-1535	15	1	c.	c.	PROPN
ejpam-1535	15	2	hollings	holling	NOUN
ejpam-1535	15	3	/	/	SYM
ejpam-1535	15	4	eur	eur	PROPN
ejpam-1535	15	5	.	.	PUNCT
ejpam-1535	16	1	j.	j.	PROPN
ejpam-1535	16	2	pure	pure	PROPN
ejpam-1535	16	3	appl	appl	PROPN
ejpam-1535	16	4	.	.	PROPN
ejpam-1535	16	5	math	math	PROPN
ejpam-1535	16	6	,	,	PUNCT
ejpam-1535	16	7	5	5	NUM
ejpam-1535	16	8	(	(	PUNCT
ejpam-1535	16	9	2012	2012	NUM
ejpam-1535	16	10	)	)	PUNCT
ejpam-1535	16	11	,	,	PUNCT
ejpam-1535	16	12	414	414	NUM
ejpam-1535	16	13	-	-	SYM
ejpam-1535	16	14	450	450	NUM
ejpam-1535	16	15	415	415	NUM
ejpam-1535	16	16	with	with	ADP
ejpam-1535	16	17	a	a	DET
ejpam-1535	16	18	partially	partially	ADV
ejpam-1535	16	19	-	-	PUNCT
ejpam-1535	16	20	defined	define	VERB
ejpam-1535	16	21	composition	composition	NOUN
ejpam-1535	16	22	of	of	ADP
ejpam-1535	16	23	such	such	ADJ
ejpam-1535	16	24	partial	partial	ADJ
ejpam-1535	16	25	transformations	transformation	NOUN
ejpam-1535	16	26	,	,	PUNCT
ejpam-1535	16	27	then	then	ADV
ejpam-1535	16	28	we	we	PRON
ejpam-1535	16	29	obtain	obtain	VERB
ejpam-1535	16	30	an	an	DET
ejpam-1535	16	31	inductive	inductive	ADJ
ejpam-1535	16	32	groupoid	groupoid	NOUN
ejpam-1535	16	33	.	.	PUNCT
ejpam-1535	17	1	on	on	ADP
ejpam-1535	17	2	the	the	DET
ejpam-1535	17	3	other	other	ADJ
ejpam-1535	17	4	hand	hand	NOUN
ejpam-1535	17	5	,	,	PUNCT
ejpam-1535	17	6	if	if	SCONJ
ejpam-1535	17	7	we	we	PRON
ejpam-1535	17	8	insist	insist	VERB
ejpam-1535	17	9	upon	upon	SCONJ
ejpam-1535	17	10	an	an	DET
ejpam-1535	17	11	everywhere	everywhere	ADV
ejpam-1535	17	12	-	-	PUNCT
ejpam-1535	17	13	defined	define	VERB
ejpam-1535	17	14	composition	composition	NOUN
ejpam-1535	17	15	,	,	PUNCT
ejpam-1535	17	16	the	the	DET
ejpam-1535	17	17	notion	notion	NOUN
ejpam-1535	17	18	of	of	ADP
ejpam-1535	17	19	an	an	DET
ejpam-1535	17	20	inverse	inverse	NOUN
ejpam-1535	17	21	semigroup	semigroup	NOUN
ejpam-1535	17	22	emerges	emerge	VERB
ejpam-1535	17	23	.	.	PUNCT
ejpam-1535	18	1	the	the	DET
ejpam-1535	18	2	esn	esn	PROPN
ejpam-1535	18	3	theorem	theorem	PROPN
ejpam-1535	18	4	expresses	express	VERB
ejpam-1535	18	5	the	the	DET
ejpam-1535	18	6	fact	fact	NOUN
ejpam-1535	18	7	that	that	SCONJ
ejpam-1535	18	8	,	,	PUNCT
ejpam-1535	18	9	given	give	VERB
ejpam-1535	18	10	any	any	DET
ejpam-1535	18	11	inverse	inverse	NOUN
ejpam-1535	18	12	semigroup	semigroup	NOUN
ejpam-1535	18	13	,	,	PUNCT
ejpam-1535	18	14	we	we	PRON
ejpam-1535	18	15	may	may	AUX
ejpam-1535	18	16	restrict	restrict	VERB
ejpam-1535	18	17	its	its	PRON
ejpam-1535	18	18	multiplication	multiplication	NOUN
ejpam-1535	18	19	in	in	ADP
ejpam-1535	18	20	such	such	DET
ejpam-1535	18	21	a	a	DET
ejpam-1535	18	22	way	way	NOUN
ejpam-1535	18	23	that	that	PRON
ejpam-1535	18	24	we	we	PRON
ejpam-1535	18	25	obtain	obtain	VERB
ejpam-1535	18	26	an	an	DET
ejpam-1535	18	27	inductive	inductive	ADJ
ejpam-1535	18	28	groupoid	groupoid	NOUN
ejpam-1535	18	29	on	on	ADP
ejpam-1535	18	30	the	the	DET
ejpam-1535	18	31	same	same	ADJ
ejpam-1535	18	32	underlying	underlying	ADJ
ejpam-1535	18	33	set	set	NOUN
ejpam-1535	18	34	:	:	PUNCT
ejpam-1535	18	35	the	the	DET
ejpam-1535	18	36	information	information	NOUN
ejpam-1535	18	37	that	that	PRON
ejpam-1535	18	38	is	be	AUX
ejpam-1535	18	39	seemingly	seemingly	ADV
ejpam-1535	18	40	lost	lose	VERB
ejpam-1535	18	41	in	in	ADP
ejpam-1535	18	42	restricting	restrict	VERB
ejpam-1535	18	43	multiplication	multiplication	NOUN
ejpam-1535	18	44	is	be	AUX
ejpam-1535	18	45	contained	contain	VERB
ejpam-1535	18	46	instead	instead	ADV
ejpam-1535	18	47	in	in	ADP
ejpam-1535	18	48	the	the	DET
ejpam-1535	18	49	partial	partial	ADJ
ejpam-1535	18	50	order	order	NOUN
ejpam-1535	18	51	structure	structure	NOUN
ejpam-1535	18	52	of	of	ADP
ejpam-1535	18	53	the	the	DET
ejpam-1535	18	54	inductive	inductive	ADJ
ejpam-1535	18	55	groupoid	groupoid	PROPN
ejpam-1535	18	56	.	.	PUNCT
ejpam-1535	19	1	conversely	conversely	ADV
ejpam-1535	19	2	,	,	PUNCT
ejpam-1535	19	3	it	it	PRON
ejpam-1535	19	4	is	be	AUX
ejpam-1535	19	5	possible	possible	ADJ
ejpam-1535	19	6	(	(	PUNCT
ejpam-1535	19	7	using	use	VERB
ejpam-1535	19	8	information	information	NOUN
ejpam-1535	19	9	encoded	encode	VERB
ejpam-1535	19	10	in	in	ADP
ejpam-1535	19	11	the	the	DET
ejpam-1535	19	12	order	order	NOUN
ejpam-1535	19	13	structure	structure	NOUN
ejpam-1535	19	14	)	)	PUNCT
ejpam-1535	19	15	to	to	PART
ejpam-1535	19	16	extend	extend	VERB
ejpam-1535	19	17	the	the	DET
ejpam-1535	19	18	partial	partial	ADJ
ejpam-1535	19	19	multiplication	multiplication	NOUN
ejpam-1535	19	20	in	in	ADP
ejpam-1535	19	21	an	an	DET
ejpam-1535	19	22	inductive	inductive	ADJ
ejpam-1535	19	23	groupoid	groupoid	NOUN
ejpam-1535	19	24	to	to	ADP
ejpam-1535	19	25	an	an	DET
ejpam-1535	19	26	everywhere	everywhere	ADV
ejpam-1535	19	27	-	-	PUNCT
ejpam-1535	19	28	defined	define	VERB
ejpam-1535	19	29	multiplication	multiplication	NOUN
ejpam-1535	19	30	,	,	PUNCT
ejpam-1535	19	31	and	and	CCONJ
ejpam-1535	19	32	thereby	thereby	ADV
ejpam-1535	19	33	construct	construct	VERB
ejpam-1535	19	34	an	an	DET
ejpam-1535	19	35	inverse	inverse	NOUN
ejpam-1535	19	36	semigroup	semigroup	NOUN
ejpam-1535	19	37	.	.	PUNCT
ejpam-1535	20	1	indeed	indeed	ADV
ejpam-1535	20	2	,	,	PUNCT
ejpam-1535	20	3	the	the	DET
ejpam-1535	20	4	esn	esn	PROPN
ejpam-1535	20	5	theorem	theorem	NOUN
ejpam-1535	20	6	goes	go	VERB
ejpam-1535	20	7	further	far	ADV
ejpam-1535	20	8	:	:	PUNCT
ejpam-1535	20	9	it	it	PRON
ejpam-1535	20	10	is	be	AUX
ejpam-1535	20	11	expressed	express	VERB
ejpam-1535	20	12	in	in	ADP
ejpam-1535	20	13	category	category	NOUN
ejpam-1535	20	14	-	-	PUNCT
ejpam-1535	20	15	theoretic	theoretic	NOUN
ejpam-1535	20	16	terms	term	NOUN
ejpam-1535	20	17	,	,	PUNCT
ejpam-1535	20	18	stating	state	VERB
ejpam-1535	20	19	that	that	SCONJ
ejpam-1535	20	20	certain	certain	ADJ
ejpam-1535	20	21	categories	category	NOUN
ejpam-1535	20	22	of	of	ADP
ejpam-1535	20	23	inverse	inverse	NOUN
ejpam-1535	20	24	semigroups	semigroup	NOUN
ejpam-1535	20	25	are	be	AUX
ejpam-1535	20	26	isomorphic	isomorphic	ADJ
ejpam-1535	20	27	to	to	ADP
ejpam-1535	20	28	certain	certain	ADJ
ejpam-1535	20	29	other	other	ADJ
ejpam-1535	20	30	categories	category	NOUN
ejpam-1535	20	31	of	of	ADP
ejpam-1535	20	32	inductive	inductive	ADJ
ejpam-1535	20	33	groupoids	groupoid	NOUN
ejpam-1535	20	34	.	.	PUNCT
ejpam-1535	21	1	in	in	ADP
ejpam-1535	21	2	this	this	DET
ejpam-1535	21	3	way	way	NOUN
ejpam-1535	21	4	,	,	PUNCT
ejpam-1535	21	5	it	it	PRON
ejpam-1535	21	6	tells	tell	VERB
ejpam-1535	21	7	us	we	PRON
ejpam-1535	21	8	that	that	SCONJ
ejpam-1535	21	9	there	there	PRON
ejpam-1535	21	10	is	be	VERB
ejpam-1535	21	11	also	also	ADV
ejpam-1535	21	12	a	a	DET
ejpam-1535	21	13	fundamental	fundamental	ADJ
ejpam-1535	21	14	connection	connection	NOUN
ejpam-1535	21	15	between	between	ADP
ejpam-1535	21	16	certain	certain	ADJ
ejpam-1535	21	17	natural	natural	ADJ
ejpam-1535	21	18	functions	function	NOUN
ejpam-1535	21	19	between	between	ADP
ejpam-1535	21	20	inverse	inverse	NOUN
ejpam-1535	21	21	semigroups	semigroup	NOUN
ejpam-1535	21	22	and	and	CCONJ
ejpam-1535	21	23	other	other	ADJ
ejpam-1535	21	24	equally	equally	ADV
ejpam-1535	21	25	natural	natural	ADJ
ejpam-1535	21	26	functions	function	NOUN
ejpam-1535	21	27	between	between	ADP
ejpam-1535	21	28	inductive	inductive	ADJ
ejpam-1535	21	29	groupoids	groupoid	NOUN
ejpam-1535	21	30	.	.	PUNCT
ejpam-1535	22	1	the	the	DET
ejpam-1535	22	2	esn	esn	PROPN
ejpam-1535	22	3	theorem	theorem	PROPN
ejpam-1535	22	4	has	have	AUX
ejpam-1535	22	5	thus	thus	ADV
ejpam-1535	22	6	proved	prove	VERB
ejpam-1535	22	7	to	to	PART
ejpam-1535	22	8	be	be	AUX
ejpam-1535	22	9	a	a	DET
ejpam-1535	22	10	useful	useful	ADJ
ejpam-1535	22	11	tool	tool	NOUN
ejpam-1535	22	12	in	in	ADP
ejpam-1535	22	13	the	the	DET
ejpam-1535	22	14	theories	theory	NOUN
ejpam-1535	22	15	of	of	ADP
ejpam-1535	22	16	both	both	DET
ejpam-1535	22	17	inverse	inverse	NOUN
ejpam-1535	22	18	semigroups	semigroup	NOUN
ejpam-1535	22	19	and	and	CCONJ
ejpam-1535	22	20	inductive	inductive	ADJ
ejpam-1535	22	21	groupoids	groupoid	NOUN
ejpam-1535	22	22	:	:	PUNCT
ejpam-1535	22	23	it	it	PRON
ejpam-1535	22	24	allows	allow	VERB
ejpam-1535	22	25	the	the	DET
ejpam-1535	22	26	study	study	NOUN
ejpam-1535	22	27	of	of	ADP
ejpam-1535	22	28	one	one	NUM
ejpam-1535	22	29	to	to	PART
ejpam-1535	22	30	inform	inform	VERB
ejpam-1535	22	31	that	that	PRON
ejpam-1535	22	32	of	of	ADP
ejpam-1535	22	33	the	the	DET
ejpam-1535	22	34	other	other	ADJ
ejpam-1535	22	35	.	.	PUNCT
ejpam-1535	23	1	the	the	DET
ejpam-1535	23	2	esn	esn	PROPN
ejpam-1535	23	3	theorem	theorem	PROPN
ejpam-1535	23	4	has	have	AUX
ejpam-1535	23	5	indeed	indeed	ADV
ejpam-1535	23	6	been	be	AUX
ejpam-1535	23	7	so	so	ADV
ejpam-1535	23	8	beneficial	beneficial	ADJ
ejpam-1535	23	9	that	that	SCONJ
ejpam-1535	23	10	it	it	PRON
ejpam-1535	23	11	has	have	AUX
ejpam-1535	23	12	been	be	AUX
ejpam-1535	23	13	highly	highly	ADV
ejpam-1535	23	14	desirable	desirable	ADJ
ejpam-1535	23	15	to	to	PART
ejpam-1535	23	16	obtain	obtain	VERB
ejpam-1535	23	17	extensions	extension	NOUN
ejpam-1535	23	18	of	of	ADP
ejpam-1535	23	19	it	it	PRON
ejpam-1535	23	20	to	to	ADP
ejpam-1535	23	21	other	other	ADJ
ejpam-1535	23	22	situations	situation	NOUN
ejpam-1535	23	23	.	.	PUNCT
ejpam-1535	24	1	in	in	ADP
ejpam-1535	24	2	particular	particular	ADJ
ejpam-1535	24	3	,	,	PUNCT
ejpam-1535	24	4	versions	version	NOUN
ejpam-1535	24	5	of	of	ADP
ejpam-1535	24	6	the	the	DET
ejpam-1535	24	7	esn	esn	PROPN
ejpam-1535	24	8	theorem	theorem	PROPN
ejpam-1535	24	9	have	have	AUX
ejpam-1535	24	10	been	be	AUX
ejpam-1535	24	11	proved	prove	VERB
ejpam-1535	24	12	in	in	ADP
ejpam-1535	24	13	the	the	DET
ejpam-1535	24	14	cases	case	NOUN
ejpam-1535	24	15	of	of	ADP
ejpam-1535	24	16	semigroups	semigroup	NOUN
ejpam-1535	24	17	which	which	PRON
ejpam-1535	24	18	are	be	AUX
ejpam-1535	24	19	more	more	ADV
ejpam-1535	24	20	general	general	ADJ
ejpam-1535	24	21	than	than	ADP
ejpam-1535	24	22	inverse	inverse	NOUN
ejpam-1535	24	23	semigroups	semigroup	NOUN
ejpam-1535	24	24	.	.	PUNCT
ejpam-1535	25	1	for	for	ADP
ejpam-1535	25	2	example	example	NOUN
ejpam-1535	25	3	,	,	PUNCT
ejpam-1535	25	4	nambooripad	nambooripad	PROPN
ejpam-1535	25	5	(	(	PUNCT
ejpam-1535	25	6	see	see	VERB
ejpam-1535	25	7	section	section	NOUN
ejpam-1535	25	8	2	2	NUM
ejpam-1535	25	9	)	)	PUNCT
ejpam-1535	25	10	arrived	arrive	VERB
ejpam-1535	25	11	at	at	ADP
ejpam-1535	25	12	a	a	DET
ejpam-1535	25	13	generalisation	generalisation	NOUN
ejpam-1535	25	14	of	of	ADP
ejpam-1535	25	15	the	the	DET
ejpam-1535	25	16	esn	esn	PROPN
ejpam-1535	25	17	theorem	theorem	NOUN
ejpam-1535	25	18	which	which	PRON
ejpam-1535	25	19	links	link	VERB
ejpam-1535	25	20	regular	regular	ADJ
ejpam-1535	25	21	semigroups	semigroup	NOUN
ejpam-1535	25	22	(	(	PUNCT
ejpam-1535	25	23	generalisations	generalisation	NOUN
ejpam-1535	25	24	of	of	ADP
ejpam-1535	25	25	inverse	inverse	NOUN
ejpam-1535	25	26	semigroups	semigroup	NOUN
ejpam-1535	25	27	in	in	ADP
ejpam-1535	25	28	which	which	PRON
ejpam-1535	25	29	every	every	DET
ejpam-1535	25	30	element	element	NOUN
ejpam-1535	25	31	is	be	AUX
ejpam-1535	25	32	assumed	assume	VERB
ejpam-1535	25	33	to	to	PART
ejpam-1535	25	34	have	have	VERB
ejpam-1535	25	35	at	at	ADV
ejpam-1535	25	36	least	least	ADV
ejpam-1535	25	37	one	one	NUM
ejpam-1535	25	38	generalised	generalised	ADJ
ejpam-1535	25	39	inverse	inverse	NOUN
ejpam-1535	25	40	)	)	PUNCT
ejpam-1535	25	41	with	with	ADP
ejpam-1535	25	42	so	so	ADV
ejpam-1535	25	43	-	-	PUNCT
ejpam-1535	25	44	called	call	VERB
ejpam-1535	25	45	“	"	PUNCT
ejpam-1535	25	46	regular	regular	ADJ
ejpam-1535	25	47	groupoids	groupoid	NOUN
ejpam-1535	25	48	”	"	PUNCT
ejpam-1535	25	49	:	:	PUNCT
ejpam-1535	25	50	generalisations	generalisation	NOUN
ejpam-1535	25	51	of	of	ADP
ejpam-1535	25	52	inductive	inductive	ADJ
ejpam-1535	25	53	groupoids	groupoid	NOUN
ejpam-1535	25	54	.	.	PUNCT
ejpam-1535	26	1	there	there	PRON
ejpam-1535	26	2	has	have	AUX
ejpam-1535	26	3	also	also	ADV
ejpam-1535	26	4	been	be	AUX
ejpam-1535	26	5	a	a	DET
ejpam-1535	26	6	great	great	ADJ
ejpam-1535	26	7	deal	deal	NOUN
ejpam-1535	26	8	of	of	ADP
ejpam-1535	26	9	activity	activity	NOUN
ejpam-1535	26	10	in	in	ADP
ejpam-1535	26	11	this	this	DET
ejpam-1535	26	12	area	area	NOUN
ejpam-1535	26	13	,	,	PUNCT
ejpam-1535	26	14	in	in	ADP
ejpam-1535	26	15	connection	connection	NOUN
ejpam-1535	26	16	with	with	ADP
ejpam-1535	26	17	the	the	DET
ejpam-1535	26	18	non	non	ADJ
ejpam-1535	26	19	-	-	ADJ
ejpam-1535	26	20	regular	regular	ADJ
ejpam-1535	26	21	generalisations	generalisation	NOUN
ejpam-1535	26	22	of	of	ADP
ejpam-1535	26	23	inverse	inverse	NOUN
ejpam-1535	26	24	semigroups	semigroup	NOUN
ejpam-1535	26	25	,	,	PUNCT
ejpam-1535	26	26	such	such	ADJ
ejpam-1535	26	27	as	as	ADP
ejpam-1535	26	28	ample	ample	ADJ
ejpam-1535	26	29	semigroups	semigroup	NOUN
ejpam-1535	26	30	and	and	CCONJ
ejpam-1535	26	31	restriction	restriction	NOUN
ejpam-1535	26	32	semigroups	semigroup	NOUN
ejpam-1535	26	33	(	(	PUNCT
ejpam-1535	26	34	see	see	VERB
ejpam-1535	26	35	section	section	NOUN
ejpam-1535	26	36	3	3	NUM
ejpam-1535	26	37	)	)	PUNCT
ejpam-1535	26	38	.	.	PUNCT
ejpam-1535	27	1	we	we	PRON
ejpam-1535	27	2	will	will	AUX
ejpam-1535	27	3	be	be	AUX
ejpam-1535	27	4	particularly	particularly	ADV
ejpam-1535	27	5	interested	interested	ADJ
ejpam-1535	27	6	in	in	ADP
ejpam-1535	27	7	the	the	DET
ejpam-1535	27	8	case	case	NOUN
ejpam-1535	27	9	of	of	ADP
ejpam-1535	27	10	restriction	restriction	NOUN
ejpam-1535	27	11	semigroups	semigroup	NOUN
ejpam-1535	27	12	,	,	PUNCT
ejpam-1535	27	13	which	which	PRON
ejpam-1535	27	14	may	may	AUX
ejpam-1535	27	15	be	be	AUX
ejpam-1535	27	16	derived	derive	VERB
ejpam-1535	27	17	from	from	ADP
ejpam-1535	27	18	semigroups	semigroup	NOUN
ejpam-1535	27	19	of	of	ADP
ejpam-1535	27	20	arbitrary	arbitrary	ADJ
ejpam-1535	27	21	partial	partial	ADJ
ejpam-1535	27	22	transformations	transformation	NOUN
ejpam-1535	27	23	.	.	PUNCT
ejpam-1535	28	1	restriction	restriction	NOUN
ejpam-1535	28	2	semigroups	semigroup	NOUN
ejpam-1535	28	3	correspond	correspond	VERB
ejpam-1535	28	4	,	,	PUNCT
ejpam-1535	28	5	in	in	ADP
ejpam-1535	28	6	an	an	DET
ejpam-1535	28	7	“	"	PUNCT
ejpam-1535	28	8	esn	esn	PROPN
ejpam-1535	28	9	-	-	PUNCT
ejpam-1535	28	10	like	like	ADJ
ejpam-1535	28	11	”	"	PUNCT
ejpam-1535	28	12	manner	manner	NOUN
ejpam-1535	28	13	,	,	PUNCT
ejpam-1535	28	14	to	to	PART
ejpam-1535	28	15	inductive	inductive	VERB
ejpam-1535	28	16	categories	category	NOUN
ejpam-1535	28	17	;	;	PUNCT
ejpam-1535	28	18	the	the	DET
ejpam-1535	28	19	order	order	NOUN
ejpam-1535	28	20	structure	structure	NOUN
ejpam-1535	28	21	on	on	ADP
ejpam-1535	28	22	the	the	DET
ejpam-1535	28	23	latter	latter	NOUN
ejpam-1535	28	24	is	be	AUX
ejpam-1535	28	25	essentially	essentially	ADV
ejpam-1535	28	26	the	the	DET
ejpam-1535	28	27	same	same	ADJ
ejpam-1535	28	28	as	as	ADP
ejpam-1535	28	29	that	that	PRON
ejpam-1535	28	30	defined	define	VERB
ejpam-1535	28	31	upon	upon	SCONJ
ejpam-1535	28	32	an	an	DET
ejpam-1535	28	33	inductive	inductive	ADJ
ejpam-1535	28	34	groupoid	groupoid	NOUN
ejpam-1535	28	35	,	,	PUNCT
ejpam-1535	28	36	but	but	CCONJ
ejpam-1535	28	37	we	we	PRON
ejpam-1535	28	38	no	no	ADV
ejpam-1535	28	39	longer	long	ADV
ejpam-1535	28	40	insist	insist	VERB
ejpam-1535	28	41	upon	upon	SCONJ
ejpam-1535	28	42	the	the	DET
ejpam-1535	28	43	invertibility	invertibility	NOUN
ejpam-1535	28	44	of	of	ADP
ejpam-1535	28	45	arrows	arrow	NOUN
ejpam-1535	28	46	.	.	PUNCT
ejpam-1535	29	1	this	this	DET
ejpam-1535	29	2	generalisation	generalisation	NOUN
ejpam-1535	29	3	of	of	ADP
ejpam-1535	29	4	the	the	DET
ejpam-1535	29	5	esn	esn	PROPN
ejpam-1535	29	6	theorem	theorem	PROPN
ejpam-1535	29	7	may	may	AUX
ejpam-1535	29	8	be	be	AUX
ejpam-1535	29	9	expressed	express	VERB
ejpam-1535	29	10	,	,	PUNCT
ejpam-1535	29	11	by	by	ADP
ejpam-1535	29	12	analogy	analogy	NOUN
ejpam-1535	29	13	with	with	ADP
ejpam-1535	29	14	the	the	DET
ejpam-1535	29	15	original	original	NOUN
ejpam-1535	29	16	,	,	PUNCT
ejpam-1535	29	17	in	in	ADP
ejpam-1535	29	18	terms	term	NOUN
ejpam-1535	29	19	of	of	ADP
ejpam-1535	29	20	isomorphisms	isomorphism	NOUN
ejpam-1535	29	21	of	of	ADP
ejpam-1535	29	22	certain	certain	ADJ
ejpam-1535	29	23	categories	category	NOUN
ejpam-1535	29	24	of	of	ADP
ejpam-1535	29	25	restriction	restriction	NOUN
ejpam-1535	29	26	semigroups	semigroup	NOUN
ejpam-1535	29	27	and	and	CCONJ
ejpam-1535	29	28	certain	certain	ADJ
ejpam-1535	29	29	other	other	ADJ
ejpam-1535	29	30	categories	category	NOUN
ejpam-1535	29	31	of	of	ADP
ejpam-1535	29	32	inductive	inductive	ADJ
ejpam-1535	29	33	categories	category	NOUN
ejpam-1535	29	34	(	(	PUNCT
ejpam-1535	29	35	see	see	VERB
ejpam-1535	29	36	below	below	ADV
ejpam-1535	29	37	for	for	ADP
ejpam-1535	29	38	comments	comment	NOUN
ejpam-1535	29	39	on	on	ADP
ejpam-1535	29	40	our	our	PRON
ejpam-1535	29	41	use	use	NOUN
ejpam-1535	29	42	of	of	ADP
ejpam-1535	29	43	the	the	DET
ejpam-1535	29	44	word	word	NOUN
ejpam-1535	29	45	“	"	PUNCT
ejpam-1535	29	46	category	category	NOUN
ejpam-1535	29	47	”	"	PUNCT
ejpam-1535	29	48	)	)	PUNCT
ejpam-1535	29	49	.	.	PUNCT
ejpam-1535	30	1	this	this	DET
ejpam-1535	30	2	theorem	theorem	NOUN
ejpam-1535	30	3	,	,	PUNCT
ejpam-1535	30	4	together	together	ADV
ejpam-1535	30	5	with	with	ADP
ejpam-1535	30	6	its	its	PRON
ejpam-1535	30	7	corollaries	corollary	NOUN
ejpam-1535	30	8	,	,	PUNCT
ejpam-1535	30	9	is	be	AUX
ejpam-1535	30	10	the	the	DET
ejpam-1535	30	11	subject	subject	NOUN
ejpam-1535	30	12	of	of	ADP
ejpam-1535	30	13	this	this	DET
ejpam-1535	30	14	survey	survey	NOUN
ejpam-1535	30	15	article	article	NOUN
ejpam-1535	30	16	,	,	PUNCT
ejpam-1535	30	17	which	which	PRON
ejpam-1535	30	18	is	be	AUX
ejpam-1535	30	19	intended	intend	VERB
ejpam-1535	30	20	as	as	ADP
ejpam-1535	30	21	a	a	DET
ejpam-1535	30	22	sequel	sequel	NOUN
ejpam-1535	30	23	to	to	ADP
ejpam-1535	30	24	a	a	DET
ejpam-1535	30	25	previous	previous	ADJ
ejpam-1535	30	26	survey	survey	NOUN
ejpam-1535	30	27	[	[	X
ejpam-1535	30	28	20	20	NUM
ejpam-1535	30	29	]	]	PUNCT
ejpam-1535	30	30	on	on	ADP
ejpam-1535	30	31	restriction	restriction	NOUN
ejpam-1535	30	32	semigroups	semigroup	NOUN
ejpam-1535	30	33	,	,	PUNCT
ejpam-1535	30	34	where	where	SCONJ
ejpam-1535	30	35	the	the	DET
ejpam-1535	30	36	use	use	NOUN
ejpam-1535	30	37	of	of	ADP
ejpam-1535	30	38	extensions	extension	NOUN
ejpam-1535	30	39	of	of	ADP
ejpam-1535	30	40	the	the	DET
ejpam-1535	30	41	esn	esn	PROPN
ejpam-1535	30	42	theorem	theorem	VERB
ejpam-1535	30	43	in	in	ADP
ejpam-1535	30	44	the	the	DET
ejpam-1535	30	45	study	study	NOUN
ejpam-1535	30	46	of	of	ADP
ejpam-1535	30	47	such	such	ADJ
ejpam-1535	30	48	semigroups	semigroup	NOUN
ejpam-1535	30	49	was	be	AUX
ejpam-1535	30	50	indicated	indicate	VERB
ejpam-1535	30	51	only	only	ADV
ejpam-1535	30	52	briefly	briefly	ADV
ejpam-1535	30	53	.	.	PUNCT
ejpam-1535	31	1	the	the	DET
ejpam-1535	31	2	present	present	ADJ
ejpam-1535	31	3	article	article	NOUN
ejpam-1535	31	4	is	be	AUX
ejpam-1535	31	5	also	also	ADV
ejpam-1535	31	6	intended	intend	VERB
ejpam-1535	31	7	as	as	ADP
ejpam-1535	31	8	a	a	DET
ejpam-1535	31	9	companion	companion	NOUN
ejpam-1535	31	10	piece	piece	NOUN
ejpam-1535	31	11	to	to	ADP
ejpam-1535	31	12	[	[	X
ejpam-1535	31	13	22	22	NUM
ejpam-1535	31	14	]	]	PUNCT
ejpam-1535	31	15	,	,	PUNCT
ejpam-1535	31	16	in	in	ADP
ejpam-1535	31	17	which	which	PRON
ejpam-1535	31	18	certain	certain	ADJ
ejpam-1535	31	19	extensions	extension	NOUN
ejpam-1535	31	20	of	of	ADP
ejpam-1535	31	21	the	the	DET
ejpam-1535	31	22	esn	esn	PROPN
ejpam-1535	31	23	theorem	theorem	PROPN
ejpam-1535	31	24	were	be	AUX
ejpam-1535	31	25	discussed	discuss	VERB
ejpam-1535	31	26	,	,	PUNCT
ejpam-1535	31	27	but	but	CCONJ
ejpam-1535	31	28	in	in	ADP
ejpam-1535	31	29	which	which	PRON
ejpam-1535	31	30	very	very	ADV
ejpam-1535	31	31	little	little	ADJ
ejpam-1535	31	32	historical	historical	ADJ
ejpam-1535	31	33	context	context	NOUN
ejpam-1535	31	34	was	be	AUX
ejpam-1535	31	35	given	give	VERB
ejpam-1535	31	36	.	.	PUNCT
ejpam-1535	32	1	our	our	PRON
ejpam-1535	32	2	approach	approach	NOUN
ejpam-1535	32	3	will	will	AUX
ejpam-1535	32	4	be	be	AUX
ejpam-1535	32	5	to	to	PART
ejpam-1535	32	6	begin	begin	VERB
ejpam-1535	32	7	with	with	ADP
ejpam-1535	32	8	the	the	DET
ejpam-1535	32	9	most	most	ADV
ejpam-1535	32	10	general	general	ADJ
ejpam-1535	32	11	situation	situation	NOUN
ejpam-1535	32	12	(	(	PUNCT
ejpam-1535	32	13	namely	namely	ADV
ejpam-1535	32	14	,	,	PUNCT
ejpam-1535	32	15	restriction	restriction	NOUN
ejpam-1535	32	16	semigroups	semigroup	NOUN
ejpam-1535	32	17	and	and	CCONJ
ejpam-1535	32	18	inductive	inductive	ADJ
ejpam-1535	32	19	categories	category	NOUN
ejpam-1535	32	20	)	)	PUNCT
ejpam-1535	32	21	and	and	CCONJ
ejpam-1535	32	22	use	use	VERB
ejpam-1535	32	23	this	this	PRON
ejpam-1535	32	24	to	to	PART
ejpam-1535	32	25	derive	derive	VERB
ejpam-1535	32	26	other	other	ADJ
ejpam-1535	32	27	cases	case	NOUN
ejpam-1535	32	28	of	of	ADP
ejpam-1535	32	29	interest	interest	NOUN
ejpam-1535	32	30	:	:	PUNCT
ejpam-1535	32	31	in	in	ADP
ejpam-1535	32	32	particular	particular	ADJ
ejpam-1535	32	33	,	,	PUNCT
ejpam-1535	32	34	that	that	PRON
ejpam-1535	32	35	of	of	ADP
ejpam-1535	32	36	inverse	inverse	NOUN
ejpam-1535	32	37	semigroups	semigroup	NOUN
ejpam-1535	32	38	and	and	CCONJ
ejpam-1535	32	39	inductive	inductive	ADJ
ejpam-1535	32	40	groupoids	groupoid	NOUN
ejpam-1535	32	41	.	.	PUNCT
ejpam-1535	33	1	we	we	PRON
ejpam-1535	33	2	will	will	AUX
ejpam-1535	33	3	not	not	PART
ejpam-1535	33	4	treat	treat	VERB
ejpam-1535	33	5	the	the	DET
ejpam-1535	33	6	case	case	NOUN
ejpam-1535	33	7	of	of	ADP
ejpam-1535	33	8	regular	regular	ADJ
ejpam-1535	33	9	semigroups	semigroup	NOUN
ejpam-1535	33	10	,	,	PUNCT
ejpam-1535	33	11	however	however	ADV
ejpam-1535	33	12	,	,	PUNCT
ejpam-1535	33	13	since	since	SCONJ
ejpam-1535	33	14	these	these	PRON
ejpam-1535	33	15	are	be	AUX
ejpam-1535	33	16	a	a	DET
ejpam-1535	33	17	generalisation	generalisation	NOUN
ejpam-1535	33	18	of	of	ADP
ejpam-1535	33	19	inverse	inverse	NOUN
ejpam-1535	33	20	semigroups	semigroup	NOUN
ejpam-1535	33	21	along	along	ADP
ejpam-1535	33	22	different	different	ADJ
ejpam-1535	33	23	lines	line	NOUN
ejpam-1535	33	24	to	to	ADP
ejpam-1535	33	25	restriction	restriction	NOUN
ejpam-1535	33	26	semigroups	semigroup	NOUN
ejpam-1535	33	27	,	,	PUNCT
ejpam-1535	33	28	and	and	CCONJ
ejpam-1535	33	29	so	so	ADV
ejpam-1535	33	30	the	the	DET
ejpam-1535	33	31	relevant	relevant	ADJ
ejpam-1535	33	32	results	result	NOUN
ejpam-1535	33	33	for	for	ADP
ejpam-1535	33	34	regular	regular	ADJ
ejpam-1535	33	35	semigroups	semigroup	NOUN
ejpam-1535	33	36	do	do	AUX
ejpam-1535	33	37	not	not	PART
ejpam-1535	33	38	follow	follow	VERB
ejpam-1535	33	39	from	from	ADP
ejpam-1535	33	40	those	those	PRON
ejpam-1535	33	41	for	for	ADP
ejpam-1535	33	42	restriction	restriction	NOUN
ejpam-1535	33	43	semigroups	semigroup	NOUN
ejpam-1535	33	44	.	.	PUNCT
ejpam-1535	34	1	as	as	SCONJ
ejpam-1535	34	2	we	we	PRON
ejpam-1535	34	3	will	will	AUX
ejpam-1535	34	4	see	see	VERB
ejpam-1535	34	5	in	in	ADP
ejpam-1535	34	6	section	section	NOUN
ejpam-1535	34	7	2	2	NUM
ejpam-1535	34	8	,	,	PUNCT
ejpam-1535	34	9	the	the	DET
ejpam-1535	34	10	original	original	ADJ
ejpam-1535	34	11	construction	construction	NOUN
ejpam-1535	34	12	of	of	ADP
ejpam-1535	34	13	an	an	DET
ejpam-1535	34	14	inverse	inverse	NOUN
ejpam-1535	34	15	semigroup	semigroup	NOUN
ejpam-1535	34	16	from	from	ADP
ejpam-1535	34	17	an	an	DET
ejpam-1535	34	18	inductive	inductive	ADJ
ejpam-1535	34	19	groupoid	groupoid	NOUN
ejpam-1535	34	20	,	,	PUNCT
ejpam-1535	34	21	and	and	CCONJ
ejpam-1535	34	22	vice	vice	ADV
ejpam-1535	34	23	versa	versa	ADV
ejpam-1535	34	24	,	,	PUNCT
ejpam-1535	34	25	was	be	AUX
ejpam-1535	34	26	provided	provide	VERB
ejpam-1535	34	27	by	by	ADP
ejpam-1535	34	28	schein	schein	PROPN
ejpam-1535	34	29	[	[	X
ejpam-1535	34	30	44	44	NUM
ejpam-1535	34	31	,	,	PUNCT
ejpam-1535	34	32	45	45	NUM
ejpam-1535	34	33	]	]	PUNCT
ejpam-1535	34	34	.	.	PUNCT
ejpam-1535	35	1	his	his	PRON
ejpam-1535	35	2	method	method	NOUN
ejpam-1535	35	3	was	be	AUX
ejpam-1535	35	4	direct	direct	ADJ
ejpam-1535	35	5	c.	c.	PROPN
ejpam-1535	35	6	hollings	holling	NOUN
ejpam-1535	35	7	/	/	SYM
ejpam-1535	35	8	eur	eur	PROPN
ejpam-1535	35	9	.	.	PUNCT
ejpam-1535	36	1	j.	j.	PROPN
ejpam-1535	36	2	pure	pure	PROPN
ejpam-1535	36	3	appl	appl	PROPN
ejpam-1535	36	4	.	.	PROPN
ejpam-1535	36	5	math	math	PROPN
ejpam-1535	36	6	,	,	PUNCT
ejpam-1535	36	7	5	5	NUM
ejpam-1535	36	8	(	(	PUNCT
ejpam-1535	36	9	2012	2012	NUM
ejpam-1535	36	10	)	)	PUNCT
ejpam-1535	36	11	,	,	PUNCT
ejpam-1535	36	12	414	414	NUM
ejpam-1535	36	13	-	-	SYM
ejpam-1535	36	14	450	450	NUM
ejpam-1535	36	15	416	416	NUM
ejpam-1535	36	16	and	and	CCONJ
ejpam-1535	36	17	entirely	entirely	ADV
ejpam-1535	36	18	algebraic	algebraic	ADJ
ejpam-1535	36	19	,	,	PUNCT
ejpam-1535	36	20	as	as	SCONJ
ejpam-1535	36	21	was	be	AUX
ejpam-1535	36	22	that	that	PRON
ejpam-1535	36	23	of	of	ADP
ejpam-1535	36	24	subsequent	subsequent	ADJ
ejpam-1535	36	25	authors	author	NOUN
ejpam-1535	36	26	in	in	ADP
ejpam-1535	36	27	connection	connection	NOUN
ejpam-1535	36	28	with	with	ADP
ejpam-1535	36	29	generalisations	generalisation	NOUN
ejpam-1535	36	30	of	of	ADP
ejpam-1535	36	31	schein	schein	PROPN
ejpam-1535	36	32	’s	’s	PART
ejpam-1535	36	33	results	result	NOUN
ejpam-1535	36	34	—	—	PUNCT
ejpam-1535	36	35	for	for	ADP
ejpam-1535	36	36	example	example	NOUN
ejpam-1535	36	37	,	,	PUNCT
ejpam-1535	36	38	armstrong	armstrong	PROPN
ejpam-1535	37	1	[	[	X
ejpam-1535	37	2	1	1	NUM
ejpam-1535	37	3	]	]	PUNCT
ejpam-1535	37	4	in	in	ADP
ejpam-1535	37	5	the	the	DET
ejpam-1535	37	6	case	case	NOUN
ejpam-1535	37	7	of	of	ADP
ejpam-1535	37	8	ample	ample	ADJ
ejpam-1535	37	9	semigroups	semigroup	NOUN
ejpam-1535	37	10	.	.	PUNCT
ejpam-1535	38	1	though	though	SCONJ
ejpam-1535	38	2	of	of	ADP
ejpam-1535	38	3	course	course	NOUN
ejpam-1535	38	4	perfectly	perfectly	ADV
ejpam-1535	38	5	valid	valid	ADJ
ejpam-1535	38	6	,	,	PUNCT
ejpam-1535	38	7	this	this	DET
ejpam-1535	38	8	approach	approach	NOUN
ejpam-1535	38	9	entails	entail	VERB
ejpam-1535	38	10	a	a	DET
ejpam-1535	38	11	somewhat	somewhat	ADV
ejpam-1535	38	12	lengthy	lengthy	ADJ
ejpam-1535	38	13	proof	proof	NOUN
ejpam-1535	38	14	,	,	PUNCT
ejpam-1535	38	15	with	with	ADP
ejpam-1535	38	16	the	the	DET
ejpam-1535	38	17	verification	verification	NOUN
ejpam-1535	38	18	of	of	ADP
ejpam-1535	38	19	associativity	associativity	NOUN
ejpam-1535	38	20	(	(	PUNCT
ejpam-1535	38	21	in	in	ADP
ejpam-1535	38	22	an	an	DET
ejpam-1535	38	23	inverse	inverse	NOUN
ejpam-1535	38	24	semigroup	semigroup	NOUN
ejpam-1535	38	25	constructed	construct	VERB
ejpam-1535	38	26	from	from	ADP
ejpam-1535	38	27	a	a	DET
ejpam-1535	38	28	given	give	VERB
ejpam-1535	38	29	inductive	inductive	ADJ
ejpam-1535	38	30	groupoid	groupoid	NOUN
ejpam-1535	38	31	)	)	PUNCT
ejpam-1535	38	32	being	be	AUX
ejpam-1535	38	33	particularly	particularly	ADV
ejpam-1535	38	34	long	long	ADJ
ejpam-1535	38	35	,	,	PUNCT
ejpam-1535	38	36	tedious	tedious	ADJ
ejpam-1535	38	37	and	and	CCONJ
ejpam-1535	38	38	fiddly	fiddly	ADV
ejpam-1535	38	39	.	.	PUNCT
ejpam-1535	39	1	a	a	DET
ejpam-1535	39	2	new	new	ADJ
ejpam-1535	39	3	approach	approach	NOUN
ejpam-1535	39	4	was	be	AUX
ejpam-1535	39	5	subsequently	subsequently	ADV
ejpam-1535	39	6	promoted	promote	VERB
ejpam-1535	39	7	by	by	ADP
ejpam-1535	39	8	lawson	lawson	PROPN
ejpam-1535	39	9	[	[	X
ejpam-1535	39	10	29	29	NUM
ejpam-1535	39	11	]	]	PUNCT
ejpam-1535	39	12	,	,	PUNCT
ejpam-1535	39	13	using	use	VERB
ejpam-1535	39	14	the	the	DET
ejpam-1535	39	15	order	order	NOUN
ejpam-1535	39	16	-	-	PUNCT
ejpam-1535	39	17	theoretic	theoretic	NOUN
ejpam-1535	39	18	techniques	technique	NOUN
ejpam-1535	39	19	of	of	ADP
ejpam-1535	39	20	ehresmann	ehresmann	NOUN
ejpam-1535	40	1	[	[	X
ejpam-1535	40	2	11	11	NUM
ejpam-1535	40	3	]	]	PUNCT
ejpam-1535	40	4	.	.	PUNCT
ejpam-1535	41	1	by	by	ADP
ejpam-1535	41	2	allowing	allow	VERB
ejpam-1535	41	3	order	order	NOUN
ejpam-1535	41	4	-	-	PUNCT
ejpam-1535	41	5	theoretic	theoretic	ADJ
ejpam-1535	41	6	considerations	consideration	NOUN
ejpam-1535	41	7	to	to	PART
ejpam-1535	41	8	play	play	VERB
ejpam-1535	41	9	a	a	DET
ejpam-1535	41	10	much	much	ADV
ejpam-1535	41	11	more	more	ADV
ejpam-1535	41	12	prominent	prominent	ADJ
ejpam-1535	41	13	role	role	NOUN
ejpam-1535	41	14	,	,	PUNCT
ejpam-1535	41	15	considerably	considerably	ADV
ejpam-1535	41	16	shorter	short	ADJ
ejpam-1535	41	17	and	and	CCONJ
ejpam-1535	41	18	more	more	ADV
ejpam-1535	41	19	elegant	elegant	ADJ
ejpam-1535	41	20	proofs	proof	NOUN
ejpam-1535	41	21	may	may	AUX
ejpam-1535	41	22	be	be	AUX
ejpam-1535	41	23	obtained	obtain	VERB
ejpam-1535	41	24	.	.	PUNCT
ejpam-1535	42	1	the	the	DET
ejpam-1535	42	2	structure	structure	NOUN
ejpam-1535	42	3	of	of	ADP
ejpam-1535	42	4	the	the	DET
ejpam-1535	42	5	article	article	NOUN
ejpam-1535	42	6	is	be	AUX
ejpam-1535	42	7	as	as	SCONJ
ejpam-1535	42	8	follows	follow	VERB
ejpam-1535	42	9	.	.	PUNCT
ejpam-1535	43	1	after	after	ADP
ejpam-1535	43	2	the	the	DET
ejpam-1535	43	3	example	example	NOUN
ejpam-1535	43	4	of	of	ADP
ejpam-1535	43	5	[	[	X
ejpam-1535	43	6	20	20	NUM
ejpam-1535	43	7	]	]	PUNCT
ejpam-1535	43	8	,	,	PUNCT
ejpam-1535	43	9	we	we	PRON
ejpam-1535	43	10	begin	begin	VERB
ejpam-1535	43	11	the	the	DET
ejpam-1535	43	12	article	article	NOUN
ejpam-1535	43	13	proper	proper	ADJ
ejpam-1535	43	14	in	in	ADP
ejpam-1535	43	15	section	section	NOUN
ejpam-1535	43	16	2	2	NUM
ejpam-1535	43	17	with	with	ADP
ejpam-1535	43	18	a	a	DET
ejpam-1535	43	19	historical	historical	ADJ
ejpam-1535	43	20	survey	survey	NOUN
ejpam-1535	43	21	of	of	ADP
ejpam-1535	43	22	the	the	DET
ejpam-1535	43	23	development	development	NOUN
ejpam-1535	43	24	of	of	ADP
ejpam-1535	43	25	the	the	DET
ejpam-1535	43	26	theorems	theorem	NOUN
ejpam-1535	43	27	of	of	ADP
ejpam-1535	43	28	interest	interest	NOUN
ejpam-1535	43	29	,	,	PUNCT
ejpam-1535	43	30	beginning	begin	VERB
ejpam-1535	43	31	with	with	ADP
ejpam-1535	43	32	the	the	DET
ejpam-1535	43	33	origins	origin	NOUN
ejpam-1535	43	34	of	of	ADP
ejpam-1535	43	35	the	the	DET
ejpam-1535	43	36	theory	theory	NOUN
ejpam-1535	43	37	of	of	ADP
ejpam-1535	43	38	inverse	inverse	NOUN
ejpam-1535	43	39	semigroups	semigroup	NOUN
ejpam-1535	43	40	,	,	PUNCT
ejpam-1535	43	41	and	and	CCONJ
ejpam-1535	43	42	arriving	arrive	VERB
ejpam-1535	43	43	eventually	eventually	ADV
ejpam-1535	43	44	at	at	ADP
ejpam-1535	43	45	the	the	DET
ejpam-1535	43	46	generalised	generalise	VERB
ejpam-1535	43	47	esn	esn	PROPN
ejpam-1535	43	48	theorem	theorem	NOUN
ejpam-1535	43	49	for	for	ADP
ejpam-1535	43	50	restriction	restriction	NOUN
ejpam-1535	43	51	semigroups	semigroup	NOUN
ejpam-1535	43	52	.	.	PUNCT
ejpam-1535	44	1	in	in	ADP
ejpam-1535	44	2	section	section	NOUN
ejpam-1535	44	3	3	3	NUM
ejpam-1535	44	4	,	,	PUNCT
ejpam-1535	44	5	we	we	PRON
ejpam-1535	44	6	give	give	VERB
ejpam-1535	44	7	a	a	DET
ejpam-1535	44	8	brief	brief	ADJ
ejpam-1535	44	9	introduction	introduction	NOUN
ejpam-1535	44	10	to	to	ADP
ejpam-1535	44	11	restriction	restriction	NOUN
ejpam-1535	44	12	semigroups	semigroup	NOUN
ejpam-1535	44	13	,	,	PUNCT
ejpam-1535	44	14	but	but	CCONJ
ejpam-1535	44	15	we	we	PRON
ejpam-1535	44	16	only	only	ADV
ejpam-1535	44	17	include	include	VERB
ejpam-1535	44	18	those	those	DET
ejpam-1535	44	19	details	detail	NOUN
ejpam-1535	44	20	which	which	PRON
ejpam-1535	44	21	are	be	AUX
ejpam-1535	44	22	pertinent	pertinent	ADJ
ejpam-1535	44	23	to	to	ADP
ejpam-1535	44	24	the	the	DET
ejpam-1535	44	25	subsequent	subsequent	ADJ
ejpam-1535	44	26	considerations	consideration	NOUN
ejpam-1535	44	27	—	—	PUNCT
ejpam-1535	44	28	for	for	ADP
ejpam-1535	44	29	a	a	DET
ejpam-1535	44	30	more	more	ADV
ejpam-1535	44	31	rounded	rounded	ADJ
ejpam-1535	44	32	account	account	NOUN
ejpam-1535	44	33	of	of	ADP
ejpam-1535	44	34	restriction	restriction	NOUN
ejpam-1535	44	35	semigroups	semigroup	NOUN
ejpam-1535	44	36	,	,	PUNCT
ejpam-1535	44	37	the	the	DET
ejpam-1535	44	38	reader	reader	NOUN
ejpam-1535	44	39	is	be	AUX
ejpam-1535	44	40	referred	refer	VERB
ejpam-1535	44	41	to	to	ADP
ejpam-1535	44	42	[	[	X
ejpam-1535	44	43	20	20	NUM
ejpam-1535	44	44	]	]	PUNCT
ejpam-1535	44	45	or	or	CCONJ
ejpam-1535	44	46	[	[	X
ejpam-1535	44	47	15	15	NUM
ejpam-1535	44	48	]	]	PUNCT
ejpam-1535	44	49	.	.	PUNCT
ejpam-1535	45	1	in	in	ADP
ejpam-1535	45	2	particular	particular	ADJ
ejpam-1535	45	3	,	,	PUNCT
ejpam-1535	45	4	these	these	DET
ejpam-1535	45	5	articles	article	NOUN
ejpam-1535	45	6	motivate	motivate	VERB
ejpam-1535	45	7	the	the	DET
ejpam-1535	45	8	study	study	NOUN
ejpam-1535	45	9	of	of	ADP
ejpam-1535	45	10	such	such	ADJ
ejpam-1535	45	11	semigroups	semigroup	NOUN
ejpam-1535	45	12	.	.	PUNCT
ejpam-1535	46	1	inductive	inductive	ADJ
ejpam-1535	46	2	categories	category	NOUN
ejpam-1535	46	3	are	be	AUX
ejpam-1535	46	4	defined	define	VERB
ejpam-1535	46	5	in	in	ADP
ejpam-1535	46	6	section	section	NOUN
ejpam-1535	46	7	4	4	NUM
ejpam-1535	46	8	.	.	PUNCT
ejpam-1535	47	1	we	we	PRON
ejpam-1535	47	2	outline	outline	VERB
ejpam-1535	47	3	the	the	DET
ejpam-1535	47	4	basics	basic	NOUN
ejpam-1535	47	5	of	of	ADP
ejpam-1535	47	6	their	their	PRON
ejpam-1535	47	7	theory	theory	NOUN
ejpam-1535	47	8	,	,	PUNCT
ejpam-1535	47	9	before	before	ADP
ejpam-1535	47	10	demonstrating	demonstrate	VERB
ejpam-1535	47	11	their	their	PRON
ejpam-1535	47	12	connection	connection	NOUN
ejpam-1535	47	13	with	with	ADP
ejpam-1535	47	14	restriction	restriction	NOUN
ejpam-1535	47	15	semigroups	semigroup	NOUN
ejpam-1535	47	16	in	in	ADP
ejpam-1535	47	17	section	section	NOUN
ejpam-1535	47	18	5	5	NUM
ejpam-1535	47	19	.	.	PUNCT
ejpam-1535	48	1	by	by	ADP
ejpam-1535	48	2	the	the	DET
ejpam-1535	48	3	end	end	NOUN
ejpam-1535	48	4	of	of	ADP
ejpam-1535	48	5	section	section	NOUN
ejpam-1535	48	6	5	5	NUM
ejpam-1535	48	7	,	,	PUNCT
ejpam-1535	48	8	we	we	PRON
ejpam-1535	48	9	will	will	AUX
ejpam-1535	48	10	have	have	AUX
ejpam-1535	48	11	shown	show	VERB
ejpam-1535	48	12	that	that	SCONJ
ejpam-1535	48	13	every	every	DET
ejpam-1535	48	14	restriction	restriction	NOUN
ejpam-1535	48	15	semigroup	semigroup	NOUN
ejpam-1535	48	16	gives	give	VERB
ejpam-1535	48	17	rise	rise	NOUN
ejpam-1535	48	18	to	to	ADP
ejpam-1535	48	19	an	an	DET
ejpam-1535	48	20	inductive	inductive	ADJ
ejpam-1535	48	21	category	category	NOUN
ejpam-1535	48	22	,	,	PUNCT
ejpam-1535	48	23	and	and	CCONJ
ejpam-1535	48	24	vice	vice	ADV
ejpam-1535	48	25	versa	versa	ADV
ejpam-1535	48	26	.	.	PUNCT
ejpam-1535	49	1	in	in	ADP
ejpam-1535	49	2	this	this	DET
ejpam-1535	49	3	way	way	NOUN
ejpam-1535	49	4	,	,	PUNCT
ejpam-1535	49	5	we	we	PRON
ejpam-1535	49	6	will	will	AUX
ejpam-1535	49	7	have	have	AUX
ejpam-1535	49	8	taken	take	VERB
ejpam-1535	49	9	care	care	NOUN
ejpam-1535	49	10	of	of	ADP
ejpam-1535	49	11	the	the	DET
ejpam-1535	49	12	“	"	PUNCT
ejpam-1535	49	13	objects	object	NOUN
ejpam-1535	49	14	”	"	PUNCT
ejpam-1535	49	15	part	part	NOUN
ejpam-1535	49	16	of	of	ADP
ejpam-1535	49	17	the	the	DET
ejpam-1535	49	18	desired	desire	VERB
ejpam-1535	49	19	correspondence	correspondence	NOUN
ejpam-1535	49	20	of	of	ADP
ejpam-1535	49	21	categories	category	NOUN
ejpam-1535	49	22	.	.	PUNCT
ejpam-1535	50	1	we	we	PRON
ejpam-1535	50	2	therefore	therefore	ADV
ejpam-1535	50	3	turn	turn	VERB
ejpam-1535	50	4	to	to	ADP
ejpam-1535	50	5	the	the	DET
ejpam-1535	50	6	“	"	PUNCT
ejpam-1535	50	7	arrows	arrow	NOUN
ejpam-1535	50	8	”	"	PUNCT
ejpam-1535	50	9	part	part	NOUN
ejpam-1535	50	10	in	in	ADP
ejpam-1535	50	11	the	the	DET
ejpam-1535	50	12	next	next	ADJ
ejpam-1535	50	13	two	two	NUM
ejpam-1535	50	14	sections	section	NOUN
ejpam-1535	50	15	.	.	PUNCT
ejpam-1535	51	1	in	in	ADP
ejpam-1535	51	2	section	section	NOUN
ejpam-1535	51	3	6	6	NUM
ejpam-1535	51	4	,	,	PUNCT
ejpam-1535	51	5	we	we	PRON
ejpam-1535	51	6	introduce	introduce	VERB
ejpam-1535	51	7	functions	function	NOUN
ejpam-1535	51	8	called	call	VERB
ejpam-1535	51	9	“	"	PUNCT
ejpam-1535	51	10	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	51	11	”	"	PUNCT
ejpam-1535	51	12	between	between	ADP
ejpam-1535	51	13	restriction	restriction	NOUN
ejpam-1535	51	14	semigroups	semigroup	NOUN
ejpam-1535	51	15	and	and	CCONJ
ejpam-1535	51	16	show	show	VERB
ejpam-1535	51	17	that	that	SCONJ
ejpam-1535	51	18	these	these	PRON
ejpam-1535	51	19	correspond	correspond	VERB
ejpam-1535	51	20	to	to	ADP
ejpam-1535	51	21	order	order	NOUN
ejpam-1535	51	22	-	-	PUNCT
ejpam-1535	51	23	preserving	preserve	VERB
ejpam-1535	51	24	functors	functor	NOUN
ejpam-1535	51	25	between	between	ADP
ejpam-1535	51	26	inductive	inductive	ADJ
ejpam-1535	51	27	categories	category	NOUN
ejpam-1535	51	28	.	.	PUNCT
ejpam-1535	52	1	in	in	ADP
ejpam-1535	52	2	section	section	NOUN
ejpam-1535	52	3	7	7	NUM
ejpam-1535	52	4	,	,	PUNCT
ejpam-1535	52	5	we	we	PRON
ejpam-1535	52	6	consider	consider	VERB
ejpam-1535	52	7	certain	certain	ADJ
ejpam-1535	52	8	morphisms	morphism	NOUN
ejpam-1535	52	9	between	between	ADP
ejpam-1535	52	10	restriction	restriction	NOUN
ejpam-1535	52	11	semigroups	semigroup	NOUN
ejpam-1535	52	12	and	and	CCONJ
ejpam-1535	52	13	show	show	VERB
ejpam-1535	52	14	that	that	SCONJ
ejpam-1535	52	15	these	these	PRON
ejpam-1535	52	16	correspond	correspond	VERB
ejpam-1535	52	17	to	to	ADP
ejpam-1535	52	18	so	so	ADV
ejpam-1535	52	19	-	-	PUNCT
ejpam-1535	52	20	called	call	VERB
ejpam-1535	52	21	“	"	PUNCT
ejpam-1535	52	22	inductive	inductive	ADJ
ejpam-1535	52	23	functors	functor	NOUN
ejpam-1535	52	24	”	"	PUNCT
ejpam-1535	52	25	between	between	ADP
ejpam-1535	52	26	inductive	inductive	ADJ
ejpam-1535	52	27	categories	category	NOUN
ejpam-1535	52	28	.	.	PUNCT
ejpam-1535	53	1	by	by	ADP
ejpam-1535	53	2	combining	combine	VERB
ejpam-1535	53	3	the	the	DET
ejpam-1535	53	4	results	result	NOUN
ejpam-1535	53	5	of	of	ADP
ejpam-1535	53	6	sections	section	NOUN
ejpam-1535	53	7	5	5	NUM
ejpam-1535	53	8	,	,	PUNCT
ejpam-1535	53	9	6	6	NUM
ejpam-1535	53	10	and	and	CCONJ
ejpam-1535	53	11	7	7	NUM
ejpam-1535	53	12	,	,	PUNCT
ejpam-1535	53	13	we	we	PRON
ejpam-1535	53	14	obtain	obtain	VERB
ejpam-1535	53	15	two	two	NUM
ejpam-1535	53	16	isomorphisms	isomorphism	NOUN
ejpam-1535	53	17	of	of	ADP
ejpam-1535	53	18	categories	category	NOUN
ejpam-1535	53	19	in	in	ADP
ejpam-1535	53	20	theorems	theorem	NOUN
ejpam-1535	53	21	5	5	NUM
ejpam-1535	53	22	and	and	CCONJ
ejpam-1535	53	23	6	6	NUM
ejpam-1535	53	24	.	.	PUNCT
ejpam-1535	54	1	together	together	ADV
ejpam-1535	54	2	,	,	PUNCT
ejpam-1535	54	3	these	these	DET
ejpam-1535	54	4	two	two	NUM
ejpam-1535	54	5	theorems	theorem	NOUN
ejpam-1535	54	6	give	give	VERB
ejpam-1535	54	7	the	the	DET
ejpam-1535	54	8	restriction	restriction	NOUN
ejpam-1535	54	9	semigroup	semigroup	NOUN
ejpam-1535	54	10	version	version	NOUN
ejpam-1535	54	11	of	of	ADP
ejpam-1535	54	12	the	the	DET
ejpam-1535	54	13	esn	esn	PROPN
ejpam-1535	54	14	theorem	theorem	PROPN
ejpam-1535	54	15	.	.	PROPN
ejpam-1535	55	1	in	in	ADP
ejpam-1535	55	2	the	the	DET
ejpam-1535	55	3	final	final	ADJ
ejpam-1535	55	4	section	section	NOUN
ejpam-1535	55	5	(	(	PUNCT
ejpam-1535	55	6	8)	8)	NUM
ejpam-1535	55	7	,	,	PUNCT
ejpam-1535	55	8	we	we	PRON
ejpam-1535	55	9	use	use	VERB
ejpam-1535	55	10	the	the	DET
ejpam-1535	55	11	results	result	NOUN
ejpam-1535	55	12	on	on	ADP
ejpam-1535	55	13	restriction	restriction	NOUN
ejpam-1535	55	14	semigroups	semigroup	NOUN
ejpam-1535	55	15	and	and	CCONJ
ejpam-1535	55	16	inductive	inductive	ADJ
ejpam-1535	55	17	categories	category	NOUN
ejpam-1535	55	18	to	to	PART
ejpam-1535	55	19	deduce	deduce	VERB
ejpam-1535	55	20	the	the	DET
ejpam-1535	55	21	original	original	ADJ
ejpam-1535	55	22	version	version	NOUN
ejpam-1535	55	23	of	of	ADP
ejpam-1535	55	24	the	the	DET
ejpam-1535	55	25	esn	esn	PROPN
ejpam-1535	55	26	theorem	theorem	PROPN
ejpam-1535	55	27	.	.	PUNCT
ejpam-1535	56	1	our	our	PRON
ejpam-1535	56	2	approach	approach	NOUN
ejpam-1535	56	3	to	to	ADP
ejpam-1535	56	4	inductive	inductive	ADJ
ejpam-1535	56	5	categories	category	NOUN
ejpam-1535	56	6	is	be	AUX
ejpam-1535	56	7	based	base	VERB
ejpam-1535	56	8	very	very	ADV
ejpam-1535	56	9	heavily	heavily	ADV
ejpam-1535	56	10	upon	upon	SCONJ
ejpam-1535	56	11	lawson	lawson	PROPN
ejpam-1535	56	12	’s	’s	PART
ejpam-1535	56	13	approach	approach	NOUN
ejpam-1535	56	14	to	to	ADP
ejpam-1535	56	15	inductive	inductive	ADJ
ejpam-1535	56	16	groupoids	groupoid	NOUN
ejpam-1535	56	17	[	[	X
ejpam-1535	56	18	29	29	NUM
ejpam-1535	56	19	]	]	PUNCT
ejpam-1535	56	20	,	,	PUNCT
ejpam-1535	56	21	but	but	CCONJ
ejpam-1535	56	22	one	one	NUM
ejpam-1535	56	23	important	important	ADJ
ejpam-1535	56	24	difference	difference	NOUN
ejpam-1535	56	25	to	to	PART
ejpam-1535	56	26	note	note	VERB
ejpam-1535	56	27	is	be	AUX
ejpam-1535	56	28	the	the	DET
ejpam-1535	56	29	fact	fact	NOUN
ejpam-1535	56	30	that	that	SCONJ
ejpam-1535	56	31	we	we	PRON
ejpam-1535	56	32	will	will	AUX
ejpam-1535	56	33	be	be	AUX
ejpam-1535	56	34	composing	compose	VERB
ejpam-1535	56	35	functions	function	NOUN
ejpam-1535	56	36	from	from	ADP
ejpam-1535	56	37	left	left	ADJ
ejpam-1535	56	38	to	to	ADP
ejpam-1535	56	39	right	right	NOUN
ejpam-1535	56	40	.	.	PUNCT
ejpam-1535	57	1	thus	thus	ADV
ejpam-1535	57	2	,	,	PUNCT
ejpam-1535	57	3	for	for	ADP
ejpam-1535	57	4	example	example	NOUN
ejpam-1535	57	5	,	,	PUNCT
ejpam-1535	57	6	our	our	PRON
ejpam-1535	57	7	domain	domain	NOUN
ejpam-1535	57	8	and	and	CCONJ
ejpam-1535	57	9	range	range	NOUN
ejpam-1535	57	10	in	in	ADP
ejpam-1535	57	11	a	a	DET
ejpam-1535	57	12	category	category	NOUN
ejpam-1535	57	13	(	(	PUNCT
ejpam-1535	57	14	see	see	VERB
ejpam-1535	57	15	section	section	NOUN
ejpam-1535	57	16	4	4	NUM
ejpam-1535	57	17	)	)	PUNCT
ejpam-1535	57	18	are	be	AUX
ejpam-1535	57	19	the	the	DET
ejpam-1535	57	20	opposite	opposite	ADJ
ejpam-1535	57	21	way	way	NOUN
ejpam-1535	57	22	round	round	ADV
ejpam-1535	57	23	to	to	ADP
ejpam-1535	57	24	those	those	PRON
ejpam-1535	57	25	in	in	ADP
ejpam-1535	57	26	[	[	X
ejpam-1535	57	27	29	29	NUM
ejpam-1535	57	28	]	]	SYM
ejpam-1535	57	29	:	:	PUNCT
ejpam-1535	57	30	for	for	ADP
ejpam-1535	57	31	lawson	lawson	PROPN
ejpam-1535	57	32	,	,	PUNCT
ejpam-1535	57	33	∃r(x	∃r(x	PROPN
ejpam-1535	57	34	)	)	PUNCT
ejpam-1535	57	35	·	·	PUNCT
ejpam-1535	58	1	x	x	PUNCT
ejpam-1535	58	2	with	with	ADP
ejpam-1535	58	3	r(x	r(x	NOUN
ejpam-1535	58	4	)	)	PUNCT
ejpam-1535	58	5	·	·	PUNCT
ejpam-1535	58	6	x	x	PUNCT
ejpam-1535	58	7	=	=	PUNCT
ejpam-1535	58	8	x	x	X
ejpam-1535	58	9	,	,	PUNCT
ejpam-1535	58	10	and	and	CCONJ
ejpam-1535	58	11	∃x	∃x	ADJ
ejpam-1535	58	12	·	·	SYM
ejpam-1535	58	13	d(x	d(x	NOUN
ejpam-1535	58	14	)	)	PUNCT
ejpam-1535	58	15	with	with	ADP
ejpam-1535	58	16	x	x	X
ejpam-1535	58	17	·	·	PUNCT
ejpam-1535	58	18	d(x	d(x	NOUN
ejpam-1535	58	19	)	)	PUNCT
ejpam-1535	59	1	=	=	PUNCT
ejpam-1535	59	2	x	x	X
ejpam-1535	59	3	(	(	PUNCT
ejpam-1535	59	4	cf	cf	NOUN
ejpam-1535	59	5	.	.	PUNCT
ejpam-1535	60	1	our	our	PRON
ejpam-1535	60	2	definition	definition	NOUN
ejpam-1535	60	3	8)	8)	NUM
ejpam-1535	60	4	.	.	PUNCT
ejpam-1535	61	1	our	our	PRON
ejpam-1535	61	2	imitation	imitation	NOUN
ejpam-1535	61	3	of	of	ADP
ejpam-1535	61	4	lawson	lawson	PROPN
ejpam-1535	61	5	[	[	X
ejpam-1535	61	6	29	29	NUM
ejpam-1535	61	7	]	]	PUNCT
ejpam-1535	61	8	extends	extend	VERB
ejpam-1535	61	9	also	also	ADV
ejpam-1535	61	10	to	to	ADP
ejpam-1535	61	11	the	the	DET
ejpam-1535	61	12	adoption	adoption	NOUN
ejpam-1535	61	13	of	of	ADP
ejpam-1535	61	14	the	the	DET
ejpam-1535	61	15	order	order	NOUN
ejpam-1535	61	16	-	-	PUNCT
ejpam-1535	61	17	theoretic	theoretic	ADJ
ejpam-1535	61	18	approach	approach	NOUN
ejpam-1535	61	19	indicated	indicate	VERB
ejpam-1535	61	20	above	above	ADV
ejpam-1535	61	21	,	,	PUNCT
ejpam-1535	61	22	rather	rather	ADV
ejpam-1535	61	23	than	than	ADP
ejpam-1535	61	24	the	the	DET
ejpam-1535	61	25	original	original	ADJ
ejpam-1535	61	26	,	,	PUNCT
ejpam-1535	61	27	direct	direct	ADJ
ejpam-1535	61	28	,	,	PUNCT
ejpam-1535	61	29	algebraic	algebraic	ADJ
ejpam-1535	61	30	approach	approach	NOUN
ejpam-1535	61	31	.	.	PUNCT
ejpam-1535	62	1	thus	thus	ADV
ejpam-1535	62	2	,	,	PUNCT
ejpam-1535	62	3	for	for	ADP
ejpam-1535	62	4	example	example	NOUN
ejpam-1535	62	5	,	,	PUNCT
ejpam-1535	62	6	our	our	PRON
ejpam-1535	62	7	auxiliary	auxiliary	ADJ
ejpam-1535	62	8	results	result	NOUN
ejpam-1535	62	9	,	,	PUNCT
ejpam-1535	62	10	propositions	proposition	NOUN
ejpam-1535	62	11	1	1	NUM
ejpam-1535	62	12	and	and	CCONJ
ejpam-1535	62	13	2	2	NUM
ejpam-1535	62	14	,	,	PUNCT
ejpam-1535	62	15	which	which	PRON
ejpam-1535	62	16	are	be	AUX
ejpam-1535	62	17	analogues	analogue	NOUN
ejpam-1535	62	18	of	of	ADP
ejpam-1535	62	19	results	result	NOUN
ejpam-1535	62	20	of	of	ADP
ejpam-1535	62	21	lawson	lawson	PROPN
ejpam-1535	62	22	in	in	ADP
ejpam-1535	62	23	the	the	DET
ejpam-1535	62	24	inverse	inverse	NOUN
ejpam-1535	62	25	case	case	NOUN
ejpam-1535	62	26	,	,	PUNCT
ejpam-1535	62	27	allow	allow	VERB
ejpam-1535	62	28	us	we	PRON
ejpam-1535	62	29	to	to	PART
ejpam-1535	62	30	sidestep	sidestep	VERB
ejpam-1535	62	31	the	the	DET
ejpam-1535	62	32	lengthy	lengthy	ADJ
ejpam-1535	62	33	associativity	associativity	NOUN
ejpam-1535	62	34	proof	proof	NOUN
ejpam-1535	62	35	mentioned	mention	VERB
ejpam-1535	62	36	above	above	ADV
ejpam-1535	62	37	.	.	PUNCT
ejpam-1535	63	1	as	as	ADV
ejpam-1535	63	2	far	far	ADV
ejpam-1535	63	3	as	as	SCONJ
ejpam-1535	63	4	we	we	PRON
ejpam-1535	63	5	are	be	AUX
ejpam-1535	63	6	aware	aware	ADJ
ejpam-1535	63	7	,	,	PUNCT
ejpam-1535	63	8	our	our	PRON
ejpam-1535	63	9	proofs	proof	NOUN
ejpam-1535	63	10	of	of	ADP
ejpam-1535	63	11	theorems	theorem	NOUN
ejpam-1535	63	12	2	2	NUM
ejpam-1535	63	13	and	and	CCONJ
ejpam-1535	63	14	3	3	NUM
ejpam-1535	63	15	(	(	PUNCT
ejpam-1535	63	16	the	the	DET
ejpam-1535	63	17	mutual	mutual	ADJ
ejpam-1535	63	18	correspondence	correspondence	NOUN
ejpam-1535	63	19	between	between	ADP
ejpam-1535	63	20	restriction	restriction	NOUN
ejpam-1535	63	21	semigroups	semigroup	NOUN
ejpam-1535	63	22	and	and	CCONJ
ejpam-1535	63	23	inductive	inductive	ADJ
ejpam-1535	63	24	categories	category	NOUN
ejpam-1535	63	25	)	)	PUNCT
ejpam-1535	63	26	are	be	AUX
ejpam-1535	63	27	the	the	DET
ejpam-1535	63	28	first	first	ADJ
ejpam-1535	63	29	direct	direct	ADJ
ejpam-1535	63	30	proofs	proof	NOUN
ejpam-1535	63	31	—	—	PUNCT
ejpam-1535	63	32	these	these	DET
ejpam-1535	63	33	theorems	theorem	NOUN
ejpam-1535	63	34	first	first	ADV
ejpam-1535	63	35	appeared	appear	VERB
ejpam-1535	63	36	in	in	ADP
ejpam-1535	63	37	[	[	X
ejpam-1535	63	38	28	28	NUM
ejpam-1535	63	39	]	]	PUNCT
ejpam-1535	63	40	,	,	PUNCT
ejpam-1535	63	41	but	but	CCONJ
ejpam-1535	63	42	were	be	AUX
ejpam-1535	63	43	deduced	deduce	VERB
ejpam-1535	63	44	there	there	ADV
ejpam-1535	63	45	from	from	ADP
ejpam-1535	63	46	other	other	ADJ
ejpam-1535	63	47	results	result	NOUN
ejpam-1535	63	48	.	.	PUNCT
ejpam-1535	64	1	however	however	ADV
ejpam-1535	64	2	,	,	PUNCT
ejpam-1535	64	3	these	these	DET
ejpam-1535	64	4	direct	direct	ADJ
ejpam-1535	64	5	proofs	proof	NOUN
ejpam-1535	64	6	differ	differ	VERB
ejpam-1535	64	7	very	very	ADV
ejpam-1535	64	8	little	little	ADJ
ejpam-1535	64	9	,	,	PUNCT
ejpam-1535	64	10	on	on	ADP
ejpam-1535	64	11	the	the	DET
ejpam-1535	64	12	whole	whole	NOUN
ejpam-1535	64	13	,	,	PUNCT
ejpam-1535	64	14	from	from	ADP
ejpam-1535	64	15	those	those	PRON
ejpam-1535	64	16	given	give	VERB
ejpam-1535	64	17	by	by	ADP
ejpam-1535	64	18	armstrong	armstrong	PROPN
ejpam-1535	64	19	[	[	X
ejpam-1535	64	20	1	1	NUM
ejpam-1535	64	21	]	]	PUNCT
ejpam-1535	64	22	in	in	ADP
ejpam-1535	64	23	the	the	DET
ejpam-1535	64	24	ample	ample	ADJ
ejpam-1535	64	25	case	case	NOUN
ejpam-1535	64	26	,	,	PUNCT
ejpam-1535	64	27	and	and	CCONJ
ejpam-1535	64	28	lawson	lawson	PROPN
ejpam-1535	65	1	[	[	X
ejpam-1535	65	2	26	26	NUM
ejpam-1535	65	3	]	]	PUNCT
ejpam-1535	65	4	in	in	ADP
ejpam-1535	65	5	the	the	DET
ejpam-1535	65	6	full	full	ADJ
ejpam-1535	65	7	restriction	restriction	NOUN
ejpam-1535	65	8	case	case	NOUN
ejpam-1535	65	9	(	(	PUNCT
ejpam-1535	65	10	and	and	CCONJ
ejpam-1535	65	11	,	,	PUNCT
ejpam-1535	65	12	indeed	indeed	ADV
ejpam-1535	65	13	,	,	PUNCT
ejpam-1535	65	14	that	that	PRON
ejpam-1535	65	15	of	of	ADP
ejpam-1535	65	16	schein	schein	PROPN
ejpam-1535	66	1	[	[	X
ejpam-1535	66	2	44	44	NUM
ejpam-1535	66	3	,	,	PUNCT
ejpam-1535	66	4	45	45	NUM
ejpam-1535	66	5	]	]	PUNCT
ejpam-1535	66	6	in	in	ADP
ejpam-1535	66	7	the	the	DET
ejpam-1535	66	8	inverse	inverse	NOUN
ejpam-1535	66	9	case	case	NOUN
ejpam-1535	66	10	)	)	PUNCT
ejpam-1535	66	11	.	.	PUNCT
ejpam-1535	67	1	the	the	DET
ejpam-1535	67	2	only	only	ADJ
ejpam-1535	67	3	significant	significant	ADJ
ejpam-1535	67	4	difference	difference	NOUN
ejpam-1535	67	5	is	be	AUX
ejpam-1535	67	6	the	the	DET
ejpam-1535	67	7	shorter	short	ADJ
ejpam-1535	67	8	proof	proof	NOUN
ejpam-1535	67	9	of	of	ADP
ejpam-1535	67	10	associativity	associativity	NOUN
ejpam-1535	67	11	.	.	PUNCT
ejpam-1535	68	1	c.	c.	PROPN
ejpam-1535	68	2	hollings	holling	NOUN
ejpam-1535	68	3	/	/	SYM
ejpam-1535	68	4	eur	eur	PROPN
ejpam-1535	68	5	.	.	PUNCT
ejpam-1535	69	1	j.	j.	PROPN
ejpam-1535	69	2	pure	pure	PROPN
ejpam-1535	69	3	appl	appl	PROPN
ejpam-1535	69	4	.	.	PROPN
ejpam-1535	69	5	math	math	PROPN
ejpam-1535	69	6	,	,	PUNCT
ejpam-1535	69	7	5	5	NUM
ejpam-1535	69	8	(	(	PUNCT
ejpam-1535	69	9	2012	2012	NUM
ejpam-1535	69	10	)	)	PUNCT
ejpam-1535	69	11	,	,	PUNCT
ejpam-1535	69	12	414	414	NUM
ejpam-1535	69	13	-	-	SYM
ejpam-1535	69	14	450	450	NUM
ejpam-1535	69	15	417	417	NUM
ejpam-1535	69	16	it	it	PRON
ejpam-1535	69	17	should	should	AUX
ejpam-1535	69	18	be	be	AUX
ejpam-1535	69	19	noted	note	VERB
ejpam-1535	69	20	that	that	SCONJ
ejpam-1535	69	21	,	,	PUNCT
ejpam-1535	69	22	as	as	SCONJ
ejpam-1535	69	23	indicated	indicate	VERB
ejpam-1535	69	24	in	in	ADP
ejpam-1535	69	25	[	[	X
ejpam-1535	69	26	20	20	NUM
ejpam-1535	69	27	]	]	PUNCT
ejpam-1535	69	28	,	,	PUNCT
ejpam-1535	69	29	there	there	PRON
ejpam-1535	69	30	are	be	VERB
ejpam-1535	69	31	three	three	NUM
ejpam-1535	69	32	types	type	NOUN
ejpam-1535	69	33	of	of	ADP
ejpam-1535	69	34	restriction	restriction	NOUN
ejpam-1535	69	35	semigroup	semigroup	NOUN
ejpam-1535	69	36	:	:	PUNCT
ejpam-1535	69	37	left	leave	VERB
ejpam-1535	69	38	,	,	PUNCT
ejpam-1535	69	39	right	right	ADJ
ejpam-1535	69	40	and	and	CCONJ
ejpam-1535	69	41	two	two	NUM
ejpam-1535	69	42	-	-	PUNCT
ejpam-1535	69	43	sided	sided	ADJ
ejpam-1535	69	44	.	.	PUNCT
ejpam-1535	70	1	we	we	PRON
ejpam-1535	70	2	will	will	AUX
ejpam-1535	70	3	only	only	ADV
ejpam-1535	70	4	be	be	AUX
ejpam-1535	70	5	concerned	concern	VERB
ejpam-1535	70	6	with	with	ADP
ejpam-1535	70	7	the	the	DET
ejpam-1535	70	8	two	two	NUM
ejpam-1535	70	9	-	-	PUNCT
ejpam-1535	70	10	sided	sided	ADJ
ejpam-1535	70	11	version	version	NOUN
ejpam-1535	70	12	here	here	ADV
ejpam-1535	70	13	,	,	PUNCT
ejpam-1535	70	14	which	which	PRON
ejpam-1535	70	15	we	we	PRON
ejpam-1535	70	16	will	will	AUX
ejpam-1535	70	17	refer	refer	VERB
ejpam-1535	70	18	to	to	ADP
ejpam-1535	70	19	throughout	throughout	ADV
ejpam-1535	70	20	simply	simply	ADV
ejpam-1535	70	21	as	as	ADP
ejpam-1535	70	22	“	"	PUNCT
ejpam-1535	70	23	restriction	restriction	NOUN
ejpam-1535	70	24	semigroups	semigroup	NOUN
ejpam-1535	70	25	”	"	PUNCT
ejpam-1535	70	26	.	.	PUNCT
ejpam-1535	71	1	an	an	DET
ejpam-1535	71	2	“	"	PUNCT
ejpam-1535	71	3	esn	esn	PROPN
ejpam-1535	71	4	-	-	PUNCT
ejpam-1535	71	5	type	type	NOUN
ejpam-1535	71	6	”	"	PUNCT
ejpam-1535	71	7	theorem	theorem	NOUN
ejpam-1535	71	8	may	may	AUX
ejpam-1535	71	9	be	be	AUX
ejpam-1535	71	10	obtained	obtain	VERB
ejpam-1535	71	11	for	for	ADP
ejpam-1535	71	12	left	left	ADJ
ejpam-1535	71	13	restriction	restriction	NOUN
ejpam-1535	71	14	semigroups	semigroup	NOUN
ejpam-1535	71	15	,	,	PUNCT
ejpam-1535	71	16	but	but	CCONJ
ejpam-1535	71	17	the	the	DET
ejpam-1535	71	18	objects	object	NOUN
ejpam-1535	71	19	to	to	PART
ejpam-1535	71	20	which	which	PRON
ejpam-1535	71	21	such	such	ADJ
ejpam-1535	71	22	semigroups	semigroup	NOUN
ejpam-1535	71	23	correspond	correspond	VERB
ejpam-1535	71	24	are	be	AUX
ejpam-1535	71	25	not	not	PART
ejpam-1535	71	26	categories	category	NOUN
ejpam-1535	71	27	,	,	PUNCT
ejpam-1535	71	28	but	but	CCONJ
ejpam-1535	71	29	“	"	PUNCT
ejpam-1535	71	30	one	one	NUM
ejpam-1535	71	31	-	-	PUNCT
ejpam-1535	71	32	sided	sided	ADJ
ejpam-1535	71	33	generalisations	generalisation	NOUN
ejpam-1535	71	34	”	"	PUNCT
ejpam-1535	71	35	of	of	ADP
ejpam-1535	71	36	categories	category	NOUN
ejpam-1535	71	37	,	,	PUNCT
ejpam-1535	71	38	termed	term	VERB
ejpam-1535	71	39	inductive	inductive	ADJ
ejpam-1535	71	40	constellations	constellation	NOUN
ejpam-1535	71	41	—	—	PUNCT
ejpam-1535	71	42	for	for	ADP
ejpam-1535	71	43	further	further	ADJ
ejpam-1535	71	44	details	detail	NOUN
ejpam-1535	71	45	,	,	PUNCT
ejpam-1535	71	46	see	see	VERB
ejpam-1535	71	47	[	[	X
ejpam-1535	71	48	17	17	NUM
ejpam-1535	71	49	]	]	PUNCT
ejpam-1535	71	50	.	.	PUNCT
ejpam-1535	72	1	some	some	DET
ejpam-1535	72	2	comments	comment	NOUN
ejpam-1535	72	3	should	should	AUX
ejpam-1535	72	4	be	be	AUX
ejpam-1535	72	5	made	make	VERB
ejpam-1535	72	6	here	here	ADV
ejpam-1535	72	7	on	on	ADP
ejpam-1535	72	8	the	the	DET
ejpam-1535	72	9	terminology	terminology	NOUN
ejpam-1535	72	10	to	to	PART
ejpam-1535	72	11	be	be	AUX
ejpam-1535	72	12	used	use	VERB
ejpam-1535	72	13	throughout	throughout	ADP
ejpam-1535	72	14	this	this	DET
ejpam-1535	72	15	article	article	NOUN
ejpam-1535	72	16	.	.	PUNCT
ejpam-1535	73	1	first	first	ADV
ejpam-1535	73	2	of	of	ADP
ejpam-1535	73	3	all	all	PRON
ejpam-1535	73	4	,	,	PUNCT
ejpam-1535	73	5	it	it	PRON
ejpam-1535	73	6	is	be	AUX
ejpam-1535	73	7	worth	worth	ADJ
ejpam-1535	73	8	emphasising	emphasise	VERB
ejpam-1535	73	9	that	that	SCONJ
ejpam-1535	73	10	we	we	PRON
ejpam-1535	73	11	will	will	AUX
ejpam-1535	73	12	be	be	AUX
ejpam-1535	73	13	using	use	VERB
ejpam-1535	73	14	the	the	DET
ejpam-1535	73	15	term	term	NOUN
ejpam-1535	73	16	“	"	PUNCT
ejpam-1535	73	17	groupoid	groupoid	PROPN
ejpam-1535	73	18	”	"	PUNCT
ejpam-1535	73	19	only	only	ADV
ejpam-1535	73	20	to	to	PART
ejpam-1535	73	21	mean	mean	VERB
ejpam-1535	73	22	a	a	DET
ejpam-1535	73	23	small	small	ADJ
ejpam-1535	73	24	category	category	NOUN
ejpam-1535	73	25	in	in	ADP
ejpam-1535	73	26	which	which	PRON
ejpam-1535	73	27	all	all	DET
ejpam-1535	73	28	arrows	arrow	NOUN
ejpam-1535	73	29	are	be	AUX
ejpam-1535	73	30	invertible	invertible	ADJ
ejpam-1535	73	31	.	.	PUNCT
ejpam-1535	74	1	“	"	PUNCT
ejpam-1535	74	2	groupoid	groupoid	PROPN
ejpam-1535	74	3	”	"	PUNCT
ejpam-1535	74	4	is	be	AUX
ejpam-1535	74	5	also	also	ADV
ejpam-1535	74	6	occasionally	occasionally	ADV
ejpam-1535	74	7	used	use	VERB
ejpam-1535	74	8	(	(	PUNCT
ejpam-1535	74	9	for	for	ADP
ejpam-1535	74	10	example	example	NOUN
ejpam-1535	74	11	,	,	PUNCT
ejpam-1535	74	12	in	in	ADP
ejpam-1535	74	13	[	[	X
ejpam-1535	74	14	23	23	NUM
ejpam-1535	74	15	,	,	PUNCT
ejpam-1535	74	16	p.	p.	NOUN
ejpam-1535	74	17	1	1	NUM
ejpam-1535	74	18	]	]	PUNCT
ejpam-1535	74	19	)	)	PUNCT
ejpam-1535	74	20	to	to	PART
ejpam-1535	74	21	refer	refer	VERB
ejpam-1535	74	22	to	to	ADP
ejpam-1535	74	23	a	a	DET
ejpam-1535	74	24	set	set	NOUN
ejpam-1535	74	25	with	with	ADP
ejpam-1535	74	26	an	an	DET
ejpam-1535	74	27	everywhere	everywhere	ADV
ejpam-1535	74	28	-	-	PUNCT
ejpam-1535	74	29	defined	define	VERB
ejpam-1535	74	30	binary	binary	ADJ
ejpam-1535	74	31	operation	operation	NOUN
ejpam-1535	74	32	(	(	PUNCT
ejpam-1535	74	33	according	accord	VERB
ejpam-1535	74	34	to	to	ADP
ejpam-1535	74	35	which	which	DET
ejpam-1535	74	36	definition	definition	NOUN
ejpam-1535	74	37	,	,	PUNCT
ejpam-1535	74	38	a	a	DET
ejpam-1535	74	39	semigroup	semigroup	NOUN
ejpam-1535	74	40	is	be	AUX
ejpam-1535	74	41	then	then	ADV
ejpam-1535	74	42	an	an	DET
ejpam-1535	74	43	“	"	PUNCT
ejpam-1535	74	44	associative	associative	ADJ
ejpam-1535	74	45	groupoid	groupoid	NOUN
ejpam-1535	74	46	”	"	PUNCT
ejpam-1535	74	47	)	)	PUNCT
ejpam-1535	74	48	—	—	PUNCT
ejpam-1535	74	49	the	the	DET
ejpam-1535	74	50	word	word	NOUN
ejpam-1535	74	51	“	"	PUNCT
ejpam-1535	74	52	groupoid	groupoid	PROPN
ejpam-1535	74	53	”	"	PUNCT
ejpam-1535	74	54	will	will	AUX
ejpam-1535	74	55	never	never	ADV
ejpam-1535	74	56	be	be	AUX
ejpam-1535	74	57	used	use	VERB
ejpam-1535	74	58	in	in	ADP
ejpam-1535	74	59	this	this	DET
ejpam-1535	74	60	sense	sense	NOUN
ejpam-1535	74	61	here	here	ADV
ejpam-1535	74	62	.	.	PUNCT
ejpam-1535	75	1	it	it	PRON
ejpam-1535	75	2	is	be	AUX
ejpam-1535	75	3	also	also	ADV
ejpam-1535	75	4	important	important	ADJ
ejpam-1535	75	5	to	to	PART
ejpam-1535	75	6	point	point	VERB
ejpam-1535	75	7	out	out	ADP
ejpam-1535	75	8	that	that	SCONJ
ejpam-1535	75	9	we	we	PRON
ejpam-1535	75	10	will	will	AUX
ejpam-1535	75	11	be	be	AUX
ejpam-1535	75	12	using	use	VERB
ejpam-1535	75	13	the	the	DET
ejpam-1535	75	14	word	word	NOUN
ejpam-1535	75	15	“	"	PUNCT
ejpam-1535	75	16	category	category	NOUN
ejpam-1535	75	17	”	"	PUNCT
ejpam-1535	75	18	in	in	ADP
ejpam-1535	75	19	two	two	NUM
ejpam-1535	75	20	slightly	slightly	ADV
ejpam-1535	75	21	different	different	ADJ
ejpam-1535	75	22	,	,	PUNCT
ejpam-1535	75	23	though	though	SCONJ
ejpam-1535	75	24	equivalent	equivalent	ADJ
ejpam-1535	75	25	,	,	PUNCT
ejpam-1535	75	26	manners	manner	NOUN
ejpam-1535	75	27	,	,	PUNCT
ejpam-1535	75	28	according	accord	VERB
ejpam-1535	75	29	to	to	ADP
ejpam-1535	75	30	the	the	DET
ejpam-1535	75	31	two	two	NUM
ejpam-1535	75	32	different	different	ADJ
ejpam-1535	75	33	ways	way	NOUN
ejpam-1535	75	34	in	in	ADP
ejpam-1535	75	35	which	which	PRON
ejpam-1535	75	36	it	it	PRON
ejpam-1535	75	37	is	be	AUX
ejpam-1535	75	38	possible	possible	ADJ
ejpam-1535	75	39	to	to	PART
ejpam-1535	75	40	view	view	VERB
ejpam-1535	75	41	a	a	DET
ejpam-1535	75	42	category	category	NOUN
ejpam-1535	75	43	:	:	PUNCT
ejpam-1535	75	44	(	(	PUNCT
ejpam-1535	75	45	♠	♠	NOUN
ejpam-1535	75	46	)	)	PUNCT
ejpam-1535	75	47	the	the	DET
ejpam-1535	75	48	“	"	PUNCT
ejpam-1535	75	49	traditional	traditional	ADJ
ejpam-1535	75	50	”	"	PUNCT
ejpam-1535	75	51	objects	object	NOUN
ejpam-1535	75	52	and	and	CCONJ
ejpam-1535	75	53	morphisms	morphism	VERB
ejpam-1535	75	54	version	version	NOUN
ejpam-1535	75	55	of	of	ADP
ejpam-1535	75	56	a	a	DET
ejpam-1535	75	57	category	category	NOUN
ejpam-1535	75	58	(	(	PUNCT
ejpam-1535	75	59	see	see	VERB
ejpam-1535	75	60	,	,	PUNCT
ejpam-1535	75	61	for	for	ADP
ejpam-1535	75	62	example	example	NOUN
ejpam-1535	75	63	,	,	PUNCT
ejpam-1535	75	64	[	[	X
ejpam-1535	75	65	24	24	NUM
ejpam-1535	75	66	,	,	PUNCT
ejpam-1535	75	67	definition	definition	NOUN
ejpam-1535	75	68	1.1	1.1	NUM
ejpam-1535	75	69	]	]	PUNCT
ejpam-1535	75	70	)	)	PUNCT
ejpam-1535	75	71	,	,	PUNCT
ejpam-1535	75	72	in	in	ADP
ejpam-1535	75	73	which	which	PRON
ejpam-1535	75	74	the	the	DET
ejpam-1535	75	75	objects	object	NOUN
ejpam-1535	75	76	are	be	AUX
ejpam-1535	75	77	mathematical	mathematical	ADJ
ejpam-1535	75	78	entities	entity	NOUN
ejpam-1535	75	79	such	such	ADJ
ejpam-1535	75	80	as	as	ADP
ejpam-1535	75	81	sets	set	NOUN
ejpam-1535	75	82	,	,	PUNCT
ejpam-1535	75	83	semigroups	semigroup	NOUN
ejpam-1535	75	84	,	,	PUNCT
ejpam-1535	75	85	groups	group	NOUN
ejpam-1535	75	86	,	,	PUNCT
ejpam-1535	75	87	rings	ring	NOUN
ejpam-1535	75	88	,	,	PUNCT
ejpam-1535	75	89	etc	etc	X
ejpam-1535	75	90	.	.	X
ejpam-1535	75	91	,	,	PUNCT
ejpam-1535	75	92	and	and	CCONJ
ejpam-1535	75	93	the	the	DET
ejpam-1535	75	94	morphisms	morphism	NOUN
ejpam-1535	75	95	are	be	AUX
ejpam-1535	75	96	functions	function	NOUN
ejpam-1535	75	97	between	between	ADP
ejpam-1535	75	98	these	these	PRON
ejpam-1535	75	99	,	,	PUNCT
ejpam-1535	75	100	such	such	ADJ
ejpam-1535	75	101	as	as	ADP
ejpam-1535	75	102	(	(	PUNCT
ejpam-1535	75	103	homo)morphisms	homo)morphism	NOUN
ejpam-1535	75	104	;	;	PUNCT
ejpam-1535	75	105	(	(	PUNCT
ejpam-1535	75	106	♣	♣	NOUN
ejpam-1535	75	107	)	)	PUNCT
ejpam-1535	75	108	the	the	DET
ejpam-1535	75	109	“	"	PUNCT
ejpam-1535	75	110	generalised	generalised	ADJ
ejpam-1535	75	111	monoid	monoid	NOUN
ejpam-1535	75	112	”	"	PUNCT
ejpam-1535	75	113	version	version	NOUN
ejpam-1535	75	114	of	of	ADP
ejpam-1535	75	115	a	a	DET
ejpam-1535	75	116	category	category	NOUN
ejpam-1535	75	117	,	,	PUNCT
ejpam-1535	75	118	which	which	PRON
ejpam-1535	75	119	sees	see	VERB
ejpam-1535	75	120	a	a	DET
ejpam-1535	75	121	category	category	NOUN
ejpam-1535	75	122	as	as	ADP
ejpam-1535	75	123	a	a	DET
ejpam-1535	75	124	set	set	NOUN
ejpam-1535	75	125	equipped	equip	VERB
ejpam-1535	75	126	with	with	ADP
ejpam-1535	75	127	a	a	DET
ejpam-1535	75	128	partially	partially	ADV
ejpam-1535	75	129	-	-	PUNCT
ejpam-1535	75	130	defined	define	VERB
ejpam-1535	75	131	binary	binary	ADJ
ejpam-1535	75	132	operation	operation	NOUN
ejpam-1535	75	133	,	,	PUNCT
ejpam-1535	75	134	subject	subject	ADJ
ejpam-1535	75	135	to	to	ADP
ejpam-1535	75	136	certain	certain	ADJ
ejpam-1535	75	137	conditions	condition	NOUN
ejpam-1535	75	138	(	(	PUNCT
ejpam-1535	75	139	see	see	VERB
ejpam-1535	75	140	definition	definition	NOUN
ejpam-1535	75	141	8)	8)	NUM
ejpam-1535	75	142	.	.	PUNCT
ejpam-1535	76	1	all	all	DET
ejpam-1535	76	2	categories	category	NOUN
ejpam-1535	76	3	viewed	view	VERB
ejpam-1535	76	4	in	in	ADP
ejpam-1535	76	5	this	this	DET
ejpam-1535	76	6	way	way	NOUN
ejpam-1535	76	7	will	will	AUX
ejpam-1535	76	8	be	be	AUX
ejpam-1535	76	9	small	small	ADJ
ejpam-1535	76	10	categories	category	NOUN
ejpam-1535	76	11	.	.	PUNCT
ejpam-1535	77	1	from	from	ADP
ejpam-1535	77	2	this	this	DET
ejpam-1535	77	3	point	point	NOUN
ejpam-1535	77	4	of	of	ADP
ejpam-1535	77	5	view	view	NOUN
ejpam-1535	77	6	,	,	PUNCT
ejpam-1535	77	7	a	a	DET
ejpam-1535	77	8	category	category	NOUN
ejpam-1535	77	9	may	may	AUX
ejpam-1535	77	10	be	be	AUX
ejpam-1535	77	11	regarded	regard	VERB
ejpam-1535	77	12	as	as	ADP
ejpam-1535	77	13	a	a	DET
ejpam-1535	77	14	directed	direct	VERB
ejpam-1535	77	15	graph	graph	NOUN
ejpam-1535	77	16	,	,	PUNCT
ejpam-1535	77	17	in	in	ADP
ejpam-1535	77	18	which	which	PRON
ejpam-1535	77	19	the	the	DET
ejpam-1535	77	20	objects	object	NOUN
ejpam-1535	77	21	(	(	PUNCT
ejpam-1535	77	22	here	here	ADV
ejpam-1535	77	23	termed	term	VERB
ejpam-1535	77	24	“	"	PUNCT
ejpam-1535	77	25	identities	identity	NOUN
ejpam-1535	77	26	”	"	PUNCT
ejpam-1535	77	27	)	)	PUNCT
ejpam-1535	77	28	are	be	AUX
ejpam-1535	77	29	the	the	DET
ejpam-1535	77	30	vertices	vertex	NOUN
ejpam-1535	77	31	and	and	CCONJ
ejpam-1535	77	32	the	the	DET
ejpam-1535	77	33	morphisms	morphism	NOUN
ejpam-1535	77	34	(	(	PUNCT
ejpam-1535	77	35	or	or	CCONJ
ejpam-1535	77	36	“	"	PUNCT
ejpam-1535	77	37	arrows	arrow	NOUN
ejpam-1535	77	38	”	"	PUNCT
ejpam-1535	77	39	)	)	PUNCT
ejpam-1535	77	40	are	be	AUX
ejpam-1535	77	41	the	the	DET
ejpam-1535	77	42	edges	edge	NOUN
ejpam-1535	77	43	.	.	PUNCT
ejpam-1535	78	1	here	here	ADV
ejpam-1535	78	2	,	,	PUNCT
ejpam-1535	78	3	two	two	NUM
ejpam-1535	78	4	arrows	arrow	NOUN
ejpam-1535	78	5	may	may	AUX
ejpam-1535	78	6	only	only	ADV
ejpam-1535	78	7	be	be	AUX
ejpam-1535	78	8	composed	compose	VERB
ejpam-1535	78	9	if	if	SCONJ
ejpam-1535	78	10	the	the	DET
ejpam-1535	78	11	terminal	terminal	ADJ
ejpam-1535	78	12	vertex	vertex	NOUN
ejpam-1535	78	13	of	of	ADP
ejpam-1535	78	14	the	the	DET
ejpam-1535	78	15	first	first	ADJ
ejpam-1535	78	16	coincides	coincide	NOUN
ejpam-1535	78	17	with	with	ADP
ejpam-1535	78	18	the	the	DET
ejpam-1535	78	19	initial	initial	ADJ
ejpam-1535	78	20	vertex	vertex	NOUN
ejpam-1535	78	21	of	of	ADP
ejpam-1535	78	22	the	the	DET
ejpam-1535	78	23	second	second	NOUN
ejpam-1535	78	24	.	.	PUNCT
ejpam-1535	79	1	wherever	wherever	SCONJ
ejpam-1535	79	2	it	it	PRON
ejpam-1535	79	3	is	be	AUX
ejpam-1535	79	4	defined	define	VERB
ejpam-1535	79	5	,	,	PUNCT
ejpam-1535	79	6	the	the	DET
ejpam-1535	79	7	composition	composition	NOUN
ejpam-1535	79	8	is	be	AUX
ejpam-1535	79	9	assumed	assume	VERB
ejpam-1535	79	10	,	,	PUNCT
ejpam-1535	79	11	amongst	amongst	ADP
ejpam-1535	79	12	other	other	ADJ
ejpam-1535	79	13	things	thing	NOUN
ejpam-1535	79	14	,	,	PUNCT
ejpam-1535	79	15	to	to	PART
ejpam-1535	79	16	be	be	AUX
ejpam-1535	79	17	associative	associative	ADJ
ejpam-1535	79	18	.	.	PUNCT
ejpam-1535	80	1	a	a	DET
ejpam-1535	80	2	monoid	monoid	NOUN
ejpam-1535	80	3	is	be	AUX
ejpam-1535	80	4	therefore	therefore	ADV
ejpam-1535	80	5	such	such	DET
ejpam-1535	80	6	a	a	DET
ejpam-1535	80	7	category	category	NOUN
ejpam-1535	80	8	with	with	ADP
ejpam-1535	80	9	precisely	precisely	ADV
ejpam-1535	80	10	one	one	NUM
ejpam-1535	80	11	identity	identity	NOUN
ejpam-1535	80	12	.	.	PUNCT
ejpam-1535	81	1	thus	thus	ADV
ejpam-1535	81	2	,	,	PUNCT
ejpam-1535	81	3	whenever	whenever	SCONJ
ejpam-1535	81	4	we	we	PRON
ejpam-1535	81	5	refer	refer	VERB
ejpam-1535	81	6	to	to	ADP
ejpam-1535	81	7	an	an	DET
ejpam-1535	81	8	inductive	inductive	ADJ
ejpam-1535	81	9	category	category	NOUN
ejpam-1535	81	10	(	(	PUNCT
ejpam-1535	81	11	or	or	CCONJ
ejpam-1535	81	12	,	,	PUNCT
ejpam-1535	81	13	indeed	indeed	ADV
ejpam-1535	81	14	,	,	PUNCT
ejpam-1535	81	15	an	an	DET
ejpam-1535	81	16	inductive	inductive	ADJ
ejpam-1535	81	17	groupoid	groupoid	NOUN
ejpam-1535	81	18	)	)	PUNCT
ejpam-1535	81	19	,	,	PUNCT
ejpam-1535	81	20	we	we	PRON
ejpam-1535	81	21	are	be	AUX
ejpam-1535	81	22	thinking	think	VERB
ejpam-1535	81	23	of	of	ADP
ejpam-1535	81	24	it	it	PRON
ejpam-1535	81	25	as	as	ADP
ejpam-1535	81	26	a	a	DET
ejpam-1535	81	27	category	category	NOUN
ejpam-1535	81	28	in	in	ADP
ejpam-1535	81	29	sense	sense	NOUN
ejpam-1535	81	30	(	(	PUNCT
ejpam-1535	81	31	♣	♣	NOUN
ejpam-1535	81	32	)	)	PUNCT
ejpam-1535	81	33	.	.	PUNCT
ejpam-1535	82	1	on	on	ADP
ejpam-1535	82	2	the	the	DET
ejpam-1535	82	3	other	other	ADJ
ejpam-1535	82	4	hand	hand	NOUN
ejpam-1535	82	5	,	,	PUNCT
ejpam-1535	82	6	when	when	SCONJ
ejpam-1535	82	7	we	we	PRON
ejpam-1535	82	8	speak	speak	VERB
ejpam-1535	82	9	of	of	ADP
ejpam-1535	82	10	a	a	DET
ejpam-1535	82	11	category	category	NOUN
ejpam-1535	82	12	of	of	ADP
ejpam-1535	82	13	inductive	inductive	ADJ
ejpam-1535	82	14	categories	category	NOUN
ejpam-1535	82	15	(	(	PUNCT
ejpam-1535	82	16	or	or	CCONJ
ejpam-1535	82	17	of	of	ADP
ejpam-1535	82	18	inverse	inverse	NOUN
ejpam-1535	82	19	semigroups	semigroup	NOUN
ejpam-1535	82	20	,	,	PUNCT
ejpam-1535	82	21	etc	etc	X
ejpam-1535	82	22	.	.	X
ejpam-1535	82	23	)	)	PUNCT
ejpam-1535	82	24	,	,	PUNCT
ejpam-1535	82	25	the	the	DET
ejpam-1535	82	26	underlined	underline	VERB
ejpam-1535	82	27	usage	usage	NOUN
ejpam-1535	82	28	of	of	ADP
ejpam-1535	82	29	the	the	DET
ejpam-1535	82	30	word	word	NOUN
ejpam-1535	82	31	category	category	NOUN
ejpam-1535	82	32	is	be	AUX
ejpam-1535	82	33	thought	think	VERB
ejpam-1535	82	34	of	of	ADP
ejpam-1535	82	35	as	as	ADP
ejpam-1535	82	36	being	be	AUX
ejpam-1535	82	37	in	in	ADP
ejpam-1535	82	38	sense	sense	NOUN
ejpam-1535	82	39	(	(	PUNCT
ejpam-1535	82	40	♠	♠	NOUN
ejpam-1535	82	41	)	)	PUNCT
ejpam-1535	82	42	.	.	PUNCT
ejpam-1535	83	1	we	we	PRON
ejpam-1535	83	2	will	will	AUX
ejpam-1535	83	3	continue	continue	VERB
ejpam-1535	83	4	to	to	PART
ejpam-1535	83	5	emphasise	emphasise	VERB
ejpam-1535	83	6	the	the	DET
ejpam-1535	83	7	distinction	distinction	NOUN
ejpam-1535	83	8	between	between	ADP
ejpam-1535	83	9	(	(	PUNCT
ejpam-1535	83	10	♠	♠	NOUN
ejpam-1535	83	11	)	)	PUNCT
ejpam-1535	83	12	and	and	CCONJ
ejpam-1535	83	13	(	(	PUNCT
ejpam-1535	83	14	♣	♣	NOUN
ejpam-1535	83	15	)	)	PUNCT
ejpam-1535	83	16	whenever	whenever	SCONJ
ejpam-1535	83	17	we	we	PRON
ejpam-1535	83	18	feel	feel	VERB
ejpam-1535	83	19	that	that	SCONJ
ejpam-1535	83	20	it	it	PRON
ejpam-1535	83	21	aids	aid	VERB
ejpam-1535	83	22	clarity	clarity	NOUN
ejpam-1535	83	23	.	.	PUNCT
ejpam-1535	84	1	in	in	ADP
ejpam-1535	84	2	the	the	DET
ejpam-1535	84	3	interests	interest	NOUN
ejpam-1535	84	4	of	of	ADP
ejpam-1535	84	5	keeping	keep	VERB
ejpam-1535	84	6	the	the	DET
ejpam-1535	84	7	length	length	NOUN
ejpam-1535	84	8	of	of	ADP
ejpam-1535	84	9	the	the	DET
ejpam-1535	84	10	article	article	NOUN
ejpam-1535	84	11	down	down	ADP
ejpam-1535	84	12	,	,	PUNCT
ejpam-1535	84	13	we	we	PRON
ejpam-1535	84	14	have	have	AUX
ejpam-1535	84	15	included	include	VERB
ejpam-1535	84	16	as	as	ADP
ejpam-1535	84	17	few	few	ADJ
ejpam-1535	84	18	proofs	proof	NOUN
ejpam-1535	84	19	as	as	ADP
ejpam-1535	84	20	possible	possible	ADJ
ejpam-1535	84	21	.	.	PUNCT
ejpam-1535	85	1	in	in	ADP
ejpam-1535	85	2	particular	particular	ADJ
ejpam-1535	85	3	,	,	PUNCT
ejpam-1535	85	4	we	we	PRON
ejpam-1535	85	5	have	have	AUX
ejpam-1535	85	6	omitted	omit	VERB
ejpam-1535	85	7	the	the	DET
ejpam-1535	85	8	proofs	proof	NOUN
ejpam-1535	85	9	of	of	ADP
ejpam-1535	85	10	most	most	ADJ
ejpam-1535	85	11	results	result	NOUN
ejpam-1535	85	12	which	which	PRON
ejpam-1535	85	13	we	we	PRON
ejpam-1535	85	14	consider	consider	VERB
ejpam-1535	85	15	to	to	PART
ejpam-1535	85	16	be	be	AUX
ejpam-1535	85	17	elementary	elementary	ADJ
ejpam-1535	85	18	,	,	PUNCT
ejpam-1535	85	19	or	or	CCONJ
ejpam-1535	85	20	which	which	PRON
ejpam-1535	85	21	may	may	AUX
ejpam-1535	85	22	easily	easily	ADV
ejpam-1535	85	23	be	be	AUX
ejpam-1535	85	24	found	find	VERB
ejpam-1535	85	25	elsewhere	elsewhere	ADV
ejpam-1535	85	26	.	.	PUNCT
ejpam-1535	86	1	nevertheless	nevertheless	ADV
ejpam-1535	86	2	,	,	PUNCT
ejpam-1535	86	3	some	some	DET
ejpam-1535	86	4	such	such	ADJ
ejpam-1535	86	5	proofs	proof	NOUN
ejpam-1535	86	6	have	have	AUX
ejpam-1535	86	7	been	be	AUX
ejpam-1535	86	8	included	include	VERB
ejpam-1535	86	9	where	where	SCONJ
ejpam-1535	86	10	they	they	PRON
ejpam-1535	86	11	are	be	AUX
ejpam-1535	86	12	particularly	particularly	ADV
ejpam-1535	86	13	instructive	instructive	ADJ
ejpam-1535	86	14	.	.	PUNCT
ejpam-1535	87	1	for	for	ADP
ejpam-1535	87	2	example	example	NOUN
ejpam-1535	87	3	,	,	PUNCT
ejpam-1535	87	4	lemma	lemma	PROPN
ejpam-1535	87	5	5	5	NUM
ejpam-1535	87	6	provides	provide	VERB
ejpam-1535	87	7	a	a	DET
ejpam-1535	87	8	good	good	ADJ
ejpam-1535	87	9	introduction	introduction	NOUN
ejpam-1535	87	10	to	to	ADP
ejpam-1535	87	11	the	the	DET
ejpam-1535	87	12	properties	property	NOUN
ejpam-1535	87	13	of	of	ADP
ejpam-1535	87	14	the	the	DET
ejpam-1535	87	15	restriction	restriction	NOUN
ejpam-1535	87	16	and	and	CCONJ
ejpam-1535	87	17	corestriction	corestriction	NOUN
ejpam-1535	87	18	in	in	ADP
ejpam-1535	87	19	an	an	DET
ejpam-1535	87	20	ordered	order	VERB
ejpam-1535	87	21	category	category	NOUN
ejpam-1535	87	22	(	(	PUNCT
ejpam-1535	87	23	see	see	VERB
ejpam-1535	87	24	definition	definition	NOUN
ejpam-1535	87	25	11	11	NUM
ejpam-1535	87	26	)	)	PUNCT
ejpam-1535	87	27	,	,	PUNCT
ejpam-1535	87	28	and	and	CCONJ
ejpam-1535	87	29	their	their	PRON
ejpam-1535	87	30	interplay	interplay	NOUN
ejpam-1535	87	31	with	with	ADP
ejpam-1535	87	32	the	the	DET
ejpam-1535	87	33	(	(	PUNCT
ejpam-1535	87	34	partial	partial	ADJ
ejpam-1535	87	35	)	)	PUNCT
ejpam-1535	87	36	multiplicative	multiplicative	ADJ
ejpam-1535	87	37	structure	structure	NOUN
ejpam-1535	87	38	.	.	PUNCT
ejpam-1535	88	1	it	it	PRON
ejpam-1535	88	2	should	should	AUX
ejpam-1535	88	3	be	be	AUX
ejpam-1535	88	4	noted	note	VERB
ejpam-1535	88	5	that	that	SCONJ
ejpam-1535	88	6	some	some	PRON
ejpam-1535	88	7	of	of	ADP
ejpam-1535	88	8	the	the	DET
ejpam-1535	88	9	citations	citation	NOUN
ejpam-1535	88	10	given	give	VERB
ejpam-1535	88	11	here	here	ADV
ejpam-1535	88	12	for	for	ADP
ejpam-1535	88	13	certain	certain	ADJ
ejpam-1535	88	14	results	result	NOUN
ejpam-1535	88	15	are	be	AUX
ejpam-1535	88	16	slightly	slightly	ADV
ejpam-1535	88	17	imprecise	imprecise	ADJ
ejpam-1535	88	18	.	.	PUNCT
ejpam-1535	89	1	for	for	ADP
ejpam-1535	89	2	example	example	NOUN
ejpam-1535	89	3	,	,	PUNCT
ejpam-1535	89	4	different	different	ADJ
ejpam-1535	89	5	parts	part	NOUN
ejpam-1535	89	6	of	of	ADP
ejpam-1535	89	7	the	the	DET
ejpam-1535	89	8	above	above	ADV
ejpam-1535	89	9	-	-	PUNCT
ejpam-1535	89	10	mentioned	mention	VERB
ejpam-1535	89	11	lemma	lemma	PROPN
ejpam-1535	89	12	5	5	NUM
ejpam-1535	89	13	have	have	AUX
ejpam-1535	89	14	been	be	AUX
ejpam-1535	89	15	attributed	attribute	VERB
ejpam-1535	89	16	c.	c.	NOUN
ejpam-1535	89	17	hollings	holling	NOUN
ejpam-1535	89	18	/	/	SYM
ejpam-1535	89	19	eur	eur	PROPN
ejpam-1535	89	20	.	.	PUNCT
ejpam-1535	90	1	j.	j.	PROPN
ejpam-1535	90	2	pure	pure	PROPN
ejpam-1535	90	3	appl	appl	PROPN
ejpam-1535	90	4	.	.	PROPN
ejpam-1535	90	5	math	math	PROPN
ejpam-1535	90	6	,	,	PUNCT
ejpam-1535	90	7	5	5	NUM
ejpam-1535	90	8	(	(	PUNCT
ejpam-1535	90	9	2012	2012	NUM
ejpam-1535	90	10	)	)	PUNCT
ejpam-1535	90	11	,	,	PUNCT
ejpam-1535	90	12	414	414	NUM
ejpam-1535	90	13	-	-	SYM
ejpam-1535	90	14	450	450	NUM
ejpam-1535	90	15	418	418	NUM
ejpam-1535	90	16	to	to	ADP
ejpam-1535	90	17	armstrong	armstrong	PROPN
ejpam-1535	91	1	[	[	X
ejpam-1535	91	2	1	1	NUM
ejpam-1535	91	3	]	]	PUNCT
ejpam-1535	91	4	and	and	CCONJ
ejpam-1535	91	5	lawson	lawson	PROPN
ejpam-1535	91	6	[	[	X
ejpam-1535	91	7	29	29	NUM
ejpam-1535	91	8	]	]	PUNCT
ejpam-1535	91	9	.	.	PUNCT
ejpam-1535	92	1	the	the	DET
ejpam-1535	92	2	imprecision	imprecision	NOUN
ejpam-1535	92	3	here	here	ADV
ejpam-1535	92	4	stems	stem	VERB
ejpam-1535	92	5	from	from	ADP
ejpam-1535	92	6	the	the	DET
ejpam-1535	92	7	fact	fact	NOUN
ejpam-1535	92	8	that	that	SCONJ
ejpam-1535	92	9	although	although	SCONJ
ejpam-1535	92	10	our	our	PRON
ejpam-1535	92	11	lemma	lemma	PROPN
ejpam-1535	92	12	5	5	NUM
ejpam-1535	92	13	concerns	concern	NOUN
ejpam-1535	92	14	arbitrary	arbitrary	ADJ
ejpam-1535	92	15	ordered	order	VERB
ejpam-1535	92	16	categories	category	NOUN
ejpam-1535	92	17	,	,	PUNCT
ejpam-1535	92	18	armstrong	armstrong	PROPN
ejpam-1535	92	19	’s	’s	PART
ejpam-1535	92	20	version	version	NOUN
ejpam-1535	92	21	deals	deal	NOUN
ejpam-1535	92	22	with	with	ADP
ejpam-1535	92	23	ordered	order	VERB
ejpam-1535	92	24	cancellative	cancellative	ADJ
ejpam-1535	92	25	categories	category	NOUN
ejpam-1535	92	26	(	(	PUNCT
ejpam-1535	92	27	see	see	VERB
ejpam-1535	92	28	definition	definition	NOUN
ejpam-1535	92	29	10	10	NUM
ejpam-1535	92	30	)	)	PUNCT
ejpam-1535	92	31	,	,	PUNCT
ejpam-1535	92	32	and	and	CCONJ
ejpam-1535	92	33	lawson	lawson	PROPN
ejpam-1535	92	34	’s	’s	X
ejpam-1535	92	35	with	with	ADP
ejpam-1535	92	36	ordered	order	VERB
ejpam-1535	92	37	groupoids	groupoid	NOUN
ejpam-1535	92	38	.	.	PUNCT
ejpam-1535	93	1	nevertheless	nevertheless	ADV
ejpam-1535	93	2	,	,	PUNCT
ejpam-1535	93	3	the	the	DET
ejpam-1535	93	4	proof	proof	NOUN
ejpam-1535	93	5	in	in	ADP
ejpam-1535	93	6	the	the	DET
ejpam-1535	93	7	case	case	NOUN
ejpam-1535	93	8	of	of	ADP
ejpam-1535	93	9	arbitrary	arbitrary	ADJ
ejpam-1535	93	10	ordered	order	VERB
ejpam-1535	93	11	categories	category	NOUN
ejpam-1535	93	12	is	be	AUX
ejpam-1535	93	13	substantially	substantially	ADV
ejpam-1535	93	14	the	the	DET
ejpam-1535	93	15	same	same	ADJ
ejpam-1535	93	16	as	as	ADP
ejpam-1535	93	17	those	those	PRON
ejpam-1535	93	18	in	in	ADP
ejpam-1535	93	19	the	the	DET
ejpam-1535	93	20	more	more	ADV
ejpam-1535	93	21	specialised	specialised	ADJ
ejpam-1535	93	22	cases	case	NOUN
ejpam-1535	93	23	—	—	PUNCT
ejpam-1535	93	24	it	it	PRON
ejpam-1535	93	25	is	be	AUX
ejpam-1535	93	26	therefore	therefore	ADV
ejpam-1535	93	27	appropriate	appropriate	ADJ
ejpam-1535	93	28	to	to	PART
ejpam-1535	93	29	cite	cite	VERB
ejpam-1535	93	30	both	both	CCONJ
ejpam-1535	93	31	armstrong	armstrong	PROPN
ejpam-1535	93	32	and	and	CCONJ
ejpam-1535	93	33	lawson	lawson	PROPN
ejpam-1535	93	34	here	here	ADV
ejpam-1535	93	35	.	.	PUNCT
ejpam-1535	94	1	any	any	DET
ejpam-1535	94	2	such	such	ADJ
ejpam-1535	94	3	imprecise	imprecise	ADJ
ejpam-1535	94	4	citations	citation	NOUN
ejpam-1535	94	5	are	be	AUX
ejpam-1535	94	6	marked	mark	VERB
ejpam-1535	94	7	with	with	ADP
ejpam-1535	94	8	an	an	DET
ejpam-1535	94	9	asterisk	asterisk	NOUN
ejpam-1535	94	10	∗.	∗.	PROPN
ejpam-1535	94	11	an	an	DET
ejpam-1535	94	12	“	"	PUNCT
ejpam-1535	94	13	[	[	X
ejpam-1535	94	14	f	f	X
ejpam-1535	94	15	]	]	X
ejpam-1535	94	16	”	"	PUNCT
ejpam-1535	94	17	given	give	VERB
ejpam-1535	94	18	as	as	ADP
ejpam-1535	94	19	a	a	DET
ejpam-1535	94	20	citation	citation	NOUN
ejpam-1535	94	21	for	for	ADP
ejpam-1535	94	22	a	a	DET
ejpam-1535	94	23	lemma	lemma	PROPN
ejpam-1535	94	24	or	or	CCONJ
ejpam-1535	94	25	theorem	theorem	NOUN
ejpam-1535	94	26	indicates	indicate	VERB
ejpam-1535	94	27	that	that	SCONJ
ejpam-1535	94	28	the	the	DET
ejpam-1535	94	29	result	result	NOUN
ejpam-1535	94	30	is	be	AUX
ejpam-1535	94	31	of	of	ADP
ejpam-1535	94	32	the	the	DET
ejpam-1535	94	33	nature	nature	NOUN
ejpam-1535	94	34	of	of	ADP
ejpam-1535	94	35	“	"	PUNCT
ejpam-1535	94	36	folklore	folklore	NOUN
ejpam-1535	94	37	”	"	PUNCT
ejpam-1535	94	38	:	:	PUNCT
ejpam-1535	94	39	it	it	PRON
ejpam-1535	94	40	is	be	AUX
ejpam-1535	94	41	both	both	CCONJ
ejpam-1535	94	42	fundamental	fundamental	ADJ
ejpam-1535	94	43	and	and	CCONJ
ejpam-1535	94	44	reasonably	reasonably	ADV
ejpam-1535	94	45	easy	easy	ADJ
ejpam-1535	94	46	to	to	PART
ejpam-1535	94	47	prove	prove	VERB
ejpam-1535	94	48	—	—	PUNCT
ejpam-1535	94	49	the	the	DET
ejpam-1535	94	50	proofs	proof	NOUN
ejpam-1535	94	51	of	of	ADP
ejpam-1535	94	52	such	such	ADJ
ejpam-1535	94	53	results	result	NOUN
ejpam-1535	94	54	will	will	AUX
ejpam-1535	94	55	therefore	therefore	ADV
ejpam-1535	94	56	be	be	AUX
ejpam-1535	94	57	omitted	omit	VERB
ejpam-1535	94	58	in	in	ADP
ejpam-1535	94	59	most	most	ADJ
ejpam-1535	94	60	cases	case	NOUN
ejpam-1535	94	61	,	,	PUNCT
ejpam-1535	94	62	unless	unless	SCONJ
ejpam-1535	94	63	the	the	DET
ejpam-1535	94	64	proof	proof	NOUN
ejpam-1535	94	65	is	be	AUX
ejpam-1535	94	66	particularly	particularly	ADV
ejpam-1535	94	67	instructive	instructive	ADJ
ejpam-1535	94	68	.	.	PUNCT
ejpam-1535	95	1	in	in	ADP
ejpam-1535	95	2	such	such	ADJ
ejpam-1535	95	3	cases	case	NOUN
ejpam-1535	95	4	,	,	PUNCT
ejpam-1535	95	5	i	i	PRON
ejpam-1535	95	6	have	have	AUX
ejpam-1535	95	7	made	make	VERB
ejpam-1535	95	8	little	little	ADJ
ejpam-1535	95	9	effort	effort	NOUN
ejpam-1535	95	10	to	to	PART
ejpam-1535	95	11	track	track	VERB
ejpam-1535	95	12	down	down	ADP
ejpam-1535	95	13	the	the	DET
ejpam-1535	95	14	first	first	ADJ
ejpam-1535	95	15	appearance	appearance	NOUN
ejpam-1535	95	16	of	of	ADP
ejpam-1535	95	17	these	these	DET
ejpam-1535	95	18	results	result	NOUN
ejpam-1535	95	19	in	in	ADP
ejpam-1535	95	20	the	the	DET
ejpam-1535	95	21	literature	literature	NOUN
ejpam-1535	95	22	.	.	PUNCT
ejpam-1535	96	1	as	as	SCONJ
ejpam-1535	96	2	the	the	DET
ejpam-1535	96	3	reader	reader	NOUN
ejpam-1535	96	4	has	have	AUX
ejpam-1535	96	5	probably	probably	ADV
ejpam-1535	96	6	concluded	conclude	VERB
ejpam-1535	96	7	from	from	ADP
ejpam-1535	96	8	this	this	DET
ejpam-1535	96	9	introduction	introduction	NOUN
ejpam-1535	96	10	,	,	PUNCT
ejpam-1535	96	11	this	this	DET
ejpam-1535	96	12	article	article	NOUN
ejpam-1535	96	13	has	have	AUX
ejpam-1535	96	14	been	be	AUX
ejpam-1535	96	15	written	write	VERB
ejpam-1535	96	16	very	very	ADV
ejpam-1535	96	17	much	much	ADV
ejpam-1535	96	18	from	from	ADP
ejpam-1535	96	19	the	the	DET
ejpam-1535	96	20	“	"	PUNCT
ejpam-1535	96	21	semigroup	semigroup	ADJ
ejpam-1535	96	22	point	point	NOUN
ejpam-1535	96	23	-	-	PUNCT
ejpam-1535	96	24	of	of	ADP
ejpam-1535	96	25	-	-	PUNCT
ejpam-1535	96	26	view	view	NOUN
ejpam-1535	96	27	”	"	PUNCT
ejpam-1535	96	28	.	.	PUNCT
ejpam-1535	97	1	we	we	PRON
ejpam-1535	97	2	therefore	therefore	ADV
ejpam-1535	97	3	assume	assume	VERB
ejpam-1535	97	4	a	a	DET
ejpam-1535	97	5	basic	basic	ADJ
ejpam-1535	97	6	knowledge	knowledge	NOUN
ejpam-1535	97	7	of	of	ADP
ejpam-1535	97	8	semigroup	semigroup	PROPN
ejpam-1535	97	9	theory	theory	NOUN
ejpam-1535	97	10	on	on	ADP
ejpam-1535	97	11	the	the	DET
ejpam-1535	97	12	part	part	NOUN
ejpam-1535	97	13	of	of	ADP
ejpam-1535	97	14	the	the	DET
ejpam-1535	97	15	reader	reader	NOUN
ejpam-1535	97	16	.	.	PUNCT
ejpam-1535	98	1	for	for	ADP
ejpam-1535	98	2	any	any	DET
ejpam-1535	98	3	undefined	undefined	ADJ
ejpam-1535	98	4	terminology	terminology	NOUN
ejpam-1535	98	5	or	or	CCONJ
ejpam-1535	98	6	notation	notation	NOUN
ejpam-1535	98	7	,	,	PUNCT
ejpam-1535	98	8	the	the	DET
ejpam-1535	98	9	reader	reader	NOUN
ejpam-1535	98	10	is	be	AUX
ejpam-1535	98	11	referred	refer	VERB
ejpam-1535	98	12	to	to	ADP
ejpam-1535	98	13	[	[	X
ejpam-1535	98	14	23	23	NUM
ejpam-1535	98	15	]	]	PUNCT
ejpam-1535	98	16	or	or	CCONJ
ejpam-1535	98	17	[	[	X
ejpam-1535	98	18	29	29	NUM
ejpam-1535	98	19	]	]	PUNCT
ejpam-1535	98	20	.	.	PUNCT
ejpam-1535	99	1	as	as	ADP
ejpam-1535	99	2	one	one	NUM
ejpam-1535	99	3	final	final	ADJ
ejpam-1535	99	4	note	note	NOUN
ejpam-1535	99	5	,	,	PUNCT
ejpam-1535	99	6	we	we	PRON
ejpam-1535	99	7	mention	mention	VERB
ejpam-1535	99	8	that	that	SCONJ
ejpam-1535	99	9	,	,	PUNCT
ejpam-1535	99	10	as	as	ADP
ejpam-1535	99	11	per	per	ADP
ejpam-1535	99	12	the	the	DET
ejpam-1535	99	13	oft	oft	ADV
ejpam-1535	99	14	-	-	PUNCT
ejpam-1535	99	15	followed	follow	VERB
ejpam-1535	99	16	convention	convention	NOUN
ejpam-1535	99	17	in	in	ADP
ejpam-1535	99	18	semigroup	semigroup	PROPN
ejpam-1535	99	19	theory	theory	NOUN
ejpam-1535	99	20	,	,	PUNCT
ejpam-1535	99	21	homomorphisms	homomorphism	NOUN
ejpam-1535	99	22	will	will	AUX
ejpam-1535	99	23	be	be	AUX
ejpam-1535	99	24	referred	refer	VERB
ejpam-1535	99	25	to	to	ADP
ejpam-1535	99	26	throughout	throughout	ADV
ejpam-1535	99	27	simply	simply	ADV
ejpam-1535	99	28	as	as	ADP
ejpam-1535	99	29	“	"	PUNCT
ejpam-1535	99	30	morphisms	morphism	NOUN
ejpam-1535	99	31	”	"	PUNCT
ejpam-1535	99	32	.	.	PUNCT
ejpam-1535	100	1	2	2	X
ejpam-1535	100	2	.	.	X
ejpam-1535	100	3	historical	historical	ADJ
ejpam-1535	100	4	background	background	NOUN
ejpam-1535	100	5	following	follow	VERB
ejpam-1535	100	6	lawson	lawson	PROPN
ejpam-1535	100	7	[	[	X
ejpam-1535	100	8	29	29	NUM
ejpam-1535	100	9	]	]	PUNCT
ejpam-1535	100	10	,	,	PUNCT
ejpam-1535	100	11	we	we	PRON
ejpam-1535	100	12	start	start	VERB
ejpam-1535	100	13	by	by	ADP
ejpam-1535	100	14	placing	place	VERB
ejpam-1535	100	15	these	these	DET
ejpam-1535	100	16	theories	theory	NOUN
ejpam-1535	100	17	in	in	ADP
ejpam-1535	100	18	the	the	DET
ejpam-1535	100	19	context	context	NOUN
ejpam-1535	100	20	of	of	ADP
ejpam-1535	100	21	klein	klein	PROPN
ejpam-1535	100	22	’s	’s	PROPN
ejpam-1535	100	23	erlanger	erlanger	PROPN
ejpam-1535	100	24	programm	programm	PROPN
ejpam-1535	100	25	.	.	PUNCT
ejpam-1535	101	1	this	this	PRON
ejpam-1535	101	2	was	be	AUX
ejpam-1535	101	3	the	the	DET
ejpam-1535	101	4	point	point	NOUN
ejpam-1535	101	5	of	of	ADP
ejpam-1535	101	6	view	view	NOUN
ejpam-1535	101	7	famously	famously	ADV
ejpam-1535	101	8	advocated	advocate	VERB
ejpam-1535	101	9	by	by	ADP
ejpam-1535	101	10	felix	felix	PROPN
ejpam-1535	101	11	klein	klein	PROPN
ejpam-1535	101	12	at	at	ADP
ejpam-1535	101	13	the	the	DET
ejpam-1535	101	14	end	end	NOUN
ejpam-1535	101	15	of	of	ADP
ejpam-1535	101	16	the	the	DET
ejpam-1535	101	17	nineteenth	nineteenth	ADJ
ejpam-1535	101	18	century	century	NOUN
ejpam-1535	101	19	that	that	PRON
ejpam-1535	101	20	every	every	DET
ejpam-1535	101	21	geometry	geometry	NOUN
ejpam-1535	101	22	(	(	PUNCT
ejpam-1535	101	23	euclidean	euclidean	ADJ
ejpam-1535	101	24	,	,	PUNCT
ejpam-1535	101	25	hyperbolic	hyperbolic	ADJ
ejpam-1535	101	26	,	,	PUNCT
ejpam-1535	101	27	projective	projective	NOUN
ejpam-1535	101	28	,	,	PUNCT
ejpam-1535	101	29	etc	etc	X
ejpam-1535	101	30	.	.	X
ejpam-1535	101	31	)	)	PUNCT
ejpam-1535	101	32	should	should	AUX
ejpam-1535	101	33	be	be	AUX
ejpam-1535	101	34	regarded	regard	VERB
ejpam-1535	101	35	as	as	ADP
ejpam-1535	101	36	the	the	DET
ejpam-1535	101	37	theory	theory	NOUN
ejpam-1535	101	38	of	of	ADP
ejpam-1535	101	39	invariants	invariant	NOUN
ejpam-1535	101	40	of	of	ADP
ejpam-1535	101	41	a	a	DET
ejpam-1535	101	42	particular	particular	ADJ
ejpam-1535	101	43	group	group	NOUN
ejpam-1535	101	44	of	of	ADP
ejpam-1535	101	45	transformations.†	transformations.†	PROPN
ejpam-1535	101	46	to	to	PART
ejpam-1535	101	47	put	put	VERB
ejpam-1535	101	48	this	this	PRON
ejpam-1535	101	49	another	another	DET
ejpam-1535	101	50	way	way	NOUN
ejpam-1535	101	51	,	,	PUNCT
ejpam-1535	101	52	not	not	PART
ejpam-1535	101	53	only	only	ADV
ejpam-1535	101	54	can	can	AUX
ejpam-1535	101	55	a	a	DET
ejpam-1535	101	56	group	group	NOUN
ejpam-1535	101	57	of	of	ADP
ejpam-1535	101	58	structure	structure	NOUN
ejpam-1535	101	59	-	-	PUNCT
ejpam-1535	101	60	preserving	preserve	VERB
ejpam-1535	101	61	bijections	bijection	NOUN
ejpam-1535	101	62	be	be	AUX
ejpam-1535	101	63	associated	associate	VERB
ejpam-1535	101	64	with	with	ADP
ejpam-1535	101	65	a	a	DET
ejpam-1535	101	66	given	give	VERB
ejpam-1535	101	67	geometry	geometry	NOUN
ejpam-1535	101	68	,	,	PUNCT
ejpam-1535	101	69	but	but	CCONJ
ejpam-1535	101	70	also	also	ADV
ejpam-1535	101	71	such	such	DET
ejpam-1535	101	72	a	a	DET
ejpam-1535	101	73	group	group	NOUN
ejpam-1535	101	74	can	can	AUX
ejpam-1535	101	75	be	be	AUX
ejpam-1535	101	76	used	use	VERB
ejpam-1535	101	77	to	to	PART
ejpam-1535	101	78	define	define	VERB
ejpam-1535	101	79	the	the	DET
ejpam-1535	101	80	geometry	geometry	NOUN
ejpam-1535	101	81	in	in	ADP
ejpam-1535	101	82	the	the	DET
ejpam-1535	101	83	first	first	ADJ
ejpam-1535	101	84	place	place	NOUN
ejpam-1535	101	85	.	.	PUNCT
ejpam-1535	102	1	this	this	DET
ejpam-1535	102	2	group	group	NOUN
ejpam-1535	102	3	-	-	PUNCT
ejpam-1535	102	4	theoretic	theoretic	NOUN
ejpam-1535	102	5	approach	approach	NOUN
ejpam-1535	102	6	to	to	ADP
ejpam-1535	102	7	geometry	geometry	NOUN
ejpam-1535	102	8	placed	place	VERB
ejpam-1535	102	9	the	the	DET
ejpam-1535	102	10	burgeoning	burgeon	VERB
ejpam-1535	102	11	theory	theory	NOUN
ejpam-1535	102	12	of	of	ADP
ejpam-1535	102	13	groups	group	NOUN
ejpam-1535	102	14	at	at	ADP
ejpam-1535	102	15	the	the	DET
ejpam-1535	102	16	centrestage	centrestage	NOUN
ejpam-1535	102	17	of	of	ADP
ejpam-1535	102	18	late	late	ADJ
ejpam-1535	102	19	-	-	PUNCT
ejpam-1535	102	20	nineteenth	nineteenth	ADJ
ejpam-1535	102	21	-	-	PUNCT
ejpam-1535	102	22	century	century	NOUN
ejpam-1535	102	23	mathematics	mathematic	NOUN
ejpam-1535	102	24	and	and	CCONJ
ejpam-1535	102	25	thus	thus	ADV
ejpam-1535	102	26	ensured	ensure	VERB
ejpam-1535	102	27	its	its	PRON
ejpam-1535	102	28	future	future	ADJ
ejpam-1535	102	29	development	development	NOUN
ejpam-1535	102	30	(	(	PUNCT
ejpam-1535	102	31	see	see	VERB
ejpam-1535	102	32	[	[	X
ejpam-1535	102	33	53	53	NUM
ejpam-1535	102	34	]	]	NUM
ejpam-1535	102	35	)	)	PUNCT
ejpam-1535	102	36	.	.	PUNCT
ejpam-1535	103	1	the	the	DET
ejpam-1535	103	2	concept	concept	NOUN
ejpam-1535	103	3	of	of	ADP
ejpam-1535	103	4	a	a	DET
ejpam-1535	103	5	group	group	NOUN
ejpam-1535	103	6	became	became	AUX
ejpam-1535	103	7	inextricably	inextricably	ADV
ejpam-1535	103	8	linked	link	VERB
ejpam-1535	103	9	to	to	ADP
ejpam-1535	103	10	the	the	DET
ejpam-1535	103	11	geometrical	geometrical	ADJ
ejpam-1535	103	12	notion	notion	NOUN
ejpam-1535	103	13	of	of	ADP
ejpam-1535	103	14	symmetry	symmetry	NOUN
ejpam-1535	103	15	.	.	PUNCT
ejpam-1535	104	1	however	however	ADV
ejpam-1535	104	2	,	,	PUNCT
ejpam-1535	104	3	despite	despite	SCONJ
ejpam-1535	104	4	the	the	DET
ejpam-1535	104	5	initial	initial	ADJ
ejpam-1535	104	6	success	success	NOUN
ejpam-1535	104	7	of	of	ADP
ejpam-1535	104	8	the	the	DET
ejpam-1535	104	9	erlanger	erlanger	PROPN
ejpam-1535	104	10	programm	programm	PROPN
ejpam-1535	104	11	,	,	PUNCT
ejpam-1535	104	12	it	it	PRON
ejpam-1535	104	13	was	be	AUX
ejpam-1535	104	14	quickly	quickly	ADV
ejpam-1535	104	15	realised	realise	VERB
ejpam-1535	104	16	that	that	SCONJ
ejpam-1535	104	17	there	there	PRON
ejpam-1535	104	18	exist	exist	VERB
ejpam-1535	104	19	geometries	geometry	NOUN
ejpam-1535	104	20	which	which	PRON
ejpam-1535	104	21	can	can	AUX
ejpam-1535	104	22	not	not	PART
ejpam-1535	104	23	be	be	AUX
ejpam-1535	104	24	slotted	slot	VERB
ejpam-1535	104	25	into	into	ADP
ejpam-1535	104	26	this	this	DET
ejpam-1535	104	27	rough	rough	ADJ
ejpam-1535	104	28	scheme	scheme	NOUN
ejpam-1535	104	29	,	,	PUNCT
ejpam-1535	104	30	that	that	ADV
ejpam-1535	104	31	is	is	ADV
ejpam-1535	104	32	,	,	PUNCT
ejpam-1535	104	33	there	there	PRON
ejpam-1535	104	34	exist	exist	VERB
ejpam-1535	104	35	geometries	geometry	NOUN
ejpam-1535	104	36	whose	whose	DET
ejpam-1535	104	37	symmetries	symmetry	NOUN
ejpam-1535	104	38	do	do	AUX
ejpam-1535	104	39	not	not	PART
ejpam-1535	104	40	form	form	VERB
ejpam-1535	104	41	groups	group	NOUN
ejpam-1535	104	42	.	.	PUNCT
ejpam-1535	105	1	a	a	DET
ejpam-1535	105	2	prime	prime	ADJ
ejpam-1535	105	3	example	example	NOUN
ejpam-1535	105	4	of	of	ADP
ejpam-1535	105	5	this	this	PRON
ejpam-1535	105	6	is	be	AUX
ejpam-1535	105	7	differential	differential	ADJ
ejpam-1535	105	8	geometry	geometry	NOUN
ejpam-1535	105	9	.	.	PUNCT
ejpam-1535	106	1	in	in	ADP
ejpam-1535	106	2	the	the	DET
ejpam-1535	106	3	early	early	ADJ
ejpam-1535	106	4	twentieth	twentieth	ADJ
ejpam-1535	106	5	century	century	NOUN
ejpam-1535	106	6	,	,	PUNCT
ejpam-1535	106	7	efforts	effort	NOUN
ejpam-1535	106	8	were	be	AUX
ejpam-1535	106	9	made	make	VERB
ejpam-1535	106	10	to	to	PART
ejpam-1535	106	11	bring	bring	VERB
ejpam-1535	106	12	such	such	ADJ
ejpam-1535	106	13	“	"	PUNCT
ejpam-1535	106	14	rogue	rogue	ADJ
ejpam-1535	106	15	geometries	geometry	NOUN
ejpam-1535	106	16	”	"	PUNCT
ejpam-1535	106	17	into	into	ADP
ejpam-1535	106	18	the	the	DET
ejpam-1535	106	19	fold	fold	NOUN
ejpam-1535	106	20	by	by	ADP
ejpam-1535	106	21	generalising	generalise	VERB
ejpam-1535	106	22	the	the	DET
ejpam-1535	106	23	group	group	NOUN
ejpam-1535	106	24	concept	concept	NOUN
ejpam-1535	106	25	,	,	PUNCT
ejpam-1535	106	26	thereby	thereby	ADV
ejpam-1535	106	27	devising	devise	VERB
ejpam-1535	106	28	an	an	DET
ejpam-1535	106	29	algebraic	algebraic	ADJ
ejpam-1535	106	30	structure	structure	NOUN
ejpam-1535	106	31	which	which	PRON
ejpam-1535	106	32	would	would	AUX
ejpam-1535	106	33	serve	serve	VERB
ejpam-1535	106	34	to	to	PART
ejpam-1535	106	35	describe	describe	VERB
ejpam-1535	106	36	the	the	DET
ejpam-1535	106	37	symmetries	symmetry	NOUN
ejpam-1535	106	38	of	of	ADP
ejpam-1535	106	39	the	the	DET
ejpam-1535	106	40	geometry	geometry	NOUN
ejpam-1535	106	41	.	.	PUNCT
ejpam-1535	107	1	the	the	DET
ejpam-1535	107	2	advent	advent	NOUN
ejpam-1535	107	3	of	of	ADP
ejpam-1535	107	4	the	the	DET
ejpam-1535	107	5	general	general	ADJ
ejpam-1535	107	6	theory	theory	NOUN
ejpam-1535	107	7	of	of	ADP
ejpam-1535	107	8	relativity	relativity	NOUN
ejpam-1535	107	9	,	,	PUNCT
ejpam-1535	107	10	with	with	ADP
ejpam-1535	107	11	its	its	PRON
ejpam-1535	107	12	reliance	reliance	NOUN
ejpam-1535	107	13	on	on	ADP
ejpam-1535	107	14	differential	differential	ADJ
ejpam-1535	107	15	geometry	geometry	NOUN
ejpam-1535	107	16	,	,	PUNCT
ejpam-1535	107	17	ensured	ensure	VERB
ejpam-1535	107	18	that	that	SCONJ
ejpam-1535	107	19	this	this	DET
ejpam-1535	107	20	problem	problem	NOUN
ejpam-1535	107	21	received	receive	VERB
ejpam-1535	107	22	a	a	DET
ejpam-1535	107	23	great	great	ADJ
ejpam-1535	107	24	deal	deal	NOUN
ejpam-1535	107	25	of	of	ADP
ejpam-1535	107	26	attention	attention	NOUN
ejpam-1535	107	27	.	.	PUNCT
ejpam-1535	108	1	the	the	DET
ejpam-1535	108	2	question	question	NOUN
ejpam-1535	108	3	of	of	ADP
ejpam-1535	108	4	how	how	SCONJ
ejpam-1535	108	5	to	to	PART
ejpam-1535	108	6	describe	describe	VERB
ejpam-1535	108	7	symmetries	symmetry	NOUN
ejpam-1535	108	8	in	in	ADP
ejpam-1535	108	9	differential	differential	ADJ
ejpam-1535	108	10	geometry	geometry	NOUN
ejpam-1535	108	11	was	be	AUX
ejpam-1535	108	12	eventually	eventually	ADV
ejpam-1535	108	13	answered	answer	VERB
ejpam-1535	108	14	by	by	ADP
ejpam-1535	108	15	veblen	veblen	PROPN
ejpam-1535	108	16	and	and	CCONJ
ejpam-1535	108	17	whitehead	whitehead	ADJ
ejpam-1535	108	18	with	with	ADP
ejpam-1535	108	19	the	the	DET
ejpam-1535	108	20	introduction	introduction	NOUN
ejpam-1535	108	21	of	of	ADP
ejpam-1535	108	22	the	the	DET
ejpam-1535	108	23	notion	notion	NOUN
ejpam-1535	108	24	of	of	ADP
ejpam-1535	108	25	a	a	DET
ejpam-1535	108	26	pseudogroup	pseudogroup	NOUN
ejpam-1535	108	27	.	.	PUNCT
ejpam-1535	109	1	this	this	PRON
ejpam-1535	109	2	was	be	AUX
ejpam-1535	109	3	a	a	DET
ejpam-1535	109	4	generalisation	generalisation	NOUN
ejpam-1535	109	5	of	of	ADP
ejpam-1535	109	6	sophus	sophus	PROPN
ejpam-1535	109	7	lie	lie	VERB
ejpam-1535	109	8	’s	’s	PART
ejpam-1535	109	9	“	"	PUNCT
ejpam-1535	109	10	(	(	PUNCT
ejpam-1535	109	11	infinite	infinite	ADJ
ejpam-1535	109	12	)	)	PUNCT
ejpam-1535	109	13	continuous	continuous	ADJ
ejpam-1535	109	14	transformation	transformation	NOUN
ejpam-1535	109	15	group	group	NOUN
ejpam-1535	109	16	”	"	PUNCT
ejpam-1535	110	1	[	[	X
ejpam-1535	110	2	31	31	NUM
ejpam-1535	110	3	]	]	PUNCT
ejpam-1535	110	4	,	,	PUNCT
ejpam-1535	110	5	now	now	ADV
ejpam-1535	110	6	termed	term	VERB
ejpam-1535	110	7	a	a	DET
ejpam-1535	110	8	lie	lie	NOUN
ejpam-1535	110	9	pseudogroup	pseudogroup	NOUN
ejpam-1535	110	10	.	.	PUNCT
ejpam-1535	111	1	definition	definition	NOUN
ejpam-1535	111	2	1	1	NUM
ejpam-1535	111	3	(	(	PUNCT
ejpam-1535	111	4	[	[	X
ejpam-1535	111	5	49	49	NUM
ejpam-1535	111	6	,	,	PUNCT
ejpam-1535	111	7	p.	p.	NOUN
ejpam-1535	111	8	38	38	NUM
ejpam-1535	111	9	]	]	PUNCT
ejpam-1535	111	10	)	)	PUNCT
ejpam-1535	111	11	.	.	PUNCT
ejpam-1535	112	1	a	a	DET
ejpam-1535	112	2	pseudogroup	pseudogroup	NOUN
ejpam-1535	112	3	γ	γ	NOUN
ejpam-1535	112	4	is	be	AUX
ejpam-1535	112	5	a	a	DET
ejpam-1535	112	6	collection	collection	NOUN
ejpam-1535	112	7	of	of	ADP
ejpam-1535	112	8	partial	partial	ADJ
ejpam-1535	112	9	homeomorphisms	homeomorphism	NOUN
ejpam-1535	112	10	between	between	ADP
ejpam-1535	112	11	†see	†see	PROPN
ejpam-1535	113	1	[	[	X
ejpam-1535	113	2	25	25	NUM
ejpam-1535	113	3	]	]	PUNCT
ejpam-1535	113	4	for	for	ADP
ejpam-1535	113	5	klein	klein	PROPN
ejpam-1535	113	6	’s	’s	PART
ejpam-1535	113	7	text	text	NOUN
ejpam-1535	113	8	,	,	PUNCT
ejpam-1535	114	1	[	[	X
ejpam-1535	114	2	19	19	NUM
ejpam-1535	114	3	,	,	PUNCT
ejpam-1535	114	4	2	2	NUM
ejpam-1535	114	5	]	]	PUNCT
ejpam-1535	114	6	for	for	ADP
ejpam-1535	114	7	comments	comment	NOUN
ejpam-1535	114	8	thereupon	thereupon	ADV
ejpam-1535	114	9	,	,	PUNCT
ejpam-1535	114	10	and	and	CCONJ
ejpam-1535	114	11	[	[	X
ejpam-1535	114	12	18	18	NUM
ejpam-1535	114	13	]	]	PUNCT
ejpam-1535	114	14	for	for	ADP
ejpam-1535	114	15	an	an	DET
ejpam-1535	114	16	english	english	ADJ
ejpam-1535	114	17	translation	translation	NOUN
ejpam-1535	114	18	.	.	PUNCT
ejpam-1535	115	1	c.	c.	PROPN
ejpam-1535	115	2	hollings	holling	NOUN
ejpam-1535	115	3	/	/	SYM
ejpam-1535	115	4	eur	eur	PROPN
ejpam-1535	115	5	.	.	PUNCT
ejpam-1535	116	1	j.	j.	PROPN
ejpam-1535	116	2	pure	pure	PROPN
ejpam-1535	116	3	appl	appl	PROPN
ejpam-1535	116	4	.	.	PROPN
ejpam-1535	116	5	math	math	PROPN
ejpam-1535	116	6	,	,	PUNCT
ejpam-1535	116	7	5	5	NUM
ejpam-1535	116	8	(	(	PUNCT
ejpam-1535	116	9	2012	2012	NUM
ejpam-1535	116	10	)	)	PUNCT
ejpam-1535	116	11	,	,	PUNCT
ejpam-1535	116	12	414	414	NUM
ejpam-1535	116	13	-	-	SYM
ejpam-1535	116	14	450	450	NUM
ejpam-1535	116	15	419	419	NUM
ejpam-1535	116	16	open	open	ADJ
ejpam-1535	116	17	subsets	subset	NOUN
ejpam-1535	116	18	of	of	ADP
ejpam-1535	116	19	a	a	DET
ejpam-1535	116	20	topological	topological	ADJ
ejpam-1535	116	21	space	space	NOUN
ejpam-1535	116	22	such	such	ADJ
ejpam-1535	116	23	that	that	SCONJ
ejpam-1535	116	24	γ	γ	PROPN
ejpam-1535	116	25	is	be	AUX
ejpam-1535	116	26	closed	close	VERB
ejpam-1535	116	27	under	under	ADP
ejpam-1535	116	28	composition	composition	NOUN
ejpam-1535	116	29	and	and	CCONJ
ejpam-1535	116	30	inverses	inverse	NOUN
ejpam-1535	116	31	,	,	PUNCT
ejpam-1535	116	32	where	where	SCONJ
ejpam-1535	116	33	we	we	PRON
ejpam-1535	116	34	compose	compose	VERB
ejpam-1535	116	35	α	α	PRON
ejpam-1535	116	36	,	,	PUNCT
ejpam-1535	116	37	β	β	PROPN
ejpam-1535	116	38	∈	∈	NOUN
ejpam-1535	116	39	γ	γ	NOUN
ejpam-1535	116	40	only	only	ADV
ejpam-1535	116	41	if	if	SCONJ
ejpam-1535	116	42	i	i	PRON
ejpam-1535	116	43	m	m	VERB
ejpam-1535	116	44	α	α	NOUN
ejpam-1535	116	45	=	=	X
ejpam-1535	116	46	dom	dom	NOUN
ejpam-1535	116	47	β	β	X
ejpam-1535	116	48	.	.	PUNCT
ejpam-1535	117	1	in	in	ADP
ejpam-1535	117	2	the	the	DET
ejpam-1535	117	3	traditional	traditional	ADJ
ejpam-1535	117	4	case	case	NOUN
ejpam-1535	117	5	of	of	ADP
ejpam-1535	117	6	groups	group	NOUN
ejpam-1535	117	7	of	of	ADP
ejpam-1535	117	8	transformations	transformation	NOUN
ejpam-1535	117	9	,	,	PUNCT
ejpam-1535	117	10	the	the	DET
ejpam-1535	117	11	move	move	NOUN
ejpam-1535	117	12	to	to	ADP
ejpam-1535	117	13	an	an	DET
ejpam-1535	117	14	abstract	abstract	ADJ
ejpam-1535	117	15	setting	setting	NOUN
ejpam-1535	117	16	had	have	AUX
ejpam-1535	117	17	yielded	yield	VERB
ejpam-1535	117	18	the	the	DET
ejpam-1535	117	19	notion	notion	NOUN
ejpam-1535	117	20	of	of	ADP
ejpam-1535	117	21	an	an	DET
ejpam-1535	117	22	abstract	abstract	ADJ
ejpam-1535	117	23	group	group	NOUN
ejpam-1535	117	24	;	;	PUNCT
ejpam-1535	117	25	researchers	researcher	NOUN
ejpam-1535	117	26	now	now	ADV
ejpam-1535	117	27	asked	ask	VERB
ejpam-1535	117	28	the	the	DET
ejpam-1535	117	29	question	question	NOUN
ejpam-1535	117	30	:	:	PUNCT
ejpam-1535	117	31	what	what	PRON
ejpam-1535	117	32	is	be	AUX
ejpam-1535	117	33	the	the	DET
ejpam-1535	117	34	corresponding	corresponding	ADJ
ejpam-1535	117	35	abstract	abstract	ADJ
ejpam-1535	117	36	structure	structure	NOUN
ejpam-1535	117	37	for	for	ADP
ejpam-1535	117	38	a	a	DET
ejpam-1535	117	39	pseudogroup	pseudogroup	NOUN
ejpam-1535	117	40	?	?	PUNCT
ejpam-1535	118	1	it	it	PRON
ejpam-1535	118	2	turned	turn	VERB
ejpam-1535	118	3	out	out	ADP
ejpam-1535	118	4	there	there	PRON
ejpam-1535	118	5	are	be	VERB
ejpam-1535	118	6	two	two	NUM
ejpam-1535	118	7	closelylinked	closelylinked	ADJ
ejpam-1535	118	8	solutions	solution	NOUN
ejpam-1535	118	9	to	to	ADP
ejpam-1535	118	10	this	this	DET
ejpam-1535	118	11	problem	problem	NOUN
ejpam-1535	118	12	,	,	PUNCT
ejpam-1535	118	13	both	both	PRON
ejpam-1535	118	14	of	of	ADP
ejpam-1535	118	15	which	which	PRON
ejpam-1535	118	16	are	be	AUX
ejpam-1535	118	17	connected	connect	VERB
ejpam-1535	118	18	with	with	ADP
ejpam-1535	118	19	the	the	DET
ejpam-1535	118	20	question	question	NOUN
ejpam-1535	118	21	of	of	ADP
ejpam-1535	118	22	how	how	SCONJ
ejpam-1535	118	23	to	to	PART
ejpam-1535	118	24	compose	compose	VERB
ejpam-1535	118	25	partial	partial	ADJ
ejpam-1535	118	26	mappings	mapping	NOUN
ejpam-1535	118	27	.	.	PUNCT
ejpam-1535	119	1	we	we	PRON
ejpam-1535	119	2	have	have	AUX
ejpam-1535	119	3	seen	see	VERB
ejpam-1535	119	4	that	that	SCONJ
ejpam-1535	119	5	veblen	veblen	PROPN
ejpam-1535	119	6	and	and	CCONJ
ejpam-1535	119	7	whitehead	whitehead	PROPN
ejpam-1535	119	8	chose	choose	VERB
ejpam-1535	119	9	to	to	PART
ejpam-1535	119	10	compose	compose	VERB
ejpam-1535	119	11	two	two	NUM
ejpam-1535	119	12	partial	partial	ADJ
ejpam-1535	119	13	mappings	mapping	NOUN
ejpam-1535	119	14	α	α	NOUN
ejpam-1535	119	15	and	and	CCONJ
ejpam-1535	119	16	β	β	PRON
ejpam-1535	119	17	only	only	ADV
ejpam-1535	119	18	if	if	SCONJ
ejpam-1535	119	19	i	i	PRON
ejpam-1535	119	20	m	m	VERB
ejpam-1535	119	21	α	α	NOUN
ejpam-1535	119	22	=	=	X
ejpam-1535	119	23	dom	dom	NOUN
ejpam-1535	119	24	β	β	X
ejpam-1535	119	25	,	,	PUNCT
ejpam-1535	119	26	thereby	thereby	ADV
ejpam-1535	119	27	giving	give	VERB
ejpam-1535	119	28	their	their	PRON
ejpam-1535	119	29	pseudogroups	pseudogroup	NOUN
ejpam-1535	119	30	a	a	DET
ejpam-1535	119	31	partial	partial	ADJ
ejpam-1535	119	32	composition	composition	NOUN
ejpam-1535	119	33	.	.	PUNCT
ejpam-1535	120	1	attempts	attempt	NOUN
ejpam-1535	120	2	were	be	AUX
ejpam-1535	120	3	subsequently	subsequently	ADV
ejpam-1535	120	4	made	make	VERB
ejpam-1535	120	5	to	to	PART
ejpam-1535	120	6	“	"	PUNCT
ejpam-1535	120	7	complete	complete	VERB
ejpam-1535	120	8	”	"	PUNCT
ejpam-1535	120	9	this	this	DET
ejpam-1535	120	10	composition	composition	NOUN
ejpam-1535	120	11	to	to	PART
ejpam-1535	120	12	give	give	VERB
ejpam-1535	120	13	a	a	DET
ejpam-1535	120	14	pseudogroup	pseudogroup	NOUN
ejpam-1535	120	15	an	an	DET
ejpam-1535	120	16	everywhere	everywhere	ADV
ejpam-1535	120	17	-	-	PUNCT
ejpam-1535	120	18	defined	define	VERB
ejpam-1535	120	19	operation	operation	NOUN
ejpam-1535	120	20	.	.	PUNCT
ejpam-1535	121	1	one	one	NUM
ejpam-1535	121	2	such	such	ADJ
ejpam-1535	121	3	attempt	attempt	NOUN
ejpam-1535	121	4	was	be	AUX
ejpam-1535	121	5	made	make	VERB
ejpam-1535	121	6	by	by	ADP
ejpam-1535	121	7	j.	j.	PROPN
ejpam-1535	121	8	a.	a.	PROPN
ejpam-1535	121	9	schouten	schouten	PROPN
ejpam-1535	121	10	and	and	CCONJ
ejpam-1535	121	11	j.	j.	PROPN
ejpam-1535	121	12	haantjes	haantjes	PROPN
ejpam-1535	121	13	,	,	PUNCT
ejpam-1535	121	14	for	for	ADP
ejpam-1535	121	15	example	example	NOUN
ejpam-1535	121	16	,	,	PUNCT
ejpam-1535	121	17	in	in	ADP
ejpam-1535	121	18	[	[	NOUN
ejpam-1535	121	19	48	48	NUM
ejpam-1535	121	20	,	,	PUNCT
ejpam-1535	121	21	p.	p.	NOUN
ejpam-1535	121	22	361	361	NUM
ejpam-1535	121	23	]	]	PUNCT
ejpam-1535	121	24	,	,	PUNCT
ejpam-1535	121	25	where	where	SCONJ
ejpam-1535	121	26	two	two	NUM
ejpam-1535	121	27	partial	partial	ADJ
ejpam-1535	121	28	mappings	mapping	NOUN
ejpam-1535	121	29	α	α	NOUN
ejpam-1535	121	30	and	and	CCONJ
ejpam-1535	121	31	β	β	X
ejpam-1535	121	32	on	on	ADP
ejpam-1535	121	33	a	a	DET
ejpam-1535	121	34	set	set	NOUN
ejpam-1535	121	35	x	x	PUNCT
ejpam-1535	121	36	were	be	AUX
ejpam-1535	121	37	composed	compose	VERB
ejpam-1535	121	38	whenever	whenever	SCONJ
ejpam-1535	121	39	i	i	PRON
ejpam-1535	121	40	m	m	VERB
ejpam-1535	121	41	α	α	PRON
ejpam-1535	121	42	∩	∩	ADJ
ejpam-1535	121	43	dom	dom	NOUN
ejpam-1535	121	44	β	β	X
ejpam-1535	121	45	6=	6=	NUM
ejpam-1535	121	46	;	;	PUNCT
ejpam-1535	121	47	.	.	PUNCT
ejpam-1535	122	1	however	however	ADV
ejpam-1535	122	2	,	,	PUNCT
ejpam-1535	122	3	this	this	DET
ejpam-1535	122	4	operation	operation	NOUN
ejpam-1535	122	5	was	be	AUX
ejpam-1535	122	6	still	still	ADV
ejpam-1535	122	7	partial	partial	ADJ
ejpam-1535	122	8	,	,	PUNCT
ejpam-1535	122	9	for	for	SCONJ
ejpam-1535	122	10	it	it	PRON
ejpam-1535	122	11	did	do	AUX
ejpam-1535	122	12	not	not	PART
ejpam-1535	122	13	take	take	VERB
ejpam-1535	122	14	into	into	ADP
ejpam-1535	122	15	account	account	NOUN
ejpam-1535	122	16	the	the	DET
ejpam-1535	122	17	possibility	possibility	NOUN
ejpam-1535	122	18	of	of	ADP
ejpam-1535	122	19	the	the	DET
ejpam-1535	122	20	“	"	PUNCT
ejpam-1535	122	21	empty	empty	ADJ
ejpam-1535	122	22	transformation	transformation	NOUN
ejpam-1535	122	23	”	"	PUNCT
ejpam-1535	122	24	:	:	PUNCT
ejpam-1535	122	25	the	the	DET
ejpam-1535	122	26	partial	partial	ADJ
ejpam-1535	122	27	transformation	transformation	NOUN
ejpam-1535	122	28	whose	whose	DET
ejpam-1535	122	29	domain	domain	NOUN
ejpam-1535	122	30	is	be	AUX
ejpam-1535	122	31	;	;	PUNCT
ejpam-1535	122	32	⊆	⊆	NUM
ejpam-1535	122	33	x	x	SYM
ejpam-1535	122	34	,	,	PUNCT
ejpam-1535	122	35	which	which	PRON
ejpam-1535	122	36	will	will	AUX
ejpam-1535	122	37	result	result	VERB
ejpam-1535	122	38	whenever	whenever	SCONJ
ejpam-1535	122	39	i	i	PRON
ejpam-1535	122	40	m	m	VERB
ejpam-1535	122	41	α	α	PRON
ejpam-1535	122	42	∩	∩	ADJ
ejpam-1535	122	43	dom	dom	NOUN
ejpam-1535	122	44	β	β	X
ejpam-1535	122	45	=	=	PUNCT
ejpam-1535	122	46	;	;	PUNCT
ejpam-1535	122	47	(	(	PUNCT
ejpam-1535	122	48	see	see	VERB
ejpam-1535	122	49	[	[	X
ejpam-1535	122	50	20	20	NUM
ejpam-1535	122	51	,	,	PUNCT
ejpam-1535	122	52	§	§	NOUN
ejpam-1535	122	53	3	3	NUM
ejpam-1535	122	54	]	]	PUNCT
ejpam-1535	122	55	for	for	ADP
ejpam-1535	122	56	a	a	DET
ejpam-1535	122	57	brief	brief	ADJ
ejpam-1535	122	58	introduction	introduction	NOUN
ejpam-1535	122	59	to	to	ADP
ejpam-1535	122	60	partial	partial	ADJ
ejpam-1535	122	61	transformations	transformation	NOUN
ejpam-1535	122	62	)	)	PUNCT
ejpam-1535	122	63	.	.	PUNCT
ejpam-1535	123	1	the	the	DET
ejpam-1535	123	2	final	final	ADJ
ejpam-1535	123	3	step	step	NOUN
ejpam-1535	123	4	came	come	VERB
ejpam-1535	123	5	in	in	ADP
ejpam-1535	123	6	the	the	DET
ejpam-1535	123	7	early	early	ADJ
ejpam-1535	123	8	1950s	1950	NOUN
ejpam-1535	123	9	with	with	ADP
ejpam-1535	123	10	the	the	DET
ejpam-1535	123	11	observation	observation	NOUN
ejpam-1535	123	12	by	by	ADP
ejpam-1535	123	13	viktor	viktor	NOUN
ejpam-1535	123	14	vladimirovich	vladimirovich	NOUN
ejpam-1535	123	15	wagner‡	wagner‡	PUNCT
ejpam-1535	123	16	that	that	SCONJ
ejpam-1535	123	17	the	the	DET
ejpam-1535	123	18	composition	composition	NOUN
ejpam-1535	123	19	of	of	ADP
ejpam-1535	123	20	partial	partial	ADJ
ejpam-1535	123	21	mappings	mapping	NOUN
ejpam-1535	123	22	is	be	AUX
ejpam-1535	123	23	a	a	DET
ejpam-1535	123	24	special	special	ADJ
ejpam-1535	123	25	case	case	NOUN
ejpam-1535	123	26	of	of	ADP
ejpam-1535	123	27	the	the	DET
ejpam-1535	123	28	composition	composition	NOUN
ejpam-1535	123	29	of	of	ADP
ejpam-1535	123	30	binary	binary	ADJ
ejpam-1535	123	31	relations	relation	NOUN
ejpam-1535	123	32	.	.	PUNCT
ejpam-1535	124	1	in	in	ADP
ejpam-1535	124	2	the	the	DET
ejpam-1535	124	3	case	case	NOUN
ejpam-1535	124	4	of	of	ADP
ejpam-1535	124	5	binary	binary	ADJ
ejpam-1535	124	6	relations	relation	NOUN
ejpam-1535	124	7	,	,	PUNCT
ejpam-1535	124	8	however	however	ADV
ejpam-1535	124	9	,	,	PUNCT
ejpam-1535	124	10	it	it	PRON
ejpam-1535	124	11	is	be	AUX
ejpam-1535	124	12	much	much	ADV
ejpam-1535	124	13	clearer	clear	ADJ
ejpam-1535	124	14	that	that	SCONJ
ejpam-1535	124	15	the	the	DET
ejpam-1535	124	16	composition	composition	NOUN
ejpam-1535	124	17	may	may	AUX
ejpam-1535	124	18	be	be	AUX
ejpam-1535	124	19	empty	empty	ADJ
ejpam-1535	124	20	.	.	PUNCT
ejpam-1535	125	1	this	this	DET
ejpam-1535	125	2	simple	simple	ADJ
ejpam-1535	125	3	observation	observation	NOUN
ejpam-1535	125	4	enabled	enable	VERB
ejpam-1535	125	5	wagner	wagner	NOUN
ejpam-1535	125	6	to	to	PART
ejpam-1535	125	7	overcome	overcome	VERB
ejpam-1535	125	8	the	the	DET
ejpam-1535	125	9	psychological	psychological	ADJ
ejpam-1535	125	10	difficulties	difficulty	NOUN
ejpam-1535	125	11	which	which	PRON
ejpam-1535	125	12	had	have	AUX
ejpam-1535	125	13	so	so	ADV
ejpam-1535	125	14	far	far	ADV
ejpam-1535	125	15	barred	bar	VERB
ejpam-1535	125	16	the	the	DET
ejpam-1535	125	17	admission	admission	NOUN
ejpam-1535	125	18	of	of	ADP
ejpam-1535	125	19	an	an	DET
ejpam-1535	125	20	empty	empty	ADJ
ejpam-1535	125	21	transformation	transformation	NOUN
ejpam-1535	125	22	into	into	ADP
ejpam-1535	125	23	the	the	DET
ejpam-1535	125	24	study	study	NOUN
ejpam-1535	125	25	of	of	ADP
ejpam-1535	125	26	partial	partial	ADJ
ejpam-1535	125	27	mappings	mapping	NOUN
ejpam-1535	125	28	.	.	PUNCT
ejpam-1535	126	1	the	the	DET
ejpam-1535	126	2	introduction	introduction	NOUN
ejpam-1535	126	3	of	of	ADP
ejpam-1535	126	4	the	the	DET
ejpam-1535	126	5	empty	empty	ADJ
ejpam-1535	126	6	transformation	transformation	NOUN
ejpam-1535	126	7	meant	mean	VERB
ejpam-1535	126	8	that	that	SCONJ
ejpam-1535	126	9	an	an	DET
ejpam-1535	126	10	everywhere	everywhere	ADV
ejpam-1535	126	11	-	-	PUNCT
ejpam-1535	126	12	defined	define	VERB
ejpam-1535	126	13	composition	composition	NOUN
ejpam-1535	126	14	of	of	ADP
ejpam-1535	126	15	partial	partial	ADJ
ejpam-1535	126	16	mappings	mapping	NOUN
ejpam-1535	126	17	could	could	AUX
ejpam-1535	126	18	finally	finally	ADV
ejpam-1535	126	19	be	be	AUX
ejpam-1535	126	20	utilised	utilise	VERB
ejpam-1535	126	21	,	,	PUNCT
ejpam-1535	126	22	namely	namely	ADV
ejpam-1535	126	23	,	,	PUNCT
ejpam-1535	126	24	the	the	DET
ejpam-1535	126	25	familiar	familiar	ADJ
ejpam-1535	126	26	(	(	PUNCT
ejpam-1535	126	27	left	leave	VERB
ejpam-1535	126	28	-	-	PUNCT
ejpam-1535	126	29	to	to	ADP
ejpam-1535	126	30	-	-	PUNCT
ejpam-1535	126	31	right	right	ADJ
ejpam-1535	126	32	)	)	PUNCT
ejpam-1535	126	33	composition	composition	NOUN
ejpam-1535	126	34	usually	usually	ADV
ejpam-1535	126	35	employed	employ	VERB
ejpam-1535	126	36	for	for	ADP
ejpam-1535	126	37	such	such	ADJ
ejpam-1535	126	38	mappings	mapping	NOUN
ejpam-1535	126	39	in	in	ADP
ejpam-1535	126	40	modern	modern	ADJ
ejpam-1535	126	41	semigroup	semigroup	NOUN
ejpam-1535	126	42	theory	theory	NOUN
ejpam-1535	126	43	[	[	X
ejpam-1535	126	44	23	23	NUM
ejpam-1535	126	45	,	,	PUNCT
ejpam-1535	126	46	p.	p.	NOUN
ejpam-1535	126	47	148	148	NUM
ejpam-1535	126	48	]	]	SYM
ejpam-1535	126	49	:	:	PUNCT
ejpam-1535	126	50	domαβ	domαβ	NOUN
ejpam-1535	126	51	=	=	SYM
ejpam-1535	126	52	�	�	PROPN
ejpam-1535	126	53	imα∩	imα∩	PROPN
ejpam-1535	126	54	domβ	domβ	PROPN
ejpam-1535	126	55	�	�	PROPN
ejpam-1535	126	56	α−1	α−1	PROPN
ejpam-1535	126	57	,	,	PUNCT
ejpam-1535	126	58	x(αβ	x(αβ	NUM
ejpam-1535	126	59	)	)	PUNCT
ejpam-1535	126	60	=	=	SYM
ejpam-1535	127	1	(	(	PUNCT
ejpam-1535	127	2	xα)β	xα)β	PROPN
ejpam-1535	127	3	,	,	PUNCT
ejpam-1535	127	4	for	for	ADP
ejpam-1535	127	5	any	any	DET
ejpam-1535	127	6	x	x	SYM
ejpam-1535	127	7	∈	∈	PROPN
ejpam-1535	127	8	domαβ	domαβ	NOUN
ejpam-1535	127	9	.	.	PUNCT
ejpam-1535	128	1	(	(	PUNCT
ejpam-1535	128	2	1	1	X
ejpam-1535	128	3	)	)	PUNCT
ejpam-1535	128	4	wagner	wagner	NOUN
ejpam-1535	128	5	now	now	ADV
ejpam-1535	128	6	turned	turn	VERB
ejpam-1535	128	7	his	his	PRON
ejpam-1535	128	8	attention	attention	NOUN
ejpam-1535	128	9	to	to	ADP
ejpam-1535	128	10	the	the	DET
ejpam-1535	128	11	study	study	NOUN
ejpam-1535	128	12	of	of	ADP
ejpam-1535	128	13	systems	system	NOUN
ejpam-1535	128	14	of	of	ADP
ejpam-1535	128	15	one	one	NUM
ejpam-1535	128	16	-	-	PUNCT
ejpam-1535	128	17	one	one	NUM
ejpam-1535	128	18	partial	partial	ADJ
ejpam-1535	128	19	transformations	transformation	NOUN
ejpam-1535	128	20	with	with	ADP
ejpam-1535	128	21	this	this	DET
ejpam-1535	128	22	everywhere	everywhere	ADV
ejpam-1535	128	23	-	-	PUNCT
ejpam-1535	128	24	defined	define	VERB
ejpam-1535	128	25	composition	composition	NOUN
ejpam-1535	128	26	[	[	X
ejpam-1535	128	27	50	50	NUM
ejpam-1535	128	28	]	]	PUNCT
ejpam-1535	128	29	.	.	PUNCT
ejpam-1535	129	1	though	though	SCONJ
ejpam-1535	129	2	a	a	DET
ejpam-1535	129	3	differential	differential	ADJ
ejpam-1535	129	4	geometer	geometer	NOUN
ejpam-1535	129	5	by	by	ADP
ejpam-1535	129	6	training	training	NOUN
ejpam-1535	129	7	,	,	PUNCT
ejpam-1535	129	8	wagner	wagner	PROPN
ejpam-1535	129	9	recognised	recognise	VERB
ejpam-1535	129	10	in	in	ADP
ejpam-1535	129	11	such	such	ADJ
ejpam-1535	129	12	systems	system	NOUN
ejpam-1535	129	13	the	the	DET
ejpam-1535	129	14	structure	structure	NOUN
ejpam-1535	129	15	of	of	ADP
ejpam-1535	129	16	a	a	DET
ejpam-1535	129	17	semigroup	semigroup	NOUN
ejpam-1535	129	18	;	;	PUNCT
ejpam-1535	129	19	given	give	VERB
ejpam-1535	129	20	a	a	DET
ejpam-1535	129	21	set	set	NOUN
ejpam-1535	129	22	x	x	SYM
ejpam-1535	129	23	,	,	PUNCT
ejpam-1535	129	24	he	he	PRON
ejpam-1535	129	25	defined	define	VERB
ejpam-1535	129	26	what	what	PRON
ejpam-1535	129	27	we	we	PRON
ejpam-1535	129	28	now	now	ADV
ejpam-1535	129	29	term	term	VERB
ejpam-1535	129	30	the	the	DET
ejpam-1535	129	31	symmetric	symmetric	ADJ
ejpam-1535	129	32	inverse	inverse	NOUN
ejpam-1535	129	33	monoid	monoid	NOUN
ejpam-1535	129	34	ix	ix	ADV
ejpam-1535	129	35	on	on	ADP
ejpam-1535	129	36	x	x	X
ejpam-1535	129	37	.	.	PUNCT
ejpam-1535	130	1	further	far	ADV
ejpam-1535	130	2	,	,	PUNCT
ejpam-1535	130	3	upon	upon	SCONJ
ejpam-1535	130	4	moving	move	VERB
ejpam-1535	130	5	to	to	ADP
ejpam-1535	130	6	an	an	DET
ejpam-1535	130	7	abstract	abstract	ADJ
ejpam-1535	130	8	setting	setting	NOUN
ejpam-1535	130	9	,	,	PUNCT
ejpam-1535	130	10	wagner	wagner	PROPN
ejpam-1535	130	11	observed	observe	VERB
ejpam-1535	130	12	that	that	SCONJ
ejpam-1535	130	13	these	these	PRON
ejpam-1535	130	14	were	be	AUX
ejpam-1535	130	15	semigroups	semigroup	NOUN
ejpam-1535	130	16	with	with	ADP
ejpam-1535	130	17	an	an	DET
ejpam-1535	130	18	involution	involution	NOUN
ejpam-1535	130	19	which	which	PRON
ejpam-1535	130	20	generalised	generalise	VERB
ejpam-1535	130	21	the	the	DET
ejpam-1535	130	22	group	group	NOUN
ejpam-1535	130	23	-	-	PUNCT
ejpam-1535	130	24	theoretic	theoretic	NOUN
ejpam-1535	130	25	notion	notion	NOUN
ejpam-1535	130	26	of	of	ADP
ejpam-1535	130	27	inversion	inversion	NOUN
ejpam-1535	130	28	.	.	PUNCT
ejpam-1535	131	1	in	in	ADP
ejpam-1535	131	2	[	[	X
ejpam-1535	131	3	51	51	NUM
ejpam-1535	131	4	]	]	PUNCT
ejpam-1535	131	5	,	,	PUNCT
ejpam-1535	131	6	he	he	PRON
ejpam-1535	131	7	gave	give	VERB
ejpam-1535	131	8	the	the	DET
ejpam-1535	131	9	modern	modern	ADJ
ejpam-1535	131	10	definition	definition	NOUN
ejpam-1535	131	11	of	of	ADP
ejpam-1535	131	12	an	an	DET
ejpam-1535	131	13	inverse	inverse	NOUN
ejpam-1535	131	14	semigroup	semigroup	NOUN
ejpam-1535	131	15	,	,	PUNCT
ejpam-1535	131	16	though	though	SCONJ
ejpam-1535	131	17	under	under	ADP
ejpam-1535	131	18	the	the	DET
ejpam-1535	131	19	name	name	NOUN
ejpam-1535	131	20	of	of	ADP
ejpam-1535	131	21	generalised	generalised	ADJ
ejpam-1535	131	22	group	group	NOUN
ejpam-1535	131	23	(	(	PUNCT
ejpam-1535	131	24	obobwenna	obobwenna	PROPN
ejpam-1535	131	25	�	�	PROPN
ejpam-1535	131	26	gruppa	gruppa	PROPN
ejpam-1535	131	27	)	)	PUNCT
ejpam-1535	131	28	.	.	PUNCT
ejpam-1535	132	1	he	he	PRON
ejpam-1535	132	2	subsequently	subsequently	ADV
ejpam-1535	132	3	developed	develop	VERB
ejpam-1535	132	4	the	the	DET
ejpam-1535	132	5	theory	theory	NOUN
ejpam-1535	132	6	of	of	ADP
ejpam-1535	132	7	generalised	generalise	VERB
ejpam-1535	132	8	groups	group	NOUN
ejpam-1535	132	9	further	far	ADV
ejpam-1535	132	10	in	in	ADP
ejpam-1535	132	11	a	a	DET
ejpam-1535	132	12	much	much	ADV
ejpam-1535	132	13	longer	long	ADJ
ejpam-1535	132	14	paper	paper	NOUN
ejpam-1535	132	15	[	[	X
ejpam-1535	132	16	52	52	NUM
ejpam-1535	132	17	]	]	PUNCT
ejpam-1535	132	18	,	,	PUNCT
ejpam-1535	132	19	where	where	SCONJ
ejpam-1535	132	20	they	they	PRON
ejpam-1535	132	21	were	be	AUX
ejpam-1535	132	22	intimately	intimately	ADV
ejpam-1535	132	23	connected	connect	VERB
ejpam-1535	132	24	with	with	ADP
ejpam-1535	132	25	the	the	DET
ejpam-1535	132	26	notion	notion	NOUN
ejpam-1535	132	27	of	of	ADP
ejpam-1535	132	28	a	a	DET
ejpam-1535	132	29	so	so	ADV
ejpam-1535	132	30	-	-	PUNCT
ejpam-1535	132	31	called	call	VERB
ejpam-1535	132	32	generalised	generalised	ADJ
ejpam-1535	132	33	heap	heap	NOUN
ejpam-1535	132	34	or	or	CCONJ
ejpam-1535	132	35	generalised	generalise	VERB
ejpam-1535	132	36	groud	groud	NOUN
ejpam-1535	132	37	(	(	PUNCT
ejpam-1535	132	38	obobwenna	obobwenna	PROPN
ejpam-1535	132	39	�	�	PROPN
ejpam-1535	132	40	gruda	gruda	NOUN
ejpam-1535	132	41	)	)	PUNCT
ejpam-1535	132	42	;	;	PUNCT
ejpam-1535	132	43	loosely	loosely	ADV
ejpam-1535	132	44	speaking	speak	VERB
ejpam-1535	132	45	,	,	PUNCT
ejpam-1535	132	46	whereas	whereas	SCONJ
ejpam-1535	132	47	an	an	DET
ejpam-1535	132	48	inverse	inverse	NOUN
ejpam-1535	132	49	semigroup	semigroup	NOUN
ejpam-1535	132	50	arises	arise	VERB
ejpam-1535	132	51	from	from	ADP
ejpam-1535	132	52	the	the	DET
ejpam-1535	132	53	study	study	NOUN
ejpam-1535	132	54	of	of	ADP
ejpam-1535	132	55	systems	system	NOUN
ejpam-1535	132	56	of	of	ADP
ejpam-1535	132	57	partial	partial	ADJ
ejpam-1535	132	58	one	one	NUM
ejpam-1535	132	59	-	-	PUNCT
ejpam-1535	132	60	one	one	NUM
ejpam-1535	132	61	transformations	transformation	NOUN
ejpam-1535	132	62	of	of	ADP
ejpam-1535	132	63	a	a	DET
ejpam-1535	132	64	single	single	ADJ
ejpam-1535	132	65	set	set	NOUN
ejpam-1535	132	66	into	into	ADP
ejpam-1535	132	67	itself	itself	PRON
ejpam-1535	132	68	,	,	PUNCT
ejpam-1535	132	69	generalised	generalise	VERB
ejpam-1535	132	70	heaps	heap	NOUN
ejpam-1535	132	71	come	come	VERB
ejpam-1535	132	72	from	from	ADP
ejpam-1535	132	73	the	the	DET
ejpam-1535	132	74	study	study	NOUN
ejpam-1535	132	75	of	of	ADP
ejpam-1535	132	76	systems	system	NOUN
ejpam-1535	132	77	of	of	ADP
ejpam-1535	132	78	partial	partial	ADJ
ejpam-1535	132	79	one	one	NUM
ejpam-1535	132	80	-	-	PUNCT
ejpam-1535	132	81	one	one	NUM
ejpam-1535	132	82	transformations	transformation	NOUN
ejpam-1535	132	83	from	from	ADP
ejpam-1535	132	84	one	one	NUM
ejpam-1535	132	85	set	set	NOUN
ejpam-1535	132	86	to	to	ADP
ejpam-1535	132	87	another	another	PRON
ejpam-1535	132	88	,	,	PUNCT
ejpam-1535	132	89	and	and	CCONJ
ejpam-1535	132	90	must	must	AUX
ejpam-1535	132	91	therefore	therefore	ADV
ejpam-1535	132	92	be	be	AUX
ejpam-1535	132	93	equipped	equip	VERB
ejpam-1535	132	94	with	with	ADP
ejpam-1535	132	95	a	a	DET
ejpam-1535	132	96	ternary	ternary	ADJ
ejpam-1535	132	97	operation	operation	NOUN
ejpam-1535	132	98	,	,	PUNCT
ejpam-1535	132	99	rather	rather	ADV
ejpam-1535	132	100	than	than	ADP
ejpam-1535	132	101	a	a	DET
ejpam-1535	132	102	binary	binary	ADJ
ejpam-1535	132	103	operation	operation	NOUN
ejpam-1535	132	104	(	(	PUNCT
ejpam-1535	132	105	given	give	VERB
ejpam-1535	132	106	partial	partial	ADJ
ejpam-1535	132	107	one	one	NUM
ejpam-1535	132	108	-	-	PUNCT
ejpam-1535	132	109	one	one	NUM
ejpam-1535	132	110	mappings	mapping	NOUN
ejpam-1535	132	111	α	α	X
ejpam-1535	132	112	,	,	PUNCT
ejpam-1535	132	113	β	β	X
ejpam-1535	132	114	,	,	PUNCT
ejpam-1535	132	115	γ	γ	PROPN
ejpam-1535	132	116	from	from	ADP
ejpam-1535	132	117	subsets	subset	NOUN
ejpam-1535	132	118	of	of	ADP
ejpam-1535	132	119	a	a	DET
ejpam-1535	132	120	set	set	NOUN
ejpam-1535	132	121	a	a	PRON
ejpam-1535	132	122	to	to	ADP
ejpam-1535	132	123	subsets	subset	NOUN
ejpam-1535	132	124	of	of	ADP
ejpam-1535	132	125	a	a	DET
ejpam-1535	132	126	set	set	NOUN
ejpam-1535	132	127	b	b	NOUN
ejpam-1535	132	128	,	,	PUNCT
ejpam-1535	132	129	the	the	DET
ejpam-1535	132	130	ternary	ternary	ADJ
ejpam-1535	132	131	operation	operation	NOUN
ejpam-1535	132	132	,	,	PUNCT
ejpam-1535	132	133	denoted	denote	VERB
ejpam-1535	132	134	[	[	X
ejpam-1535	132	135	·	·	PUNCT
ejpam-1535	132	136	·	·	PUNCT
ejpam-1535	132	137	·	·	PUNCT
ejpam-1535	132	138	]	]	PUNCT
ejpam-1535	132	139	,	,	PUNCT
ejpam-1535	132	140	is	be	AUX
ejpam-1535	132	141	defined	define	VERB
ejpam-1535	132	142	to	to	PART
ejpam-1535	132	143	be	be	AUX
ejpam-1535	132	144	the	the	DET
ejpam-1535	132	145	composition	composition	NOUN
ejpam-1535	133	1	[	[	X
ejpam-1535	133	2	α	α	X
ejpam-1535	133	3	β	β	X
ejpam-1535	133	4	γ	γ	X
ejpam-1535	133	5	]	]	X
ejpam-1535	133	6	=	=	SYM
ejpam-1535	133	7	αβ−1γ	αβ−1γ	NUM
ejpam-1535	133	8	)	)	PUNCT
ejpam-1535	133	9	.	.	PUNCT
ejpam-1535	134	1	‡	‡	X
ejpam-1535	135	1	viktor	viktor	PROPN
ejpam-1535	135	2	vladimiroviq	vladimiroviq	PROPN
ejpam-1535	135	3	vagner	vagner	NOUN
ejpam-1535	135	4	.	.	PUNCT
ejpam-1535	136	1	i	i	PRON
ejpam-1535	136	2	have	have	AUX
ejpam-1535	136	3	chosen	choose	VERB
ejpam-1535	136	4	to	to	PART
ejpam-1535	136	5	transliterate	transliterate	VERB
ejpam-1535	136	6	the	the	DET
ejpam-1535	136	7	“	"	PUNCT
ejpam-1535	136	8	v	v	NOUN
ejpam-1535	136	9	”	"	PUNCT
ejpam-1535	136	10	of	of	ADP
ejpam-1535	136	11	“	"	PUNCT
ejpam-1535	136	12	vagner	vagner	NOUN
ejpam-1535	136	13	”	"	PUNCT
ejpam-1535	136	14	as	as	ADP
ejpam-1535	136	15	“	"	PUNCT
ejpam-1535	136	16	w	w	NOUN
ejpam-1535	136	17	”	"	PUNCT
ejpam-1535	136	18	,	,	PUNCT
ejpam-1535	136	19	as	as	SCONJ
ejpam-1535	136	20	this	this	PRON
ejpam-1535	136	21	was	be	AUX
ejpam-1535	136	22	apparently	apparently	ADV
ejpam-1535	136	23	wagner	wagner	PROPN
ejpam-1535	136	24	’s	’s	PART
ejpam-1535	136	25	own	own	ADJ
ejpam-1535	136	26	preference	preference	NOUN
ejpam-1535	136	27	—	—	PUNCT
ejpam-1535	136	28	see	see	VERB
ejpam-1535	136	29	[	[	X
ejpam-1535	136	30	47	47	NUM
ejpam-1535	136	31	,	,	PUNCT
ejpam-1535	136	32	p.	p.	NOUN
ejpam-1535	136	33	152	152	NUM
ejpam-1535	136	34	]	]	X
ejpam-1535	136	35	c.	c.	PROPN
ejpam-1535	136	36	hollings	holling	NOUN
ejpam-1535	136	37	/	/	SYM
ejpam-1535	136	38	eur	eur	PROPN
ejpam-1535	136	39	.	.	PUNCT
ejpam-1535	137	1	j.	j.	PROPN
ejpam-1535	137	2	pure	pure	PROPN
ejpam-1535	137	3	appl	appl	PROPN
ejpam-1535	137	4	.	.	PROPN
ejpam-1535	137	5	math	math	PROPN
ejpam-1535	137	6	,	,	PUNCT
ejpam-1535	137	7	5	5	NUM
ejpam-1535	137	8	(	(	PUNCT
ejpam-1535	137	9	2012	2012	NUM
ejpam-1535	137	10	)	)	PUNCT
ejpam-1535	137	11	,	,	PUNCT
ejpam-1535	137	12	414	414	NUM
ejpam-1535	137	13	-	-	SYM
ejpam-1535	137	14	450	450	NUM
ejpam-1535	137	15	420	420	NUM
ejpam-1535	137	16	inverse	inverse	NOUN
ejpam-1535	137	17	semigroups	semigroup	NOUN
ejpam-1535	137	18	were	be	AUX
ejpam-1535	137	19	introduced	introduce	VERB
ejpam-1535	137	20	and	and	CCONJ
ejpam-1535	137	21	studied	study	VERB
ejpam-1535	137	22	independently	independently	ADV
ejpam-1535	137	23	by	by	ADP
ejpam-1535	137	24	gordon	gordon	PROPN
ejpam-1535	137	25	preston	preston	PROPN
ejpam-1535	137	26	,	,	PUNCT
ejpam-1535	137	27	first	first	ADV
ejpam-1535	137	28	in	in	ADP
ejpam-1535	137	29	his	his	PRON
ejpam-1535	137	30	1953	1953	NUM
ejpam-1535	137	31	dphil	dphil	ADJ
ejpam-1535	137	32	thesis	thesis	NOUN
ejpam-1535	137	33	[	[	X
ejpam-1535	137	34	38	38	NUM
ejpam-1535	137	35	]	]	PUNCT
ejpam-1535	137	36	,	,	PUNCT
ejpam-1535	137	37	under	under	ADP
ejpam-1535	137	38	the	the	DET
ejpam-1535	137	39	name	name	NOUN
ejpam-1535	137	40	“	"	PUNCT
ejpam-1535	137	41	mapping	mapping	NOUN
ejpam-1535	137	42	semigroups	semigroup	NOUN
ejpam-1535	137	43	”	"	PUNCT
ejpam-1535	137	44	,	,	PUNCT
ejpam-1535	137	45	and	and	CCONJ
ejpam-1535	137	46	then	then	ADV
ejpam-1535	137	47	in	in	ADP
ejpam-1535	137	48	a	a	DET
ejpam-1535	137	49	much	much	ADV
ejpam-1535	137	50	more	more	ADV
ejpam-1535	137	51	polished	polished	ADJ
ejpam-1535	137	52	form	form	NOUN
ejpam-1535	137	53	in	in	ADP
ejpam-1535	137	54	three	three	NUM
ejpam-1535	137	55	papers	paper	NOUN
ejpam-1535	137	56	of	of	ADP
ejpam-1535	137	57	1954	1954	NUM
ejpam-1535	137	58	[	[	X
ejpam-1535	137	59	39	39	NUM
ejpam-1535	137	60	,	,	PUNCT
ejpam-1535	137	61	40	40	NUM
ejpam-1535	137	62	,	,	PUNCT
ejpam-1535	137	63	41	41	NUM
ejpam-1535	137	64	]	]	PUNCT
ejpam-1535	137	65	.	.	PUNCT
ejpam-1535	138	1	it	it	PRON
ejpam-1535	138	2	was	be	AUX
ejpam-1535	138	3	in	in	ADP
ejpam-1535	138	4	these	these	DET
ejpam-1535	138	5	latter	latter	ADJ
ejpam-1535	138	6	three	three	NUM
ejpam-1535	138	7	papers	paper	NOUN
ejpam-1535	138	8	that	that	SCONJ
ejpam-1535	138	9	the	the	DET
ejpam-1535	138	10	term	term	NOUN
ejpam-1535	138	11	“	"	PUNCT
ejpam-1535	138	12	inverse	inverse	NOUN
ejpam-1535	138	13	semigroup	semigroup	NOUN
ejpam-1535	138	14	”	"	PUNCT
ejpam-1535	138	15	appeared	appear	VERB
ejpam-1535	138	16	for	for	ADP
ejpam-1535	138	17	the	the	DET
ejpam-1535	138	18	very	very	ADV
ejpam-1535	138	19	first	first	ADJ
ejpam-1535	138	20	time	time	NOUN
ejpam-1535	138	21	.	.	PUNCT
ejpam-1535	139	1	preston	preston	PROPN
ejpam-1535	139	2	was	be	AUX
ejpam-1535	139	3	influenced	influence	VERB
ejpam-1535	139	4	by	by	ADP
ejpam-1535	139	5	earlier	early	ADJ
ejpam-1535	139	6	work	work	NOUN
ejpam-1535	139	7	on	on	ADP
ejpam-1535	139	8	systems	system	NOUN
ejpam-1535	139	9	of	of	ADP
ejpam-1535	139	10	one	one	NUM
ejpam-1535	139	11	-	-	PUNCT
ejpam-1535	139	12	one	one	NUM
ejpam-1535	139	13	partial	partial	ADJ
ejpam-1535	139	14	transformations	transformation	NOUN
ejpam-1535	139	15	:	:	PUNCT
ejpam-1535	139	16	his	his	PRON
ejpam-1535	139	17	initial	initial	ADJ
ejpam-1535	139	18	motivation	motivation	NOUN
ejpam-1535	139	19	was	be	AUX
ejpam-1535	139	20	the	the	DET
ejpam-1535	139	21	axiomatisation	axiomatisation	NOUN
ejpam-1535	139	22	of	of	ADP
ejpam-1535	139	23	certain	certain	ADJ
ejpam-1535	139	24	semigroups	semigroup	NOUN
ejpam-1535	139	25	of	of	ADP
ejpam-1535	139	26	one	one	NUM
ejpam-1535	139	27	-	-	PUNCT
ejpam-1535	139	28	one	one	NUM
ejpam-1535	139	29	partial	partial	ADJ
ejpam-1535	139	30	transformations	transformation	NOUN
ejpam-1535	139	31	that	that	PRON
ejpam-1535	139	32	had	have	AUX
ejpam-1535	139	33	been	be	AUX
ejpam-1535	139	34	studied	study	VERB
ejpam-1535	139	35	by	by	ADP
ejpam-1535	139	36	david	david	PROPN
ejpam-1535	139	37	rees	rees	PROPN
ejpam-1535	139	38	[	[	X
ejpam-1535	139	39	43	43	NUM
ejpam-1535	139	40	]	]	PUNCT
ejpam-1535	139	41	.	.	PUNCT
ejpam-1535	140	1	for	for	ADP
ejpam-1535	140	2	more	more	ADJ
ejpam-1535	140	3	details	detail	NOUN
ejpam-1535	140	4	on	on	ADP
ejpam-1535	140	5	preston	preston	PROPN
ejpam-1535	140	6	’s	’s	PART
ejpam-1535	140	7	development	development	NOUN
ejpam-1535	140	8	of	of	ADP
ejpam-1535	140	9	inverse	inverse	NOUN
ejpam-1535	140	10	semigroups	semigroup	NOUN
ejpam-1535	140	11	,	,	PUNCT
ejpam-1535	140	12	see	see	VERB
ejpam-1535	140	13	[	[	X
ejpam-1535	140	14	42	42	NUM
ejpam-1535	140	15	]	]	X
ejpam-1535	140	16	;	;	PUNCT
ejpam-1535	140	17	on	on	ADP
ejpam-1535	140	18	the	the	DET
ejpam-1535	140	19	history	history	NOUN
ejpam-1535	140	20	of	of	ADP
ejpam-1535	140	21	inverse	inverse	NOUN
ejpam-1535	140	22	semigroups	semigroup	NOUN
ejpam-1535	140	23	more	more	ADV
ejpam-1535	140	24	generally	generally	ADV
ejpam-1535	140	25	,	,	PUNCT
ejpam-1535	140	26	see	see	VERB
ejpam-1535	140	27	[	[	X
ejpam-1535	140	28	46	46	NUM
ejpam-1535	140	29	,	,	PUNCT
ejpam-1535	140	30	47	47	NUM
ejpam-1535	140	31	]	]	PUNCT
ejpam-1535	140	32	.	.	PUNCT
ejpam-1535	141	1	with	with	ADP
ejpam-1535	141	2	the	the	DET
ejpam-1535	141	3	definition	definition	NOUN
ejpam-1535	141	4	of	of	ADP
ejpam-1535	141	5	an	an	DET
ejpam-1535	141	6	inverse	inverse	NOUN
ejpam-1535	141	7	semigroup	semigroup	NOUN
ejpam-1535	141	8	established	establish	VERB
ejpam-1535	141	9	,	,	PUNCT
ejpam-1535	141	10	it	it	PRON
ejpam-1535	141	11	was	be	AUX
ejpam-1535	141	12	clear	clear	ADJ
ejpam-1535	141	13	that	that	SCONJ
ejpam-1535	141	14	the	the	DET
ejpam-1535	141	15	desired	desire	VERB
ejpam-1535	141	16	abstract	abstract	ADJ
ejpam-1535	141	17	model	model	NOUN
ejpam-1535	141	18	for	for	ADP
ejpam-1535	141	19	a	a	DET
ejpam-1535	141	20	pseudogroup	pseudogroup	NOUN
ejpam-1535	141	21	had	have	AUX
ejpam-1535	141	22	been	be	AUX
ejpam-1535	141	23	obtained	obtain	VERB
ejpam-1535	141	24	.	.	PUNCT
ejpam-1535	142	1	if	if	SCONJ
ejpam-1535	142	2	a	a	DET
ejpam-1535	142	3	pseudogroup	pseudogroup	NOUN
ejpam-1535	142	4	is	be	AUX
ejpam-1535	142	5	given	give	VERB
ejpam-1535	142	6	the	the	DET
ejpam-1535	142	7	composition	composition	NOUN
ejpam-1535	142	8	of	of	ADP
ejpam-1535	142	9	(	(	PUNCT
ejpam-1535	142	10	1	1	NUM
ejpam-1535	142	11	)	)	PUNCT
ejpam-1535	142	12	,	,	PUNCT
ejpam-1535	142	13	then	then	ADV
ejpam-1535	142	14	it	it	PRON
ejpam-1535	142	15	is	be	AUX
ejpam-1535	142	16	simply	simply	ADV
ejpam-1535	142	17	an	an	DET
ejpam-1535	142	18	inverse	inverse	NOUN
ejpam-1535	142	19	semigroup	semigroup	NOUN
ejpam-1535	142	20	of	of	ADP
ejpam-1535	142	21	homeomorphisms	homeomorphisms	PROPN
ejpam-1535	142	22	between	between	ADP
ejpam-1535	142	23	open	open	ADJ
ejpam-1535	142	24	sets	set	NOUN
ejpam-1535	142	25	of	of	ADP
ejpam-1535	142	26	a	a	DET
ejpam-1535	142	27	topological	topological	ADJ
ejpam-1535	142	28	space	space	NOUN
ejpam-1535	142	29	.	.	PUNCT
ejpam-1535	143	1	the	the	DET
ejpam-1535	143	2	second	second	ADJ
ejpam-1535	143	3	solution	solution	NOUN
ejpam-1535	143	4	to	to	ADP
ejpam-1535	143	5	the	the	DET
ejpam-1535	143	6	problem	problem	NOUN
ejpam-1535	143	7	of	of	ADP
ejpam-1535	143	8	finding	find	VERB
ejpam-1535	143	9	an	an	DET
ejpam-1535	143	10	abstract	abstract	ADJ
ejpam-1535	143	11	model	model	NOUN
ejpam-1535	143	12	for	for	ADP
ejpam-1535	143	13	a	a	DET
ejpam-1535	143	14	pseudogroup	pseudogroup	NOUN
ejpam-1535	143	15	is	be	AUX
ejpam-1535	143	16	due	due	ADJ
ejpam-1535	143	17	to	to	ADP
ejpam-1535	143	18	charles	charles	PROPN
ejpam-1535	143	19	ehresmann	ehresmann	PROPN
ejpam-1535	143	20	and	and	CCONJ
ejpam-1535	143	21	goes	go	VERB
ejpam-1535	143	22	back	back	ADV
ejpam-1535	143	23	to	to	ADP
ejpam-1535	143	24	the	the	DET
ejpam-1535	143	25	composition	composition	NOUN
ejpam-1535	143	26	of	of	ADP
ejpam-1535	143	27	partial	partial	ADJ
ejpam-1535	143	28	mappings	mapping	NOUN
ejpam-1535	143	29	.	.	PUNCT
ejpam-1535	144	1	rather	rather	ADV
ejpam-1535	144	2	than	than	ADP
ejpam-1535	144	3	trying	try	VERB
ejpam-1535	144	4	to	to	PART
ejpam-1535	144	5	“	"	PUNCT
ejpam-1535	144	6	complete	complete	VERB
ejpam-1535	144	7	”	"	PUNCT
ejpam-1535	144	8	the	the	DET
ejpam-1535	144	9	operation	operation	NOUN
ejpam-1535	144	10	on	on	ADP
ejpam-1535	144	11	a	a	DET
ejpam-1535	144	12	pseudogroup	pseudogroup	NOUN
ejpam-1535	144	13	,	,	PUNCT
ejpam-1535	144	14	ehresmann	ehresmann	PROPN
ejpam-1535	144	15	realised	realise	VERB
ejpam-1535	144	16	that	that	SCONJ
ejpam-1535	144	17	if	if	SCONJ
ejpam-1535	144	18	the	the	DET
ejpam-1535	144	19	partial	partial	ADJ
ejpam-1535	144	20	composition	composition	NOUN
ejpam-1535	144	21	defined	define	VERB
ejpam-1535	144	22	by	by	ADP
ejpam-1535	144	23	veblen	veblen	PROPN
ejpam-1535	144	24	and	and	CCONJ
ejpam-1535	144	25	whitehead	whitehead	PROPN
ejpam-1535	144	26	is	be	AUX
ejpam-1535	144	27	retained	retain	VERB
ejpam-1535	144	28	,	,	PUNCT
ejpam-1535	144	29	then	then	ADV
ejpam-1535	144	30	a	a	DET
ejpam-1535	144	31	pseudogroup	pseudogroup	NOUN
ejpam-1535	144	32	has	have	VERB
ejpam-1535	144	33	the	the	DET
ejpam-1535	144	34	structure	structure	NOUN
ejpam-1535	144	35	of	of	ADP
ejpam-1535	144	36	a	a	DET
ejpam-1535	144	37	groupoid	groupoid	NOUN
ejpam-1535	144	38	,	,	PUNCT
ejpam-1535	144	39	that	that	ADV
ejpam-1535	144	40	is	is	ADV
ejpam-1535	144	41	,	,	PUNCT
ejpam-1535	144	42	a	a	DET
ejpam-1535	144	43	small	small	ADJ
ejpam-1535	144	44	category	category	NOUN
ejpam-1535	144	45	in	in	ADP
ejpam-1535	144	46	which	which	PRON
ejpam-1535	144	47	all	all	DET
ejpam-1535	144	48	arrows	arrow	NOUN
ejpam-1535	144	49	are	be	AUX
ejpam-1535	144	50	invertible.§	invertible.§	NOUN
ejpam-1535	144	51	in	in	ADP
ejpam-1535	144	52	fact	fact	NOUN
ejpam-1535	144	53	,	,	PUNCT
ejpam-1535	144	54	as	as	SCONJ
ejpam-1535	144	55	ehresmann	ehresmann	PROPN
ejpam-1535	144	56	also	also	ADV
ejpam-1535	144	57	observed	observe	VERB
ejpam-1535	144	58	,	,	PUNCT
ejpam-1535	144	59	pseudogroups	pseudogroup	NOUN
ejpam-1535	144	60	form	form	VERB
ejpam-1535	144	61	ordered	order	VERB
ejpam-1535	144	62	groupoids	groupoid	NOUN
ejpam-1535	144	63	,	,	PUNCT
ejpam-1535	144	64	with	with	ADP
ejpam-1535	144	65	the	the	DET
ejpam-1535	144	66	obvious	obvious	ADJ
ejpam-1535	144	67	partial	partial	ADJ
ejpam-1535	144	68	order	order	NOUN
ejpam-1535	144	69	of	of	ADP
ejpam-1535	144	70	restriction	restriction	NOUN
ejpam-1535	144	71	of	of	ADP
ejpam-1535	144	72	mappings	mapping	NOUN
ejpam-1535	144	73	.	.	PUNCT
ejpam-1535	145	1	by	by	ADP
ejpam-1535	145	2	imposing	impose	VERB
ejpam-1535	145	3	extra	extra	ADJ
ejpam-1535	145	4	conditions	condition	NOUN
ejpam-1535	145	5	on	on	ADP
ejpam-1535	145	6	ordered	order	VERB
ejpam-1535	145	7	groupoids	groupoid	NOUN
ejpam-1535	145	8	,	,	PUNCT
ejpam-1535	145	9	ehresmann	ehresmann	PROPN
ejpam-1535	145	10	went	go	VERB
ejpam-1535	145	11	even	even	ADV
ejpam-1535	145	12	further	far	ADV
ejpam-1535	145	13	and	and	CCONJ
ejpam-1535	145	14	studied	study	VERB
ejpam-1535	145	15	the	the	DET
ejpam-1535	145	16	special	special	ADJ
ejpam-1535	145	17	case	case	NOUN
ejpam-1535	145	18	of	of	ADP
ejpam-1535	145	19	so	so	ADV
ejpam-1535	145	20	-	-	PUNCT
ejpam-1535	145	21	called	call	VERB
ejpam-1535	145	22	inductive	inductive	ADJ
ejpam-1535	145	23	groupoids	groupoid	NOUN
ejpam-1535	145	24	,	,	PUNCT
ejpam-1535	145	25	although	although	SCONJ
ejpam-1535	145	26	his	his	PRON
ejpam-1535	145	27	notion	notion	NOUN
ejpam-1535	145	28	of	of	ADP
ejpam-1535	145	29	“	"	PUNCT
ejpam-1535	145	30	inductivity	inductivity	NOUN
ejpam-1535	145	31	”	"	PUNCT
ejpam-1535	145	32	was	be	AUX
ejpam-1535	145	33	a	a	DET
ejpam-1535	145	34	little	little	ADV
ejpam-1535	145	35	more	more	ADV
ejpam-1535	145	36	stringent	stringent	ADJ
ejpam-1535	145	37	than	than	ADP
ejpam-1535	145	38	in	in	ADP
ejpam-1535	145	39	the	the	DET
ejpam-1535	145	40	modern	modern	ADJ
ejpam-1535	145	41	definition	definition	NOUN
ejpam-1535	145	42	.	.	PUNCT
ejpam-1535	146	1	the	the	DET
ejpam-1535	146	2	ordering	ordering	NOUN
ejpam-1535	146	3	in	in	ADP
ejpam-1535	146	4	the	the	DET
ejpam-1535	146	5	groupoid	groupoid	NOUN
ejpam-1535	146	6	played	play	VERB
ejpam-1535	146	7	a	a	DET
ejpam-1535	146	8	much	much	ADV
ejpam-1535	146	9	more	more	ADV
ejpam-1535	146	10	prominent	prominent	ADJ
ejpam-1535	146	11	role	role	NOUN
ejpam-1535	146	12	in	in	ADP
ejpam-1535	146	13	ehresmann	ehresmann	PROPN
ejpam-1535	146	14	’s	’s	PART
ejpam-1535	146	15	work	work	NOUN
ejpam-1535	146	16	than	than	SCONJ
ejpam-1535	146	17	it	it	PRON
ejpam-1535	146	18	had	have	VERB
ejpam-1535	146	19	in	in	ADP
ejpam-1535	146	20	the	the	DET
ejpam-1535	146	21	work	work	NOUN
ejpam-1535	146	22	of	of	ADP
ejpam-1535	146	23	previous	previous	ADJ
ejpam-1535	146	24	authors	author	NOUN
ejpam-1535	146	25	.	.	PUNCT
ejpam-1535	147	1	in	in	ADP
ejpam-1535	147	2	essence	essence	NOUN
ejpam-1535	147	3	,	,	PUNCT
ejpam-1535	147	4	whereas	whereas	SCONJ
ejpam-1535	147	5	both	both	DET
ejpam-1535	147	6	wagner	wagner	PROPN
ejpam-1535	147	7	and	and	CCONJ
ejpam-1535	147	8	preston	preston	PROPN
ejpam-1535	147	9	axiomatised	axiomatise	VERB
ejpam-1535	147	10	(	(	PUNCT
ejpam-1535	147	11	ix	ix	ADV
ejpam-1535	147	12	,	,	PUNCT
ejpam-1535	147	13	◦	◦	NOUN
ejpam-1535	147	14	)	)	PUNCT
ejpam-1535	147	15	to	to	PART
ejpam-1535	147	16	obtain	obtain	VERB
ejpam-1535	147	17	an	an	DET
ejpam-1535	147	18	inverse	inverse	NOUN
ejpam-1535	147	19	semigroup	semigroup	NOUN
ejpam-1535	147	20	(	(	PUNCT
ejpam-1535	147	21	where	where	SCONJ
ejpam-1535	147	22	◦	◦	NOUN
ejpam-1535	147	23	is	be	AUX
ejpam-1535	147	24	the	the	DET
ejpam-1535	147	25	composition	composition	NOUN
ejpam-1535	147	26	of	of	ADP
ejpam-1535	147	27	(	(	PUNCT
ejpam-1535	147	28	1	1	NUM
ejpam-1535	147	29	)	)	PUNCT
ejpam-1535	147	30	)	)	PUNCT
ejpam-1535	147	31	,	,	PUNCT
ejpam-1535	147	32	ehresmann	ehresmann	PROPN
ejpam-1535	147	33	axiomatised	axiomatise	VERB
ejpam-1535	147	34	(	(	PUNCT
ejpam-1535	147	35	ix	ix	ADV
ejpam-1535	147	36	,	,	PUNCT
ejpam-1535	147	37	·	·	PUNCT
ejpam-1535	147	38	,	,	PUNCT
ejpam-1535	147	39	⊆	⊆	NOUN
ejpam-1535	147	40	)	)	PUNCT
ejpam-1535	147	41	to	to	PART
ejpam-1535	147	42	obtain	obtain	VERB
ejpam-1535	147	43	an	an	DET
ejpam-1535	147	44	inductive	inductive	ADJ
ejpam-1535	147	45	groupoid	groupoid	NOUN
ejpam-1535	147	46	(	(	PUNCT
ejpam-1535	147	47	where	where	SCONJ
ejpam-1535	147	48	·	·	PUNCT
ejpam-1535	147	49	is	be	AUX
ejpam-1535	147	50	veblen	veblen	PROPN
ejpam-1535	147	51	and	and	CCONJ
ejpam-1535	147	52	whitehead	whitehead	PROPN
ejpam-1535	147	53	’s	’s	PART
ejpam-1535	147	54	partial	partial	ADJ
ejpam-1535	147	55	composition	composition	NOUN
ejpam-1535	147	56	,	,	PUNCT
ejpam-1535	147	57	and	and	CCONJ
ejpam-1535	147	58	⊆	⊆	NUM
ejpam-1535	147	59	denotes	denote	VERB
ejpam-1535	147	60	the	the	DET
ejpam-1535	147	61	ordering	ordering	NOUN
ejpam-1535	147	62	of	of	ADP
ejpam-1535	147	63	partial	partial	ADJ
ejpam-1535	147	64	transformations	transformation	NOUN
ejpam-1535	147	65	)	)	PUNCT
ejpam-1535	147	66	—	—	PUNCT
ejpam-1535	147	67	see	see	VERB
ejpam-1535	147	68	[	[	X
ejpam-1535	147	69	29	29	NUM
ejpam-1535	147	70	,	,	PUNCT
ejpam-1535	147	71	p.	p.	NOUN
ejpam-1535	147	72	9	9	NUM
ejpam-1535	147	73	]	]	PUNCT
ejpam-1535	147	74	.	.	PUNCT
ejpam-1535	148	1	the	the	DET
ejpam-1535	148	2	motivation	motivation	NOUN
ejpam-1535	148	3	for	for	ADP
ejpam-1535	148	4	ehresmann	ehresmann	PROPN
ejpam-1535	148	5	’s	’s	PART
ejpam-1535	148	6	work	work	NOUN
ejpam-1535	148	7	came	come	VERB
ejpam-1535	148	8	from	from	ADP
ejpam-1535	148	9	the	the	DET
ejpam-1535	148	10	study	study	NOUN
ejpam-1535	148	11	of	of	ADP
ejpam-1535	148	12	local	local	ADJ
ejpam-1535	148	13	structures	structure	NOUN
ejpam-1535	148	14	:	:	PUNCT
ejpam-1535	148	15	structures	structure	NOUN
ejpam-1535	148	16	defined	define	VERB
ejpam-1535	148	17	on	on	ADP
ejpam-1535	148	18	topological	topological	ADJ
ejpam-1535	148	19	spaces	space	NOUN
ejpam-1535	148	20	by	by	ADP
ejpam-1535	148	21	using	use	VERB
ejpam-1535	148	22	pseudogroups	pseudogroup	NOUN
ejpam-1535	148	23	in	in	ADP
ejpam-1535	148	24	a	a	DET
ejpam-1535	148	25	manner	manner	NOUN
ejpam-1535	148	26	analogous	analogous	ADJ
ejpam-1535	148	27	to	to	ADP
ejpam-1535	148	28	the	the	DET
ejpam-1535	148	29	way	way	NOUN
ejpam-1535	148	30	in	in	ADP
ejpam-1535	148	31	which	which	PRON
ejpam-1535	148	32	groups	group	NOUN
ejpam-1535	148	33	are	be	AUX
ejpam-1535	148	34	used	use	VERB
ejpam-1535	148	35	to	to	PART
ejpam-1535	148	36	define	define	VERB
ejpam-1535	148	37	geometries	geometry	NOUN
ejpam-1535	148	38	(	(	PUNCT
ejpam-1535	148	39	see	see	VERB
ejpam-1535	148	40	[	[	X
ejpam-1535	148	41	29	29	NUM
ejpam-1535	148	42	,	,	PUNCT
ejpam-1535	148	43	§	§	NOUN
ejpam-1535	148	44	1.2	1.2	NUM
ejpam-1535	148	45	]	]	NUM
ejpam-1535	148	46	)	)	PUNCT
ejpam-1535	148	47	.	.	PUNCT
ejpam-1535	149	1	ehresmann	ehresmann	PROPN
ejpam-1535	149	2	’s	’s	PART
ejpam-1535	149	3	category	category	NOUN
ejpam-1535	149	4	-	-	PUNCT
ejpam-1535	149	5	theoretic	theoretic	NOUN
ejpam-1535	149	6	work	work	NOUN
ejpam-1535	149	7	began	begin	VERB
ejpam-1535	149	8	in	in	ADP
ejpam-1535	149	9	[	[	X
ejpam-1535	149	10	9	9	NUM
ejpam-1535	149	11	]	]	PUNCT
ejpam-1535	149	12	and	and	CCONJ
ejpam-1535	149	13	continued	continue	VERB
ejpam-1535	149	14	through	through	ADP
ejpam-1535	149	15	a	a	DET
ejpam-1535	149	16	number	number	NOUN
ejpam-1535	149	17	of	of	ADP
ejpam-1535	149	18	further	further	ADJ
ejpam-1535	149	19	papers	paper	NOUN
ejpam-1535	149	20	,	,	PUNCT
ejpam-1535	149	21	which	which	PRON
ejpam-1535	149	22	may	may	AUX
ejpam-1535	149	23	all	all	PRON
ejpam-1535	149	24	be	be	AUX
ejpam-1535	149	25	found	find	VERB
ejpam-1535	149	26	in	in	ADP
ejpam-1535	149	27	his	his	PRON
ejpam-1535	149	28	collected	collect	VERB
ejpam-1535	149	29	works	work	NOUN
ejpam-1535	149	30	[	[	X
ejpam-1535	149	31	11	11	NUM
ejpam-1535	149	32	]	]	PUNCT
ejpam-1535	149	33	—	—	PUNCT
ejpam-1535	149	34	see	see	VERB
ejpam-1535	149	35	[	[	X
ejpam-1535	149	36	29	29	NUM
ejpam-1535	149	37	,	,	PUNCT
ejpam-1535	149	38	§	§	NOUN
ejpam-1535	149	39	§	§	PROPN
ejpam-1535	149	40	1.6	1.6	NUM
ejpam-1535	149	41	and	and	CCONJ
ejpam-1535	149	42	4.4	4.4	NUM
ejpam-1535	149	43	]	]	PUNCT
ejpam-1535	149	44	for	for	ADP
ejpam-1535	149	45	more	more	ADJ
ejpam-1535	149	46	details	detail	NOUN
ejpam-1535	149	47	on	on	ADP
ejpam-1535	149	48	ehresmann	ehresmann	PROPN
ejpam-1535	149	49	’s	’s	PART
ejpam-1535	149	50	publications	publication	NOUN
ejpam-1535	149	51	.	.	PUNCT
ejpam-1535	150	1	see	see	VERB
ejpam-1535	150	2	also	also	ADV
ejpam-1535	150	3	[	[	X
ejpam-1535	150	4	4	4	NUM
ejpam-1535	150	5	,	,	PUNCT
ejpam-1535	150	6	5	5	NUM
ejpam-1535	150	7	,	,	PUNCT
ejpam-1535	150	8	6	6	NUM
ejpam-1535	150	9	]	]	PUNCT
ejpam-1535	150	10	on	on	ADP
ejpam-1535	150	11	the	the	DET
ejpam-1535	150	12	history	history	NOUN
ejpam-1535	150	13	of	of	ADP
ejpam-1535	150	14	groupoids	groupoid	NOUN
ejpam-1535	150	15	.	.	PUNCT
ejpam-1535	151	1	the	the	DET
ejpam-1535	151	2	theories	theory	NOUN
ejpam-1535	151	3	of	of	ADP
ejpam-1535	151	4	inverse	inverse	NOUN
ejpam-1535	151	5	semigroups	semigroup	NOUN
ejpam-1535	151	6	and	and	CCONJ
ejpam-1535	151	7	ordered	order	VERB
ejpam-1535	151	8	groupoids	groupoid	NOUN
ejpam-1535	151	9	developed	develop	VERB
ejpam-1535	151	10	along	along	ADP
ejpam-1535	151	11	their	their	PRON
ejpam-1535	151	12	separate	separate	ADJ
ejpam-1535	151	13	paths	path	NOUN
ejpam-1535	151	14	for	for	ADP
ejpam-1535	151	15	some	some	DET
ejpam-1535	151	16	time	time	NOUN
ejpam-1535	151	17	after	after	ADP
ejpam-1535	151	18	their	their	PRON
ejpam-1535	151	19	inceptions	inception	NOUN
ejpam-1535	151	20	.	.	PUNCT
ejpam-1535	152	1	it	it	PRON
ejpam-1535	152	2	seems	seem	VERB
ejpam-1535	152	3	that	that	SCONJ
ejpam-1535	152	4	ehresmann	ehresmann	PROPN
ejpam-1535	152	5	was	be	AUX
ejpam-1535	152	6	aware	aware	ADJ
ejpam-1535	152	7	of	of	ADP
ejpam-1535	152	8	the	the	DET
ejpam-1535	152	9	connection	connection	NOUN
ejpam-1535	152	10	between	between	ADP
ejpam-1535	152	11	his	his	PRON
ejpam-1535	152	12	work	work	NOUN
ejpam-1535	152	13	and	and	CCONJ
ejpam-1535	152	14	that	that	PRON
ejpam-1535	152	15	of	of	ADP
ejpam-1535	152	16	wagner	wagner	PROPN
ejpam-1535	152	17	(	(	PUNCT
ejpam-1535	152	18	see	see	VERB
ejpam-1535	152	19	[	[	X
ejpam-1535	152	20	29	29	NUM
ejpam-1535	152	21	,	,	PUNCT
ejpam-1535	152	22	p.	p.	NOUN
ejpam-1535	152	23	131	131	NUM
ejpam-1535	152	24	]	]	PUNCT
ejpam-1535	152	25	)	)	PUNCT
ejpam-1535	152	26	;	;	PUNCT
ejpam-1535	152	27	indeed	indeed	ADV
ejpam-1535	152	28	,	,	PUNCT
ejpam-1535	152	29	it	it	PRON
ejpam-1535	152	30	was	be	AUX
ejpam-1535	152	31	ehresmann	ehresmann	PROPN
ejpam-1535	152	32	who	who	PRON
ejpam-1535	152	33	first	first	ADV
ejpam-1535	152	34	defined	define	VERB
ejpam-1535	152	35	the	the	DET
ejpam-1535	152	36	pseudoproduct	pseudoproduct	NOUN
ejpam-1535	152	37	which	which	PRON
ejpam-1535	152	38	is	be	AUX
ejpam-1535	152	39	necessary	necessary	ADJ
ejpam-1535	152	40	for	for	ADP
ejpam-1535	152	41	the	the	DET
ejpam-1535	152	42	construction	construction	NOUN
ejpam-1535	152	43	of	of	ADP
ejpam-1535	152	44	an	an	DET
ejpam-1535	152	45	inverse	inverse	NOUN
ejpam-1535	152	46	semi§the	semi§the	PRON
ejpam-1535	152	47	notion	notion	NOUN
ejpam-1535	152	48	of	of	ADP
ejpam-1535	152	49	a	a	DET
ejpam-1535	152	50	groupoid	groupoid	NOUN
ejpam-1535	152	51	seems	seem	VERB
ejpam-1535	152	52	to	to	PART
ejpam-1535	152	53	have	have	AUX
ejpam-1535	152	54	originated	originate	VERB
ejpam-1535	152	55	with	with	ADP
ejpam-1535	152	56	heinrich	heinrich	NOUN
ejpam-1535	152	57	brandt	brandt	PROPN
ejpam-1535	153	1	[	[	X
ejpam-1535	153	2	3	3	NUM
ejpam-1535	153	3	]	]	PUNCT
ejpam-1535	153	4	,	,	PUNCT
ejpam-1535	153	5	although	although	SCONJ
ejpam-1535	153	6	brandt	brandt	PROPN
ejpam-1535	153	7	’s	’s	PART
ejpam-1535	153	8	groupoids	groupoid	NOUN
ejpam-1535	153	9	had	have	VERB
ejpam-1535	153	10	a	a	DET
ejpam-1535	153	11	slightly	slightly	ADV
ejpam-1535	153	12	stronger	strong	ADJ
ejpam-1535	153	13	definition	definition	NOUN
ejpam-1535	153	14	than	than	ADP
ejpam-1535	153	15	the	the	DET
ejpam-1535	153	16	modern	modern	ADJ
ejpam-1535	153	17	one	one	NOUN
ejpam-1535	153	18	.	.	PUNCT
ejpam-1535	154	1	in	in	ADP
ejpam-1535	154	2	modern	modern	ADJ
ejpam-1535	154	3	terminology	terminology	NOUN
ejpam-1535	154	4	[	[	X
ejpam-1535	154	5	29	29	NUM
ejpam-1535	154	6	,	,	PUNCT
ejpam-1535	154	7	p.	p.	NOUN
ejpam-1535	154	8	105	105	NUM
ejpam-1535	154	9	]	]	PUNCT
ejpam-1535	154	10	,	,	PUNCT
ejpam-1535	154	11	brandt	brandt	PROPN
ejpam-1535	154	12	groupoids	groupoids	PROPN
ejpam-1535	154	13	are	be	AUX
ejpam-1535	154	14	connected	connected	ADJ
ejpam-1535	154	15	groupoids	groupoid	NOUN
ejpam-1535	154	16	:	:	PUNCT
ejpam-1535	154	17	for	for	ADP
ejpam-1535	154	18	any	any	DET
ejpam-1535	154	19	identities	identity	NOUN
ejpam-1535	154	20	x	x	SYM
ejpam-1535	154	21	,	,	PUNCT
ejpam-1535	154	22	y	y	PROPN
ejpam-1535	154	23	in	in	ADP
ejpam-1535	154	24	the	the	DET
ejpam-1535	154	25	groupoid	groupoid	NOUN
ejpam-1535	154	26	,	,	PUNCT
ejpam-1535	154	27	there	there	PRON
ejpam-1535	154	28	is	be	VERB
ejpam-1535	154	29	an	an	DET
ejpam-1535	154	30	arrow	arrow	NOUN
ejpam-1535	154	31	s	s	NOUN
ejpam-1535	154	32	with	with	ADP
ejpam-1535	154	33	d(s	d(s	PROPN
ejpam-1535	154	34	)	)	PUNCT
ejpam-1535	155	1	=	=	SYM
ejpam-1535	155	2	x	x	X
ejpam-1535	155	3	and	and	CCONJ
ejpam-1535	155	4	r(s	r(s	PROPN
ejpam-1535	155	5	)	)	PUNCT
ejpam-1535	156	1	=	=	SYM
ejpam-1535	156	2	y	y	PROPN
ejpam-1535	156	3	(	(	PUNCT
ejpam-1535	156	4	see	see	VERB
ejpam-1535	156	5	section	section	NOUN
ejpam-1535	156	6	4	4	NUM
ejpam-1535	156	7	for	for	ADP
ejpam-1535	156	8	the	the	DET
ejpam-1535	156	9	definition	definition	NOUN
ejpam-1535	156	10	of	of	ADP
ejpam-1535	156	11	this	this	DET
ejpam-1535	156	12	notation	notation	NOUN
ejpam-1535	156	13	)	)	PUNCT
ejpam-1535	156	14	.	.	PUNCT
ejpam-1535	157	1	an	an	DET
ejpam-1535	157	2	observation	observation	NOUN
ejpam-1535	157	3	later	later	ADV
ejpam-1535	157	4	made	make	VERB
ejpam-1535	157	5	by	by	ADP
ejpam-1535	157	6	schein	schein	PROPN
ejpam-1535	157	7	[	[	X
ejpam-1535	157	8	44	44	NUM
ejpam-1535	157	9	,	,	PUNCT
ejpam-1535	157	10	45	45	NUM
ejpam-1535	157	11	]	]	PUNCT
ejpam-1535	157	12	is	be	AUX
ejpam-1535	157	13	thus	thus	ADV
ejpam-1535	157	14	reasonably	reasonably	ADV
ejpam-1535	157	15	clear	clear	ADJ
ejpam-1535	157	16	:	:	PUNCT
ejpam-1535	157	17	an	an	DET
ejpam-1535	157	18	arbitrary	arbitrary	ADJ
ejpam-1535	157	19	groupoid	groupoid	NOUN
ejpam-1535	157	20	is	be	AUX
ejpam-1535	157	21	a	a	DET
ejpam-1535	157	22	union	union	NOUN
ejpam-1535	157	23	of	of	ADP
ejpam-1535	157	24	brandt	brandt	PROPN
ejpam-1535	157	25	groupoids	groupoids	PROPN
ejpam-1535	157	26	,	,	PUNCT
ejpam-1535	157	27	since	since	SCONJ
ejpam-1535	157	28	each	each	DET
ejpam-1535	157	29	“	"	PUNCT
ejpam-1535	157	30	connected	connected	ADJ
ejpam-1535	157	31	component	component	NOUN
ejpam-1535	157	32	”	"	PUNCT
ejpam-1535	157	33	is	be	AUX
ejpam-1535	157	34	a	a	DET
ejpam-1535	157	35	brandt	brandt	PROPN
ejpam-1535	157	36	groupoid	groupoid	PROPN
ejpam-1535	157	37	.	.	PUNCT
ejpam-1535	158	1	on	on	ADP
ejpam-1535	158	2	the	the	DET
ejpam-1535	158	3	origins	origin	NOUN
ejpam-1535	158	4	of	of	ADP
ejpam-1535	158	5	brandt	brandt	PROPN
ejpam-1535	158	6	groupoids	groupoids	PROPN
ejpam-1535	158	7	,	,	PUNCT
ejpam-1535	158	8	see	see	VERB
ejpam-1535	158	9	[	[	X
ejpam-1535	158	10	21	21	NUM
ejpam-1535	158	11	,	,	PUNCT
ejpam-1535	158	12	§	§	NOUN
ejpam-1535	158	13	4	4	NUM
ejpam-1535	158	14	]	]	PUNCT
ejpam-1535	158	15	.	.	PUNCT
ejpam-1535	159	1	we	we	PRON
ejpam-1535	159	2	note	note	VERB
ejpam-1535	159	3	also	also	ADV
ejpam-1535	159	4	that	that	SCONJ
ejpam-1535	159	5	the	the	DET
ejpam-1535	159	6	theory	theory	NOUN
ejpam-1535	159	7	of	of	ADP
ejpam-1535	159	8	groupoids	groupoid	NOUN
ejpam-1535	159	9	predates	predate	VERB
ejpam-1535	159	10	that	that	PRON
ejpam-1535	159	11	of	of	ADP
ejpam-1535	159	12	categories	category	NOUN
ejpam-1535	159	13	,	,	PUNCT
ejpam-1535	159	14	which	which	PRON
ejpam-1535	159	15	was	be	AUX
ejpam-1535	159	16	initiated	initiate	VERB
ejpam-1535	159	17	by	by	ADP
ejpam-1535	159	18	a	a	DET
ejpam-1535	159	19	1945	1945	NUM
ejpam-1535	159	20	paper	paper	NOUN
ejpam-1535	159	21	of	of	ADP
ejpam-1535	159	22	eilenberg	eilenberg	PROPN
ejpam-1535	159	23	and	and	CCONJ
ejpam-1535	159	24	mac	mac	PROPN
ejpam-1535	159	25	lane	lane	NOUN
ejpam-1535	160	1	[	[	X
ejpam-1535	160	2	12	12	NUM
ejpam-1535	160	3	]	]	X
ejpam-1535	160	4	—	—	PUNCT
ejpam-1535	160	5	see	see	VERB
ejpam-1535	160	6	[	[	X
ejpam-1535	160	7	7	7	NUM
ejpam-1535	160	8	,	,	PUNCT
ejpam-1535	160	9	chapter	chapter	NOUN
ejpam-1535	160	10	8	8	NUM
ejpam-1535	160	11	]	]	PUNCT
ejpam-1535	160	12	for	for	ADP
ejpam-1535	160	13	further	further	ADJ
ejpam-1535	160	14	details	detail	NOUN
ejpam-1535	160	15	on	on	ADP
ejpam-1535	160	16	the	the	DET
ejpam-1535	160	17	development	development	NOUN
ejpam-1535	160	18	of	of	ADP
ejpam-1535	160	19	category	category	NOUN
ejpam-1535	160	20	theory	theory	NOUN
ejpam-1535	160	21	.	.	PUNCT
ejpam-1535	161	1	c.	c.	PROPN
ejpam-1535	161	2	hollings	holling	NOUN
ejpam-1535	161	3	/	/	SYM
ejpam-1535	161	4	eur	eur	PROPN
ejpam-1535	161	5	.	.	PUNCT
ejpam-1535	162	1	j.	j.	PROPN
ejpam-1535	162	2	pure	pure	PROPN
ejpam-1535	162	3	appl	appl	PROPN
ejpam-1535	162	4	.	.	PROPN
ejpam-1535	162	5	math	math	PROPN
ejpam-1535	162	6	,	,	PUNCT
ejpam-1535	162	7	5	5	NUM
ejpam-1535	162	8	(	(	PUNCT
ejpam-1535	162	9	2012	2012	NUM
ejpam-1535	162	10	)	)	PUNCT
ejpam-1535	162	11	,	,	PUNCT
ejpam-1535	162	12	414	414	NUM
ejpam-1535	162	13	-	-	SYM
ejpam-1535	162	14	450	450	NUM
ejpam-1535	162	15	421	421	NUM
ejpam-1535	162	16	group	group	NOUN
ejpam-1535	162	17	from	from	ADP
ejpam-1535	162	18	an	an	DET
ejpam-1535	162	19	inductive	inductive	ADJ
ejpam-1535	162	20	groupoid	groupoid	NOUN
ejpam-1535	163	1	[	[	X
ejpam-1535	163	2	9	9	NUM
ejpam-1535	163	3	,	,	PUNCT
ejpam-1535	163	4	10	10	NUM
ejpam-1535	163	5	]	]	PUNCT
ejpam-1535	163	6	(	(	PUNCT
ejpam-1535	163	7	viz	viz	NUM
ejpam-1535	163	8	.	.	PUNCT
ejpam-1535	164	1	our	our	PRON
ejpam-1535	164	2	equation	equation	NOUN
ejpam-1535	164	3	(	(	PUNCT
ejpam-1535	164	4	6	6	NUM
ejpam-1535	164	5	)	)	PUNCT
ejpam-1535	164	6	)	)	PUNCT
ejpam-1535	164	7	.	.	PUNCT
ejpam-1535	165	1	however	however	ADV
ejpam-1535	165	2	,	,	PUNCT
ejpam-1535	165	3	it	it	PRON
ejpam-1535	165	4	was	be	AUX
ejpam-1535	165	5	left	leave	VERB
ejpam-1535	165	6	to	to	ADP
ejpam-1535	165	7	boris	boris	PROPN
ejpam-1535	165	8	schein	schein	PROPN
ejpam-1535	165	9	[	[	X
ejpam-1535	165	10	44	44	NUM
ejpam-1535	165	11	,	,	PUNCT
ejpam-1535	165	12	45	45	NUM
ejpam-1535	165	13	]	]	PUNCT
ejpam-1535	165	14	to	to	PART
ejpam-1535	165	15	make	make	VERB
ejpam-1535	165	16	the	the	DET
ejpam-1535	165	17	connection	connection	NOUN
ejpam-1535	165	18	explicit	explicit	ADJ
ejpam-1535	165	19	.	.	PUNCT
ejpam-1535	166	1	by	by	ADP
ejpam-1535	166	2	relaxing	relax	VERB
ejpam-1535	166	3	ehresmann	ehresmann	PROPN
ejpam-1535	166	4	’s	’s	PART
ejpam-1535	166	5	original	original	ADJ
ejpam-1535	166	6	conditions	condition	NOUN
ejpam-1535	166	7	for	for	ADP
ejpam-1535	166	8	“	"	PUNCT
ejpam-1535	166	9	inductivity	inductivity	NOUN
ejpam-1535	166	10	”	"	PUNCT
ejpam-1535	166	11	,	,	PUNCT
ejpam-1535	166	12	schein	schein	PROPN
ejpam-1535	166	13	arrived	arrive	VERB
ejpam-1535	166	14	at	at	ADP
ejpam-1535	166	15	the	the	DET
ejpam-1535	166	16	modern	modern	ADJ
ejpam-1535	166	17	notion	notion	NOUN
ejpam-1535	166	18	of	of	ADP
ejpam-1535	166	19	an	an	DET
ejpam-1535	166	20	inductive	inductive	ADJ
ejpam-1535	166	21	groupoid	groupoid	NOUN
ejpam-1535	166	22	:	:	PUNCT
ejpam-1535	166	23	an	an	DET
ejpam-1535	166	24	ordered	order	VERB
ejpam-1535	166	25	groupoid	groupoid	NOUN
ejpam-1535	166	26	in	in	ADP
ejpam-1535	166	27	which	which	PRON
ejpam-1535	166	28	every	every	DET
ejpam-1535	166	29	pair	pair	NOUN
ejpam-1535	166	30	of	of	ADP
ejpam-1535	166	31	identities	identity	NOUN
ejpam-1535	166	32	has	have	VERB
ejpam-1535	166	33	a	a	DET
ejpam-1535	166	34	greatest	greatest	ADV
ejpam-1535	166	35	lower	lower	ADV
ejpam-1535	166	36	bound	bind	VERB
ejpam-1535	166	37	,	,	PUNCT
ejpam-1535	166	38	or	or	CCONJ
ejpam-1535	166	39	meet	meet	VERB
ejpam-1535	166	40	.	.	PUNCT
ejpam-1535	167	1	furthermore	furthermore	ADV
ejpam-1535	167	2	,	,	PUNCT
ejpam-1535	167	3	he	he	PRON
ejpam-1535	167	4	observed	observe	VERB
ejpam-1535	167	5	that	that	SCONJ
ejpam-1535	167	6	,	,	PUNCT
ejpam-1535	167	7	without	without	ADP
ejpam-1535	167	8	the	the	DET
ejpam-1535	167	9	order	order	NOUN
ejpam-1535	167	10	structure	structure	NOUN
ejpam-1535	167	11	,	,	PUNCT
ejpam-1535	167	12	such	such	ADJ
ejpam-1535	167	13	objects	object	NOUN
ejpam-1535	167	14	had	have	AUX
ejpam-1535	167	15	in	in	ADP
ejpam-1535	167	16	fact	fact	NOUN
ejpam-1535	167	17	already	already	ADV
ejpam-1535	167	18	been	be	AUX
ejpam-1535	167	19	studied	study	VERB
ejpam-1535	167	20	(	(	PUNCT
ejpam-1535	167	21	under	under	ADP
ejpam-1535	167	22	the	the	DET
ejpam-1535	167	23	name	name	NOUN
ejpam-1535	167	24	“	"	PUNCT
ejpam-1535	167	25	partial	partial	ADJ
ejpam-1535	167	26	group	group	NOUN
ejpam-1535	167	27	”	"	PUNCT
ejpam-1535	167	28	:	:	PUNCT
ejpam-1535	167	29	textquotedblleft	textquotedblleft	NOUN
ejpam-1535	167	30	groupe	groupe	PROPN
ejpam-1535	167	31	partiel	partiel	PROPN
ejpam-1535	167	32	”	"	PUNCT
ejpam-1535	167	33	)	)	PUNCT
ejpam-1535	167	34	by	by	ADP
ejpam-1535	167	35	robert	robert	PROPN
ejpam-1535	167	36	croisot	croisot	PROPN
ejpam-1535	167	37	in	in	ADP
ejpam-1535	167	38	1948	1948	NUM
ejpam-1535	167	39	[	[	X
ejpam-1535	167	40	8	8	NUM
ejpam-1535	167	41	]	]	PUNCT
ejpam-1535	167	42	.	.	PUNCT
ejpam-1535	168	1	for	for	ADP
ejpam-1535	168	2	this	this	DET
ejpam-1535	168	3	reason	reason	NOUN
ejpam-1535	168	4	,	,	PUNCT
ejpam-1535	168	5	the	the	DET
ejpam-1535	168	6	modern	modern	ADJ
ejpam-1535	168	7	notion	notion	NOUN
ejpam-1535	168	8	of	of	ADP
ejpam-1535	168	9	a	a	DET
ejpam-1535	168	10	groupoid	groupoid	NOUN
ejpam-1535	168	11	was	be	AUX
ejpam-1535	168	12	termed	term	VERB
ejpam-1535	168	13	by	by	ADP
ejpam-1535	168	14	schein	schein	PROPN
ejpam-1535	168	15	a	a	DET
ejpam-1535	168	16	croisot	croisot	NOUN
ejpam-1535	168	17	groupoid	groupoid	PROPN
ejpam-1535	168	18	.	.	PUNCT
ejpam-1535	169	1	a	a	DET
ejpam-1535	169	2	croisot	croisot	NOUN
ejpam-1535	169	3	groupoid	groupoid	PROPN
ejpam-1535	169	4	was	be	AUX
ejpam-1535	169	5	said	say	VERB
ejpam-1535	169	6	further	far	ADV
ejpam-1535	169	7	to	to	PART
ejpam-1535	169	8	be	be	AUX
ejpam-1535	169	9	replenishable	replenishable	ADJ
ejpam-1535	169	10	if	if	SCONJ
ejpam-1535	169	11	its	its	PRON
ejpam-1535	169	12	multiplication	multiplication	NOUN
ejpam-1535	169	13	could	could	AUX
ejpam-1535	169	14	be	be	AUX
ejpam-1535	169	15	extended	extend	VERB
ejpam-1535	169	16	to	to	ADP
ejpam-1535	169	17	an	an	DET
ejpam-1535	169	18	everywhere	everywhere	ADV
ejpam-1535	169	19	-	-	PUNCT
ejpam-1535	169	20	defined	define	VERB
ejpam-1535	169	21	operation	operation	NOUN
ejpam-1535	169	22	;	;	PUNCT
ejpam-1535	169	23	schein	schein	PROPN
ejpam-1535	169	24	showed	show	VERB
ejpam-1535	169	25	that	that	SCONJ
ejpam-1535	169	26	a	a	DET
ejpam-1535	169	27	croisot	croisot	NOUN
ejpam-1535	169	28	groupoid	groupoid	NOUN
ejpam-1535	169	29	is	be	AUX
ejpam-1535	169	30	replenishable	replenishable	ADJ
ejpam-1535	169	31	if	if	SCONJ
ejpam-1535	169	32	and	and	CCONJ
ejpam-1535	169	33	only	only	ADV
ejpam-1535	169	34	if	if	SCONJ
ejpam-1535	169	35	it	it	PRON
ejpam-1535	169	36	can	can	AUX
ejpam-1535	169	37	be	be	AUX
ejpam-1535	169	38	ordered	order	VERB
ejpam-1535	169	39	in	in	ADP
ejpam-1535	169	40	such	such	DET
ejpam-1535	169	41	a	a	DET
ejpam-1535	169	42	way	way	NOUN
ejpam-1535	169	43	as	as	SCONJ
ejpam-1535	169	44	to	to	PART
ejpam-1535	169	45	make	make	VERB
ejpam-1535	169	46	it	it	PRON
ejpam-1535	169	47	inductive	inductive	VERB
ejpam-1535	169	48	.	.	PUNCT
ejpam-1535	170	1	any	any	DET
ejpam-1535	170	2	inductive	inductive	ADJ
ejpam-1535	170	3	croisot	croisot	NOUN
ejpam-1535	170	4	groupoid	groupoid	PROPN
ejpam-1535	170	5	may	may	AUX
ejpam-1535	170	6	be	be	AUX
ejpam-1535	170	7	replenished	replenish	VERB
ejpam-1535	170	8	in	in	ADP
ejpam-1535	170	9	such	such	DET
ejpam-1535	170	10	a	a	DET
ejpam-1535	170	11	way	way	NOUN
ejpam-1535	170	12	that	that	PRON
ejpam-1535	170	13	an	an	DET
ejpam-1535	170	14	inverse	inverse	NOUN
ejpam-1535	170	15	semigroup	semigroup	NOUN
ejpam-1535	170	16	is	be	AUX
ejpam-1535	170	17	obtained	obtain	VERB
ejpam-1535	170	18	[	[	X
ejpam-1535	170	19	45	45	NUM
ejpam-1535	170	20	,	,	PUNCT
ejpam-1535	170	21	theorem	theorem	VERB
ejpam-1535	170	22	3.4	3.4	NUM
ejpam-1535	170	23	]	]	PUNCT
ejpam-1535	170	24	.	.	PUNCT
ejpam-1535	171	1	conversely	conversely	ADV
ejpam-1535	171	2	,	,	PUNCT
ejpam-1535	171	3	schein	schein	PROPN
ejpam-1535	171	4	demonstrated	demonstrate	VERB
ejpam-1535	171	5	that	that	SCONJ
ejpam-1535	171	6	if	if	SCONJ
ejpam-1535	171	7	we	we	PRON
ejpam-1535	171	8	take	take	VERB
ejpam-1535	171	9	any	any	DET
ejpam-1535	171	10	inverse	inverse	NOUN
ejpam-1535	171	11	semigroup	semigroup	NOUN
ejpam-1535	171	12	s	s	PART
ejpam-1535	171	13	and	and	CCONJ
ejpam-1535	171	14	define	define	VERB
ejpam-1535	171	15	in	in	ADP
ejpam-1535	171	16	it	it	PRON
ejpam-1535	171	17	a	a	DET
ejpam-1535	171	18	partial	partial	ADJ
ejpam-1535	171	19	operation	operation	NOUN
ejpam-1535	171	20	,	,	PUNCT
ejpam-1535	171	21	which	which	PRON
ejpam-1535	171	22	he	he	PRON
ejpam-1535	171	23	termed	term	VERB
ejpam-1535	171	24	the	the	DET
ejpam-1535	171	25	abutting	abut	VERB
ejpam-1535	171	26	multiplication	multiplication	NOUN
ejpam-1535	171	27	(	(	PUNCT
ejpam-1535	171	28	defined	define	VERB
ejpam-1535	171	29	in	in	ADP
ejpam-1535	171	30	our	our	PRON
ejpam-1535	171	31	equation	equation	NOUN
ejpam-1535	171	32	(	(	PUNCT
ejpam-1535	171	33	9	9	NUM
ejpam-1535	171	34	)	)	PUNCT
ejpam-1535	171	35	)	)	PUNCT
ejpam-1535	171	36	,	,	PUNCT
ejpam-1535	171	37	then	then	ADV
ejpam-1535	171	38	the	the	DET
ejpam-1535	171	39	semigroup	semigroup	NOUN
ejpam-1535	171	40	becomes	become	VERB
ejpam-1535	171	41	a	a	DET
ejpam-1535	171	42	croisot	croisot	NOUN
ejpam-1535	171	43	groupoid	groupoid	NOUN
ejpam-1535	171	44	tr(s	tr(s	PUNCT
ejpam-1535	171	45	)	)	PUNCT
ejpam-1535	171	46	(	(	PUNCT
ejpam-1535	171	47	the	the	DET
ejpam-1535	171	48	trace	trace	NOUN
ejpam-1535	171	49	of	of	ADP
ejpam-1535	171	50	s	s	NOUN
ejpam-1535	171	51	)	)	PUNCT
ejpam-1535	171	52	with	with	ADP
ejpam-1535	171	53	respect	respect	NOUN
ejpam-1535	171	54	to	to	ADP
ejpam-1535	171	55	this	this	DET
ejpam-1535	171	56	new	new	ADJ
ejpam-1535	171	57	multiplication	multiplication	NOUN
ejpam-1535	171	58	;	;	PUNCT
ejpam-1535	171	59	furthermore	furthermore	ADV
ejpam-1535	171	60	,	,	PUNCT
ejpam-1535	171	61	the	the	DET
ejpam-1535	171	62	natural	natural	ADJ
ejpam-1535	171	63	partial	partial	ADJ
ejpam-1535	171	64	order	order	NOUN
ejpam-1535	171	65	of	of	ADP
ejpam-1535	171	66	s	s	PRON
ejpam-1535	171	67	makes	make	VERB
ejpam-1535	171	68	tr(s	tr(s	PUNCT
ejpam-1535	171	69	)	)	PUNCT
ejpam-1535	171	70	inductive	inductive	ADJ
ejpam-1535	171	71	cite[p	cite[p	PROPN
ejpam-1535	171	72	.	.	PROPN
ejpam-1535	171	73	109]schein1979	109]schein1979	NUM
ejpam-1535	171	74	.	.	PUNCT
ejpam-1535	172	1	thus	thus	ADV
ejpam-1535	172	2	,	,	PUNCT
ejpam-1535	172	3	given	give	VERB
ejpam-1535	172	4	any	any	DET
ejpam-1535	172	5	inverse	inverse	NOUN
ejpam-1535	172	6	semigroup	semigroup	NOUN
ejpam-1535	172	7	,	,	PUNCT
ejpam-1535	172	8	we	we	PRON
ejpam-1535	172	9	may	may	AUX
ejpam-1535	172	10	construct	construct	VERB
ejpam-1535	172	11	an	an	DET
ejpam-1535	172	12	inductive	inductive	ADJ
ejpam-1535	172	13	(	(	PUNCT
ejpam-1535	172	14	croisot	croisot	NOUN
ejpam-1535	172	15	)	)	PUNCT
ejpam-1535	172	16	groupoid	groupoid	NOUN
ejpam-1535	172	17	,	,	PUNCT
ejpam-1535	172	18	and	and	CCONJ
ejpam-1535	172	19	vice	vice	ADV
ejpam-1535	172	20	versa	versa	ADV
ejpam-1535	172	21	.	.	PUNCT
ejpam-1535	173	1	we	we	PRON
ejpam-1535	173	2	see	see	VERB
ejpam-1535	173	3	then	then	ADV
ejpam-1535	173	4	that	that	DET
ejpam-1535	173	5	inverse	inverse	NOUN
ejpam-1535	173	6	semigroups	semigroup	NOUN
ejpam-1535	173	7	and	and	CCONJ
ejpam-1535	173	8	inductive	inductive	ADJ
ejpam-1535	173	9	groupoids	groupoid	NOUN
ejpam-1535	173	10	share	share	VERB
ejpam-1535	173	11	a	a	DET
ejpam-1535	173	12	very	very	ADV
ejpam-1535	173	13	close	close	ADJ
ejpam-1535	173	14	connection	connection	NOUN
ejpam-1535	173	15	which	which	PRON
ejpam-1535	173	16	reflects	reflect	VERB
ejpam-1535	173	17	their	their	PRON
ejpam-1535	173	18	common	common	ADJ
ejpam-1535	173	19	origins	origin	NOUN
ejpam-1535	173	20	in	in	ADP
ejpam-1535	173	21	the	the	DET
ejpam-1535	173	22	theory	theory	NOUN
ejpam-1535	173	23	of	of	ADP
ejpam-1535	173	24	pseudogroups	pseudogroup	NOUN
ejpam-1535	173	25	.	.	PUNCT
ejpam-1535	174	1	the	the	DET
ejpam-1535	174	2	results	result	NOUN
ejpam-1535	174	3	of	of	ADP
ejpam-1535	174	4	schein	schein	PROPN
ejpam-1535	174	5	were	be	AUX
ejpam-1535	174	6	subsequently	subsequently	ADV
ejpam-1535	174	7	generalised	generalise	VERB
ejpam-1535	174	8	to	to	ADP
ejpam-1535	174	9	the	the	DET
ejpam-1535	174	10	case	case	NOUN
ejpam-1535	174	11	of	of	ADP
ejpam-1535	174	12	regular	regular	ADJ
ejpam-1535	174	13	semigroups	semigroup	NOUN
ejpam-1535	174	14	by	by	ADP
ejpam-1535	174	15	k.	k.	PROPN
ejpam-1535	174	16	s.	s.	PROPN
ejpam-1535	174	17	s.	s.	PROPN
ejpam-1535	174	18	nambooripad	nambooripad	PROPN
ejpam-1535	174	19	.	.	PUNCT
ejpam-1535	175	1	beginning	begin	VERB
ejpam-1535	175	2	in	in	ADP
ejpam-1535	175	3	his	his	PRON
ejpam-1535	175	4	1973	1973	NUM
ejpam-1535	175	5	phd	phd	NOUN
ejpam-1535	175	6	thesis	thesis	NOUN
ejpam-1535	175	7	[	[	X
ejpam-1535	175	8	34	34	NUM
ejpam-1535	175	9	]	]	PUNCT
ejpam-1535	175	10	,	,	PUNCT
ejpam-1535	175	11	and	and	CCONJ
ejpam-1535	175	12	developing	develop	VERB
ejpam-1535	175	13	his	his	PRON
ejpam-1535	175	14	ideas	idea	NOUN
ejpam-1535	175	15	through	through	ADP
ejpam-1535	175	16	a	a	DET
ejpam-1535	175	17	series	series	NOUN
ejpam-1535	175	18	of	of	ADP
ejpam-1535	175	19	papers	paper	NOUN
ejpam-1535	175	20	based	base	VERB
ejpam-1535	175	21	thereupon	thereupon	ADV
ejpam-1535	175	22	[	[	X
ejpam-1535	175	23	35	35	NUM
ejpam-1535	175	24	,	,	PUNCT
ejpam-1535	175	25	36	36	NUM
ejpam-1535	175	26	]	]	PUNCT
ejpam-1535	175	27	,	,	PUNCT
ejpam-1535	175	28	nambooripad	nambooripad	PROPN
ejpam-1535	175	29	showed	show	VERB
ejpam-1535	175	30	that	that	SCONJ
ejpam-1535	175	31	every	every	DET
ejpam-1535	175	32	regular	regular	ADJ
ejpam-1535	175	33	semigroup	semigroup	NOUN
ejpam-1535	175	34	gives	give	VERB
ejpam-1535	175	35	rise	rise	NOUN
ejpam-1535	175	36	to	to	ADP
ejpam-1535	175	37	a	a	DET
ejpam-1535	175	38	generalisation	generalisation	NOUN
ejpam-1535	175	39	of	of	ADP
ejpam-1535	175	40	an	an	DET
ejpam-1535	175	41	inductive	inductive	ADJ
ejpam-1535	175	42	groupoid	groupoid	NOUN
ejpam-1535	175	43	,	,	PUNCT
ejpam-1535	175	44	which	which	PRON
ejpam-1535	175	45	he	he	PRON
ejpam-1535	175	46	termed	term	VERB
ejpam-1535	175	47	a	a	DET
ejpam-1535	175	48	regular	regular	ADJ
ejpam-1535	175	49	groupoid	groupoid	NOUN
ejpam-1535	175	50	,	,	PUNCT
ejpam-1535	175	51	and	and	CCONJ
ejpam-1535	175	52	,	,	PUNCT
ejpam-1535	175	53	conversely	conversely	ADV
ejpam-1535	175	54	,	,	PUNCT
ejpam-1535	175	55	that	that	SCONJ
ejpam-1535	175	56	a	a	DET
ejpam-1535	175	57	regular	regular	ADJ
ejpam-1535	175	58	semigroup	semigroup	NOUN
ejpam-1535	175	59	may	may	AUX
ejpam-1535	175	60	be	be	AUX
ejpam-1535	175	61	obtained	obtain	VERB
ejpam-1535	175	62	from	from	ADP
ejpam-1535	175	63	any	any	DET
ejpam-1535	175	64	such	such	ADJ
ejpam-1535	175	65	regular	regular	ADJ
ejpam-1535	175	66	groupoid	groupoid	NOUN
ejpam-1535	175	67	.	.	PUNCT
ejpam-1535	176	1	a	a	DET
ejpam-1535	176	2	regular	regular	ADJ
ejpam-1535	176	3	groupoid	groupoid	NOUN
ejpam-1535	176	4	,	,	PUNCT
ejpam-1535	176	5	together	together	ADV
ejpam-1535	176	6	with	with	ADP
ejpam-1535	176	7	a	a	DET
ejpam-1535	176	8	certain	certain	ADJ
ejpam-1535	176	9	collection	collection	NOUN
ejpam-1535	176	10	of	of	ADP
ejpam-1535	176	11	mappings	mapping	NOUN
ejpam-1535	176	12	between	between	ADP
ejpam-1535	176	13	rclasses	rclasse	NOUN
ejpam-1535	176	14	of	of	ADP
ejpam-1535	176	15	the	the	DET
ejpam-1535	176	16	idempotents	idempotent	NOUN
ejpam-1535	176	17	of	of	ADP
ejpam-1535	176	18	the	the	DET
ejpam-1535	176	19	corresponding	correspond	VERB
ejpam-1535	176	20	regular	regular	ADJ
ejpam-1535	176	21	semigroup	semigroup	NOUN
ejpam-1535	176	22	,	,	PUNCT
ejpam-1535	176	23	and	and	CCONJ
ejpam-1535	176	24	another	another	DET
ejpam-1535	176	25	collection	collection	NOUN
ejpam-1535	176	26	of	of	ADP
ejpam-1535	176	27	mappings	mapping	NOUN
ejpam-1535	176	28	between	between	ADP
ejpam-1535	176	29	l	l	NOUN
ejpam-1535	176	30	-classes	-classe	NOUN
ejpam-1535	176	31	of	of	ADP
ejpam-1535	176	32	the	the	DET
ejpam-1535	176	33	idempotents	idempotent	NOUN
ejpam-1535	176	34	,	,	PUNCT
ejpam-1535	176	35	was	be	AUX
ejpam-1535	176	36	termed	term	VERB
ejpam-1535	176	37	by	by	ADP
ejpam-1535	176	38	nambooripad	nambooripad	PROPN
ejpam-1535	176	39	a	a	DET
ejpam-1535	176	40	regular	regular	ADJ
ejpam-1535	176	41	system	system	NOUN
ejpam-1535	176	42	.	.	PUNCT
ejpam-1535	177	1	he	he	PRON
ejpam-1535	177	2	showed	show	VERB
ejpam-1535	177	3	that	that	SCONJ
ejpam-1535	177	4	there	there	PRON
ejpam-1535	177	5	is	be	VERB
ejpam-1535	177	6	a	a	DET
ejpam-1535	177	7	one	one	NUM
ejpam-1535	177	8	-	-	PUNCT
ejpam-1535	177	9	one	one	NUM
ejpam-1535	177	10	correspondence	correspondence	NOUN
ejpam-1535	177	11	between	between	ADP
ejpam-1535	177	12	regular	regular	ADJ
ejpam-1535	177	13	systems	system	NOUN
ejpam-1535	177	14	and	and	CCONJ
ejpam-1535	177	15	regular	regular	ADJ
ejpam-1535	177	16	semigroups	semigroup	NOUN
ejpam-1535	177	17	[	[	X
ejpam-1535	177	18	35	35	NUM
ejpam-1535	177	19	,	,	PUNCT
ejpam-1535	177	20	part	part	PROPN
ejpam-1535	177	21	ii	ii	PROPN
ejpam-1535	177	22	,	,	PUNCT
ejpam-1535	177	23	theorems	theorem	NOUN
ejpam-1535	177	24	1	1	NUM
ejpam-1535	177	25	and	and	CCONJ
ejpam-1535	177	26	2	2	NUM
ejpam-1535	177	27	]	]	PUNCT
ejpam-1535	177	28	.	.	PUNCT
ejpam-1535	178	1	indeed	indeed	ADV
ejpam-1535	178	2	,	,	PUNCT
ejpam-1535	178	3	going	go	VERB
ejpam-1535	178	4	further	far	ADV
ejpam-1535	178	5	,	,	PUNCT
ejpam-1535	178	6	he	he	PRON
ejpam-1535	178	7	also	also	ADV
ejpam-1535	178	8	demonstrated	demonstrate	VERB
ejpam-1535	178	9	that	that	SCONJ
ejpam-1535	178	10	there	there	PRON
ejpam-1535	178	11	is	be	VERB
ejpam-1535	178	12	a	a	DET
ejpam-1535	178	13	similar	similar	ADJ
ejpam-1535	178	14	correspondence	correspondence	NOUN
ejpam-1535	178	15	between	between	ADP
ejpam-1535	178	16	morphisms	morphism	NOUN
ejpam-1535	178	17	of	of	ADP
ejpam-1535	178	18	regular	regular	ADJ
ejpam-1535	178	19	systems	system	NOUN
ejpam-1535	178	20	(	(	PUNCT
ejpam-1535	178	21	which	which	PRON
ejpam-1535	178	22	are	be	AUX
ejpam-1535	178	23	defined	define	VERB
ejpam-1535	178	24	in	in	ADP
ejpam-1535	178	25	an	an	DET
ejpam-1535	178	26	appropriate	appropriate	ADJ
ejpam-1535	178	27	manner	manner	NOUN
ejpam-1535	178	28	)	)	PUNCT
ejpam-1535	178	29	and	and	CCONJ
ejpam-1535	178	30	morphisms	morphism	NOUN
ejpam-1535	178	31	of	of	ADP
ejpam-1535	178	32	the	the	DET
ejpam-1535	178	33	associated	associated	ADJ
ejpam-1535	178	34	regular	regular	ADJ
ejpam-1535	178	35	semigroups	semigroup	NOUN
ejpam-1535	178	36	,	,	PUNCT
ejpam-1535	178	37	and	and	CCONJ
ejpam-1535	178	38	vice	vice	ADV
ejpam-1535	178	39	versa	versa	ADV
ejpam-1535	178	40	.	.	PUNCT
ejpam-1535	179	1	in	in	ADP
ejpam-1535	179	2	this	this	DET
ejpam-1535	179	3	way	way	NOUN
ejpam-1535	179	4	,	,	PUNCT
ejpam-1535	179	5	without	without	ADP
ejpam-1535	179	6	ever	ever	ADV
ejpam-1535	179	7	using	use	VERB
ejpam-1535	179	8	the	the	DET
ejpam-1535	179	9	word	word	NOUN
ejpam-1535	179	10	“	"	PUNCT
ejpam-1535	179	11	category	category	NOUN
ejpam-1535	179	12	”	"	PUNCT
ejpam-1535	179	13	,	,	PUNCT
ejpam-1535	179	14	nambooripad	nambooripad	PROPN
ejpam-1535	179	15	showed	show	VERB
ejpam-1535	179	16	that	that	SCONJ
ejpam-1535	179	17	there	there	PRON
ejpam-1535	179	18	is	be	VERB
ejpam-1535	179	19	an	an	DET
ejpam-1535	179	20	isomorphism	isomorphism	NOUN
ejpam-1535	179	21	between	between	ADP
ejpam-1535	179	22	the	the	DET
ejpam-1535	179	23	category	category	NOUN
ejpam-1535	179	24	of	of	ADP
ejpam-1535	179	25	regular	regular	ADJ
ejpam-1535	179	26	systems	system	NOUN
ejpam-1535	179	27	and	and	CCONJ
ejpam-1535	179	28	morphisms	morphism	NOUN
ejpam-1535	179	29	and	and	CCONJ
ejpam-1535	179	30	the	the	DET
ejpam-1535	179	31	category	category	NOUN
ejpam-1535	179	32	of	of	ADP
ejpam-1535	179	33	regular	regular	ADJ
ejpam-1535	179	34	semigroups	semigroup	NOUN
ejpam-1535	179	35	and	and	CCONJ
ejpam-1535	179	36	morphisms	morphism	NOUN
ejpam-1535	179	37	.	.	PUNCT
ejpam-1535	180	1	we	we	PRON
ejpam-1535	180	2	may	may	AUX
ejpam-1535	180	3	then	then	ADV
ejpam-1535	180	4	deduce	deduce	VERB
ejpam-1535	180	5	the	the	DET
ejpam-1535	180	6	specialisation	specialisation	NOUN
ejpam-1535	180	7	of	of	ADP
ejpam-1535	180	8	this	this	DET
ejpam-1535	180	9	result	result	NOUN
ejpam-1535	180	10	to	to	ADP
ejpam-1535	180	11	the	the	DET
ejpam-1535	180	12	inverse	inverse	NOUN
ejpam-1535	180	13	case	case	NOUN
ejpam-1535	180	14	:	:	PUNCT
ejpam-1535	180	15	that	that	SCONJ
ejpam-1535	180	16	the	the	DET
ejpam-1535	180	17	category	category	NOUN
ejpam-1535	180	18	of	of	ADP
ejpam-1535	180	19	inductive	inductive	ADJ
ejpam-1535	180	20	groupoids	groupoid	NOUN
ejpam-1535	180	21	and	and	CCONJ
ejpam-1535	180	22	inductive	inductive	ADJ
ejpam-1535	180	23	functors	functor	NOUN
ejpam-1535	180	24	is	be	AUX
ejpam-1535	180	25	isomorphic	isomorphic	ADJ
ejpam-1535	180	26	to	to	ADP
ejpam-1535	180	27	the	the	DET
ejpam-1535	180	28	category	category	NOUN
ejpam-1535	180	29	of	of	ADP
ejpam-1535	180	30	inverse	inverse	NOUN
ejpam-1535	180	31	semigroups	semigroup	NOUN
ejpam-1535	180	32	and	and	CCONJ
ejpam-1535	180	33	morphisms	morphism	NOUN
ejpam-1535	180	34	,	,	PUNCT
ejpam-1535	180	35	where	where	SCONJ
ejpam-1535	180	36	we	we	PRON
ejpam-1535	180	37	have	have	AUX
ejpam-1535	180	38	switched	switch	VERB
ejpam-1535	180	39	to	to	ADP
ejpam-1535	180	40	the	the	DET
ejpam-1535	180	41	terminology	terminology	NOUN
ejpam-1535	180	42	to	to	PART
ejpam-1535	180	43	be	be	AUX
ejpam-1535	180	44	used	use	VERB
ejpam-1535	180	45	throughout	throughout	ADP
ejpam-1535	180	46	the	the	DET
ejpam-1535	180	47	present	present	ADJ
ejpam-1535	180	48	article	article	NOUN
ejpam-1535	180	49	:	:	PUNCT
ejpam-1535	180	50	an	an	DET
ejpam-1535	180	51	inductive	inductive	ADJ
ejpam-1535	180	52	functor	functor	NOUN
ejpam-1535	180	53	is	be	AUX
ejpam-1535	180	54	an	an	DET
ejpam-1535	180	55	order	order	NOUN
ejpam-1535	180	56	-	-	PUNCT
ejpam-1535	180	57	preserving	preserve	VERB
ejpam-1535	180	58	functor	functor	NOUN
ejpam-1535	180	59	(	(	PUNCT
ejpam-1535	180	60	or	or	CCONJ
ejpam-1535	180	61	ordered	order	VERB
ejpam-1535	180	62	functor	functor	PROPN
ejpam-1535	180	63	)	)	PUNCT
ejpam-1535	180	64	which	which	PRON
ejpam-1535	180	65	preserves	preserve	VERB
ejpam-1535	180	66	meet	meet	VERB
ejpam-1535	180	67	.	.	PUNCT
ejpam-1535	181	1	it	it	PRON
ejpam-1535	181	2	was	be	AUX
ejpam-1535	181	3	shown	show	VERB
ejpam-1535	181	4	further	far	ADV
ejpam-1535	181	5	[	[	X
ejpam-1535	181	6	37	37	NUM
ejpam-1535	181	7	,	,	PUNCT
ejpam-1535	181	8	pp	pp	ADJ
ejpam-1535	181	9	.	.	PUNCT
ejpam-1535	182	1	286–7	286–7	X
ejpam-1535	182	2	]	]	X
ejpam-1535	182	3	that	that	SCONJ
ejpam-1535	182	4	if	if	SCONJ
ejpam-1535	182	5	we	we	PRON
ejpam-1535	182	6	require	require	VERB
ejpam-1535	182	7	our	our	PRON
ejpam-1535	182	8	functors	functor	NOUN
ejpam-1535	182	9	between	between	ADP
ejpam-1535	182	10	inductive	inductive	ADJ
ejpam-1535	182	11	groupoids	groupoid	NOUN
ejpam-1535	182	12	to	to	PART
ejpam-1535	182	13	be	be	AUX
ejpam-1535	182	14	merely	merely	ADV
ejpam-1535	182	15	ordered	order	VERB
ejpam-1535	182	16	,	,	PUNCT
ejpam-1535	182	17	and	and	CCONJ
ejpam-1535	182	18	not	not	PART
ejpam-1535	182	19	necessarily	necessarily	ADV
ejpam-1535	182	20	inductive	inductive	ADJ
ejpam-1535	182	21	,	,	PUNCT
ejpam-1535	182	22	then	then	ADV
ejpam-1535	182	23	these	these	PRON
ejpam-1535	182	24	correspond	correspond	VERB
ejpam-1535	182	25	to	to	ADP
ejpam-1535	182	26	functions	function	NOUN
ejpam-1535	182	27	between	between	ADP
ejpam-1535	182	28	inverse	inverse	NOUN
ejpam-1535	182	29	semigroups	semigroup	NOUN
ejpam-1535	182	30	,	,	PUNCT
ejpam-1535	182	31	termed	term	VERB
ejpam-1535	182	32	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	182	33	;	;	PUNCT
ejpam-1535	182	34	a	a	DET
ejpam-1535	182	35	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	182	36	,	,	PUNCT
ejpam-1535	182	37	as	as	SCONJ
ejpam-1535	182	38	introduced	introduce	VERB
ejpam-1535	182	39	by	by	ADP
ejpam-1535	182	40	mcalister	mcalister	NOUN
ejpam-1535	183	1	[	[	X
ejpam-1535	183	2	32	32	NUM
ejpam-1535	183	3	]	]	PUNCT
ejpam-1535	183	4	,	,	PUNCT
ejpam-1535	183	5	is	be	AUX
ejpam-1535	183	6	a	a	DET
ejpam-1535	183	7	function	function	NOUN
ejpam-1535	183	8	θ	θ	NOUN
ejpam-1535	183	9	:	:	PUNCT
ejpam-1535	183	10	s	s	X
ejpam-1535	183	11	→	→	SYM
ejpam-1535	183	12	t	t	NOUN
ejpam-1535	183	13	between	between	ADP
ejpam-1535	183	14	inverse	inverse	NOUN
ejpam-1535	183	15	semigroups	semigroup	NOUN
ejpam-1535	183	16	s	s	PART
ejpam-1535	183	17	and	and	CCONJ
ejpam-1535	183	18	t	t	NOUN
ejpam-1535	183	19	such	such	ADJ
ejpam-1535	183	20	that	that	PRON
ejpam-1535	183	21	(	(	PUNCT
ejpam-1535	183	22	st)θ	st)θ	PROPN
ejpam-1535	183	23	≤	≤	NOUN
ejpam-1535	183	24	(	(	PUNCT
ejpam-1535	183	25	sθ)(tθ	sθ)(tθ	PROPN
ejpam-1535	183	26	)	)	PUNCT
ejpam-1535	183	27	.	.	PUNCT
ejpam-1535	184	1	we	we	PRON
ejpam-1535	184	2	may	may	AUX
ejpam-1535	184	3	thus	thus	ADV
ejpam-1535	184	4	establish	establish	VERB
ejpam-1535	184	5	an	an	DET
ejpam-1535	184	6	isomorphism	isomorphism	NOUN
ejpam-1535	184	7	between	between	ADP
ejpam-1535	184	8	the	the	DET
ejpam-1535	184	9	category	category	NOUN
ejpam-1535	184	10	of	of	ADP
ejpam-1535	184	11	inductive	inductive	ADJ
ejpam-1535	184	12	groupoids	groupoid	NOUN
ejpam-1535	184	13	and	and	CCONJ
ejpam-1535	184	14	ordered	order	VERB
ejpam-1535	184	15	functors	functor	NOUN
ejpam-1535	184	16	,	,	PUNCT
ejpam-1535	184	17	and	and	CCONJ
ejpam-1535	184	18	the	the	DET
ejpam-1535	184	19	catec	catec	ADJ
ejpam-1535	184	20	.	.	PUNCT
ejpam-1535	185	1	hollings	holling	NOUN
ejpam-1535	185	2	/	/	SYM
ejpam-1535	185	3	eur	eur	PROPN
ejpam-1535	185	4	.	.	PUNCT
ejpam-1535	186	1	j.	j.	PROPN
ejpam-1535	186	2	pure	pure	PROPN
ejpam-1535	186	3	appl	appl	PROPN
ejpam-1535	186	4	.	.	PROPN
ejpam-1535	186	5	math	math	PROPN
ejpam-1535	186	6	,	,	PUNCT
ejpam-1535	186	7	5	5	NUM
ejpam-1535	186	8	(	(	PUNCT
ejpam-1535	186	9	2012	2012	NUM
ejpam-1535	186	10	)	)	PUNCT
ejpam-1535	186	11	,	,	PUNCT
ejpam-1535	186	12	414	414	NUM
ejpam-1535	186	13	-	-	SYM
ejpam-1535	186	14	450	450	NUM
ejpam-1535	186	15	422	422	NUM
ejpam-1535	186	16	gory	gory	NOUN
ejpam-1535	186	17	of	of	ADP
ejpam-1535	186	18	inverse	inverse	NOUN
ejpam-1535	186	19	semigroups	semigroup	NOUN
ejpam-1535	186	20	and	and	CCONJ
ejpam-1535	186	21	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	186	22	.	.	PUNCT
ejpam-1535	187	1	as	as	SCONJ
ejpam-1535	187	2	noted	note	VERB
ejpam-1535	187	3	in	in	ADP
ejpam-1535	187	4	the	the	DET
ejpam-1535	187	5	introduction	introduction	NOUN
ejpam-1535	187	6	,	,	PUNCT
ejpam-1535	187	7	these	these	DET
ejpam-1535	187	8	categorytheoretic	categorytheoretic	ADJ
ejpam-1535	187	9	results	result	NOUN
ejpam-1535	187	10	,	,	PUNCT
ejpam-1535	187	11	which	which	PRON
ejpam-1535	187	12	very	very	ADV
ejpam-1535	187	13	nicely	nicely	ADV
ejpam-1535	187	14	sum	sum	VERB
ejpam-1535	187	15	up	up	ADP
ejpam-1535	187	16	the	the	DET
ejpam-1535	187	17	connection	connection	NOUN
ejpam-1535	187	18	between	between	ADP
ejpam-1535	187	19	inverse	inverse	NOUN
ejpam-1535	187	20	semigroups	semigroup	NOUN
ejpam-1535	187	21	and	and	CCONJ
ejpam-1535	187	22	inductive	inductive	ADJ
ejpam-1535	187	23	groupoids	groupoid	NOUN
ejpam-1535	187	24	,	,	PUNCT
ejpam-1535	187	25	were	be	AUX
ejpam-1535	187	26	gathered	gather	VERB
ejpam-1535	187	27	together	together	ADV
ejpam-1535	187	28	into	into	ADP
ejpam-1535	187	29	a	a	DET
ejpam-1535	187	30	single	single	ADJ
ejpam-1535	187	31	theorem	theorem	NOUN
ejpam-1535	187	32	(	(	PUNCT
ejpam-1535	187	33	theorem	theorem	VERB
ejpam-1535	187	34	4.1.8	4.1.8	NUM
ejpam-1535	187	35	)	)	PUNCT
ejpam-1535	187	36	in	in	ADP
ejpam-1535	187	37	[	[	X
ejpam-1535	187	38	29	29	NUM
ejpam-1535	187	39	]	]	X
ejpam-1535	187	40	;	;	PUNCT
ejpam-1535	187	41	this	this	PRON
ejpam-1535	187	42	was	be	AUX
ejpam-1535	187	43	named	name	VERB
ejpam-1535	187	44	the	the	DET
ejpam-1535	187	45	ehresmann	ehresmann	PROPN
ejpam-1535	187	46	-	-	PUNCT
ejpam-1535	187	47	schein	schein	PROPN
ejpam-1535	187	48	-	-	PUNCT
ejpam-1535	187	49	nambooripad	nambooripad	NOUN
ejpam-1535	187	50	theorem	theorem	NOUN
ejpam-1535	187	51	to	to	PART
ejpam-1535	187	52	reflect	reflect	VERB
ejpam-1535	187	53	its	its	PRON
ejpam-1535	187	54	disparate	disparate	ADJ
ejpam-1535	187	55	origins	origin	NOUN
ejpam-1535	187	56	:	:	PUNCT
ejpam-1535	187	57	theorem	theorem	NOUN
ejpam-1535	187	58	1	1	NUM
ejpam-1535	187	59	.	.	PUNCT
ejpam-1535	188	1	the	the	DET
ejpam-1535	188	2	category	category	NOUN
ejpam-1535	188	3	of	of	ADP
ejpam-1535	188	4	inverse	inverse	NOUN
ejpam-1535	188	5	semigroups	semigroup	NOUN
ejpam-1535	188	6	and	and	CCONJ
ejpam-1535	188	7	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	188	8	is	be	AUX
ejpam-1535	188	9	isomorphic	isomorphic	ADJ
ejpam-1535	188	10	to	to	ADP
ejpam-1535	188	11	the	the	DET
ejpam-1535	188	12	category	category	NOUN
ejpam-1535	188	13	of	of	ADP
ejpam-1535	188	14	inductive	inductive	ADJ
ejpam-1535	188	15	groupoids	groupoid	NOUN
ejpam-1535	188	16	and	and	CCONJ
ejpam-1535	188	17	ordered	order	VERB
ejpam-1535	188	18	functors	functor	NOUN
ejpam-1535	188	19	;	;	PUNCT
ejpam-1535	188	20	the	the	DET
ejpam-1535	188	21	category	category	NOUN
ejpam-1535	188	22	of	of	ADP
ejpam-1535	188	23	inverse	inverse	NOUN
ejpam-1535	188	24	semigroups	semigroup	NOUN
ejpam-1535	188	25	and	and	CCONJ
ejpam-1535	188	26	morphisms	morphism	NOUN
ejpam-1535	188	27	is	be	AUX
ejpam-1535	188	28	isomorphic	isomorphic	ADJ
ejpam-1535	188	29	to	to	ADP
ejpam-1535	188	30	the	the	DET
ejpam-1535	188	31	category	category	NOUN
ejpam-1535	188	32	of	of	ADP
ejpam-1535	188	33	inductive	inductive	ADJ
ejpam-1535	188	34	groupoids	groupoid	NOUN
ejpam-1535	188	35	and	and	CCONJ
ejpam-1535	188	36	inductive	inductive	ADJ
ejpam-1535	188	37	functors.¶	functors.¶	VERB
ejpam-1535	188	38	with	with	ADP
ejpam-1535	188	39	this	this	DET
ejpam-1535	188	40	connection	connection	NOUN
ejpam-1535	188	41	between	between	ADP
ejpam-1535	188	42	inverse	inverse	NOUN
ejpam-1535	188	43	semigroups	semigroup	NOUN
ejpam-1535	188	44	and	and	CCONJ
ejpam-1535	188	45	inductive	inductive	ADJ
ejpam-1535	188	46	groupoids	groupoid	NOUN
ejpam-1535	188	47	established	establish	VERB
ejpam-1535	188	48	,	,	PUNCT
ejpam-1535	188	49	it	it	PRON
ejpam-1535	188	50	was	be	AUX
ejpam-1535	188	51	natural	natural	ADJ
ejpam-1535	188	52	to	to	PART
ejpam-1535	188	53	seek	seek	VERB
ejpam-1535	188	54	other	other	ADJ
ejpam-1535	188	55	generalisations	generalisation	NOUN
ejpam-1535	188	56	.	.	PUNCT
ejpam-1535	189	1	we	we	PRON
ejpam-1535	189	2	have	have	AUX
ejpam-1535	189	3	seen	see	VERB
ejpam-1535	189	4	that	that	SCONJ
ejpam-1535	189	5	there	there	PRON
ejpam-1535	189	6	is	be	VERB
ejpam-1535	189	7	an	an	DET
ejpam-1535	189	8	extension	extension	NOUN
ejpam-1535	189	9	of	of	ADP
ejpam-1535	189	10	this	this	DET
ejpam-1535	189	11	result	result	NOUN
ejpam-1535	189	12	to	to	ADP
ejpam-1535	189	13	the	the	DET
ejpam-1535	189	14	regular	regular	ADJ
ejpam-1535	189	15	case	case	NOUN
ejpam-1535	189	16	,	,	PUNCT
ejpam-1535	189	17	due	due	ADP
ejpam-1535	189	18	to	to	ADP
ejpam-1535	189	19	nambooripad	nambooripad	PROPN
ejpam-1535	189	20	,	,	PUNCT
ejpam-1535	189	21	but	but	CCONJ
ejpam-1535	189	22	what	what	PRON
ejpam-1535	189	23	of	of	ADP
ejpam-1535	189	24	the	the	DET
ejpam-1535	189	25	non	non	ADJ
ejpam-1535	189	26	-	-	ADJ
ejpam-1535	189	27	regular	regular	ADJ
ejpam-1535	189	28	generalisations	generalisation	NOUN
ejpam-1535	189	29	of	of	ADP
ejpam-1535	189	30	inverse	inverse	NOUN
ejpam-1535	189	31	semigroups	semigroup	NOUN
ejpam-1535	189	32	,	,	PUNCT
ejpam-1535	189	33	such	such	ADJ
ejpam-1535	189	34	as	as	ADP
ejpam-1535	189	35	the	the	DET
ejpam-1535	189	36	ample	ample	ADJ
ejpam-1535	189	37	(	(	PUNCT
ejpam-1535	189	38	a.k.a	a.k.a	ADJ
ejpam-1535	189	39	.	.	PROPN
ejpam-1535	189	40	type	type	NOUN
ejpam-1535	189	41	-	-	PUNCT
ejpam-1535	189	42	a	a	NOUN
ejpam-1535	189	43	)	)	PUNCT
ejpam-1535	189	44	semigroups	semigroup	NOUN
ejpam-1535	189	45	developed	develop	VERB
ejpam-1535	189	46	by	by	ADP
ejpam-1535	189	47	john	john	PROPN
ejpam-1535	189	48	fountain	fountain	PROPN
ejpam-1535	189	49	[	[	X
ejpam-1535	189	50	13	13	NUM
ejpam-1535	189	51	,	,	PUNCT
ejpam-1535	189	52	14	14	NUM
ejpam-1535	189	53	]	]	PUNCT
ejpam-1535	189	54	,	,	PUNCT
ejpam-1535	189	55	and	and	CCONJ
ejpam-1535	189	56	the	the	DET
ejpam-1535	189	57	related	relate	VERB
ejpam-1535	189	58	semigroups	semigroup	NOUN
ejpam-1535	189	59	surveyed	survey	VERB
ejpam-1535	189	60	in	in	ADP
ejpam-1535	189	61	[	[	X
ejpam-1535	189	62	20	20	NUM
ejpam-1535	189	63	]	]	PUNCT
ejpam-1535	189	64	?	?	PUNCT
ejpam-1535	190	1	furthermore	furthermore	ADV
ejpam-1535	190	2	,	,	PUNCT
ejpam-1535	190	3	since	since	SCONJ
ejpam-1535	190	4	a	a	DET
ejpam-1535	190	5	groupoid	groupoid	NOUN
ejpam-1535	190	6	is	be	AUX
ejpam-1535	190	7	a	a	DET
ejpam-1535	190	8	very	very	ADV
ejpam-1535	190	9	specialised	specialised	ADJ
ejpam-1535	190	10	type	type	NOUN
ejpam-1535	190	11	of	of	ADP
ejpam-1535	190	12	category	category	NOUN
ejpam-1535	190	13	,	,	PUNCT
ejpam-1535	190	14	we	we	PRON
ejpam-1535	190	15	might	might	AUX
ejpam-1535	190	16	ask	ask	VERB
ejpam-1535	190	17	what	what	DET
ejpam-1535	190	18	type	type	NOUN
ejpam-1535	190	19	of	of	ADP
ejpam-1535	190	20	semigroup	semigroup	NOUN
ejpam-1535	190	21	may	may	AUX
ejpam-1535	190	22	be	be	AUX
ejpam-1535	190	23	associated	associate	VERB
ejpam-1535	190	24	with	with	ADP
ejpam-1535	190	25	a	a	DET
ejpam-1535	190	26	more	more	ADV
ejpam-1535	190	27	general	general	ADJ
ejpam-1535	190	28	inductive	inductive	ADJ
ejpam-1535	190	29	category	category	NOUN
ejpam-1535	190	30	,	,	PUNCT
ejpam-1535	190	31	or	or	CCONJ
ejpam-1535	190	32	even	even	ADV
ejpam-1535	190	33	with	with	ADP
ejpam-1535	190	34	an	an	DET
ejpam-1535	190	35	arbitrary	arbitrary	ADJ
ejpam-1535	190	36	inductive	inductive	ADJ
ejpam-1535	190	37	category	category	NOUN
ejpam-1535	190	38	(	(	PUNCT
ejpam-1535	190	39	in	in	ADP
ejpam-1535	190	40	sense	sense	NOUN
ejpam-1535	190	41	(	(	PUNCT
ejpam-1535	190	42	♣	♣	NOUN
ejpam-1535	190	43	)	)	PUNCT
ejpam-1535	190	44	)	)	PUNCT
ejpam-1535	190	45	.	.	PUNCT
ejpam-1535	191	1	this	this	DET
ejpam-1535	191	2	question	question	NOUN
ejpam-1535	191	3	has	have	AUX
ejpam-1535	191	4	indeed	indeed	ADV
ejpam-1535	191	5	been	be	AUX
ejpam-1535	191	6	answered	answer	VERB
ejpam-1535	191	7	,	,	PUNCT
ejpam-1535	191	8	via	via	ADP
ejpam-1535	191	9	a	a	DET
ejpam-1535	191	10	succession	succession	NOUN
ejpam-1535	191	11	of	of	ADP
ejpam-1535	191	12	generalisations	generalisation	NOUN
ejpam-1535	191	13	of	of	ADP
ejpam-1535	191	14	the	the	DET
ejpam-1535	191	15	esn	esn	PROPN
ejpam-1535	191	16	theorem	theorem	PROPN
ejpam-1535	191	17	,	,	PUNCT
ejpam-1535	191	18	which	which	PRON
ejpam-1535	191	19	we	we	PRON
ejpam-1535	191	20	now	now	ADV
ejpam-1535	191	21	discuss	discuss	VERB
ejpam-1535	191	22	.	.	PUNCT
ejpam-1535	192	1	the	the	DET
ejpam-1535	192	2	first	first	ADJ
ejpam-1535	192	3	of	of	ADP
ejpam-1535	192	4	these	these	DET
ejpam-1535	192	5	generalisations	generalisation	NOUN
ejpam-1535	192	6	is	be	AUX
ejpam-1535	192	7	due	due	ADJ
ejpam-1535	192	8	to	to	ADP
ejpam-1535	192	9	sheena	sheena	PROPN
ejpam-1535	192	10	armstrong	armstrong	PROPN
ejpam-1535	193	1	[	[	X
ejpam-1535	193	2	1	1	NUM
ejpam-1535	193	3	]	]	PUNCT
ejpam-1535	193	4	and	and	CCONJ
ejpam-1535	193	5	is	be	AUX
ejpam-1535	193	6	rooted	root	VERB
ejpam-1535	193	7	in	in	ADP
ejpam-1535	193	8	the	the	DET
ejpam-1535	193	9	work	work	NOUN
ejpam-1535	193	10	of	of	ADP
ejpam-1535	193	11	john	john	PROPN
ejpam-1535	193	12	meakin	meakin	PROPN
ejpam-1535	194	1	[	[	X
ejpam-1535	194	2	33	33	NUM
ejpam-1535	194	3	]	]	PUNCT
ejpam-1535	194	4	.	.	PUNCT
ejpam-1535	195	1	we	we	PRON
ejpam-1535	195	2	saw	see	VERB
ejpam-1535	195	3	above	above	ADP
ejpam-1535	195	4	that	that	PRON
ejpam-1535	195	5	,	,	PUNCT
ejpam-1535	195	6	at	at	ADP
ejpam-1535	195	7	one	one	NUM
ejpam-1535	195	8	point	point	NOUN
ejpam-1535	195	9	,	,	PUNCT
ejpam-1535	195	10	nambooripad	nambooripad	NOUN
ejpam-1535	195	11	used	use	VERB
ejpam-1535	195	12	mappings	mapping	NOUN
ejpam-1535	195	13	between	between	ADP
ejpam-1535	195	14	rand	rand	NOUN
ejpam-1535	195	15	l	l	NOUN
ejpam-1535	195	16	-classes	-classe	NOUN
ejpam-1535	195	17	as	as	ADP
ejpam-1535	195	18	part	part	NOUN
ejpam-1535	195	19	of	of	ADP
ejpam-1535	195	20	his	his	PRON
ejpam-1535	195	21	description	description	NOUN
ejpam-1535	195	22	of	of	ADP
ejpam-1535	195	23	the	the	DET
ejpam-1535	195	24	structure	structure	NOUN
ejpam-1535	195	25	of	of	ADP
ejpam-1535	195	26	regular	regular	ADJ
ejpam-1535	195	27	semigroups	semigroup	NOUN
ejpam-1535	195	28	.	.	PUNCT
ejpam-1535	196	1	inspired	inspire	VERB
ejpam-1535	196	2	by	by	ADP
ejpam-1535	196	3	some	some	DET
ejpam-1535	196	4	observations	observation	NOUN
ejpam-1535	196	5	of	of	ADP
ejpam-1535	196	6	schein	schein	PROPN
ejpam-1535	197	1	[	[	X
ejpam-1535	197	2	44	44	NUM
ejpam-1535	197	3	]	]	PUNCT
ejpam-1535	197	4	,	,	PUNCT
ejpam-1535	197	5	meakin	meakin	PROPN
ejpam-1535	197	6	had	have	AUX
ejpam-1535	197	7	,	,	PUNCT
ejpam-1535	197	8	entirely	entirely	ADV
ejpam-1535	197	9	independently	independently	ADV
ejpam-1535	197	10	of	of	ADP
ejpam-1535	197	11	nambooripad	nambooripad	PROPN
ejpam-1535	197	12	,	,	PUNCT
ejpam-1535	197	13	embarked	embark	VERB
ejpam-1535	197	14	upon	upon	SCONJ
ejpam-1535	197	15	a	a	DET
ejpam-1535	197	16	similar	similar	ADJ
ejpam-1535	197	17	approach	approach	NOUN
ejpam-1535	197	18	to	to	ADP
ejpam-1535	197	19	the	the	DET
ejpam-1535	197	20	structure	structure	NOUN
ejpam-1535	197	21	of	of	ADP
ejpam-1535	197	22	an	an	DET
ejpam-1535	197	23	inverse	inverse	NOUN
ejpam-1535	197	24	semigroup	semigroup	NOUN
ejpam-1535	197	25	s	s	X
ejpam-1535	197	26	by	by	ADP
ejpam-1535	197	27	means	mean	NOUN
ejpam-1535	197	28	of	of	ADP
ejpam-1535	197	29	so	so	ADV
ejpam-1535	197	30	-	-	PUNCT
ejpam-1535	197	31	called	call	VERB
ejpam-1535	197	32	“	"	PUNCT
ejpam-1535	197	33	structure	structure	NOUN
ejpam-1535	197	34	mappings	mapping	NOUN
ejpam-1535	197	35	”	"	PUNCT
ejpam-1535	197	36	,	,	PUNCT
ejpam-1535	197	37	that	that	ADV
ejpam-1535	197	38	is	is	ADV
ejpam-1535	197	39	,	,	PUNCT
ejpam-1535	197	40	mappings	mapping	NOUN
ejpam-1535	197	41	between	between	ADP
ejpam-1535	197	42	r	r	NOUN
ejpam-1535	197	43	-	-	PUNCT
ejpam-1535	197	44	classes	class	NOUN
ejpam-1535	197	45	of	of	ADP
ejpam-1535	197	46	s.	s.	PROPN
ejpam-1535	197	47	in	in	ADP
ejpam-1535	197	48	essence	essence	NOUN
ejpam-1535	197	49	,	,	PUNCT
ejpam-1535	197	50	given	give	VERB
ejpam-1535	197	51	an	an	DET
ejpam-1535	197	52	inverse	inverse	NOUN
ejpam-1535	197	53	semigroup	semigroup	NOUN
ejpam-1535	197	54	s	s	PROPN
ejpam-1535	197	55	,	,	PUNCT
ejpam-1535	197	56	meakin	meakin	PROPN
ejpam-1535	197	57	’s	’s	PART
ejpam-1535	197	58	structure	structure	NOUN
ejpam-1535	197	59	mappings	mapping	NOUN
ejpam-1535	197	60	permit	permit	VERB
ejpam-1535	197	61	the	the	DET
ejpam-1535	197	62	location	location	NOUN
ejpam-1535	197	63	of	of	ADP
ejpam-1535	197	64	those	those	DET
ejpam-1535	197	65	products	product	NOUN
ejpam-1535	197	66	which	which	PRON
ejpam-1535	197	67	do	do	AUX
ejpam-1535	197	68	not	not	PART
ejpam-1535	197	69	belong	belong	VERB
ejpam-1535	197	70	to	to	ADP
ejpam-1535	197	71	tr(s	tr(	NOUN
ejpam-1535	197	72	)	)	PUNCT
ejpam-1535	197	73	.	.	PUNCT
ejpam-1535	198	1	indeed	indeed	ADV
ejpam-1535	198	2	,	,	PUNCT
ejpam-1535	198	3	these	these	DET
ejpam-1535	198	4	structure	structure	NOUN
ejpam-1535	198	5	mappings	mapping	NOUN
ejpam-1535	198	6	encode	encode	VERB
ejpam-1535	198	7	the	the	DET
ejpam-1535	198	8	same	same	ADJ
ejpam-1535	198	9	information	information	NOUN
ejpam-1535	198	10	as	as	ADP
ejpam-1535	198	11	the	the	DET
ejpam-1535	198	12	“	"	PUNCT
ejpam-1535	198	13	restriction	restriction	NOUN
ejpam-1535	198	14	”	"	PUNCT
ejpam-1535	198	15	and	and	CCONJ
ejpam-1535	198	16	“	"	PUNCT
ejpam-1535	198	17	corestriction	corestriction	NOUN
ejpam-1535	198	18	”	"	PUNCT
ejpam-1535	198	19	that	that	PRON
ejpam-1535	198	20	we	we	PRON
ejpam-1535	198	21	will	will	AUX
ejpam-1535	198	22	introduce	introduce	VERB
ejpam-1535	198	23	in	in	ADP
ejpam-1535	198	24	definition	definition	NOUN
ejpam-1535	198	25	11	11	NUM
ejpam-1535	198	26	.	.	PUNCT
ejpam-1535	199	1	armstrong	armstrong	PROPN
ejpam-1535	199	2	generalised	generalise	VERB
ejpam-1535	199	3	this	this	DET
ejpam-1535	199	4	approach	approach	NOUN
ejpam-1535	199	5	to	to	ADP
ejpam-1535	199	6	the	the	DET
ejpam-1535	199	7	study	study	NOUN
ejpam-1535	199	8	of	of	ADP
ejpam-1535	199	9	ample	ample	ADJ
ejpam-1535	199	10	semigroups	semigroup	NOUN
ejpam-1535	199	11	by	by	ADP
ejpam-1535	199	12	considering	consider	VERB
ejpam-1535	199	13	mappings	mapping	NOUN
ejpam-1535	199	14	between	between	ADP
ejpam-1535	199	15	classes	class	NOUN
ejpam-1535	199	16	of	of	ADP
ejpam-1535	199	17	the	the	DET
ejpam-1535	199	18	generalised	generalise	VERB
ejpam-1535	199	19	green	green	NOUN
ejpam-1535	199	20	’s	’s	PART
ejpam-1535	199	21	relations	relation	NOUN
ejpam-1535	199	22	,	,	PUNCT
ejpam-1535	199	23	r∗	r∗	VERB
ejpam-1535	199	24	and	and	CCONJ
ejpam-1535	199	25	l	l	NOUN
ejpam-1535	199	26	∗	∗	NOUN
ejpam-1535	199	27	,	,	PUNCT
ejpam-1535	199	28	in	in	ADP
ejpam-1535	199	29	terms	term	NOUN
ejpam-1535	199	30	of	of	ADP
ejpam-1535	199	31	which	which	PRON
ejpam-1535	199	32	ample	ample	ADJ
ejpam-1535	199	33	semigroups	semigroup	NOUN
ejpam-1535	199	34	are	be	AUX
ejpam-1535	199	35	defined	define	VERB
ejpam-1535	199	36	(	(	PUNCT
ejpam-1535	199	37	see	see	VERB
ejpam-1535	199	38	section	section	NOUN
ejpam-1535	199	39	3	3	NUM
ejpam-1535	199	40	)	)	PUNCT
ejpam-1535	199	41	.	.	PUNCT
ejpam-1535	200	1	in	in	ADP
ejpam-1535	200	2	her	she	PRON
ejpam-1535	200	3	theorem	theorem	ADJ
ejpam-1535	200	4	3.9	3.9	NUM
ejpam-1535	200	5	(	(	PUNCT
ejpam-1535	200	6	our	our	PRON
ejpam-1535	200	7	corollaries	corollary	NOUN
ejpam-1535	200	8	4	4	NUM
ejpam-1535	200	9	and	and	CCONJ
ejpam-1535	200	10	6	6	NUM
ejpam-1535	200	11	)	)	PUNCT
ejpam-1535	200	12	,	,	PUNCT
ejpam-1535	200	13	armstrong	armstrong	PROPN
ejpam-1535	200	14	extended	extend	VERB
ejpam-1535	200	15	the	the	DET
ejpam-1535	200	16	esn	esn	PROPN
ejpam-1535	200	17	theorem	theorem	VERB
ejpam-1535	200	18	to	to	ADP
ejpam-1535	200	19	the	the	DET
ejpam-1535	200	20	case	case	NOUN
ejpam-1535	200	21	of	of	ADP
ejpam-1535	200	22	ample	ample	ADJ
ejpam-1535	200	23	semigroups	semigroup	NOUN
ejpam-1535	200	24	and	and	CCONJ
ejpam-1535	200	25	inductive	inductive	ADJ
ejpam-1535	200	26	cancellative	cancellative	ADJ
ejpam-1535	200	27	categories	category	NOUN
ejpam-1535	200	28	(	(	PUNCT
ejpam-1535	200	29	to	to	PART
ejpam-1535	200	30	be	be	AUX
ejpam-1535	200	31	defined	define	VERB
ejpam-1535	200	32	in	in	ADP
ejpam-1535	200	33	section	section	NOUN
ejpam-1535	200	34	4	4	NUM
ejpam-1535	200	35	)	)	PUNCT
ejpam-1535	200	36	,	,	PUNCT
ejpam-1535	200	37	although	although	SCONJ
ejpam-1535	200	38	,	,	PUNCT
ejpam-1535	200	39	adapting	adapt	VERB
ejpam-1535	200	40	schein	schein	PROPN
ejpam-1535	200	41	’s	’s	PART
ejpam-1535	200	42	terminology	terminology	NOUN
ejpam-1535	200	43	,	,	PUNCT
ejpam-1535	200	44	she	she	PRON
ejpam-1535	200	45	referred	refer	VERB
ejpam-1535	200	46	to	to	ADP
ejpam-1535	200	47	these	these	PRON
ejpam-1535	200	48	as	as	ADP
ejpam-1535	200	49	inductive	inductive	ADJ
ejpam-1535	200	50	weak	weak	ADJ
ejpam-1535	200	51	croisot	croisot	NOUN
ejpam-1535	200	52	groupoids	groupoid	NOUN
ejpam-1535	200	53	.	.	PUNCT
ejpam-1535	201	1	like	like	PROPN
ejpam-1535	201	2	schein	schein	PROPN
ejpam-1535	201	3	,	,	PUNCT
ejpam-1535	201	4	armstrong	armstrong	PROPN
ejpam-1535	201	5	did	do	AUX
ejpam-1535	201	6	not	not	PART
ejpam-1535	201	7	give	give	VERB
ejpam-1535	201	8	her	she	PRON
ejpam-1535	201	9	result	result	NOUN
ejpam-1535	201	10	a	a	DET
ejpam-1535	201	11	categorytheoretic	categorytheoretic	ADJ
ejpam-1535	201	12	formulation	formulation	NOUN
ejpam-1535	201	13	such	such	ADJ
ejpam-1535	201	14	as	as	ADP
ejpam-1535	201	15	theorem	theorem	NOUN
ejpam-1535	201	16	1	1	NUM
ejpam-1535	201	17	.	.	PUNCT
ejpam-1535	202	1	in	in	ADP
ejpam-1535	202	2	the	the	DET
ejpam-1535	202	3	presentation	presentation	NOUN
ejpam-1535	202	4	of	of	ADP
ejpam-1535	202	5	[	[	X
ejpam-1535	202	6	20	20	NUM
ejpam-1535	202	7	]	]	PUNCT
ejpam-1535	202	8	,	,	PUNCT
ejpam-1535	202	9	ample	ample	ADJ
ejpam-1535	202	10	semigroups	semigroup	NOUN
ejpam-1535	202	11	have	have	VERB
ejpam-1535	202	12	two	two	NUM
ejpam-1535	202	13	successive	successive	ADJ
ejpam-1535	202	14	generalisations	generalisation	NOUN
ejpam-1535	202	15	:	:	PUNCT
ejpam-1535	202	16	full	full	ADJ
ejpam-1535	202	17	restriction	restriction	NOUN
ejpam-1535	202	18	semigroups	semigroup	NOUN
ejpam-1535	202	19	(	(	PUNCT
ejpam-1535	202	20	formerly	formerly	ADV
ejpam-1535	202	21	termed	term	VERB
ejpam-1535	202	22	weakly	weakly	ADJ
ejpam-1535	202	23	ample	ample	ADJ
ejpam-1535	202	24	semigroups	semigroup	NOUN
ejpam-1535	202	25	)	)	PUNCT
ejpam-1535	202	26	and	and	CCONJ
ejpam-1535	202	27	restriction	restriction	NOUN
ejpam-1535	202	28	semigroups	semigroup	NOUN
ejpam-1535	202	29	(	(	PUNCT
ejpam-1535	202	30	formerly	formerly	ADV
ejpam-1535	202	31	,	,	PUNCT
ejpam-1535	202	32	weakly	weakly	ADJ
ejpam-1535	202	33	e	e	NOUN
ejpam-1535	202	34	-	-	ADJ
ejpam-1535	202	35	ample	ample	ADJ
ejpam-1535	202	36	semigroups	semigroup	NOUN
ejpam-1535	202	37	)	)	PUNCT
ejpam-1535	202	38	.	.	PUNCT
ejpam-1535	203	1	each	each	PRON
ejpam-1535	203	2	of	of	ADP
ejpam-1535	203	3	the	the	DET
ejpam-1535	203	4	two	two	NUM
ejpam-1535	203	5	further	further	ADJ
ejpam-1535	203	6	generalisations	generalisation	NOUN
ejpam-1535	203	7	of	of	ADP
ejpam-1535	203	8	the	the	DET
ejpam-1535	203	9	esn	esn	PROPN
ejpam-1535	203	10	theorem	theorem	VERB
ejpam-1535	203	11	to	to	ADP
ejpam-1535	203	12	these	these	DET
ejpam-1535	203	13	cases	case	NOUN
ejpam-1535	203	14	is	be	AUX
ejpam-1535	203	15	due	due	ADJ
ejpam-1535	203	16	to	to	PART
ejpam-1535	203	17	mark	mark	PROPN
ejpam-1535	203	18	lawson	lawson	PROPN
ejpam-1535	203	19	.	.	PUNCT
ejpam-1535	204	1	the	the	DET
ejpam-1535	204	2	case	case	NOUN
ejpam-1535	204	3	of	of	ADP
ejpam-1535	204	4	full	full	ADJ
ejpam-1535	204	5	restriction	restriction	NOUN
ejpam-1535	204	6	semigroups	semigroup	NOUN
ejpam-1535	204	7	and	and	CCONJ
ejpam-1535	204	8	inductive	inductive	ADJ
ejpam-1535	204	9	unipotent	unipotent	ADJ
ejpam-1535	204	10	categories	category	NOUN
ejpam-1535	204	11	(	(	PUNCT
ejpam-1535	204	12	see	see	VERB
ejpam-1535	204	13	section	section	NOUN
ejpam-1535	204	14	4	4	NUM
ejpam-1535	204	15	)	)	PUNCT
ejpam-1535	204	16	appears	appear	VERB
ejpam-1535	204	17	in	in	ADP
ejpam-1535	204	18	his	his	PRON
ejpam-1535	204	19	dphil	dphil	ADJ
ejpam-1535	204	20	thesis	thesis	NOUN
ejpam-1535	204	21	[	[	X
ejpam-1535	204	22	26	26	NUM
ejpam-1535	204	23	,	,	PUNCT
ejpam-1535	204	24	theorem	theorem	VERB
ejpam-1535	204	25	3.16	3.16	NUM
ejpam-1535	204	26	]	]	PUNCT
ejpam-1535	204	27	(	(	PUNCT
ejpam-1535	204	28	our	our	PRON
ejpam-1535	204	29	corollary	corollary	ADJ
ejpam-1535	204	30	9	9	NUM
ejpam-1535	204	31	)	)	PUNCT
ejpam-1535	204	32	as	as	ADP
ejpam-1535	204	33	a	a	DET
ejpam-1535	204	34	generalisation	generalisation	NOUN
ejpam-1535	204	35	of	of	ADP
ejpam-1535	204	36	armstrong	armstrong	PROPN
ejpam-1535	204	37	’s	’s	PART
ejpam-1535	204	38	result	result	NOUN
ejpam-1535	204	39	,	,	PUNCT
ejpam-1535	204	40	whilst	whilst	SCONJ
ejpam-1535	204	41	that	that	PRON
ejpam-1535	204	42	of	of	ADP
ejpam-1535	204	43	restriction	restriction	NOUN
ejpam-1535	204	44	semigroups	semigroup	NOUN
ejpam-1535	204	45	and	and	CCONJ
ejpam-1535	204	46	arbitrary	arbitrary	ADJ
ejpam-1535	204	47	inductive	inductive	ADJ
ejpam-1535	204	48	categories	category	NOUN
ejpam-1535	204	49	may	may	AUX
ejpam-1535	204	50	be	be	AUX
ejpam-1535	204	51	found	find	VERB
ejpam-1535	204	52	in	in	ADP
ejpam-1535	204	53	a	a	DET
ejpam-1535	204	54	later	later	ADJ
ejpam-1535	204	55	paper	paper	NOUN
ejpam-1535	205	1	[	[	X
ejpam-1535	205	2	28	28	NUM
ejpam-1535	205	3	,	,	PUNCT
ejpam-1535	205	4	theorem	theorem	VERB
ejpam-1535	205	5	5.7	5.7	NUM
ejpam-1535	205	6	]	]	PUNCT
ejpam-1535	205	7	(	(	PUNCT
ejpam-1535	205	8	our	our	PRON
ejpam-1535	205	9	theorem	theorem	NOUN
ejpam-1535	205	10	6	6	NUM
ejpam-1535	205	11	)	)	PUNCT
ejpam-1535	205	12	.	.	PUNCT
ejpam-1535	206	1	this	this	DET
ejpam-1535	206	2	second	second	ADJ
ejpam-1535	206	3	generalisation	generalisation	NOUN
ejpam-1535	206	4	is	be	AUX
ejpam-1535	206	5	carried	carry	VERB
ejpam-1535	206	6	out	out	ADP
ejpam-1535	206	7	in	in	ADP
ejpam-1535	206	8	the	the	DET
ejpam-1535	206	9	order	order	NOUN
ejpam-1535	206	10	-	-	PUNCT
ejpam-1535	206	11	theoretic	theoretic	ADJ
ejpam-1535	206	12	style	style	NOUN
ejpam-1535	206	13	of	of	ADP
ejpam-1535	206	14	¶every	¶every	DET
ejpam-1535	206	15	occurrence	occurrence	NOUN
ejpam-1535	206	16	of	of	ADP
ejpam-1535	206	17	the	the	DET
ejpam-1535	206	18	word	word	NOUN
ejpam-1535	206	19	“	"	PUNCT
ejpam-1535	206	20	category	category	NOUN
ejpam-1535	206	21	”	"	PUNCT
ejpam-1535	206	22	in	in	ADP
ejpam-1535	206	23	this	this	DET
ejpam-1535	206	24	theorem	theorem	NOUN
ejpam-1535	206	25	is	be	AUX
ejpam-1535	206	26	used	use	VERB
ejpam-1535	206	27	in	in	ADP
ejpam-1535	206	28	sense	sense	NOUN
ejpam-1535	206	29	(	(	PUNCT
ejpam-1535	206	30	♠	♠	NOUN
ejpam-1535	206	31	)	)	PUNCT
ejpam-1535	206	32	.	.	PUNCT
ejpam-1535	207	1	c.	c.	PROPN
ejpam-1535	207	2	hollings	holling	NOUN
ejpam-1535	207	3	/	/	SYM
ejpam-1535	207	4	eur	eur	PROPN
ejpam-1535	207	5	.	.	PUNCT
ejpam-1535	208	1	j.	j.	PROPN
ejpam-1535	208	2	pure	pure	PROPN
ejpam-1535	208	3	appl	appl	PROPN
ejpam-1535	208	4	.	.	PROPN
ejpam-1535	208	5	math	math	PROPN
ejpam-1535	208	6	,	,	PUNCT
ejpam-1535	208	7	5	5	NUM
ejpam-1535	208	8	(	(	PUNCT
ejpam-1535	208	9	2012	2012	NUM
ejpam-1535	208	10	)	)	PUNCT
ejpam-1535	208	11	,	,	PUNCT
ejpam-1535	208	12	414	414	NUM
ejpam-1535	208	13	-	-	SYM
ejpam-1535	208	14	450	450	NUM
ejpam-1535	208	15	423	423	NUM
ejpam-1535	208	16	ehresmann	ehresmann	NOUN
ejpam-1535	208	17	,	,	PUNCT
ejpam-1535	208	18	whereas	whereas	SCONJ
ejpam-1535	208	19	the	the	DET
ejpam-1535	208	20	work	work	NOUN
ejpam-1535	208	21	of	of	ADP
ejpam-1535	208	22	lawson	lawson	PROPN
ejpam-1535	208	23	’s	’s	PART
ejpam-1535	208	24	thesis	thesis	NOUN
ejpam-1535	208	25	,	,	PUNCT
ejpam-1535	208	26	and	and	CCONJ
ejpam-1535	208	27	that	that	PRON
ejpam-1535	208	28	of	of	ADP
ejpam-1535	208	29	armstrong	armstrong	PROPN
ejpam-1535	208	30	,	,	PUNCT
ejpam-1535	208	31	simply	simply	ADV
ejpam-1535	208	32	adapts	adapt	VERB
ejpam-1535	208	33	the	the	DET
ejpam-1535	208	34	direct	direct	ADJ
ejpam-1535	208	35	approach	approach	NOUN
ejpam-1535	208	36	of	of	ADP
ejpam-1535	208	37	schein	schein	PROPN
ejpam-1535	209	1	[	[	X
ejpam-1535	209	2	44	44	NUM
ejpam-1535	209	3	,	,	PUNCT
ejpam-1535	209	4	45	45	NUM
ejpam-1535	209	5	]	]	PUNCT
ejpam-1535	209	6	,	,	PUNCT
ejpam-1535	209	7	complete	complete	ADJ
ejpam-1535	209	8	with	with	ADP
ejpam-1535	209	9	the	the	DET
ejpam-1535	209	10	consequent	consequent	ADJ
ejpam-1535	209	11	lengthy	lengthy	ADJ
ejpam-1535	209	12	associativity	associativity	NOUN
ejpam-1535	209	13	proof	proof	NOUN
ejpam-1535	209	14	noted	note	VERB
ejpam-1535	209	15	in	in	ADP
ejpam-1535	209	16	the	the	DET
ejpam-1535	209	17	introduction	introduction	NOUN
ejpam-1535	209	18	.	.	PUNCT
ejpam-1535	210	1	indeed	indeed	ADV
ejpam-1535	210	2	,	,	PUNCT
ejpam-1535	210	3	in	in	ADP
ejpam-1535	210	4	a	a	DET
ejpam-1535	210	5	parallel	parallel	ADJ
ejpam-1535	210	6	paper	paper	NOUN
ejpam-1535	210	7	[	[	X
ejpam-1535	210	8	27	27	NUM
ejpam-1535	210	9	]	]	PUNCT
ejpam-1535	210	10	,	,	PUNCT
ejpam-1535	210	11	lawson	lawson	PROPN
ejpam-1535	210	12	also	also	ADV
ejpam-1535	210	13	gave	give	VERB
ejpam-1535	210	14	an	an	DET
ejpam-1535	210	15	ordertheoretic	ordertheoretic	ADJ
ejpam-1535	210	16	treatment	treatment	NOUN
ejpam-1535	210	17	of	of	ADP
ejpam-1535	210	18	the	the	DET
ejpam-1535	210	19	inverse	inverse	NOUN
ejpam-1535	210	20	case	case	NOUN
ejpam-1535	210	21	;	;	PUNCT
ejpam-1535	210	22	this	this	DET
ejpam-1535	210	23	last	last	ADJ
ejpam-1535	210	24	paper	paper	NOUN
ejpam-1535	210	25	appears	appear	VERB
ejpam-1535	210	26	to	to	PART
ejpam-1535	210	27	contains	contain	VERB
ejpam-1535	210	28	the	the	DET
ejpam-1535	210	29	seeds	seed	NOUN
ejpam-1535	210	30	of	of	ADP
ejpam-1535	210	31	[	[	X
ejpam-1535	210	32	29	29	NUM
ejpam-1535	210	33	]	]	PUNCT
ejpam-1535	210	34	,	,	PUNCT
ejpam-1535	210	35	for	for	ADP
ejpam-1535	210	36	which	which	DET
ejpam-1535	210	37	book	book	NOUN
ejpam-1535	210	38	the	the	DET
ejpam-1535	210	39	esn	esn	PROPN
ejpam-1535	210	40	theorem	theorem	NOUN
ejpam-1535	210	41	provides	provide	VERB
ejpam-1535	210	42	the	the	DET
ejpam-1535	210	43	main	main	ADJ
ejpam-1535	210	44	focus	focus	NOUN
ejpam-1535	210	45	.	.	PUNCT
ejpam-1535	211	1	we	we	PRON
ejpam-1535	211	2	conclude	conclude	VERB
ejpam-1535	211	3	this	this	DET
ejpam-1535	211	4	historical	historical	ADJ
ejpam-1535	211	5	introduction	introduction	NOUN
ejpam-1535	211	6	by	by	ADP
ejpam-1535	211	7	noting	note	VERB
ejpam-1535	211	8	that	that	SCONJ
ejpam-1535	211	9	,	,	PUNCT
ejpam-1535	211	10	although	although	SCONJ
ejpam-1535	211	11	lawson	lawson	PROPN
ejpam-1535	211	12	[	[	X
ejpam-1535	211	13	28	28	NUM
ejpam-1535	211	14	]	]	PUNCT
ejpam-1535	211	15	did	do	AUX
ejpam-1535	211	16	phrase	phrase	VERB
ejpam-1535	211	17	his	his	PRON
ejpam-1535	211	18	results	result	NOUN
ejpam-1535	211	19	in	in	ADP
ejpam-1535	211	20	category	category	NOUN
ejpam-1535	211	21	-	-	PUNCT
ejpam-1535	211	22	theoretic	theoretic	NOUN
ejpam-1535	211	23	terms	term	NOUN
ejpam-1535	211	24	,	,	PUNCT
ejpam-1535	211	25	he	he	PRON
ejpam-1535	211	26	only	only	ADV
ejpam-1535	211	27	considered	consider	VERB
ejpam-1535	211	28	the	the	DET
ejpam-1535	211	29	case	case	NOUN
ejpam-1535	211	30	where	where	SCONJ
ejpam-1535	211	31	the	the	DET
ejpam-1535	211	32	arrows	arrow	NOUN
ejpam-1535	211	33	between	between	ADP
ejpam-1535	211	34	(	(	PUNCT
ejpam-1535	211	35	full	full	ADJ
ejpam-1535	211	36	)	)	PUNCT
ejpam-1535	211	37	restriction	restriction	NOUN
ejpam-1535	211	38	semigroups	semigroup	NOUN
ejpam-1535	211	39	are	be	AUX
ejpam-1535	211	40	morphisms	morphism	NOUN
ejpam-1535	211	41	;	;	PUNCT
ejpam-1535	211	42	he	he	PRON
ejpam-1535	211	43	did	do	AUX
ejpam-1535	211	44	not	not	PART
ejpam-1535	211	45	consider	consider	VERB
ejpam-1535	211	46	a	a	DET
ejpam-1535	211	47	“	"	PUNCT
ejpam-1535	211	48	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	211	49	”	"	PUNCT
ejpam-1535	211	50	version	version	NOUN
ejpam-1535	211	51	.	.	PUNCT
ejpam-1535	212	1	such	such	DET
ejpam-1535	212	2	a	a	DET
ejpam-1535	212	3	treatment	treatment	NOUN
ejpam-1535	212	4	may	may	AUX
ejpam-1535	212	5	be	be	AUX
ejpam-1535	212	6	found	find	VERB
ejpam-1535	212	7	instead	instead	ADV
ejpam-1535	212	8	in	in	ADP
ejpam-1535	212	9	[	[	X
ejpam-1535	212	10	22	22	NUM
ejpam-1535	212	11	]	]	PUNCT
ejpam-1535	212	12	.	.	PUNCT
ejpam-1535	213	1	we	we	PRON
ejpam-1535	213	2	note	note	VERB
ejpam-1535	213	3	also	also	ADV
ejpam-1535	213	4	that	that	SCONJ
ejpam-1535	213	5	[	[	X
ejpam-1535	213	6	22	22	NUM
ejpam-1535	213	7	]	]	PUNCT
ejpam-1535	213	8	contains	contain	VERB
ejpam-1535	213	9	“	"	PUNCT
ejpam-1535	213	10	esntype	esntype	NOUN
ejpam-1535	213	11	”	"	PUNCT
ejpam-1535	213	12	theorems	theorem	NOUN
ejpam-1535	213	13	(	(	PUNCT
ejpam-1535	213	14	not	not	PART
ejpam-1535	213	15	only	only	ADV
ejpam-1535	213	16	for	for	ADP
ejpam-1535	213	17	restriction	restriction	NOUN
ejpam-1535	213	18	semigroups	semigroup	NOUN
ejpam-1535	213	19	,	,	PUNCT
ejpam-1535	213	20	but	but	CCONJ
ejpam-1535	213	21	also	also	ADV
ejpam-1535	213	22	in	in	ADP
ejpam-1535	213	23	the	the	DET
ejpam-1535	213	24	special	special	ADJ
ejpam-1535	213	25	case	case	NOUN
ejpam-1535	213	26	of	of	ADP
ejpam-1535	213	27	inverse	inverse	NOUN
ejpam-1535	213	28	semigroups	semigroup	NOUN
ejpam-1535	213	29	)	)	PUNCT
ejpam-1535	213	30	involving	involve	VERB
ejpam-1535	213	31	the	the	DET
ejpam-1535	213	32	functions	function	NOUN
ejpam-1535	213	33	dual	dual	ADJ
ejpam-1535	213	34	to	to	ADP
ejpam-1535	213	35	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	213	36	,	,	PUNCT
ejpam-1535	213	37	so	so	ADV
ejpam-1535	213	38	-	-	PUNCT
ejpam-1535	213	39	called	call	VERB
ejpam-1535	213	40	“	"	PUNCT
ejpam-1535	213	41	∧-premorphisms	∧-premorphism	NOUN
ejpam-1535	213	42	”	"	PUNCT
ejpam-1535	213	43	,	,	PUNCT
ejpam-1535	213	44	which	which	PRON
ejpam-1535	213	45	have	have	VERB
ejpam-1535	213	46	an	an	DET
ejpam-1535	213	47	important	important	ADJ
ejpam-1535	213	48	role	role	NOUN
ejpam-1535	213	49	to	to	PART
ejpam-1535	213	50	play	play	VERB
ejpam-1535	213	51	in	in	ADP
ejpam-1535	213	52	the	the	DET
ejpam-1535	213	53	theory	theory	NOUN
ejpam-1535	213	54	of	of	ADP
ejpam-1535	213	55	partial	partial	ADJ
ejpam-1535	213	56	actions	action	NOUN
ejpam-1535	213	57	(	(	PUNCT
ejpam-1535	213	58	see	see	VERB
ejpam-1535	213	59	,	,	PUNCT
ejpam-1535	213	60	for	for	ADP
ejpam-1535	213	61	example	example	NOUN
ejpam-1535	213	62	,	,	PUNCT
ejpam-1535	213	63	[	[	X
ejpam-1535	213	64	16	16	NUM
ejpam-1535	213	65	,	,	PUNCT
ejpam-1535	213	66	30	30	NUM
ejpam-1535	213	67	]	]	PUNCT
ejpam-1535	213	68	)	)	PUNCT
ejpam-1535	213	69	.	.	PUNCT
ejpam-1535	214	1	however	however	ADV
ejpam-1535	214	2	,	,	PUNCT
ejpam-1535	214	3	we	we	PRON
ejpam-1535	214	4	will	will	AUX
ejpam-1535	214	5	not	not	PART
ejpam-1535	214	6	consider	consider	VERB
ejpam-1535	214	7	these	these	DET
ejpam-1535	214	8	functions	function	NOUN
ejpam-1535	214	9	in	in	ADP
ejpam-1535	214	10	the	the	DET
ejpam-1535	214	11	present	present	ADJ
ejpam-1535	214	12	article	article	NOUN
ejpam-1535	214	13	.	.	PUNCT
ejpam-1535	215	1	3	3	X
ejpam-1535	215	2	.	.	X
ejpam-1535	215	3	restriction	restriction	NOUN
ejpam-1535	215	4	semigroups	semigroup	NOUN
ejpam-1535	215	5	in	in	ADP
ejpam-1535	215	6	this	this	DET
ejpam-1535	215	7	section	section	NOUN
ejpam-1535	215	8	,	,	PUNCT
ejpam-1535	215	9	we	we	PRON
ejpam-1535	215	10	provide	provide	VERB
ejpam-1535	215	11	a	a	DET
ejpam-1535	215	12	brief	brief	ADJ
ejpam-1535	215	13	introduction	introduction	NOUN
ejpam-1535	215	14	to	to	ADP
ejpam-1535	215	15	the	the	DET
ejpam-1535	215	16	notion	notion	NOUN
ejpam-1535	215	17	of	of	ADP
ejpam-1535	215	18	a	a	DET
ejpam-1535	215	19	two	two	NUM
ejpam-1535	215	20	-	-	PUNCT
ejpam-1535	215	21	sided	side	VERB
ejpam-1535	215	22	restriction	restriction	NOUN
ejpam-1535	215	23	semigroup	semigroup	NOUN
ejpam-1535	215	24	,	,	PUNCT
ejpam-1535	215	25	which	which	PRON
ejpam-1535	215	26	we	we	PRON
ejpam-1535	215	27	will	will	AUX
ejpam-1535	215	28	refer	refer	VERB
ejpam-1535	215	29	to	to	ADP
ejpam-1535	215	30	here	here	ADV
ejpam-1535	215	31	simply	simply	ADV
ejpam-1535	215	32	as	as	ADP
ejpam-1535	215	33	a	a	DET
ejpam-1535	215	34	restriction	restriction	NOUN
ejpam-1535	215	35	semigroup	semigroup	NOUN
ejpam-1535	215	36	.	.	PUNCT
ejpam-1535	216	1	these	these	PRON
ejpam-1535	216	2	are	be	AUX
ejpam-1535	216	3	semigroups	semigroup	NOUN
ejpam-1535	216	4	which	which	PRON
ejpam-1535	216	5	arise	arise	VERB
ejpam-1535	216	6	from	from	ADP
ejpam-1535	216	7	semigroups	semigroup	NOUN
ejpam-1535	216	8	of	of	ADP
ejpam-1535	216	9	arbitrary	arbitrary	ADJ
ejpam-1535	216	10	partial	partial	ADJ
ejpam-1535	216	11	transformations	transformation	NOUN
ejpam-1535	216	12	in	in	ADP
ejpam-1535	216	13	much	much	ADV
ejpam-1535	216	14	the	the	DET
ejpam-1535	216	15	same	same	ADJ
ejpam-1535	216	16	way	way	NOUN
ejpam-1535	216	17	that	that	PRON
ejpam-1535	216	18	inverse	inverse	NOUN
ejpam-1535	216	19	semigroups	semigroup	NOUN
ejpam-1535	216	20	arise	arise	VERB
ejpam-1535	216	21	from	from	ADP
ejpam-1535	216	22	semigroups	semigroup	NOUN
ejpam-1535	216	23	of	of	ADP
ejpam-1535	216	24	one	one	NUM
ejpam-1535	216	25	-	-	PUNCT
ejpam-1535	216	26	one	one	NUM
ejpam-1535	216	27	partial	partial	ADJ
ejpam-1535	216	28	transformations	transformation	NOUN
ejpam-1535	216	29	.	.	PUNCT
ejpam-1535	217	1	a	a	DET
ejpam-1535	217	2	sketch	sketch	NOUN
ejpam-1535	217	3	of	of	ADP
ejpam-1535	217	4	the	the	DET
ejpam-1535	217	5	history	history	NOUN
ejpam-1535	217	6	of	of	ADP
ejpam-1535	217	7	these	these	DET
ejpam-1535	217	8	semigroups	semigroup	NOUN
ejpam-1535	217	9	is	be	AUX
ejpam-1535	217	10	given	give	VERB
ejpam-1535	217	11	in	in	ADP
ejpam-1535	217	12	[	[	X
ejpam-1535	217	13	20	20	NUM
ejpam-1535	217	14	]	]	PUNCT
ejpam-1535	217	15	,	,	PUNCT
ejpam-1535	217	16	and	and	CCONJ
ejpam-1535	217	17	it	it	PRON
ejpam-1535	217	18	to	to	ADP
ejpam-1535	217	19	this	this	DET
ejpam-1535	217	20	article	article	NOUN
ejpam-1535	217	21	(	(	PUNCT
ejpam-1535	217	22	as	as	ADV
ejpam-1535	217	23	well	well	ADV
ejpam-1535	217	24	as	as	ADP
ejpam-1535	217	25	to	to	ADP
ejpam-1535	217	26	[	[	X
ejpam-1535	217	27	15	15	NUM
ejpam-1535	217	28	]	]	PUNCT
ejpam-1535	217	29	)	)	PUNCT
ejpam-1535	217	30	that	that	SCONJ
ejpam-1535	217	31	we	we	PRON
ejpam-1535	217	32	direct	direct	VERB
ejpam-1535	217	33	the	the	DET
ejpam-1535	217	34	interested	interested	ADJ
ejpam-1535	217	35	reader	reader	NOUN
ejpam-1535	217	36	for	for	ADP
ejpam-1535	217	37	further	further	ADJ
ejpam-1535	217	38	details	detail	NOUN
ejpam-1535	217	39	(	(	PUNCT
ejpam-1535	217	40	including	include	VERB
ejpam-1535	217	41	proofs	proof	NOUN
ejpam-1535	217	42	)	)	PUNCT
ejpam-1535	217	43	and	and	CCONJ
ejpam-1535	217	44	references	reference	NOUN
ejpam-1535	217	45	.	.	PUNCT
ejpam-1535	218	1	indeed	indeed	ADV
ejpam-1535	218	2	,	,	PUNCT
ejpam-1535	218	3	in	in	ADP
ejpam-1535	218	4	the	the	DET
ejpam-1535	218	5	very	very	ADV
ejpam-1535	218	6	brief	brief	ADJ
ejpam-1535	218	7	account	account	NOUN
ejpam-1535	218	8	of	of	ADP
ejpam-1535	218	9	these	these	DET
ejpam-1535	218	10	semigroups	semigroup	NOUN
ejpam-1535	218	11	given	give	VERB
ejpam-1535	218	12	here	here	ADV
ejpam-1535	218	13	,	,	PUNCT
ejpam-1535	218	14	we	we	PRON
ejpam-1535	218	15	do	do	AUX
ejpam-1535	218	16	not	not	PART
ejpam-1535	218	17	include	include	VERB
ejpam-1535	218	18	any	any	DET
ejpam-1535	218	19	justification	justification	NOUN
ejpam-1535	218	20	for	for	ADP
ejpam-1535	218	21	their	their	PRON
ejpam-1535	218	22	study	study	NOUN
ejpam-1535	218	23	,	,	PUNCT
ejpam-1535	218	24	usually	usually	ADV
ejpam-1535	218	25	provided	provide	VERB
ejpam-1535	218	26	by	by	ADP
ejpam-1535	218	27	means	mean	NOUN
ejpam-1535	218	28	of	of	ADP
ejpam-1535	218	29	partial	partial	ADJ
ejpam-1535	218	30	transformations	transformation	NOUN
ejpam-1535	218	31	,	,	PUNCT
ejpam-1535	218	32	and	and	CCONJ
ejpam-1535	218	33	move	move	VERB
ejpam-1535	218	34	straight	straight	ADV
ejpam-1535	218	35	to	to	ADP
ejpam-1535	218	36	the	the	DET
ejpam-1535	218	37	abstract	abstract	ADJ
ejpam-1535	218	38	definition	definition	NOUN
ejpam-1535	218	39	;	;	PUNCT
ejpam-1535	218	40	said	say	VERB
ejpam-1535	218	41	justification	justification	NOUN
ejpam-1535	218	42	may	may	AUX
ejpam-1535	218	43	be	be	AUX
ejpam-1535	218	44	found	find	VERB
ejpam-1535	218	45	in	in	ADP
ejpam-1535	218	46	[	[	X
ejpam-1535	218	47	20	20	NUM
ejpam-1535	218	48	]	]	PUNCT
ejpam-1535	218	49	.	.	PUNCT
ejpam-1535	219	1	let	let	VERB
ejpam-1535	219	2	s	s	PRON
ejpam-1535	219	3	be	be	AUX
ejpam-1535	219	4	a	a	DET
ejpam-1535	219	5	semigroup	semigroup	NOUN
ejpam-1535	219	6	and	and	CCONJ
ejpam-1535	219	7	suppose	suppose	VERB
ejpam-1535	219	8	that	that	SCONJ
ejpam-1535	219	9	s	s	VERB
ejpam-1535	219	10	has	have	VERB
ejpam-1535	219	11	some	some	DET
ejpam-1535	219	12	distinguished	distinguished	ADJ
ejpam-1535	219	13	subsemilattice	subsemilattice	NOUN
ejpam-1535	219	14	of	of	ADP
ejpam-1535	219	15	idempotents	idempotent	NOUN
ejpam-1535	219	16	e	e	PROPN
ejpam-1535	219	17	⊆	⊆	NUM
ejpam-1535	219	18	e(s	e(s	PROPN
ejpam-1535	219	19	)	)	PUNCT
ejpam-1535	219	20	,	,	PUNCT
ejpam-1535	219	21	where	where	SCONJ
ejpam-1535	219	22	,	,	PUNCT
ejpam-1535	219	23	as	as	ADP
ejpam-1535	219	24	usual	usual	ADJ
ejpam-1535	219	25	,	,	PUNCT
ejpam-1535	219	26	e(s	e(s	NUM
ejpam-1535	219	27	)	)	PUNCT
ejpam-1535	219	28	denotes	denote	VERB
ejpam-1535	219	29	the	the	DET
ejpam-1535	219	30	subset	subset	NOUN
ejpam-1535	219	31	of	of	ADP
ejpam-1535	219	32	idempotents	idempotent	NOUN
ejpam-1535	219	33	of	of	ADP
ejpam-1535	219	34	a	a	DET
ejpam-1535	219	35	semigroup	semigroup	PROPN
ejpam-1535	219	36	s.	s.	PROPN
ejpam-1535	219	37	we	we	PRON
ejpam-1535	219	38	define	define	VERB
ejpam-1535	219	39	two	two	NUM
ejpam-1535	219	40	(	(	PUNCT
ejpam-1535	219	41	equivalence	equivalence	NOUN
ejpam-1535	219	42	)	)	PUNCT
ejpam-1535	219	43	relations	relation	NOUN
ejpam-1535	219	44	in	in	ADP
ejpam-1535	219	45	s	s	PRON
ejpam-1535	219	46	with	with	ADP
ejpam-1535	219	47	respect	respect	NOUN
ejpam-1535	219	48	to	to	ADP
ejpam-1535	219	49	e	e	NOUN
ejpam-1535	219	50	:	:	PUNCT
ejpam-1535	219	51	a	a	DET
ejpam-1535	219	52	ere	ere	PROPN
ejpam-1535	219	53	b	b	PROPN
ejpam-1535	219	54	⇐	⇐	PROPN
ejpam-1535	220	1	⇒∀e	⇒∀e	PROPN
ejpam-1535	220	2	∈	∈	PROPN
ejpam-1535	220	3	e	e	X
ejpam-1535	221	1	[	[	X
ejpam-1535	221	2	ea	ea	X
ejpam-1535	221	3	=	=	PUNCT
ejpam-1535	221	4	a⇔	a⇔	PROPN
ejpam-1535	221	5	eb	eb	PROPN
ejpam-1535	221	6	=	=	SYM
ejpam-1535	221	7	b	b	PROPN
ejpam-1535	221	8	]	]	X
ejpam-1535	221	9	;	;	PUNCT
ejpam-1535	221	10	a	a	DET
ejpam-1535	221	11	fle	fle	NOUN
ejpam-1535	221	12	b	b	SYM
ejpam-1535	221	13	⇐	⇐	PROPN
ejpam-1535	221	14	⇒∀e	⇒∀e	PROPN
ejpam-1535	221	15	∈	∈	PROPN
ejpam-1535	221	16	e	e	X
ejpam-1535	222	1	[	[	X
ejpam-1535	222	2	ae	ae	X
ejpam-1535	222	3	=	=	PUNCT
ejpam-1535	222	4	a⇔	a⇔	NOUN
ejpam-1535	222	5	be	be	AUX
ejpam-1535	222	6	=	=	ADJ
ejpam-1535	222	7	b	b	NOUN
ejpam-1535	222	8	]	]	PUNCT
ejpam-1535	222	9	.	.	PUNCT
ejpam-1535	223	1	thus	thus	ADV
ejpam-1535	223	2	,	,	PUNCT
ejpam-1535	223	3	two	two	NUM
ejpam-1535	223	4	elements	element	NOUN
ejpam-1535	223	5	of	of	ADP
ejpam-1535	223	6	s	s	NOUN
ejpam-1535	223	7	are	be	AUX
ejpam-1535	223	8	ere	ere	PROPN
ejpam-1535	223	9	(	(	PUNCT
ejpam-1535	223	10	fle-)related	fle-)relate	VERB
ejpam-1535	223	11	if	if	SCONJ
ejpam-1535	223	12	and	and	CCONJ
ejpam-1535	223	13	only	only	ADV
ejpam-1535	223	14	if	if	SCONJ
ejpam-1535	223	15	they	they	PRON
ejpam-1535	223	16	have	have	VERB
ejpam-1535	223	17	the	the	DET
ejpam-1535	223	18	same	same	ADJ
ejpam-1535	223	19	left	left	NOUN
ejpam-1535	223	20	(	(	PUNCT
ejpam-1535	223	21	right	right	ADJ
ejpam-1535	223	22	)	)	PUNCT
ejpam-1535	223	23	identities	identity	NOUN
ejpam-1535	223	24	in	in	ADP
ejpam-1535	223	25	e.	e.	PROPN
ejpam-1535	223	26	in	in	ADP
ejpam-1535	223	27	the	the	DET
ejpam-1535	223	28	case	case	NOUN
ejpam-1535	223	29	where	where	SCONJ
ejpam-1535	223	30	e	e	NOUN
ejpam-1535	223	31	=	=	SYM
ejpam-1535	223	32	e(s	e(s	PROPN
ejpam-1535	223	33	)	)	PUNCT
ejpam-1535	223	34	,	,	PUNCT
ejpam-1535	223	35	we	we	PRON
ejpam-1535	223	36	omit	omit	VERB
ejpam-1535	223	37	the	the	DET
ejpam-1535	223	38	subscripts	subscript	NOUN
ejpam-1535	223	39	from	from	ADP
ejpam-1535	223	40	the	the	DET
ejpam-1535	223	41	relations	relation	NOUN
ejpam-1535	223	42	and	and	CCONJ
ejpam-1535	223	43	write	write	VERB
ejpam-1535	223	44	er	er	INTJ
ejpam-1535	223	45	for	for	ADP
ejpam-1535	223	46	ere(s	ere(s	PROPN
ejpam-1535	223	47	)	)	PUNCT
ejpam-1535	223	48	and	and	CCONJ
ejpam-1535	223	49	fl	fl	PROPN
ejpam-1535	223	50	for	for	ADP
ejpam-1535	223	51	fle(s	fle(s	PROPN
ejpam-1535	223	52	)	)	PUNCT
ejpam-1535	223	53	.	.	PUNCT
ejpam-1535	224	1	as	as	SCONJ
ejpam-1535	224	2	the	the	DET
ejpam-1535	224	3	notation	notation	NOUN
ejpam-1535	224	4	suggests	suggest	VERB
ejpam-1535	224	5	,	,	PUNCT
ejpam-1535	224	6	ere	ere	PROPN
ejpam-1535	224	7	and	and	CCONJ
ejpam-1535	224	8	fle	fle	NOUN
ejpam-1535	224	9	are	be	AUX
ejpam-1535	224	10	generalisations	generalisation	NOUN
ejpam-1535	224	11	of	of	ADP
ejpam-1535	224	12	green	green	PROPN
ejpam-1535	224	13	’s	’s	PART
ejpam-1535	224	14	relations	relation	NOUN
ejpam-1535	224	15	r	r	NOUN
ejpam-1535	224	16	and	and	CCONJ
ejpam-1535	224	17	l	l	NOUN
ejpam-1535	224	18	in	in	ADP
ejpam-1535	224	19	the	the	DET
ejpam-1535	224	20	sense	sense	NOUN
ejpam-1535	224	21	that	that	SCONJ
ejpam-1535	224	22	,	,	PUNCT
ejpam-1535	224	23	for	for	ADP
ejpam-1535	224	24	any	any	DET
ejpam-1535	224	25	e	e	NOUN
ejpam-1535	224	26	⊆	⊆	NUM
ejpam-1535	224	27	e(s	e(s	PROPN
ejpam-1535	224	28	)	)	PUNCT
ejpam-1535	224	29	,	,	PUNCT
ejpam-1535	224	30	r	r	NOUN
ejpam-1535	224	31	⊆	⊆	NUM
ejpam-1535	224	32	er	er	INTJ
ejpam-1535	224	33	⊆	⊆	NUM
ejpam-1535	224	34	ere	ere	NOUN
ejpam-1535	224	35	and	and	CCONJ
ejpam-1535	224	36	l	l	NOUN
ejpam-1535	224	37	⊆	⊆	NUM
ejpam-1535	224	38	fl	fl	NUM
ejpam-1535	224	39	⊆	⊆	NUM
ejpam-1535	224	40	fle	fle	NOUN
ejpam-1535	224	41	.	.	PUNCT
ejpam-1535	225	1	it	it	PRON
ejpam-1535	225	2	is	be	AUX
ejpam-1535	225	3	useful	useful	ADJ
ejpam-1535	225	4	to	to	PART
ejpam-1535	225	5	note	note	VERB
ejpam-1535	225	6	the	the	DET
ejpam-1535	225	7	following	follow	VERB
ejpam-1535	225	8	conditions	condition	NOUN
ejpam-1535	225	9	,	,	PUNCT
ejpam-1535	225	10	derived	derive	VERB
ejpam-1535	225	11	from	from	ADP
ejpam-1535	225	12	the	the	DET
ejpam-1535	225	13	above	above	NOUN
ejpam-1535	225	14	,	,	PUNCT
ejpam-1535	225	15	for	for	ADP
ejpam-1535	225	16	an	an	DET
ejpam-1535	225	17	element	element	NOUN
ejpam-1535	225	18	a	a	DET
ejpam-1535	225	19	∈	∈	NOUN
ejpam-1535	225	20	s	s	VERB
ejpam-1535	225	21	to	to	PART
ejpam-1535	225	22	be	be	AUX
ejpam-1535	225	23	ereor	ereor	NOUN
ejpam-1535	225	24	fle	fle	ADV
ejpam-1535	225	25	-	-	PUNCT
ejpam-1535	225	26	related	relate	VERB
ejpam-1535	225	27	to	to	ADP
ejpam-1535	225	28	an	an	DET
ejpam-1535	225	29	idempotent	idempotent	NOUN
ejpam-1535	225	30	e	e	NOUN
ejpam-1535	225	31	∈	∈	PROPN
ejpam-1535	225	32	e	e	NOUN
ejpam-1535	225	33	:	:	PUNCT
ejpam-1535	225	34	a	a	DET
ejpam-1535	225	35	ere	ere	PROPN
ejpam-1535	225	36	e	e	NOUN
ejpam-1535	225	37	⇐	⇐	ADJ
ejpam-1535	225	38	⇒	⇒	NOUN
ejpam-1535	225	39	ea	ea	PUNCT
ejpam-1535	226	1	=	=	PUNCT
ejpam-1535	226	2	a	a	PRON
ejpam-1535	226	3	and	and	CCONJ
ejpam-1535	226	4	∀	∀	PUNCT
ejpam-1535	227	1	f	f	NOUN
ejpam-1535	227	2	∈	∈	PROPN
ejpam-1535	227	3	e	e	X
ejpam-1535	227	4	�	�	PROPN
ejpam-1535	227	5	f	f	PROPN
ejpam-1535	227	6	a	a	PROPN
ejpam-1535	227	7	=	=	X
ejpam-1535	227	8	a⇒	a⇒	PROPN
ejpam-1535	227	9	f	f	X
ejpam-1535	227	10	e	e	PROPN
ejpam-1535	227	11	=	=	SYM
ejpam-1535	227	12	e	e	X
ejpam-1535	227	13	�	�	PROPN
ejpam-1535	227	14	;	;	PUNCT
ejpam-1535	227	15	a	a	DET
ejpam-1535	227	16	fle	fle	NOUN
ejpam-1535	227	17	e	e	X
ejpam-1535	227	18	⇐	⇐	ADJ
ejpam-1535	227	19	⇒	⇒	NOUN
ejpam-1535	227	20	ae	ae	PROPN
ejpam-1535	227	21	=	=	PUNCT
ejpam-1535	227	22	a	a	PROPN
ejpam-1535	227	23	and	and	CCONJ
ejpam-1535	227	24	∀	∀	PUNCT
ejpam-1535	227	25	f	f	NOUN
ejpam-1535	227	26	∈	∈	PROPN
ejpam-1535	227	27	e	e	X
ejpam-1535	227	28	�	�	PROPN
ejpam-1535	227	29	a	a	DET
ejpam-1535	227	30	f	f	X
ejpam-1535	227	31	=	=	PUNCT
ejpam-1535	227	32	a⇒	a⇒	PROPN
ejpam-1535	228	1	e	e	X
ejpam-1535	228	2	f	f	PROPN
ejpam-1535	228	3	=	=	SYM
ejpam-1535	228	4	e	e	X
ejpam-1535	228	5	�	�	PROPN
ejpam-1535	228	6	.	.	PUNCT
ejpam-1535	229	1	without	without	ADP
ejpam-1535	229	2	giving	give	VERB
ejpam-1535	229	3	any	any	DET
ejpam-1535	229	4	justification	justification	NOUN
ejpam-1535	229	5	,	,	PUNCT
ejpam-1535	229	6	we	we	PRON
ejpam-1535	229	7	define	define	VERB
ejpam-1535	229	8	left	left	ADJ
ejpam-1535	229	9	and	and	CCONJ
ejpam-1535	229	10	right	right	ADJ
ejpam-1535	229	11	restriction	restriction	NOUN
ejpam-1535	229	12	semigroups	semigroup	NOUN
ejpam-1535	229	13	in	in	ADP
ejpam-1535	229	14	terms	term	NOUN
ejpam-1535	229	15	of	of	ADP
ejpam-1535	229	16	ere	ere	NOUN
ejpam-1535	229	17	and	and	CCONJ
ejpam-1535	229	18	fle	fle	NOUN
ejpam-1535	229	19	,	,	PUNCT
ejpam-1535	229	20	respectively	respectively	ADV
ejpam-1535	229	21	:	:	PUNCT
ejpam-1535	229	22	c.	c.	PROPN
ejpam-1535	229	23	hollings	holling	NOUN
ejpam-1535	229	24	/	/	SYM
ejpam-1535	229	25	eur	eur	PROPN
ejpam-1535	229	26	.	.	PUNCT
ejpam-1535	230	1	j.	j.	PROPN
ejpam-1535	230	2	pure	pure	PROPN
ejpam-1535	230	3	appl	appl	PROPN
ejpam-1535	230	4	.	.	PROPN
ejpam-1535	230	5	math	math	PROPN
ejpam-1535	230	6	,	,	PUNCT
ejpam-1535	230	7	5	5	NUM
ejpam-1535	230	8	(	(	PUNCT
ejpam-1535	230	9	2012	2012	NUM
ejpam-1535	230	10	)	)	PUNCT
ejpam-1535	230	11	,	,	PUNCT
ejpam-1535	230	12	414	414	NUM
ejpam-1535	230	13	-	-	SYM
ejpam-1535	230	14	450	450	NUM
ejpam-1535	230	15	424	424	NUM
ejpam-1535	230	16	definition	definition	NOUN
ejpam-1535	230	17	2	2	NUM
ejpam-1535	230	18	.	.	PUNCT
ejpam-1535	231	1	let	let	VERB
ejpam-1535	231	2	s	s	PRON
ejpam-1535	231	3	be	be	AUX
ejpam-1535	231	4	a	a	DET
ejpam-1535	231	5	semigroup	semigroup	NOUN
ejpam-1535	231	6	with	with	ADP
ejpam-1535	231	7	distinguished	distinguished	ADJ
ejpam-1535	231	8	subsemilattice	subsemilattice	NOUN
ejpam-1535	231	9	of	of	ADP
ejpam-1535	231	10	idempotents	idempotent	NOUN
ejpam-1535	231	11	e	e	PROPN
ejpam-1535	231	12	⊆	⊆	NUM
ejpam-1535	231	13	e(s	e(s	PROPN
ejpam-1535	231	14	)	)	PUNCT
ejpam-1535	231	15	.	.	PUNCT
ejpam-1535	232	1	we	we	PRON
ejpam-1535	232	2	call	call	VERB
ejpam-1535	232	3	s	s	PRON
ejpam-1535	232	4	a	a	DET
ejpam-1535	232	5	left	left	ADJ
ejpam-1535	232	6	restriction	restriction	NOUN
ejpam-1535	232	7	semigroup	semigroup	NOUN
ejpam-1535	232	8	(	(	PUNCT
ejpam-1535	232	9	with	with	ADP
ejpam-1535	232	10	respect	respect	NOUN
ejpam-1535	232	11	to	to	ADP
ejpam-1535	232	12	e	e	NOUN
ejpam-1535	232	13	)	)	PUNCT
ejpam-1535	232	14	if	if	SCONJ
ejpam-1535	232	15	(	(	PUNCT
ejpam-1535	232	16	1	1	X
ejpam-1535	232	17	)	)	PUNCT
ejpam-1535	232	18	every	every	DET
ejpam-1535	232	19	element	element	NOUN
ejpam-1535	232	20	a	a	DET
ejpam-1535	232	21	∈	∈	NOUN
ejpam-1535	232	22	s	s	NOUN
ejpam-1535	232	23	is	be	AUX
ejpam-1535	232	24	ere	ere	NOUN
ejpam-1535	232	25	-	-	PUNCT
ejpam-1535	232	26	related	relate	VERB
ejpam-1535	232	27	to	to	ADP
ejpam-1535	232	28	a	a	DET
ejpam-1535	232	29	(	(	PUNCT
ejpam-1535	232	30	necessarily	necessarily	ADV
ejpam-1535	232	31	unique	unique	ADJ
ejpam-1535	232	32	)	)	PUNCT
ejpam-1535	232	33	element	element	NOUN
ejpam-1535	232	34	of	of	ADP
ejpam-1535	232	35	e	e	NOUN
ejpam-1535	232	36	,	,	PUNCT
ejpam-1535	232	37	which	which	PRON
ejpam-1535	232	38	we	we	PRON
ejpam-1535	232	39	denote	denote	VERB
ejpam-1535	232	40	by	by	ADP
ejpam-1535	232	41	a+	a+	NOUN
ejpam-1535	232	42	;	;	PUNCT
ejpam-1535	232	43	(	(	PUNCT
ejpam-1535	232	44	2	2	X
ejpam-1535	232	45	)	)	PUNCT
ejpam-1535	232	46	ere	ere	NOUN
ejpam-1535	232	47	is	be	AUX
ejpam-1535	232	48	a	a	DET
ejpam-1535	232	49	left	left	ADJ
ejpam-1535	232	50	congruence	congruence	NOUN
ejpam-1535	232	51	;	;	PUNCT
ejpam-1535	232	52	(	(	PUNCT
ejpam-1535	232	53	3	3	X
ejpam-1535	232	54	)	)	PUNCT
ejpam-1535	232	55	for	for	ADP
ejpam-1535	232	56	all	all	DET
ejpam-1535	232	57	a	a	DET
ejpam-1535	232	58	∈	∈	NOUN
ejpam-1535	232	59	s	s	PART
ejpam-1535	232	60	and	and	CCONJ
ejpam-1535	232	61	all	all	DET
ejpam-1535	232	62	e	e	X
ejpam-1535	232	63	∈	∈	PROPN
ejpam-1535	232	64	e	e	NOUN
ejpam-1535	232	65	,	,	PUNCT
ejpam-1535	232	66	ae	ae	PROPN
ejpam-1535	232	67	=	=	PUNCT
ejpam-1535	232	68	(	(	PUNCT
ejpam-1535	232	69	ae)+a	ae)+a	NOUN
ejpam-1535	232	70	.	.	PUNCT
ejpam-1535	233	1	if	if	SCONJ
ejpam-1535	233	2	e	e	PROPN
ejpam-1535	233	3	=	=	SYM
ejpam-1535	233	4	e(s	e(s	PROPN
ejpam-1535	233	5	)	)	PUNCT
ejpam-1535	233	6	,	,	PUNCT
ejpam-1535	233	7	we	we	PRON
ejpam-1535	233	8	term	term	VERB
ejpam-1535	233	9	s	s	VERB
ejpam-1535	233	10	a	a	DET
ejpam-1535	233	11	full	full	ADJ
ejpam-1535	233	12	left	left	NOUN
ejpam-1535	233	13	restriction	restriction	NOUN
ejpam-1535	233	14	semigroup	semigroup	NOUN
ejpam-1535	233	15	.	.	PUNCT
ejpam-1535	234	1	definition	definition	NOUN
ejpam-1535	234	2	3	3	NUM
ejpam-1535	234	3	.	.	PUNCT
ejpam-1535	235	1	let	let	VERB
ejpam-1535	235	2	s	s	PRON
ejpam-1535	235	3	be	be	AUX
ejpam-1535	235	4	a	a	DET
ejpam-1535	235	5	semigroup	semigroup	NOUN
ejpam-1535	235	6	with	with	ADP
ejpam-1535	235	7	distinguished	distinguished	ADJ
ejpam-1535	235	8	subsemilattice	subsemilattice	NOUN
ejpam-1535	235	9	of	of	ADP
ejpam-1535	235	10	idempotents	idempotent	NOUN
ejpam-1535	235	11	e	e	PROPN
ejpam-1535	235	12	⊆	⊆	NUM
ejpam-1535	235	13	e(s	e(s	PROPN
ejpam-1535	235	14	)	)	PUNCT
ejpam-1535	235	15	.	.	PUNCT
ejpam-1535	236	1	we	we	PRON
ejpam-1535	236	2	call	call	VERB
ejpam-1535	236	3	s	s	PRON
ejpam-1535	236	4	a	a	DET
ejpam-1535	236	5	right	right	ADJ
ejpam-1535	236	6	restriction	restriction	NOUN
ejpam-1535	236	7	semigroup	semigroup	NOUN
ejpam-1535	236	8	(	(	PUNCT
ejpam-1535	236	9	with	with	ADP
ejpam-1535	236	10	respect	respect	NOUN
ejpam-1535	236	11	to	to	ADP
ejpam-1535	236	12	e	e	NOUN
ejpam-1535	236	13	)	)	PUNCT
ejpam-1535	236	14	if	if	SCONJ
ejpam-1535	236	15	(	(	PUNCT
ejpam-1535	236	16	1	1	X
ejpam-1535	236	17	)	)	PUNCT
ejpam-1535	236	18	every	every	DET
ejpam-1535	236	19	element	element	NOUN
ejpam-1535	236	20	a	a	DET
ejpam-1535	236	21	∈	∈	NOUN
ejpam-1535	236	22	s	s	VERB
ejpam-1535	236	23	is	be	AUX
ejpam-1535	236	24	fle	fle	NOUN
ejpam-1535	236	25	-	-	PUNCT
ejpam-1535	236	26	related	relate	VERB
ejpam-1535	236	27	to	to	ADP
ejpam-1535	236	28	a	a	DET
ejpam-1535	236	29	(	(	PUNCT
ejpam-1535	236	30	necessarily	necessarily	ADV
ejpam-1535	236	31	unique	unique	ADJ
ejpam-1535	236	32	)	)	PUNCT
ejpam-1535	236	33	element	element	NOUN
ejpam-1535	236	34	of	of	ADP
ejpam-1535	236	35	e	e	NOUN
ejpam-1535	236	36	,	,	PUNCT
ejpam-1535	236	37	which	which	PRON
ejpam-1535	236	38	we	we	PRON
ejpam-1535	236	39	denote	denote	VERB
ejpam-1535	236	40	by	by	ADP
ejpam-1535	236	41	a∗	a∗	PROPN
ejpam-1535	236	42	;	;	PUNCT
ejpam-1535	236	43	(	(	PUNCT
ejpam-1535	236	44	2	2	X
ejpam-1535	236	45	)	)	PUNCT
ejpam-1535	236	46	fle	fle	NOUN
ejpam-1535	236	47	is	be	AUX
ejpam-1535	236	48	a	a	DET
ejpam-1535	236	49	left	left	ADJ
ejpam-1535	236	50	congruence	congruence	NOUN
ejpam-1535	236	51	;	;	PUNCT
ejpam-1535	236	52	(	(	PUNCT
ejpam-1535	236	53	3	3	X
ejpam-1535	236	54	)	)	PUNCT
ejpam-1535	236	55	for	for	ADP
ejpam-1535	236	56	all	all	DET
ejpam-1535	236	57	a	a	DET
ejpam-1535	236	58	∈	∈	NOUN
ejpam-1535	236	59	s	s	PART
ejpam-1535	236	60	and	and	CCONJ
ejpam-1535	236	61	all	all	DET
ejpam-1535	236	62	e	e	X
ejpam-1535	236	63	∈	∈	PROPN
ejpam-1535	236	64	e	e	NOUN
ejpam-1535	236	65	,	,	PUNCT
ejpam-1535	236	66	ea	ea	X
ejpam-1535	236	67	=	=	SYM
ejpam-1535	236	68	a(ea)∗.	a(ea)∗.	PROPN
ejpam-1535	236	69	if	if	SCONJ
ejpam-1535	236	70	e	e	NOUN
ejpam-1535	236	71	=	=	SYM
ejpam-1535	236	72	e(s	e(s	PROPN
ejpam-1535	236	73	)	)	PUNCT
ejpam-1535	236	74	,	,	PUNCT
ejpam-1535	236	75	we	we	PRON
ejpam-1535	236	76	term	term	VERB
ejpam-1535	236	77	s	s	VERB
ejpam-1535	236	78	a	a	DET
ejpam-1535	236	79	full	full	ADJ
ejpam-1535	236	80	right	right	ADJ
ejpam-1535	236	81	restriction	restriction	NOUN
ejpam-1535	236	82	semigroup	semigroup	NOUN
ejpam-1535	236	83	.	.	PUNCT
ejpam-1535	237	1	as	as	SCONJ
ejpam-1535	237	2	might	might	AUX
ejpam-1535	237	3	be	be	AUX
ejpam-1535	237	4	expected	expect	VERB
ejpam-1535	237	5	,	,	PUNCT
ejpam-1535	237	6	we	we	PRON
ejpam-1535	237	7	obtain	obtain	VERB
ejpam-1535	237	8	a	a	DET
ejpam-1535	237	9	(	(	PUNCT
ejpam-1535	237	10	two	two	NUM
ejpam-1535	237	11	-	-	PUNCT
ejpam-1535	237	12	sided	sided	ADJ
ejpam-1535	237	13	)	)	PUNCT
ejpam-1535	237	14	restriction	restriction	NOUN
ejpam-1535	237	15	semigroup	semigroup	NOUN
ejpam-1535	237	16	by	by	ADP
ejpam-1535	237	17	combining	combine	VERB
ejpam-1535	237	18	the	the	DET
ejpam-1535	237	19	preceding	precede	VERB
ejpam-1535	237	20	two	two	NUM
ejpam-1535	237	21	definitions	definition	NOUN
ejpam-1535	237	22	:	:	PUNCT
ejpam-1535	237	23	definition	definition	NOUN
ejpam-1535	237	24	4	4	NUM
ejpam-1535	237	25	.	.	PUNCT
ejpam-1535	238	1	let	let	VERB
ejpam-1535	238	2	s	s	PRON
ejpam-1535	238	3	be	be	AUX
ejpam-1535	238	4	a	a	DET
ejpam-1535	238	5	semigroup	semigroup	NOUN
ejpam-1535	238	6	with	with	ADP
ejpam-1535	238	7	distinguished	distinguished	ADJ
ejpam-1535	238	8	subsemilattice	subsemilattice	NOUN
ejpam-1535	238	9	of	of	ADP
ejpam-1535	238	10	idempotents	idempotent	NOUN
ejpam-1535	238	11	e	e	PROPN
ejpam-1535	238	12	⊆	⊆	NUM
ejpam-1535	238	13	e(s	e(s	PROPN
ejpam-1535	238	14	)	)	PUNCT
ejpam-1535	238	15	.	.	PUNCT
ejpam-1535	239	1	we	we	PRON
ejpam-1535	239	2	call	call	VERB
ejpam-1535	239	3	s	s	PRON
ejpam-1535	239	4	a	a	DET
ejpam-1535	239	5	(	(	PUNCT
ejpam-1535	239	6	two	two	NUM
ejpam-1535	239	7	-	-	PUNCT
ejpam-1535	239	8	sided	sided	ADJ
ejpam-1535	239	9	)	)	PUNCT
ejpam-1535	239	10	restriction	restriction	NOUN
ejpam-1535	239	11	semigroup	semigroup	NOUN
ejpam-1535	239	12	(	(	PUNCT
ejpam-1535	239	13	with	with	ADP
ejpam-1535	239	14	respect	respect	NOUN
ejpam-1535	239	15	to	to	ADP
ejpam-1535	239	16	e	e	NOUN
ejpam-1535	239	17	)	)	PUNCT
ejpam-1535	239	18	if	if	SCONJ
ejpam-1535	239	19	it	it	PRON
ejpam-1535	239	20	is	be	AUX
ejpam-1535	239	21	both	both	CCONJ
ejpam-1535	239	22	a	a	DET
ejpam-1535	239	23	left	left	ADJ
ejpam-1535	239	24	restriction	restriction	NOUN
ejpam-1535	239	25	semigroup	semigroup	NOUN
ejpam-1535	239	26	with	with	ADP
ejpam-1535	239	27	respect	respect	NOUN
ejpam-1535	239	28	to	to	ADP
ejpam-1535	239	29	e	e	NOUN
ejpam-1535	239	30	and	and	CCONJ
ejpam-1535	239	31	a	a	DET
ejpam-1535	239	32	right	right	ADJ
ejpam-1535	239	33	restriction	restriction	NOUN
ejpam-1535	239	34	semigroup	semigroup	NOUN
ejpam-1535	239	35	with	with	ADP
ejpam-1535	239	36	respect	respect	NOUN
ejpam-1535	239	37	to	to	ADP
ejpam-1535	239	38	e.	e.	PROPN
ejpam-1535	239	39	note	note	VERB
ejpam-1535	239	40	that	that	SCONJ
ejpam-1535	239	41	e+	e+	ADP
ejpam-1535	239	42	=	=	SYM
ejpam-1535	239	43	e∗	e∗	NOUN
ejpam-1535	239	44	=	=	SYM
ejpam-1535	239	45	e	e	NOUN
ejpam-1535	239	46	,	,	PUNCT
ejpam-1535	239	47	for	for	ADP
ejpam-1535	239	48	any	any	DET
ejpam-1535	239	49	e	e	PROPN
ejpam-1535	239	50	∈	∈	PROPN
ejpam-1535	239	51	e.	e.	PROPN
ejpam-1535	239	52	we	we	PRON
ejpam-1535	239	53	observe	observe	VERB
ejpam-1535	239	54	also	also	ADV
ejpam-1535	239	55	that	that	SCONJ
ejpam-1535	239	56	any	any	DET
ejpam-1535	239	57	inverse	inverse	NOUN
ejpam-1535	239	58	semigroup	semigroup	NOUN
ejpam-1535	239	59	is	be	AUX
ejpam-1535	239	60	a	a	DET
ejpam-1535	239	61	left	left	ADJ
ejpam-1535	239	62	/	/	SYM
ejpam-1535	239	63	right	right	ADJ
ejpam-1535	239	64	/	/	SYM
ejpam-1535	239	65	two	two	NUM
ejpam-1535	239	66	-	-	PUNCT
ejpam-1535	239	67	sided	side	VERB
ejpam-1535	239	68	restriction	restriction	NOUN
ejpam-1535	239	69	semigroup	semigroup	NOUN
ejpam-1535	239	70	with	with	ADP
ejpam-1535	239	71	respect	respect	NOUN
ejpam-1535	239	72	to	to	ADP
ejpam-1535	239	73	e(s	e(s	PROPN
ejpam-1535	239	74	)	)	PUNCT
ejpam-1535	239	75	,	,	PUNCT
ejpam-1535	239	76	with	with	ADP
ejpam-1535	239	77	a+	a+	PUNCT
ejpam-1535	239	78	=	=	SYM
ejpam-1535	239	79	aa−1	aa−1	PROPN
ejpam-1535	239	80	and	and	CCONJ
ejpam-1535	239	81	a∗	a∗	PROPN
ejpam-1535	239	82	=	=	SYM
ejpam-1535	239	83	a−1a	a−1a	PROPN
ejpam-1535	239	84	;	;	PUNCT
ejpam-1535	239	85	thus	thus	ADV
ejpam-1535	239	86	,	,	PUNCT
ejpam-1535	239	87	in	in	ADP
ejpam-1535	239	88	an	an	DET
ejpam-1535	239	89	inverse	inverse	NOUN
ejpam-1535	239	90	semigroup	semigroup	NOUN
ejpam-1535	239	91	,	,	PUNCT
ejpam-1535	239	92	er	er	INTJ
ejpam-1535	239	93	=	=	NOUN
ejpam-1535	239	94	r	r	NOUN
ejpam-1535	239	95	and	and	CCONJ
ejpam-1535	239	96	fl	fl	NOUN
ejpam-1535	239	97	=	=	NOUN
ejpam-1535	239	98	l	l	NOUN
ejpam-1535	239	99	.	.	PUNCT
ejpam-1535	240	1	it	it	PRON
ejpam-1535	240	2	should	should	AUX
ejpam-1535	240	3	be	be	AUX
ejpam-1535	240	4	noted	note	VERB
ejpam-1535	240	5	that	that	SCONJ
ejpam-1535	240	6	left	leave	VERB
ejpam-1535	240	7	restriction	restriction	NOUN
ejpam-1535	240	8	semigroups	semigroup	NOUN
ejpam-1535	240	9	form	form	VERB
ejpam-1535	240	10	a	a	DET
ejpam-1535	240	11	variety	variety	NOUN
ejpam-1535	240	12	of	of	ADP
ejpam-1535	240	13	algebras	algebra	NOUN
ejpam-1535	240	14	of	of	ADP
ejpam-1535	240	15	type	type	NOUN
ejpam-1535	240	16	(	(	PUNCT
ejpam-1535	240	17	2,1	2,1	NUM
ejpam-1535	240	18	)	)	PUNCT
ejpam-1535	240	19	,	,	PUNCT
ejpam-1535	240	20	as	as	SCONJ
ejpam-1535	240	21	do	do	VERB
ejpam-1535	240	22	right	right	ADJ
ejpam-1535	240	23	restriction	restriction	NOUN
ejpam-1535	240	24	semigroups	semigroup	NOUN
ejpam-1535	240	25	;	;	PUNCT
ejpam-1535	240	26	two	two	NUM
ejpam-1535	240	27	-	-	PUNCT
ejpam-1535	240	28	sided	side	VERB
ejpam-1535	240	29	restriction	restriction	NOUN
ejpam-1535	240	30	semigroups	semigroup	NOUN
ejpam-1535	240	31	form	form	VERB
ejpam-1535	240	32	a	a	DET
ejpam-1535	240	33	variety	variety	NOUN
ejpam-1535	240	34	of	of	ADP
ejpam-1535	240	35	algebras	algebra	NOUN
ejpam-1535	240	36	of	of	ADP
ejpam-1535	240	37	type	type	NOUN
ejpam-1535	240	38	(	(	PUNCT
ejpam-1535	240	39	2,1,1	2,1,1	NUM
ejpam-1535	240	40	)	)	PUNCT
ejpam-1535	240	41	.	.	PUNCT
ejpam-1535	241	1	in	in	ADP
ejpam-1535	241	2	all	all	DET
ejpam-1535	241	3	three	three	NUM
ejpam-1535	241	4	cases	case	NOUN
ejpam-1535	241	5	,	,	PUNCT
ejpam-1535	241	6	the	the	DET
ejpam-1535	241	7	“	"	PUNCT
ejpam-1535	241	8	full	full	ADJ
ejpam-1535	241	9	”	"	PUNCT
ejpam-1535	241	10	versions	version	NOUN
ejpam-1535	241	11	form	form	VERB
ejpam-1535	241	12	only	only	ADV
ejpam-1535	241	13	quasi	quasi	NOUN
ejpam-1535	241	14	-	-	NOUN
ejpam-1535	241	15	varieties	variety	NOUN
ejpam-1535	241	16	.	.	PUNCT
ejpam-1535	242	1	the	the	DET
ejpam-1535	242	2	“	"	PUNCT
ejpam-1535	242	3	varieties	variety	NOUN
ejpam-1535	242	4	”	"	PUNCT
ejpam-1535	242	5	standpoint	standpoint	NOUN
ejpam-1535	242	6	has	have	AUX
ejpam-1535	242	7	become	become	VERB
ejpam-1535	242	8	an	an	DET
ejpam-1535	242	9	extremely	extremely	ADV
ejpam-1535	242	10	useful	useful	ADJ
ejpam-1535	242	11	way	way	NOUN
ejpam-1535	242	12	of	of	ADP
ejpam-1535	242	13	viewing	view	VERB
ejpam-1535	242	14	these	these	DET
ejpam-1535	242	15	semigroups	semigroup	NOUN
ejpam-1535	242	16	,	,	PUNCT
ejpam-1535	242	17	but	but	CCONJ
ejpam-1535	242	18	we	we	PRON
ejpam-1535	242	19	will	will	AUX
ejpam-1535	242	20	have	have	VERB
ejpam-1535	242	21	no	no	DET
ejpam-1535	242	22	occasion	occasion	NOUN
ejpam-1535	242	23	to	to	PART
ejpam-1535	242	24	adopt	adopt	VERB
ejpam-1535	242	25	this	this	DET
ejpam-1535	242	26	view	view	NOUN
ejpam-1535	242	27	here	here	ADV
ejpam-1535	242	28	—	—	PUNCT
ejpam-1535	242	29	the	the	DET
ejpam-1535	242	30	interested	interested	ADJ
ejpam-1535	242	31	reader	reader	NOUN
ejpam-1535	242	32	is	be	AUX
ejpam-1535	242	33	directed	direct	VERB
ejpam-1535	242	34	to	to	ADP
ejpam-1535	242	35	[	[	X
ejpam-1535	242	36	15	15	NUM
ejpam-1535	242	37	]	]	PUNCT
ejpam-1535	242	38	.	.	PUNCT
ejpam-1535	243	1	for	for	ADP
ejpam-1535	243	2	the	the	DET
ejpam-1535	243	3	rest	rest	NOUN
ejpam-1535	243	4	of	of	ADP
ejpam-1535	243	5	this	this	DET
ejpam-1535	243	6	article	article	NOUN
ejpam-1535	243	7	,	,	PUNCT
ejpam-1535	243	8	the	the	DET
ejpam-1535	243	9	distinguished	distinguished	ADJ
ejpam-1535	243	10	subsemilattice	subsemilattice	NOUN
ejpam-1535	243	11	of	of	ADP
ejpam-1535	243	12	a	a	DET
ejpam-1535	243	13	given	give	VERB
ejpam-1535	243	14	restriction	restriction	NOUN
ejpam-1535	243	15	semigroup	semigroup	NOUN
ejpam-1535	243	16	s	s	PART
ejpam-1535	243	17	will	will	AUX
ejpam-1535	243	18	be	be	AUX
ejpam-1535	243	19	denoted	denote	VERB
ejpam-1535	243	20	by	by	ADP
ejpam-1535	243	21	e	e	NOUN
ejpam-1535	243	22	,	,	PUNCT
ejpam-1535	243	23	unless	unless	SCONJ
ejpam-1535	243	24	stated	state	VERB
ejpam-1535	243	25	otherwise	otherwise	ADV
ejpam-1535	243	26	.	.	PUNCT
ejpam-1535	244	1	we	we	PRON
ejpam-1535	244	2	will	will	AUX
ejpam-1535	244	3	therefore	therefore	ADV
ejpam-1535	244	4	suppress	suppress	VERB
ejpam-1535	244	5	mention	mention	NOUN
ejpam-1535	244	6	of	of	ADP
ejpam-1535	244	7	e	e	NOUN
ejpam-1535	244	8	,	,	PUNCT
ejpam-1535	244	9	except	except	SCONJ
ejpam-1535	244	10	where	where	SCONJ
ejpam-1535	244	11	clarity	clarity	NOUN
ejpam-1535	244	12	demands	demand	VERB
ejpam-1535	244	13	it	it	PRON
ejpam-1535	244	14	,	,	PUNCT
ejpam-1535	244	15	and	and	CCONJ
ejpam-1535	244	16	refer	refer	VERB
ejpam-1535	244	17	simply	simply	ADV
ejpam-1535	244	18	to	to	ADP
ejpam-1535	244	19	“	"	PUNCT
ejpam-1535	244	20	the	the	DET
ejpam-1535	244	21	restriction	restriction	NOUN
ejpam-1535	244	22	semigroup	semigroup	NOUN
ejpam-1535	244	23	s	s	PART
ejpam-1535	244	24	”	"	PUNCT
ejpam-1535	244	25	.	.	PUNCT
ejpam-1535	245	1	we	we	PRON
ejpam-1535	245	2	record	record	VERB
ejpam-1535	245	3	here	here	ADV
ejpam-1535	245	4	some	some	DET
ejpam-1535	245	5	very	very	ADV
ejpam-1535	245	6	useful	useful	ADJ
ejpam-1535	245	7	properties	property	NOUN
ejpam-1535	245	8	of	of	ADP
ejpam-1535	245	9	restriction	restriction	NOUN
ejpam-1535	245	10	semigroups	semigroup	NOUN
ejpam-1535	245	11	which	which	PRON
ejpam-1535	245	12	will	will	AUX
ejpam-1535	245	13	be	be	AUX
ejpam-1535	245	14	used	use	VERB
ejpam-1535	245	15	many	many	ADJ
ejpam-1535	245	16	times	time	NOUN
ejpam-1535	245	17	in	in	ADP
ejpam-1535	245	18	the	the	DET
ejpam-1535	245	19	course	course	NOUN
ejpam-1535	245	20	of	of	ADP
ejpam-1535	245	21	this	this	DET
ejpam-1535	245	22	article	article	NOUN
ejpam-1535	245	23	;	;	PUNCT
ejpam-1535	245	24	these	these	DET
ejpam-1535	245	25	properties	property	NOUN
ejpam-1535	245	26	follow	follow	VERB
ejpam-1535	245	27	immediately	immediately	ADV
ejpam-1535	245	28	the	the	DET
ejpam-1535	245	29	left	left	ADJ
ejpam-1535	245	30	(	(	PUNCT
ejpam-1535	245	31	right	right	ADJ
ejpam-1535	245	32	)	)	PUNCT
ejpam-1535	245	33	congruence	congruence	NOUN
ejpam-1535	245	34	properties	property	NOUN
ejpam-1535	245	35	of	of	ADP
ejpam-1535	245	36	ere	ere	PROPN
ejpam-1535	245	37	(	(	PUNCT
ejpam-1535	245	38	respectively	respectively	ADV
ejpam-1535	245	39	,	,	PUNCT
ejpam-1535	245	40	fle	fle	PROPN
ejpam-1535	245	41	):	):	PUNCT
ejpam-1535	245	42	lemma	lemma	PROPN
ejpam-1535	245	43	1	1	NUM
ejpam-1535	245	44	(	(	PUNCT
ejpam-1535	245	45	[	[	X
ejpam-1535	245	46	f	f	X
ejpam-1535	245	47	]	]	X
ejpam-1535	245	48	)	)	PUNCT
ejpam-1535	245	49	.	.	PUNCT
ejpam-1535	246	1	let	let	VERB
ejpam-1535	246	2	s	s	PRON
ejpam-1535	246	3	be	be	AUX
ejpam-1535	246	4	a	a	DET
ejpam-1535	246	5	restriction	restriction	NOUN
ejpam-1535	246	6	semigroup	semigroup	NOUN
ejpam-1535	246	7	.	.	PUNCT
ejpam-1535	247	1	for	for	ADP
ejpam-1535	247	2	any	any	DET
ejpam-1535	247	3	s	s	NOUN
ejpam-1535	247	4	,	,	PUNCT
ejpam-1535	247	5	t	t	PROPN
ejpam-1535	247	6	∈	∈	PROPN
ejpam-1535	247	7	s	s	PROPN
ejpam-1535	247	8	,	,	PUNCT
ejpam-1535	247	9	(	(	PUNCT
ejpam-1535	247	10	st)+	st)+	NOUN
ejpam-1535	247	11	=	=	SYM
ejpam-1535	247	12	(	(	PUNCT
ejpam-1535	247	13	st+)+	st+)+	ADJ
ejpam-1535	247	14	and	and	CCONJ
ejpam-1535	247	15	(	(	PUNCT
ejpam-1535	247	16	st)∗	st)∗	PROPN
ejpam-1535	247	17	=	=	SYM
ejpam-1535	247	18	(	(	PUNCT
ejpam-1535	247	19	s∗	s∗	PROPN
ejpam-1535	247	20	t)∗.	t)∗.	PROPN
ejpam-1535	247	21	c.	c.	PROPN
ejpam-1535	247	22	hollings	hollings	PROPN
ejpam-1535	247	23	/	/	SYM
ejpam-1535	247	24	eur	eur	PROPN
ejpam-1535	247	25	.	.	PUNCT
ejpam-1535	248	1	j.	j.	PROPN
ejpam-1535	248	2	pure	pure	PROPN
ejpam-1535	248	3	appl	appl	PROPN
ejpam-1535	248	4	.	.	PROPN
ejpam-1535	248	5	math	math	PROPN
ejpam-1535	248	6	,	,	PUNCT
ejpam-1535	248	7	5	5	NUM
ejpam-1535	248	8	(	(	PUNCT
ejpam-1535	248	9	2012	2012	NUM
ejpam-1535	248	10	)	)	PUNCT
ejpam-1535	248	11	,	,	PUNCT
ejpam-1535	248	12	414	414	NUM
ejpam-1535	248	13	-	-	SYM
ejpam-1535	248	14	450	450	NUM
ejpam-1535	248	15	425	425	NUM
ejpam-1535	248	16	just	just	ADV
ejpam-1535	248	17	like	like	ADP
ejpam-1535	248	18	an	an	DET
ejpam-1535	248	19	inverse	inverse	NOUN
ejpam-1535	248	20	semigroup	semigroup	NOUN
ejpam-1535	249	1	,	,	PUNCT
ejpam-1535	249	2	any	any	DET
ejpam-1535	249	3	restriction	restriction	NOUN
ejpam-1535	249	4	semigroup	semigroup	NOUN
ejpam-1535	249	5	possesses	possess	VERB
ejpam-1535	249	6	a	a	DET
ejpam-1535	249	7	partial	partial	ADJ
ejpam-1535	249	8	order	order	NOUN
ejpam-1535	249	9	which	which	PRON
ejpam-1535	249	10	is	be	AUX
ejpam-1535	249	11	natural	natural	ADJ
ejpam-1535	249	12	in	in	ADP
ejpam-1535	249	13	the	the	DET
ejpam-1535	249	14	sense	sense	NOUN
ejpam-1535	249	15	that	that	SCONJ
ejpam-1535	249	16	it	it	PRON
ejpam-1535	249	17	is	be	AUX
ejpam-1535	249	18	compatible	compatible	ADJ
ejpam-1535	249	19	with	with	ADP
ejpam-1535	249	20	the	the	DET
ejpam-1535	249	21	semigroup	semigroup	ADJ
ejpam-1535	249	22	multiplication	multiplication	NOUN
ejpam-1535	249	23	,	,	PUNCT
ejpam-1535	249	24	and	and	CCONJ
ejpam-1535	249	25	that	that	SCONJ
ejpam-1535	249	26	it	it	PRON
ejpam-1535	249	27	restricts	restrict	VERB
ejpam-1535	249	28	to	to	ADP
ejpam-1535	249	29	the	the	DET
ejpam-1535	249	30	usual	usual	ADJ
ejpam-1535	249	31	partial	partial	ADJ
ejpam-1535	249	32	order	order	NOUN
ejpam-1535	249	33	on	on	ADP
ejpam-1535	249	34	idempotents	idempotent	NOUN
ejpam-1535	249	35	from	from	ADP
ejpam-1535	249	36	e	e	NOUN
ejpam-1535	249	37	(	(	PUNCT
ejpam-1535	249	38	namely	namely	ADV
ejpam-1535	249	39	,	,	PUNCT
ejpam-1535	249	40	e	e	X
ejpam-1535	249	41	≤	≤	NUM
ejpam-1535	249	42	f	f	NOUN
ejpam-1535	250	1	if	if	SCONJ
ejpam-1535	250	2	and	and	CCONJ
ejpam-1535	250	3	only	only	ADV
ejpam-1535	250	4	if	if	SCONJ
ejpam-1535	250	5	e	e	X
ejpam-1535	250	6	=	=	SYM
ejpam-1535	250	7	e	e	X
ejpam-1535	250	8	f	f	PROPN
ejpam-1535	250	9	)	)	PUNCT
ejpam-1535	250	10	.	.	PUNCT
ejpam-1535	251	1	the	the	DET
ejpam-1535	251	2	partial	partial	ADJ
ejpam-1535	251	3	order	order	NOUN
ejpam-1535	251	4	in	in	ADP
ejpam-1535	251	5	a	a	DET
ejpam-1535	251	6	restriction	restriction	NOUN
ejpam-1535	251	7	semigroup	semigroup	NOUN
ejpam-1535	251	8	may	may	AUX
ejpam-1535	251	9	be	be	AUX
ejpam-1535	251	10	given	give	VERB
ejpam-1535	251	11	by	by	ADP
ejpam-1535	251	12	a	a	DET
ejpam-1535	251	13	≤	≤	NUM
ejpam-1535	251	14	b	b	ADP
ejpam-1535	251	15	⇐	⇐	ADJ
ejpam-1535	251	16	⇒	⇒	NOUN
ejpam-1535	251	17	a	a	DET
ejpam-1535	251	18	=	=	SYM
ejpam-1535	251	19	eb	eb	PROPN
ejpam-1535	251	20	,	,	PUNCT
ejpam-1535	251	21	for	for	ADP
ejpam-1535	251	22	some	some	DET
ejpam-1535	251	23	e	e	NOUN
ejpam-1535	251	24	∈	∈	PROPN
ejpam-1535	251	25	e	e	NOUN
ejpam-1535	251	26	,	,	PUNCT
ejpam-1535	251	27	(	(	PUNCT
ejpam-1535	251	28	2	2	NUM
ejpam-1535	251	29	)	)	PUNCT
ejpam-1535	251	30	or	or	CCONJ
ejpam-1535	251	31	,	,	PUNCT
ejpam-1535	251	32	equivalently	equivalently	ADV
ejpam-1535	251	33	:	:	PUNCT
ejpam-1535	251	34	a	a	DET
ejpam-1535	251	35	≤	≤	NUM
ejpam-1535	251	36	b	b	NUM
ejpam-1535	251	37	⇐	⇐	ADJ
ejpam-1535	251	38	⇒	⇒	NOUN
ejpam-1535	251	39	a	a	DET
ejpam-1535	251	40	=	=	SYM
ejpam-1535	251	41	b	b	PROPN
ejpam-1535	251	42	f	f	PROPN
ejpam-1535	251	43	,	,	PUNCT
ejpam-1535	251	44	for	for	ADP
ejpam-1535	251	45	some	some	DET
ejpam-1535	251	46	f	f	PROPN
ejpam-1535	251	47	∈	∈	PROPN
ejpam-1535	251	48	e.	e.	PROPN
ejpam-1535	251	49	(	(	PUNCT
ejpam-1535	251	50	3	3	NUM
ejpam-1535	251	51	)	)	PUNCT
ejpam-1535	251	52	in	in	ADP
ejpam-1535	251	53	fact	fact	NOUN
ejpam-1535	251	54	,	,	PUNCT
ejpam-1535	251	55	the	the	DET
ejpam-1535	251	56	idempotents	idempotent	NOUN
ejpam-1535	251	57	e	e	NOUN
ejpam-1535	251	58	and	and	CCONJ
ejpam-1535	251	59	f	f	PROPN
ejpam-1535	251	60	in	in	ADP
ejpam-1535	251	61	(	(	PUNCT
ejpam-1535	251	62	2	2	NUM
ejpam-1535	251	63	)	)	PUNCT
ejpam-1535	251	64	and	and	CCONJ
ejpam-1535	251	65	(	(	PUNCT
ejpam-1535	251	66	3	3	X
ejpam-1535	251	67	)	)	PUNCT
ejpam-1535	251	68	can	can	AUX
ejpam-1535	251	69	be	be	AUX
ejpam-1535	251	70	taken	take	VERB
ejpam-1535	251	71	to	to	PART
ejpam-1535	251	72	be	be	AUX
ejpam-1535	251	73	a+	a+	PUNCT
ejpam-1535	251	74	and	and	CCONJ
ejpam-1535	251	75	a∗	a∗	PROPN
ejpam-1535	251	76	,	,	PUNCT
ejpam-1535	251	77	respectively	respectively	ADV
ejpam-1535	251	78	:	:	PUNCT
ejpam-1535	251	79	a	a	DET
ejpam-1535	251	80	≤	≤	NUM
ejpam-1535	251	81	b	b	NUM
ejpam-1535	251	82	⇐	⇐	ADJ
ejpam-1535	251	83	⇒	⇒	NOUN
ejpam-1535	251	84	a	a	DET
ejpam-1535	251	85	=	=	SYM
ejpam-1535	251	86	a+b	a+b	NUM
ejpam-1535	251	87	⇐	⇐	ADJ
ejpam-1535	251	88	⇒	⇒	NOUN
ejpam-1535	251	89	a	a	DET
ejpam-1535	251	90	=	=	NOUN
ejpam-1535	251	91	ba∗.	ba∗.	PROPN
ejpam-1535	251	92	(	(	PUNCT
ejpam-1535	251	93	4	4	NUM
ejpam-1535	251	94	)	)	PUNCT
ejpam-1535	251	95	given	give	VERB
ejpam-1535	251	96	the	the	DET
ejpam-1535	251	97	above	above	ADJ
ejpam-1535	251	98	comments	comment	NOUN
ejpam-1535	251	99	on	on	ADP
ejpam-1535	251	100	inverse	inverse	NOUN
ejpam-1535	251	101	semigroups	semigroup	NOUN
ejpam-1535	251	102	,	,	PUNCT
ejpam-1535	251	103	it	it	PRON
ejpam-1535	251	104	is	be	AUX
ejpam-1535	251	105	easy	easy	ADJ
ejpam-1535	251	106	to	to	PART
ejpam-1535	251	107	see	see	VERB
ejpam-1535	251	108	that	that	SCONJ
ejpam-1535	251	109	if	if	SCONJ
ejpam-1535	251	110	the	the	DET
ejpam-1535	251	111	restriction	restriction	NOUN
ejpam-1535	251	112	semigroup	semigroup	VERB
ejpam-1535	251	113	in	in	ADP
ejpam-1535	251	114	question	question	NOUN
ejpam-1535	251	115	is	be	AUX
ejpam-1535	251	116	in	in	ADP
ejpam-1535	251	117	fact	fact	NOUN
ejpam-1535	251	118	inverse	inverse	NOUN
ejpam-1535	251	119	,	,	PUNCT
ejpam-1535	251	120	then	then	ADV
ejpam-1535	251	121	the	the	DET
ejpam-1535	251	122	above	above	ADJ
ejpam-1535	251	123	ordering	order	VERB
ejpam-1535	251	124	coincides	coincide	NOUN
ejpam-1535	251	125	with	with	ADP
ejpam-1535	251	126	the	the	DET
ejpam-1535	251	127	usual	usual	ADJ
ejpam-1535	251	128	partial	partial	ADJ
ejpam-1535	251	129	order	order	NOUN
ejpam-1535	251	130	on	on	ADP
ejpam-1535	251	131	an	an	DET
ejpam-1535	251	132	inverse	inverse	NOUN
ejpam-1535	251	133	semigroup	semigroup	NOUN
ejpam-1535	251	134	.	.	PUNCT
ejpam-1535	252	1	we	we	PRON
ejpam-1535	252	2	have	have	AUX
ejpam-1535	252	3	already	already	ADV
ejpam-1535	252	4	observed	observe	VERB
ejpam-1535	252	5	that	that	SCONJ
ejpam-1535	252	6	any	any	DET
ejpam-1535	252	7	inverse	inverse	NOUN
ejpam-1535	252	8	semigroup	semigroup	NOUN
ejpam-1535	252	9	is	be	AUX
ejpam-1535	252	10	a	a	DET
ejpam-1535	252	11	restriction	restriction	NOUN
ejpam-1535	252	12	semigroup	semigroup	NOUN
ejpam-1535	252	13	.	.	PUNCT
ejpam-1535	253	1	in	in	ADP
ejpam-1535	253	2	fact	fact	NOUN
ejpam-1535	253	3	,	,	PUNCT
ejpam-1535	253	4	there	there	PRON
ejpam-1535	253	5	is	be	VERB
ejpam-1535	253	6	another	another	DET
ejpam-1535	253	7	special	special	ADJ
ejpam-1535	253	8	type	type	NOUN
ejpam-1535	253	9	of	of	ADP
ejpam-1535	253	10	restriction	restriction	NOUN
ejpam-1535	253	11	semigroup	semigroup	NOUN
ejpam-1535	253	12	which	which	PRON
ejpam-1535	253	13	we	we	PRON
ejpam-1535	253	14	will	will	AUX
ejpam-1535	253	15	have	have	VERB
ejpam-1535	253	16	occasion	occasion	NOUN
ejpam-1535	253	17	to	to	PART
ejpam-1535	253	18	consider	consider	VERB
ejpam-1535	253	19	:	:	PUNCT
ejpam-1535	253	20	so	so	ADV
ejpam-1535	253	21	-	-	PUNCT
ejpam-1535	253	22	called	call	VERB
ejpam-1535	253	23	ample	ample	ADJ
ejpam-1535	253	24	semigroups	semigroup	NOUN
ejpam-1535	253	25	.	.	PUNCT
ejpam-1535	254	1	these	these	PRON
ejpam-1535	254	2	form	form	VERB
ejpam-1535	254	3	a	a	DET
ejpam-1535	254	4	class	class	NOUN
ejpam-1535	254	5	of	of	ADP
ejpam-1535	254	6	semigroups	semigroup	NOUN
ejpam-1535	254	7	intermediate	intermediate	ADJ
ejpam-1535	254	8	between	between	ADP
ejpam-1535	254	9	restriction	restriction	NOUN
ejpam-1535	254	10	semigroups	semigroup	NOUN
ejpam-1535	254	11	and	and	CCONJ
ejpam-1535	254	12	inverse	inverse	NOUN
ejpam-1535	254	13	semigroups	semigroup	NOUN
ejpam-1535	254	14	,	,	PUNCT
ejpam-1535	254	15	and	and	CCONJ
ejpam-1535	254	16	are	be	AUX
ejpam-1535	254	17	defined	define	VERB
ejpam-1535	254	18	in	in	ADP
ejpam-1535	254	19	terms	term	NOUN
ejpam-1535	254	20	of	of	ADP
ejpam-1535	254	21	the	the	DET
ejpam-1535	254	22	following	follow	VERB
ejpam-1535	254	23	specialisations	specialisation	NOUN
ejpam-1535	254	24	of	of	ADP
ejpam-1535	254	25	ere	ere	PROPN
ejpam-1535	254	26	and	and	CCONJ
ejpam-1535	254	27	fle	fle	PROPN
ejpam-1535	254	28	:	:	PUNCT
ejpam-1535	254	29	ar∗	ar∗	PROPN
ejpam-1535	254	30	b	b	NUM
ejpam-1535	254	31	⇐	⇐	PROPN
ejpam-1535	254	32	⇒∀x	⇒∀x	NOUN
ejpam-1535	254	33	,	,	PUNCT
ejpam-1535	254	34	y	y	PROPN
ejpam-1535	254	35	∈	∈	PROPN
ejpam-1535	254	36	s1[xa	s1[xa	NOUN
ejpam-1535	254	37	=	=	PUNCT
ejpam-1535	254	38	ya⇔	ya⇔	NOUN
ejpam-1535	254	39	x	x	X
ejpam-1535	254	40	b	b	X
ejpam-1535	254	41	=	=	SYM
ejpam-1535	254	42	y	y	PROPN
ejpam-1535	254	43	b	b	PROPN
ejpam-1535	254	44	]	]	X
ejpam-1535	254	45	;	;	PUNCT
ejpam-1535	254	46	al	al	PROPN
ejpam-1535	254	47	∗	∗	PROPN
ejpam-1535	254	48	b	b	PROPN
ejpam-1535	254	49	⇐	⇐	PROPN
ejpam-1535	254	50	⇒∀x	⇒∀x	NOUN
ejpam-1535	254	51	,	,	PUNCT
ejpam-1535	254	52	y	y	PROPN
ejpam-1535	254	53	∈	∈	PROPN
ejpam-1535	254	54	s1[ax	s1[ax	NOUN
ejpam-1535	254	55	=	=	PRON
ejpam-1535	254	56	a	a	DET
ejpam-1535	254	57	y⇔	y⇔	NOUN
ejpam-1535	254	58	bx	bx	NOUN
ejpam-1535	254	59	=	=	SYM
ejpam-1535	255	1	b	b	PROPN
ejpam-1535	255	2	y	y	NOUN
ejpam-1535	255	3	]	]	X
ejpam-1535	255	4	.	.	PUNCT
ejpam-1535	256	1	these	these	DET
ejpam-1535	256	2	equivalence	equivalence	NOUN
ejpam-1535	256	3	relations	relation	NOUN
ejpam-1535	256	4	are	be	AUX
ejpam-1535	256	5	again	again	ADV
ejpam-1535	256	6	generalisations	generalisation	NOUN
ejpam-1535	256	7	of	of	ADP
ejpam-1535	256	8	green	green	PROPN
ejpam-1535	256	9	’s	’s	PART
ejpam-1535	256	10	relations	relation	NOUN
ejpam-1535	256	11	r	r	NOUN
ejpam-1535	256	12	and	and	CCONJ
ejpam-1535	256	13	l	l	NOUN
ejpam-1535	256	14	,	,	PUNCT
ejpam-1535	256	15	and	and	CCONJ
ejpam-1535	256	16	,	,	PUNCT
ejpam-1535	256	17	indeed	indeed	ADV
ejpam-1535	256	18	,	,	PUNCT
ejpam-1535	256	19	we	we	PRON
ejpam-1535	256	20	have	have	VERB
ejpam-1535	256	21	r	r	NOUN
ejpam-1535	256	22	⊆	⊆	NUM
ejpam-1535	256	23	r∗	r∗	PROPN
ejpam-1535	256	24	⊆	⊆	NUM
ejpam-1535	256	25	er	er	INTJ
ejpam-1535	256	26	⊆	⊆	NUM
ejpam-1535	256	27	ere	ere	NOUN
ejpam-1535	256	28	and	and	CCONJ
ejpam-1535	256	29	l	l	NOUN
ejpam-1535	256	30	⊆	⊆	NUM
ejpam-1535	256	31	l	l	NOUN
ejpam-1535	256	32	∗	∗	NOUN
ejpam-1535	256	33	⊆	⊆	NUM
ejpam-1535	256	34	fl	fl	NUM
ejpam-1535	256	35	⊆	⊆	NUM
ejpam-1535	256	36	fle	fle	NOUN
ejpam-1535	256	37	on	on	ADP
ejpam-1535	256	38	any	any	DET
ejpam-1535	256	39	semigroup	semigroup	NOUN
ejpam-1535	256	40	s	s	NOUN
ejpam-1535	256	41	,	,	PUNCT
ejpam-1535	256	42	for	for	ADP
ejpam-1535	256	43	any	any	DET
ejpam-1535	256	44	subsemilattice	subsemilattice	NOUN
ejpam-1535	256	45	e.	e.	PROPN
ejpam-1535	256	46	as	as	ADP
ejpam-1535	256	47	with	with	ADP
ejpam-1535	256	48	ere	ere	NOUN
ejpam-1535	256	49	and	and	CCONJ
ejpam-1535	256	50	fle	fle	NOUN
ejpam-1535	256	51	,	,	PUNCT
ejpam-1535	256	52	we	we	PRON
ejpam-1535	256	53	have	have	VERB
ejpam-1535	256	54	simpler	simple	ADJ
ejpam-1535	256	55	conditions	condition	NOUN
ejpam-1535	256	56	for	for	ADP
ejpam-1535	256	57	an	an	DET
ejpam-1535	256	58	element	element	NOUN
ejpam-1535	256	59	a	a	DET
ejpam-1535	256	60	∈	∈	NOUN
ejpam-1535	256	61	s	s	VERB
ejpam-1535	256	62	to	to	PART
ejpam-1535	256	63	be	be	AUX
ejpam-1535	256	64	r∗or	r∗or	PROPN
ejpam-1535	256	65	l	l	NOUN
ejpam-1535	256	66	∗-related	∗-relate	VERB
ejpam-1535	256	67	to	to	ADP
ejpam-1535	256	68	an	an	DET
ejpam-1535	256	69	idempotent	idempotent	ADJ
ejpam-1535	256	70	e	e	NOUN
ejpam-1535	256	71	∈	∈	PROPN
ejpam-1535	256	72	e(s	e(s	PROPN
ejpam-1535	256	73	):	):	PUNCT
ejpam-1535	256	74	ar∗	ar∗	NOUN
ejpam-1535	256	75	e	e	X
ejpam-1535	256	76	⇐	⇐	ADJ
ejpam-1535	256	77	⇒	⇒	NOUN
ejpam-1535	256	78	ea	ea	PUNCT
ejpam-1535	257	1	=	=	PUNCT
ejpam-1535	257	2	a	a	PROPN
ejpam-1535	257	3	and	and	CCONJ
ejpam-1535	257	4	∀x	∀x	NUM
ejpam-1535	257	5	,	,	PUNCT
ejpam-1535	257	6	y	y	PROPN
ejpam-1535	257	7	∈	∈	PROPN
ejpam-1535	257	8	s1[xa	s1[xa	NOUN
ejpam-1535	257	9	=	=	SYM
ejpam-1535	257	10	ya⇒	ya⇒	PROPN
ejpam-1535	257	11	xe	xe	PROPN
ejpam-1535	257	12	=	=	PROPN
ejpam-1535	257	13	ye	ye	PROPN
ejpam-1535	257	14	]	]	X
ejpam-1535	257	15	;	;	PUNCT
ejpam-1535	257	16	(	(	PUNCT
ejpam-1535	257	17	5	5	X
ejpam-1535	257	18	)	)	PUNCT
ejpam-1535	257	19	al	al	PROPN
ejpam-1535	257	20	∗	∗	PROPN
ejpam-1535	257	21	e	e	NOUN
ejpam-1535	257	22	⇐	⇐	PROPN
ejpam-1535	257	23	⇒	⇒	NOUN
ejpam-1535	257	24	ae	ae	PROPN
ejpam-1535	257	25	=	=	PUNCT
ejpam-1535	257	26	a	a	PROPN
ejpam-1535	257	27	and	and	CCONJ
ejpam-1535	257	28	∀x	∀x	NUM
ejpam-1535	257	29	,	,	PUNCT
ejpam-1535	257	30	y	y	PROPN
ejpam-1535	257	31	∈	∈	PROPN
ejpam-1535	257	32	s1[ax	s1[ax	PROPN
ejpam-1535	257	33	=	=	PRON
ejpam-1535	257	34	a	a	DET
ejpam-1535	257	35	y	y	PROPN
ejpam-1535	257	36	⇒	⇒	VERB
ejpam-1535	257	37	ex	ex	X
ejpam-1535	257	38	=	=	PUNCT
ejpam-1535	257	39	e	e	PART
ejpam-1535	257	40	y	y	NOUN
ejpam-1535	257	41	]	]	PUNCT
ejpam-1535	257	42	.	.	PUNCT
ejpam-1535	258	1	we	we	PRON
ejpam-1535	258	2	may	may	AUX
ejpam-1535	258	3	now	now	ADV
ejpam-1535	258	4	define	define	VERB
ejpam-1535	258	5	left	left	ADJ
ejpam-1535	258	6	and	and	CCONJ
ejpam-1535	258	7	right	right	ADJ
ejpam-1535	258	8	ample	ample	ADJ
ejpam-1535	258	9	semigroups	semigroup	NOUN
ejpam-1535	258	10	:	:	PUNCT
ejpam-1535	258	11	definition	definition	NOUN
ejpam-1535	258	12	5	5	NUM
ejpam-1535	258	13	.	.	PUNCT
ejpam-1535	259	1	we	we	PRON
ejpam-1535	259	2	call	call	VERB
ejpam-1535	259	3	a	a	DET
ejpam-1535	259	4	semigroup	semigroup	NOUN
ejpam-1535	259	5	s	s	VERB
ejpam-1535	259	6	a	a	DET
ejpam-1535	259	7	left	left	ADJ
ejpam-1535	259	8	ample	ample	ADJ
ejpam-1535	259	9	semigroup	semigroup	NOUN
ejpam-1535	259	10	if	if	SCONJ
ejpam-1535	259	11	(	(	PUNCT
ejpam-1535	259	12	1	1	X
ejpam-1535	259	13	)	)	PUNCT
ejpam-1535	259	14	every	every	DET
ejpam-1535	259	15	element	element	NOUN
ejpam-1535	259	16	a	a	DET
ejpam-1535	259	17	∈	∈	NOUN
ejpam-1535	259	18	s	s	VERB
ejpam-1535	259	19	is	be	AUX
ejpam-1535	259	20	r∗-related	r∗-relate	VERB
ejpam-1535	259	21	to	to	ADP
ejpam-1535	259	22	a	a	DET
ejpam-1535	259	23	(	(	PUNCT
ejpam-1535	259	24	necessarily	necessarily	ADV
ejpam-1535	259	25	unique	unique	ADJ
ejpam-1535	259	26	)	)	PUNCT
ejpam-1535	259	27	element	element	NOUN
ejpam-1535	259	28	of	of	ADP
ejpam-1535	259	29	e(s	e(s	PROPN
ejpam-1535	259	30	)	)	PUNCT
ejpam-1535	259	31	,	,	PUNCT
ejpam-1535	259	32	which	which	PRON
ejpam-1535	259	33	we	we	PRON
ejpam-1535	259	34	denote	denote	VERB
ejpam-1535	259	35	by	by	ADP
ejpam-1535	259	36	a+	a+	NOUN
ejpam-1535	259	37	;	;	PUNCT
ejpam-1535	259	38	(	(	PUNCT
ejpam-1535	259	39	2	2	X
ejpam-1535	259	40	)	)	PUNCT
ejpam-1535	259	41	for	for	ADP
ejpam-1535	259	42	all	all	DET
ejpam-1535	259	43	a	a	DET
ejpam-1535	259	44	∈	∈	NOUN
ejpam-1535	259	45	s	s	PART
ejpam-1535	259	46	and	and	CCONJ
ejpam-1535	259	47	all	all	DET
ejpam-1535	259	48	e	e	PROPN
ejpam-1535	259	49	∈	∈	PROPN
ejpam-1535	259	50	e(s	e(s	PROPN
ejpam-1535	259	51	)	)	PUNCT
ejpam-1535	259	52	,	,	PUNCT
ejpam-1535	259	53	ae	ae	PROPN
ejpam-1535	259	54	=	=	SYM
ejpam-1535	259	55	(	(	PUNCT
ejpam-1535	259	56	ae)+a	ae)+a	PROPN
ejpam-1535	259	57	.	.	PUNCT
ejpam-1535	260	1	definition	definition	NOUN
ejpam-1535	260	2	6	6	NUM
ejpam-1535	260	3	.	.	PUNCT
ejpam-1535	261	1	we	we	PRON
ejpam-1535	261	2	call	call	VERB
ejpam-1535	261	3	a	a	DET
ejpam-1535	261	4	semigroup	semigroup	NOUN
ejpam-1535	261	5	s	s	VERB
ejpam-1535	261	6	a	a	DET
ejpam-1535	261	7	right	right	ADJ
ejpam-1535	261	8	ample	ample	ADJ
ejpam-1535	261	9	semigroup	semigroup	NOUN
ejpam-1535	261	10	if	if	SCONJ
ejpam-1535	261	11	(	(	PUNCT
ejpam-1535	261	12	1	1	X
ejpam-1535	261	13	)	)	PUNCT
ejpam-1535	261	14	every	every	DET
ejpam-1535	261	15	element	element	NOUN
ejpam-1535	261	16	a	a	DET
ejpam-1535	261	17	∈	∈	NOUN
ejpam-1535	261	18	s	s	PART
ejpam-1535	261	19	is	be	AUX
ejpam-1535	261	20	l	l	NOUN
ejpam-1535	261	21	∗-related	∗-relate	VERB
ejpam-1535	261	22	to	to	ADP
ejpam-1535	261	23	a	a	DET
ejpam-1535	261	24	(	(	PUNCT
ejpam-1535	261	25	necessarily	necessarily	ADV
ejpam-1535	261	26	unique	unique	ADJ
ejpam-1535	261	27	)	)	PUNCT
ejpam-1535	261	28	element	element	NOUN
ejpam-1535	261	29	of	of	ADP
ejpam-1535	261	30	e(s	e(s	PROPN
ejpam-1535	261	31	)	)	PUNCT
ejpam-1535	261	32	,	,	PUNCT
ejpam-1535	261	33	which	which	PRON
ejpam-1535	261	34	we	we	PRON
ejpam-1535	261	35	denote	denote	VERB
ejpam-1535	261	36	by	by	ADP
ejpam-1535	261	37	a∗	a∗	PROPN
ejpam-1535	261	38	;	;	PUNCT
ejpam-1535	261	39	c.	c.	PROPN
ejpam-1535	261	40	hollings	holling	NOUN
ejpam-1535	261	41	/	/	SYM
ejpam-1535	261	42	eur	eur	PROPN
ejpam-1535	261	43	.	.	PUNCT
ejpam-1535	262	1	j.	j.	PROPN
ejpam-1535	262	2	pure	pure	PROPN
ejpam-1535	262	3	appl	appl	PROPN
ejpam-1535	262	4	.	.	PROPN
ejpam-1535	262	5	math	math	PROPN
ejpam-1535	262	6	,	,	PUNCT
ejpam-1535	262	7	5	5	NUM
ejpam-1535	262	8	(	(	PUNCT
ejpam-1535	262	9	2012	2012	NUM
ejpam-1535	262	10	)	)	PUNCT
ejpam-1535	262	11	,	,	PUNCT
ejpam-1535	262	12	414	414	NUM
ejpam-1535	262	13	-	-	SYM
ejpam-1535	262	14	450	450	NUM
ejpam-1535	262	15	426	426	NUM
ejpam-1535	262	16	(	(	PUNCT
ejpam-1535	262	17	2	2	NUM
ejpam-1535	262	18	)	)	PUNCT
ejpam-1535	262	19	for	for	ADP
ejpam-1535	262	20	all	all	DET
ejpam-1535	262	21	a	a	DET
ejpam-1535	262	22	∈	∈	NOUN
ejpam-1535	262	23	s	s	PART
ejpam-1535	262	24	and	and	CCONJ
ejpam-1535	262	25	all	all	DET
ejpam-1535	262	26	e	e	PROPN
ejpam-1535	262	27	∈	∈	PROPN
ejpam-1535	262	28	e(s	e(s	PROPN
ejpam-1535	262	29	)	)	PUNCT
ejpam-1535	262	30	,	,	PUNCT
ejpam-1535	262	31	ea	ea	X
ejpam-1535	262	32	=	=	SYM
ejpam-1535	262	33	a(ea)∗.	a(ea)∗.	PROPN
ejpam-1535	262	34	thus	thus	ADV
ejpam-1535	262	35	,	,	PUNCT
ejpam-1535	262	36	the	the	DET
ejpam-1535	262	37	definition	definition	NOUN
ejpam-1535	262	38	of	of	ADP
ejpam-1535	262	39	a	a	DET
ejpam-1535	262	40	left	left	ADJ
ejpam-1535	262	41	(	(	PUNCT
ejpam-1535	262	42	right	right	ADJ
ejpam-1535	262	43	)	)	PUNCT
ejpam-1535	262	44	ample	ample	ADJ
ejpam-1535	262	45	semigroup	semigroup	NOUN
ejpam-1535	262	46	is	be	AUX
ejpam-1535	262	47	broadly	broadly	ADV
ejpam-1535	262	48	similar	similar	ADJ
ejpam-1535	262	49	to	to	ADP
ejpam-1535	262	50	that	that	PRON
ejpam-1535	262	51	of	of	ADP
ejpam-1535	262	52	a	a	DET
ejpam-1535	262	53	left	left	ADJ
ejpam-1535	262	54	(	(	PUNCT
ejpam-1535	262	55	right	right	ADJ
ejpam-1535	262	56	)	)	PUNCT
ejpam-1535	262	57	restriction	restriction	NOUN
ejpam-1535	262	58	semigroup	semigroup	NOUN
ejpam-1535	262	59	,	,	PUNCT
ejpam-1535	262	60	but	but	CCONJ
ejpam-1535	262	61	with	with	ADP
ejpam-1535	262	62	ere	ere	PROPN
ejpam-1535	262	63	(	(	PUNCT
ejpam-1535	262	64	fle	fle	NOUN
ejpam-1535	262	65	)	)	PUNCT
ejpam-1535	262	66	replaced	replace	VERB
ejpam-1535	262	67	by	by	ADP
ejpam-1535	262	68	r∗	r∗	PROPN
ejpam-1535	262	69	(	(	PUNCT
ejpam-1535	262	70	l	l	NOUN
ejpam-1535	262	71	∗	∗	NOUN
ejpam-1535	262	72	)	)	PUNCT
ejpam-1535	262	73	.	.	PUNCT
ejpam-1535	263	1	the	the	DET
ejpam-1535	263	2	notable	notable	ADJ
ejpam-1535	263	3	omission	omission	NOUN
ejpam-1535	263	4	from	from	ADP
ejpam-1535	263	5	the	the	DET
ejpam-1535	263	6	left	left	ADJ
ejpam-1535	263	7	(	(	PUNCT
ejpam-1535	263	8	right	right	ADJ
ejpam-1535	263	9	)	)	PUNCT
ejpam-1535	263	10	ample	ample	ADJ
ejpam-1535	263	11	definition	definition	NOUN
ejpam-1535	263	12	,	,	PUNCT
ejpam-1535	263	13	however	however	ADV
ejpam-1535	263	14	,	,	PUNCT
ejpam-1535	263	15	is	be	AUX
ejpam-1535	263	16	the	the	DET
ejpam-1535	263	17	left	left	ADJ
ejpam-1535	263	18	(	(	PUNCT
ejpam-1535	263	19	right	right	ADJ
ejpam-1535	263	20	)	)	PUNCT
ejpam-1535	263	21	congruence	congruence	NOUN
ejpam-1535	263	22	condition	condition	NOUN
ejpam-1535	263	23	;	;	PUNCT
ejpam-1535	263	24	in	in	ADP
ejpam-1535	263	25	fact	fact	NOUN
ejpam-1535	263	26	,	,	PUNCT
ejpam-1535	263	27	r∗	r∗	PROPN
ejpam-1535	263	28	(	(	PUNCT
ejpam-1535	263	29	l	l	NOUN
ejpam-1535	263	30	∗	∗	NOUN
ejpam-1535	263	31	)	)	PUNCT
ejpam-1535	263	32	is	be	AUX
ejpam-1535	263	33	always	always	ADV
ejpam-1535	263	34	a	a	DET
ejpam-1535	263	35	left	left	ADJ
ejpam-1535	263	36	(	(	PUNCT
ejpam-1535	263	37	right	right	ADJ
ejpam-1535	263	38	)	)	PUNCT
ejpam-1535	263	39	congruence	congruence	NOUN
ejpam-1535	263	40	,	,	PUNCT
ejpam-1535	263	41	so	so	SCONJ
ejpam-1535	263	42	this	this	PRON
ejpam-1535	263	43	need	need	AUX
ejpam-1535	263	44	not	not	PART
ejpam-1535	263	45	be	be	AUX
ejpam-1535	263	46	demanded	demand	VERB
ejpam-1535	263	47	explicitly	explicitly	ADV
ejpam-1535	263	48	.	.	PUNCT
ejpam-1535	264	1	moreover	moreover	ADV
ejpam-1535	264	2	,	,	PUNCT
ejpam-1535	264	3	we	we	PRON
ejpam-1535	264	4	have	have	VERB
ejpam-1535	264	5	er	er	INTJ
ejpam-1535	264	6	=	=	ADJ
ejpam-1535	264	7	r∗	r∗	PROPN
ejpam-1535	264	8	(	(	PUNCT
ejpam-1535	264	9	fl	fl	NOUN
ejpam-1535	264	10	=	=	PUNCT
ejpam-1535	264	11	l	l	NOUN
ejpam-1535	264	12	∗	∗	NOUN
ejpam-1535	264	13	)	)	PUNCT
ejpam-1535	264	14	in	in	ADP
ejpam-1535	264	15	a	a	DET
ejpam-1535	264	16	left	left	ADJ
ejpam-1535	264	17	(	(	PUNCT
ejpam-1535	264	18	right	right	ADJ
ejpam-1535	264	19	)	)	PUNCT
ejpam-1535	264	20	ample	ample	ADJ
ejpam-1535	264	21	semigroup	semigroup	NOUN
ejpam-1535	264	22	,	,	PUNCT
ejpam-1535	264	23	so	so	CCONJ
ejpam-1535	264	24	there	there	PRON
ejpam-1535	264	25	is	be	VERB
ejpam-1535	264	26	no	no	DET
ejpam-1535	264	27	ambiguity	ambiguity	NOUN
ejpam-1535	264	28	in	in	ADP
ejpam-1535	264	29	our	our	PRON
ejpam-1535	264	30	use	use	NOUN
ejpam-1535	264	31	of	of	ADP
ejpam-1535	264	32	a+	a+	PRON
ejpam-1535	264	33	(	(	PUNCT
ejpam-1535	264	34	a∗	a∗	NOUN
ejpam-1535	264	35	)	)	PUNCT
ejpam-1535	264	36	to	to	PART
ejpam-1535	264	37	denote	denote	VERB
ejpam-1535	264	38	the	the	DET
ejpam-1535	264	39	idempotent	idempotent	NOUN
ejpam-1535	264	40	which	which	PRON
ejpam-1535	264	41	is	be	AUX
ejpam-1535	264	42	r∗(l	r∗(l	PROPN
ejpam-1535	264	43	∗-)related	∗-)relate	VERB
ejpam-1535	264	44	to	to	ADP
ejpam-1535	264	45	a	a	DET
ejpam-1535	264	46	∈	∈	NOUN
ejpam-1535	264	47	s.	s.	NOUN
ejpam-1535	265	1	we	we	PRON
ejpam-1535	265	2	of	of	ADP
ejpam-1535	265	3	course	course	NOUN
ejpam-1535	265	4	obtain	obtain	VERB
ejpam-1535	265	5	the	the	DET
ejpam-1535	265	6	notion	notion	NOUN
ejpam-1535	265	7	of	of	ADP
ejpam-1535	265	8	a	a	DET
ejpam-1535	265	9	(	(	PUNCT
ejpam-1535	265	10	two	two	NUM
ejpam-1535	265	11	-	-	PUNCT
ejpam-1535	265	12	sided	sided	ADJ
ejpam-1535	265	13	)	)	PUNCT
ejpam-1535	265	14	ample	ample	ADJ
ejpam-1535	265	15	semigroup	semigroup	NOUN
ejpam-1535	265	16	by	by	ADP
ejpam-1535	265	17	combining	combine	VERB
ejpam-1535	265	18	the	the	DET
ejpam-1535	265	19	preceding	precede	VERB
ejpam-1535	265	20	two	two	NUM
ejpam-1535	265	21	definitions	definition	NOUN
ejpam-1535	265	22	:	:	PUNCT
ejpam-1535	265	23	definition	definition	NOUN
ejpam-1535	265	24	7	7	NUM
ejpam-1535	265	25	.	.	PUNCT
ejpam-1535	266	1	we	we	PRON
ejpam-1535	266	2	call	call	VERB
ejpam-1535	266	3	a	a	DET
ejpam-1535	266	4	semigroup	semigroup	NOUN
ejpam-1535	266	5	s	s	X
ejpam-1535	266	6	(	(	PUNCT
ejpam-1535	266	7	two	two	NUM
ejpam-1535	266	8	-	-	PUNCT
ejpam-1535	266	9	sided	sided	ADJ
ejpam-1535	266	10	)	)	PUNCT
ejpam-1535	266	11	ample	ample	ADJ
ejpam-1535	266	12	if	if	SCONJ
ejpam-1535	266	13	it	it	PRON
ejpam-1535	266	14	is	be	AUX
ejpam-1535	266	15	both	both	PRON
ejpam-1535	266	16	left	leave	VERB
ejpam-1535	266	17	ample	ample	ADJ
ejpam-1535	266	18	and	and	CCONJ
ejpam-1535	266	19	right	right	ADJ
ejpam-1535	266	20	ample	ample	ADJ
ejpam-1535	266	21	.	.	PUNCT
ejpam-1535	267	1	it	it	PRON
ejpam-1535	267	2	is	be	AUX
ejpam-1535	267	3	clear	clear	ADJ
ejpam-1535	267	4	from	from	ADP
ejpam-1535	267	5	the	the	DET
ejpam-1535	267	6	definitions	definition	NOUN
ejpam-1535	267	7	that	that	PRON
ejpam-1535	267	8	any	any	DET
ejpam-1535	267	9	ample	ample	ADJ
ejpam-1535	267	10	semigroup	semigroup	NOUN
ejpam-1535	267	11	is	be	AUX
ejpam-1535	267	12	a	a	DET
ejpam-1535	267	13	restriction	restriction	NOUN
ejpam-1535	267	14	semigroup	semigroup	NOUN
ejpam-1535	267	15	,	,	PUNCT
ejpam-1535	267	16	and	and	CCONJ
ejpam-1535	267	17	so	so	ADV
ejpam-1535	267	18	everything	everything	PRON
ejpam-1535	267	19	we	we	PRON
ejpam-1535	267	20	have	have	AUX
ejpam-1535	267	21	said	say	VERB
ejpam-1535	267	22	about	about	ADP
ejpam-1535	267	23	restriction	restriction	NOUN
ejpam-1535	267	24	semigroups	semigroup	NOUN
ejpam-1535	267	25	may	may	AUX
ejpam-1535	267	26	be	be	AUX
ejpam-1535	267	27	applied	apply	VERB
ejpam-1535	267	28	to	to	ADP
ejpam-1535	267	29	ample	ample	ADJ
ejpam-1535	267	30	semigroups	semigroup	NOUN
ejpam-1535	267	31	.	.	PUNCT
ejpam-1535	268	1	in	in	ADP
ejpam-1535	268	2	particular	particular	ADJ
ejpam-1535	268	3	,	,	PUNCT
ejpam-1535	268	4	lemma	lemma	PROPN
ejpam-1535	268	5	1	1	NUM
ejpam-1535	268	6	holds	hold	VERB
ejpam-1535	268	7	in	in	ADP
ejpam-1535	268	8	any	any	DET
ejpam-1535	268	9	ample	ample	ADJ
ejpam-1535	268	10	semigroup	semigroup	NOUN
ejpam-1535	268	11	,	,	PUNCT
ejpam-1535	268	12	and	and	CCONJ
ejpam-1535	268	13	such	such	DET
ejpam-1535	268	14	a	a	DET
ejpam-1535	268	15	semigroup	semigroup	PROPN
ejpam-1535	268	16	possesses	possess	VERB
ejpam-1535	268	17	a	a	DET
ejpam-1535	268	18	partial	partial	ADJ
ejpam-1535	268	19	order	order	NOUN
ejpam-1535	268	20	defined	define	VERB
ejpam-1535	268	21	by	by	ADP
ejpam-1535	268	22	(	(	PUNCT
ejpam-1535	268	23	2	2	NUM
ejpam-1535	268	24	)	)	PUNCT
ejpam-1535	268	25	,	,	PUNCT
ejpam-1535	268	26	(	(	PUNCT
ejpam-1535	268	27	3	3	X
ejpam-1535	268	28	)	)	PUNCT
ejpam-1535	268	29	or	or	CCONJ
ejpam-1535	268	30	(	(	PUNCT
ejpam-1535	268	31	4	4	NUM
ejpam-1535	268	32	)	)	PUNCT
ejpam-1535	268	33	.	.	PUNCT
ejpam-1535	269	1	once	once	ADV
ejpam-1535	269	2	again	again	ADV
ejpam-1535	269	3	,	,	PUNCT
ejpam-1535	269	4	any	any	DET
ejpam-1535	269	5	inverse	inverse	NOUN
ejpam-1535	269	6	semigroup	semigroup	NOUN
ejpam-1535	269	7	is	be	AUX
ejpam-1535	269	8	ample	ample	ADJ
ejpam-1535	269	9	,	,	PUNCT
ejpam-1535	269	10	with	with	ADP
ejpam-1535	269	11	a+	a+	PRON
ejpam-1535	269	12	=	=	SYM
ejpam-1535	269	13	aa−1	aa−1	PROPN
ejpam-1535	269	14	and	and	CCONJ
ejpam-1535	269	15	a∗	a∗	NOUN
ejpam-1535	269	16	=	=	SYM
ejpam-1535	269	17	a−1a	a−1a	PROPN
ejpam-1535	269	18	.	.	PUNCT
ejpam-1535	270	1	in	in	ADP
ejpam-1535	270	2	contrast	contrast	NOUN
ejpam-1535	270	3	to	to	ADP
ejpam-1535	270	4	the	the	DET
ejpam-1535	270	5	situation	situation	NOUN
ejpam-1535	270	6	with	with	ADP
ejpam-1535	270	7	restriction	restriction	NOUN
ejpam-1535	270	8	semigroups	semigroup	NOUN
ejpam-1535	270	9	,	,	PUNCT
ejpam-1535	270	10	left	leave	VERB
ejpam-1535	270	11	/	/	SYM
ejpam-1535	270	12	right	right	ADJ
ejpam-1535	270	13	ample	ample	ADJ
ejpam-1535	270	14	semigroups	semigroup	NOUN
ejpam-1535	270	15	form	form	VERB
ejpam-1535	270	16	only	only	ADV
ejpam-1535	270	17	a	a	DET
ejpam-1535	270	18	quasi	quasi	NOUN
ejpam-1535	270	19	-	-	NOUN
ejpam-1535	270	20	variety	variety	NOUN
ejpam-1535	270	21	of	of	ADP
ejpam-1535	270	22	algebras	algebra	NOUN
ejpam-1535	270	23	of	of	ADP
ejpam-1535	270	24	type	type	NOUN
ejpam-1535	270	25	(	(	PUNCT
ejpam-1535	270	26	2,1	2,1	NUM
ejpam-1535	270	27	)	)	PUNCT
ejpam-1535	270	28	,	,	PUNCT
ejpam-1535	270	29	whilst	whilst	SCONJ
ejpam-1535	270	30	two	two	NUM
ejpam-1535	270	31	-	-	PUNCT
ejpam-1535	270	32	sided	sided	ADJ
ejpam-1535	270	33	ample	ample	ADJ
ejpam-1535	270	34	semigroups	semigroup	NOUN
ejpam-1535	270	35	form	form	VERB
ejpam-1535	270	36	a	a	DET
ejpam-1535	270	37	quasi	quasi	NOUN
ejpam-1535	270	38	-	-	NOUN
ejpam-1535	270	39	variety	variety	NOUN
ejpam-1535	270	40	of	of	ADP
ejpam-1535	270	41	algebras	algebra	NOUN
ejpam-1535	270	42	of	of	ADP
ejpam-1535	270	43	type	type	NOUN
ejpam-1535	270	44	(	(	PUNCT
ejpam-1535	270	45	2,1,1	2,1,1	NUM
ejpam-1535	270	46	)	)	PUNCT
ejpam-1535	270	47	.	.	PUNCT
ejpam-1535	271	1	as	as	ADP
ejpam-1535	271	2	a	a	DET
ejpam-1535	271	3	final	final	ADJ
ejpam-1535	271	4	comment	comment	NOUN
ejpam-1535	271	5	on	on	ADP
ejpam-1535	271	6	the	the	DET
ejpam-1535	271	7	ample	ample	ADJ
ejpam-1535	271	8	case	case	NOUN
ejpam-1535	271	9	,	,	PUNCT
ejpam-1535	271	10	we	we	PRON
ejpam-1535	271	11	observe	observe	VERB
ejpam-1535	271	12	that	that	SCONJ
ejpam-1535	271	13	,	,	PUNCT
ejpam-1535	271	14	unlike	unlike	ADP
ejpam-1535	271	15	for	for	ADP
ejpam-1535	271	16	restriction	restriction	NOUN
ejpam-1535	271	17	semigroups	semigroup	NOUN
ejpam-1535	271	18	,	,	PUNCT
ejpam-1535	271	19	we	we	PRON
ejpam-1535	271	20	have	have	AUX
ejpam-1535	271	21	not	not	PART
ejpam-1535	271	22	defined	define	VERB
ejpam-1535	271	23	ample	ample	ADJ
ejpam-1535	271	24	semigroups	semigroup	NOUN
ejpam-1535	271	25	with	with	ADP
ejpam-1535	271	26	respect	respect	NOUN
ejpam-1535	271	27	to	to	ADP
ejpam-1535	271	28	a	a	DET
ejpam-1535	271	29	distinguished	distinguished	ADJ
ejpam-1535	271	30	subsemilattice	subsemilattice	NOUN
ejpam-1535	271	31	.	.	PUNCT
ejpam-1535	272	1	this	this	PRON
ejpam-1535	272	2	is	be	AUX
ejpam-1535	272	3	because	because	SCONJ
ejpam-1535	272	4	there	there	PRON
ejpam-1535	272	5	is	be	VERB
ejpam-1535	272	6	no	no	DET
ejpam-1535	272	7	need	need	NOUN
ejpam-1535	272	8	to	to	PART
ejpam-1535	272	9	do	do	AUX
ejpam-1535	272	10	so	so	ADV
ejpam-1535	272	11	:	:	PUNCT
ejpam-1535	272	12	any	any	DET
ejpam-1535	272	13	left	left	ADJ
ejpam-1535	272	14	/	/	SYM
ejpam-1535	272	15	right	right	ADJ
ejpam-1535	272	16	/	/	SYM
ejpam-1535	272	17	two	two	NUM
ejpam-1535	272	18	-	-	PUNCT
ejpam-1535	272	19	sided	sided	ADJ
ejpam-1535	272	20	ample	ample	ADJ
ejpam-1535	272	21	semigroup	semigroup	NOUN
ejpam-1535	272	22	is	be	AUX
ejpam-1535	272	23	necessary	necessary	ADJ
ejpam-1535	272	24	full	full	ADJ
ejpam-1535	272	25	in	in	ADP
ejpam-1535	272	26	the	the	DET
ejpam-1535	272	27	sense	sense	NOUN
ejpam-1535	272	28	of	of	ADP
ejpam-1535	272	29	definition	definition	NOUN
ejpam-1535	272	30	2	2	NUM
ejpam-1535	272	31	(	(	PUNCT
ejpam-1535	272	32	3	3	NUM
ejpam-1535	272	33	)	)	PUNCT
ejpam-1535	272	34	.	.	PUNCT
ejpam-1535	273	1	to	to	PART
ejpam-1535	273	2	see	see	VERB
ejpam-1535	273	3	this	this	PRON
ejpam-1535	273	4	,	,	PUNCT
ejpam-1535	273	5	we	we	PRON
ejpam-1535	273	6	suppose	suppose	VERB
ejpam-1535	273	7	that	that	SCONJ
ejpam-1535	273	8	we	we	PRON
ejpam-1535	273	9	have	have	AUX
ejpam-1535	273	10	defined	define	VERB
ejpam-1535	273	11	a	a	DET
ejpam-1535	273	12	“	"	PUNCT
ejpam-1535	273	13	left	left	ADJ
ejpam-1535	273	14	e	e	NOUN
ejpam-1535	273	15	-	-	ADJ
ejpam-1535	273	16	ample	ample	ADJ
ejpam-1535	273	17	semigroup	semigroup	NOUN
ejpam-1535	273	18	”	"	PUNCT
ejpam-1535	273	19	s	s	NOUN
ejpam-1535	273	20	by	by	ADP
ejpam-1535	273	21	replacing	replace	VERB
ejpam-1535	273	22	all	all	DET
ejpam-1535	273	23	occurrences	occurrence	NOUN
ejpam-1535	273	24	of	of	ADP
ejpam-1535	273	25	“	"	PUNCT
ejpam-1535	273	26	e(s	e(s	PROPN
ejpam-1535	273	27	)	)	PUNCT
ejpam-1535	273	28	”	"	PUNCT
ejpam-1535	273	29	in	in	ADP
ejpam-1535	273	30	definition	definition	NOUN
ejpam-1535	273	31	5	5	NUM
ejpam-1535	273	32	by	by	ADP
ejpam-1535	273	33	“	"	PUNCT
ejpam-1535	273	34	e	e	NOUN
ejpam-1535	273	35	”	"	PUNCT
ejpam-1535	273	36	,	,	PUNCT
ejpam-1535	273	37	where	where	SCONJ
ejpam-1535	273	38	e	e	NOUN
ejpam-1535	273	39	is	be	AUX
ejpam-1535	273	40	some	some	DET
ejpam-1535	273	41	distinguished	distinguished	ADJ
ejpam-1535	273	42	subsemilattice	subsemilattice	NOUN
ejpam-1535	273	43	of	of	ADP
ejpam-1535	273	44	s.	s.	PROPN
ejpam-1535	273	45	we	we	PRON
ejpam-1535	273	46	take	take	VERB
ejpam-1535	273	47	an	an	DET
ejpam-1535	273	48	arbitrary	arbitrary	ADJ
ejpam-1535	273	49	idempotent	idempotent	NOUN
ejpam-1535	273	50	e	e	PROPN
ejpam-1535	273	51	∈	∈	PROPN
ejpam-1535	273	52	s	s	PART
ejpam-1535	273	53	and	and	CCONJ
ejpam-1535	273	54	observe	observe	VERB
ejpam-1535	273	55	,	,	PUNCT
ejpam-1535	273	56	using	use	VERB
ejpam-1535	273	57	the	the	DET
ejpam-1535	273	58	second	second	ADJ
ejpam-1535	273	59	condition	condition	NOUN
ejpam-1535	273	60	of	of	ADP
ejpam-1535	273	61	definition	definition	NOUN
ejpam-1535	273	62	5	5	NUM
ejpam-1535	273	63	,	,	PUNCT
ejpam-1535	273	64	together	together	ADV
ejpam-1535	273	65	with	with	ADP
ejpam-1535	273	66	lemma	lemma	PROPN
ejpam-1535	273	67	1	1	NUM
ejpam-1535	273	68	,	,	PUNCT
ejpam-1535	273	69	that	that	ADV
ejpam-1535	273	70	ee+	ee+	ADJ
ejpam-1535	273	71	=	=	PUNCT
ejpam-1535	273	72	(	(	PUNCT
ejpam-1535	273	73	ee+)+e	ee+)+e	NOUN
ejpam-1535	273	74	=	=	SYM
ejpam-1535	273	75	(	(	PUNCT
ejpam-1535	273	76	ee)+e	ee)+e	NOUN
ejpam-1535	273	77	=	=	PUNCT
ejpam-1535	273	78	e+e	e+e	PUNCT
ejpam-1535	273	79	=	=	PUNCT
ejpam-1535	273	80	e.	e.	PROPN
ejpam-1535	273	81	however	however	ADV
ejpam-1535	273	82	,	,	PUNCT
ejpam-1535	273	83	since	since	SCONJ
ejpam-1535	273	84	ee	ee	PROPN
ejpam-1535	273	85	=	=	SYM
ejpam-1535	273	86	e+e	e+e	PROPN
ejpam-1535	273	87	and	and	CCONJ
ejpam-1535	273	88	er∗	er∗	VERB
ejpam-1535	273	89	e+	e+	VERB
ejpam-1535	273	90	,	,	PUNCT
ejpam-1535	273	91	we	we	PRON
ejpam-1535	273	92	have	have	VERB
ejpam-1535	273	93	ee+	ee+	ADJ
ejpam-1535	273	94	=	=	SYM
ejpam-1535	273	95	e+e+	e+e+	NOUN
ejpam-1535	273	96	,	,	PUNCT
ejpam-1535	273	97	hence	hence	ADV
ejpam-1535	273	98	e	e	NOUN
ejpam-1535	273	99	=	=	PUNCT
ejpam-1535	273	100	e+	e+	X
ejpam-1535	273	101	,	,	PUNCT
ejpam-1535	273	102	from	from	ADP
ejpam-1535	273	103	which	which	PRON
ejpam-1535	273	104	we	we	PRON
ejpam-1535	273	105	conclude	conclude	VERB
ejpam-1535	273	106	that	that	SCONJ
ejpam-1535	273	107	e	e	NOUN
ejpam-1535	273	108	=	=	SYM
ejpam-1535	273	109	e(s	e(s	PROPN
ejpam-1535	273	110	)	)	PUNCT
ejpam-1535	273	111	.	.	PUNCT
ejpam-1535	274	1	a	a	DET
ejpam-1535	274	2	similar	similar	ADJ
ejpam-1535	274	3	argument	argument	NOUN
ejpam-1535	274	4	may	may	AUX
ejpam-1535	274	5	be	be	AUX
ejpam-1535	274	6	made	make	VERB
ejpam-1535	274	7	for	for	ADP
ejpam-1535	274	8	the	the	DET
ejpam-1535	274	9	right	right	ADJ
ejpam-1535	274	10	-	-	PUNCT
ejpam-1535	274	11	hand	hand	NOUN
ejpam-1535	274	12	version	version	NOUN
ejpam-1535	274	13	of	of	ADP
ejpam-1535	274	14	these	these	DET
ejpam-1535	274	15	semigroups	semigroup	NOUN
ejpam-1535	274	16	.	.	PUNCT
ejpam-1535	275	1	the	the	DET
ejpam-1535	275	2	notion	notion	NOUN
ejpam-1535	275	3	of	of	ADP
ejpam-1535	275	4	a	a	DET
ejpam-1535	275	5	“	"	PUNCT
ejpam-1535	275	6	left	left	ADJ
ejpam-1535	275	7	/	/	SYM
ejpam-1535	275	8	right	right	ADJ
ejpam-1535	275	9	/	/	SYM
ejpam-1535	275	10	two	two	NUM
ejpam-1535	275	11	-	-	PUNCT
ejpam-1535	275	12	sided	sided	ADJ
ejpam-1535	275	13	e	e	ADJ
ejpam-1535	275	14	-	-	ADJ
ejpam-1535	275	15	ample	ample	ADJ
ejpam-1535	275	16	semigroup	semigroup	NOUN
ejpam-1535	275	17	”	"	PUNCT
ejpam-1535	275	18	is	be	AUX
ejpam-1535	275	19	therefore	therefore	ADV
ejpam-1535	275	20	redundant	redundant	ADJ
ejpam-1535	275	21	.	.	PUNCT
ejpam-1535	276	1	4	4	X
ejpam-1535	276	2	.	.	NUM
ejpam-1535	276	3	inductive	inductive	ADJ
ejpam-1535	276	4	categories	category	NOUN
ejpam-1535	276	5	having	having	AUX
ejpam-1535	276	6	defined	define	VERB
ejpam-1535	276	7	the	the	DET
ejpam-1535	276	8	semigroups	semigroup	NOUN
ejpam-1535	276	9	of	of	ADP
ejpam-1535	276	10	interest	interest	NOUN
ejpam-1535	276	11	,	,	PUNCT
ejpam-1535	276	12	we	we	PRON
ejpam-1535	276	13	now	now	ADV
ejpam-1535	276	14	turn	turn	VERB
ejpam-1535	276	15	our	our	PRON
ejpam-1535	276	16	attention	attention	NOUN
ejpam-1535	276	17	to	to	ADP
ejpam-1535	276	18	the	the	DET
ejpam-1535	276	19	definition	definition	NOUN
ejpam-1535	276	20	of	of	ADP
ejpam-1535	276	21	a	a	DET
ejpam-1535	276	22	category	category	NOUN
ejpam-1535	276	23	(	(	PUNCT
ejpam-1535	276	24	in	in	ADP
ejpam-1535	276	25	sense	sense	NOUN
ejpam-1535	276	26	(	(	PUNCT
ejpam-1535	276	27	♣	♣	NOUN
ejpam-1535	276	28	)	)	PUNCT
ejpam-1535	276	29	of	of	ADP
ejpam-1535	276	30	the	the	DET
ejpam-1535	276	31	introduction	introduction	NOUN
ejpam-1535	276	32	)	)	PUNCT
ejpam-1535	276	33	.	.	PUNCT
ejpam-1535	277	1	let	let	VERB
ejpam-1535	277	2	c	c	PRON
ejpam-1535	277	3	be	be	AUX
ejpam-1535	277	4	a	a	DET
ejpam-1535	277	5	class	class	NOUN
ejpam-1535	277	6	and	and	CCONJ
ejpam-1535	277	7	let	let	VERB
ejpam-1535	277	8	·	·	PUNCT
ejpam-1535	277	9	be	be	AUX
ejpam-1535	277	10	a	a	DET
ejpam-1535	277	11	partial	partial	ADJ
ejpam-1535	277	12	binary	binary	ADJ
ejpam-1535	277	13	operation	operation	NOUN
ejpam-1535	277	14	on	on	ADP
ejpam-1535	277	15	c	c	PROPN
ejpam-1535	277	16	,	,	PUNCT
ejpam-1535	277	17	i.e.	i.e.	X
ejpam-1535	277	18	,	,	PUNCT
ejpam-1535	277	19	an	an	DET
ejpam-1535	277	20	operation	operation	NOUN
ejpam-1535	277	21	which	which	PRON
ejpam-1535	277	22	is	be	AUX
ejpam-1535	277	23	not	not	PART
ejpam-1535	277	24	necessarily	necessarily	ADV
ejpam-1535	277	25	defined	define	VERB
ejpam-1535	277	26	for	for	ADP
ejpam-1535	277	27	all	all	DET
ejpam-1535	277	28	pairs	pair	NOUN
ejpam-1535	277	29	(	(	PUNCT
ejpam-1535	277	30	x	x	NOUN
ejpam-1535	277	31	,	,	PUNCT
ejpam-1535	277	32	y	y	PROPN
ejpam-1535	277	33	)	)	PUNCT
ejpam-1535	277	34	∈	∈	PROPN
ejpam-1535	278	1	c	c	AUX
ejpam-1535	278	2	×	×	NOUN
ejpam-1535	278	3	c	c	NOUN
ejpam-1535	278	4	;	;	PUNCT
ejpam-1535	278	5	whenever	whenever	SCONJ
ejpam-1535	278	6	the	the	DET
ejpam-1535	278	7	product	product	NOUN
ejpam-1535	278	8	x	x	X
ejpam-1535	278	9	·	·	PUNCT
ejpam-1535	278	10	y	y	NOUN
ejpam-1535	278	11	is	be	AUX
ejpam-1535	278	12	defined	define	VERB
ejpam-1535	278	13	,	,	PUNCT
ejpam-1535	278	14	we	we	PRON
ejpam-1535	278	15	denote	denote	VERB
ejpam-1535	278	16	the	the	DET
ejpam-1535	278	17	fact	fact	NOUN
ejpam-1535	278	18	by	by	ADP
ejpam-1535	278	19	“	"	PUNCT
ejpam-1535	278	20	∃x	∃x	PROPN
ejpam-1535	278	21	·	·	PUNCT
ejpam-1535	278	22	y	y	NOUN
ejpam-1535	278	23	”	"	PUNCT
ejpam-1535	278	24	.	.	PUNCT
ejpam-1535	279	1	when	when	SCONJ
ejpam-1535	279	2	we	we	PRON
ejpam-1535	279	3	write	write	VERB
ejpam-1535	279	4	expressions	expression	NOUN
ejpam-1535	279	5	such	such	ADJ
ejpam-1535	279	6	as	as	ADP
ejpam-1535	279	7	“	"	PUNCT
ejpam-1535	279	8	∃(x	∃(x	PROPN
ejpam-1535	279	9	·	·	PUNCT
ejpam-1535	279	10	y	y	X
ejpam-1535	279	11	)	)	PUNCT
ejpam-1535	279	12	·	·	PUNCT
ejpam-1535	280	1	z	z	X
ejpam-1535	280	2	”	"	PUNCT
ejpam-1535	280	3	,	,	PUNCT
ejpam-1535	280	4	for	for	ADP
ejpam-1535	280	5	example	example	NOUN
ejpam-1535	280	6	,	,	PUNCT
ejpam-1535	280	7	we	we	PRON
ejpam-1535	280	8	mean	mean	VERB
ejpam-1535	280	9	that	that	SCONJ
ejpam-1535	280	10	∃x	∃x	ADJ
ejpam-1535	280	11	·	·	PUNCT
ejpam-1535	280	12	y	y	PROPN
ejpam-1535	280	13	and	and	CCONJ
ejpam-1535	280	14	∃(x	∃(x	PROPN
ejpam-1535	280	15	·	·	PUNCT
ejpam-1535	280	16	y	y	X
ejpam-1535	280	17	)	)	PUNCT
ejpam-1535	280	18	·	·	PUNCT
ejpam-1535	281	1	z.	z.	PROPN
ejpam-1535	282	1	an	an	DET
ejpam-1535	282	2	element	element	NOUN
ejpam-1535	282	3	e	e	PROPN
ejpam-1535	282	4	∈	∈	PROPN
ejpam-1535	282	5	c	c	PROPN
ejpam-1535	282	6	is	be	AUX
ejpam-1535	282	7	termed	term	VERB
ejpam-1535	282	8	idempotent	idempotent	ADJ
ejpam-1535	282	9	if	if	SCONJ
ejpam-1535	282	10	∃e	∃e	NUM
ejpam-1535	282	11	·	·	PUNCT
ejpam-1535	282	12	e	e	NOUN
ejpam-1535	282	13	and	and	CCONJ
ejpam-1535	282	14	e	e	X
ejpam-1535	282	15	·	·	PUNCT
ejpam-1535	282	16	e	e	X
ejpam-1535	282	17	=	=	PUNCT
ejpam-1535	282	18	e.	e.	PROPN
ejpam-1535	283	1	the	the	DET
ejpam-1535	283	2	identities	identity	NOUN
ejpam-1535	283	3	of	of	ADP
ejpam-1535	283	4	c	c	PROPN
ejpam-1535	283	5	are	be	AUX
ejpam-1535	283	6	those	those	DET
ejpam-1535	283	7	idempotents	idempotent	NOUN
ejpam-1535	283	8	e	e	X
ejpam-1535	283	9	which	which	PRON
ejpam-1535	283	10	satisfy	satisfy	VERB
ejpam-1535	283	11	the	the	DET
ejpam-1535	283	12	following	follow	VERB
ejpam-1535	283	13	conditions	condition	NOUN
ejpam-1535	283	14	,	,	PUNCT
ejpam-1535	283	15	for	for	ADP
ejpam-1535	283	16	any	any	DET
ejpam-1535	283	17	x	x	SYM
ejpam-1535	283	18	∈	∈	PROPN
ejpam-1535	283	19	c	c	NOUN
ejpam-1535	283	20	:	:	PUNCT
ejpam-1535	283	21	∃e	∃e	NUM
ejpam-1535	283	22	·	·	PUNCT
ejpam-1535	283	23	x	x	PUNCT
ejpam-1535	284	1	=	=	NOUN
ejpam-1535	284	2	⇒	⇒	X
ejpam-1535	284	3	e	e	X
ejpam-1535	284	4	·	·	PUNCT
ejpam-1535	284	5	x	x	SYM
ejpam-1535	284	6	=	=	PUNCT
ejpam-1535	284	7	x	x	PROPN
ejpam-1535	284	8	;	;	PUNCT
ejpam-1535	284	9	c.	c.	PROPN
ejpam-1535	284	10	hollings	holling	NOUN
ejpam-1535	284	11	/	/	SYM
ejpam-1535	284	12	eur	eur	PROPN
ejpam-1535	284	13	.	.	PUNCT
ejpam-1535	285	1	j.	j.	PROPN
ejpam-1535	285	2	pure	pure	PROPN
ejpam-1535	285	3	appl	appl	PROPN
ejpam-1535	285	4	.	.	PROPN
ejpam-1535	285	5	math	math	PROPN
ejpam-1535	285	6	,	,	PUNCT
ejpam-1535	285	7	5	5	NUM
ejpam-1535	285	8	(	(	PUNCT
ejpam-1535	285	9	2012	2012	NUM
ejpam-1535	285	10	)	)	PUNCT
ejpam-1535	285	11	,	,	PUNCT
ejpam-1535	285	12	414	414	NUM
ejpam-1535	285	13	-	-	SYM
ejpam-1535	285	14	450	450	NUM
ejpam-1535	285	15	427	427	NUM
ejpam-1535	285	16	∃x	∃x	NOUN
ejpam-1535	285	17	·	·	PUNCT
ejpam-1535	285	18	e	e	X
ejpam-1535	286	1	=	=	NOUN
ejpam-1535	286	2	⇒	⇒	NOUN
ejpam-1535	286	3	x	x	X
ejpam-1535	286	4	·	·	PUNCT
ejpam-1535	286	5	e	e	X
ejpam-1535	286	6	=	=	PUNCT
ejpam-1535	286	7	x	x	X
ejpam-1535	286	8	.	.	PUNCT
ejpam-1535	287	1	we	we	PRON
ejpam-1535	287	2	denote	denote	VERB
ejpam-1535	287	3	the	the	DET
ejpam-1535	287	4	subset	subset	NOUN
ejpam-1535	287	5	of	of	ADP
ejpam-1535	287	6	identities	identity	NOUN
ejpam-1535	287	7	of	of	ADP
ejpam-1535	287	8	c	c	PROPN
ejpam-1535	287	9	by	by	ADP
ejpam-1535	287	10	co	co	PROPN
ejpam-1535	287	11	(	(	PUNCT
ejpam-1535	287	12	“	"	PUNCT
ejpam-1535	287	13	o	o	NOUN
ejpam-1535	287	14	”	"	PUNCT
ejpam-1535	287	15	for	for	ADP
ejpam-1535	287	16	“	"	PUNCT
ejpam-1535	287	17	objects	object	NOUN
ejpam-1535	287	18	”	"	PUNCT
ejpam-1535	287	19	)	)	PUNCT
ejpam-1535	287	20	.	.	PUNCT
ejpam-1535	288	1	definition	definition	NOUN
ejpam-1535	288	2	8	8	NUM
ejpam-1535	288	3	.	.	PUNCT
ejpam-1535	289	1	let	let	VERB
ejpam-1535	289	2	c	c	PRON
ejpam-1535	289	3	be	be	AUX
ejpam-1535	289	4	a	a	DET
ejpam-1535	289	5	class	class	NOUN
ejpam-1535	289	6	and	and	CCONJ
ejpam-1535	289	7	let	let	VERB
ejpam-1535	289	8	·	·	PUNCT
ejpam-1535	289	9	be	be	AUX
ejpam-1535	289	10	a	a	DET
ejpam-1535	289	11	partial	partial	ADJ
ejpam-1535	289	12	binary	binary	ADJ
ejpam-1535	289	13	operation	operation	NOUN
ejpam-1535	289	14	on	on	ADP
ejpam-1535	289	15	c.	c.	PROPN
ejpam-1535	289	16	the	the	DET
ejpam-1535	289	17	pair	pair	NOUN
ejpam-1535	289	18	(	(	PUNCT
ejpam-1535	289	19	c	c	NOUN
ejpam-1535	289	20	,	,	PUNCT
ejpam-1535	289	21	·	·	PUNCT
ejpam-1535	289	22	)	)	PUNCT
ejpam-1535	289	23	is	be	AUX
ejpam-1535	289	24	a	a	DET
ejpam-1535	289	25	category	category	NOUN
ejpam-1535	289	26	if	if	SCONJ
ejpam-1535	289	27	the	the	DET
ejpam-1535	289	28	following	follow	VERB
ejpam-1535	289	29	conditions	condition	NOUN
ejpam-1535	289	30	hold	hold	VERB
ejpam-1535	289	31	:	:	PUNCT
ejpam-1535	289	32	(	(	PUNCT
ejpam-1535	289	33	ca1	ca1	NOUN
ejpam-1535	289	34	)	)	PUNCT
ejpam-1535	289	35	∃x	∃x	NOUN
ejpam-1535	289	36	·	·	PUNCT
ejpam-1535	289	37	(	(	PUNCT
ejpam-1535	289	38	y	y	PROPN
ejpam-1535	289	39	·	·	PUNCT
ejpam-1535	290	1	z)	z)	NUM
ejpam-1535	290	2	⇐	⇐	PROPN
ejpam-1535	290	3	⇒∃(x	⇒∃(x	SYM
ejpam-1535	290	4	·	·	SYM
ejpam-1535	290	5	y	y	X
ejpam-1535	290	6	)	)	PUNCT
ejpam-1535	290	7	·	·	PUNCT
ejpam-1535	291	1	z	z	X
ejpam-1535	291	2	,	,	PUNCT
ejpam-1535	291	3	in	in	ADP
ejpam-1535	291	4	which	which	DET
ejpam-1535	291	5	case	case	NOUN
ejpam-1535	291	6	x	x	X
ejpam-1535	291	7	·	·	PUNCT
ejpam-1535	291	8	(	(	PUNCT
ejpam-1535	291	9	y	y	PROPN
ejpam-1535	291	10	·	·	PUNCT
ejpam-1535	291	11	z	z	X
ejpam-1535	291	12	)	)	PUNCT
ejpam-1535	291	13	=	=	SYM
ejpam-1535	291	14	(	(	PUNCT
ejpam-1535	291	15	x	x	X
ejpam-1535	291	16	·	·	PUNCT
ejpam-1535	291	17	y	y	X
ejpam-1535	291	18	)	)	PUNCT
ejpam-1535	291	19	·	·	PUNCT
ejpam-1535	292	1	z	z	X
ejpam-1535	292	2	;	;	PUNCT
ejpam-1535	292	3	(	(	PUNCT
ejpam-1535	292	4	ca2	ca2	NOUN
ejpam-1535	292	5	)	)	PUNCT
ejpam-1535	292	6	∃x	∃x	NOUN
ejpam-1535	292	7	·	·	PUNCT
ejpam-1535	292	8	(	(	PUNCT
ejpam-1535	292	9	y	y	PROPN
ejpam-1535	292	10	·	·	PUNCT
ejpam-1535	292	11	z)	z)	NUM
ejpam-1535	292	12	⇐	⇐	ADJ
ejpam-1535	292	13	⇒∃x	⇒∃x	SYM
ejpam-1535	292	14	·	·	PUNCT
ejpam-1535	292	15	y	y	PROPN
ejpam-1535	292	16	and	and	CCONJ
ejpam-1535	292	17	∃y	∃y	PROPN
ejpam-1535	292	18	·	·	PUNCT
ejpam-1535	293	1	z	z	NOUN
ejpam-1535	293	2	;	;	PUNCT
ejpam-1535	293	3	(	(	PUNCT
ejpam-1535	293	4	ca3	ca3	NOUN
ejpam-1535	293	5	)	)	PUNCT
ejpam-1535	293	6	for	for	ADP
ejpam-1535	293	7	each	each	DET
ejpam-1535	293	8	x	x	SYM
ejpam-1535	293	9	∈	∈	PROPN
ejpam-1535	293	10	c	c	X
ejpam-1535	293	11	,	,	PUNCT
ejpam-1535	293	12	there	there	PRON
ejpam-1535	293	13	exist	exist	VERB
ejpam-1535	293	14	unique	unique	ADJ
ejpam-1535	293	15	identities	identity	NOUN
ejpam-1535	293	16	d(x	d(x	PROPN
ejpam-1535	293	17	)	)	PUNCT
ejpam-1535	293	18	,	,	PUNCT
ejpam-1535	294	1	r(x	r(x	PROPN
ejpam-1535	294	2	)	)	PUNCT
ejpam-1535	294	3	∈	∈	PROPN
ejpam-1535	294	4	co	co	NOUN
ejpam-1535	294	5	such	such	ADJ
ejpam-1535	294	6	that	that	PRON
ejpam-1535	294	7	∃d(x	∃d(x	NOUN
ejpam-1535	294	8	)	)	PUNCT
ejpam-1535	294	9	·	·	PUNCT
ejpam-1535	295	1	x	x	PUNCT
ejpam-1535	295	2	and	and	CCONJ
ejpam-1535	295	3	∃x	∃x	PROPN
ejpam-1535	295	4	·	·	PUNCT
ejpam-1535	295	5	r(x	r(x	NOUN
ejpam-1535	295	6	)	)	PUNCT
ejpam-1535	295	7	.	.	PUNCT
ejpam-1535	296	1	if	if	SCONJ
ejpam-1535	296	2	c	c	PROPN
ejpam-1535	296	3	is	be	AUX
ejpam-1535	296	4	simply	simply	ADV
ejpam-1535	296	5	a	a	DET
ejpam-1535	296	6	set	set	NOUN
ejpam-1535	296	7	,	,	PUNCT
ejpam-1535	296	8	then	then	ADV
ejpam-1535	296	9	we	we	PRON
ejpam-1535	296	10	call	call	VERB
ejpam-1535	296	11	(	(	PUNCT
ejpam-1535	296	12	c	c	NOUN
ejpam-1535	296	13	,	,	PUNCT
ejpam-1535	296	14	·	·	PUNCT
ejpam-1535	296	15	)	)	PUNCT
ejpam-1535	296	16	a	a	DET
ejpam-1535	296	17	small	small	ADJ
ejpam-1535	296	18	category	category	NOUN
ejpam-1535	296	19	.	.	PUNCT
ejpam-1535	297	1	whenever	whenever	SCONJ
ejpam-1535	297	2	the	the	DET
ejpam-1535	297	3	partial	partial	ADJ
ejpam-1535	297	4	multiplication	multiplication	NOUN
ejpam-1535	297	5	in	in	ADP
ejpam-1535	297	6	a	a	DET
ejpam-1535	297	7	category	category	NOUN
ejpam-1535	297	8	(	(	PUNCT
ejpam-1535	297	9	c	c	NOUN
ejpam-1535	297	10	,	,	PUNCT
ejpam-1535	297	11	·	·	PUNCT
ejpam-1535	297	12	)	)	PUNCT
ejpam-1535	297	13	is	be	AUX
ejpam-1535	297	14	clear	clear	ADJ
ejpam-1535	297	15	,	,	PUNCT
ejpam-1535	297	16	we	we	PRON
ejpam-1535	297	17	will	will	AUX
ejpam-1535	297	18	refer	refer	VERB
ejpam-1535	297	19	simply	simply	ADV
ejpam-1535	297	20	to	to	ADP
ejpam-1535	297	21	“	"	PUNCT
ejpam-1535	297	22	the	the	DET
ejpam-1535	297	23	category	category	NOUN
ejpam-1535	297	24	c	c	NOUN
ejpam-1535	297	25	”	"	PUNCT
ejpam-1535	297	26	.	.	PUNCT
ejpam-1535	298	1	the	the	DET
ejpam-1535	298	2	identity	identity	NOUN
ejpam-1535	298	3	d(x	d(x	NOUN
ejpam-1535	298	4	)	)	PUNCT
ejpam-1535	298	5	is	be	AUX
ejpam-1535	298	6	called	call	VERB
ejpam-1535	298	7	the	the	DET
ejpam-1535	298	8	domain	domain	NOUN
ejpam-1535	298	9	of	of	ADP
ejpam-1535	298	10	x	x	X
ejpam-1535	298	11	and	and	CCONJ
ejpam-1535	298	12	r(x	r(x	PROPN
ejpam-1535	298	13	)	)	PUNCT
ejpam-1535	298	14	is	be	AUX
ejpam-1535	298	15	the	the	DET
ejpam-1535	298	16	range	range	NOUN
ejpam-1535	298	17	of	of	ADP
ejpam-1535	298	18	x	x	X
ejpam-1535	298	19	.	.	PUNCT
ejpam-1535	299	1	notice	notice	VERB
ejpam-1535	299	2	that	that	SCONJ
ejpam-1535	299	3	by	by	ADP
ejpam-1535	299	4	the	the	DET
ejpam-1535	299	5	definition	definition	NOUN
ejpam-1535	299	6	of	of	ADP
ejpam-1535	299	7	identities	identity	NOUN
ejpam-1535	299	8	,	,	PUNCT
ejpam-1535	299	9	d(x	d(x	PROPN
ejpam-1535	299	10	)	)	PUNCT
ejpam-1535	299	11	·	·	PUNCT
ejpam-1535	299	12	x	x	PUNCT
ejpam-1535	300	1	=	=	PUNCT
ejpam-1535	300	2	x	x	X
ejpam-1535	300	3	and	and	CCONJ
ejpam-1535	300	4	x	x	X
ejpam-1535	300	5	·	·	PUNCT
ejpam-1535	300	6	r(x	r(x	NOUN
ejpam-1535	300	7	)	)	PUNCT
ejpam-1535	300	8	=	=	PUNCT
ejpam-1535	301	1	x	x	X
ejpam-1535	301	2	.	.	PUNCT
ejpam-1535	302	1	moreover	moreover	ADV
ejpam-1535	302	2	,	,	PUNCT
ejpam-1535	302	3	for	for	ADP
ejpam-1535	302	4	any	any	DET
ejpam-1535	302	5	identity	identity	NOUN
ejpam-1535	302	6	e	e	NOUN
ejpam-1535	302	7	,	,	PUNCT
ejpam-1535	302	8	d(e	d(e	PROPN
ejpam-1535	302	9	)	)	PUNCT
ejpam-1535	302	10	=	=	SYM
ejpam-1535	302	11	r(e	r(e	NOUN
ejpam-1535	302	12	)	)	PUNCT
ejpam-1535	303	1	=	=	SYM
ejpam-1535	303	2	e.	e.	PROPN
ejpam-1535	304	1	all	all	DET
ejpam-1535	304	2	categories	category	NOUN
ejpam-1535	304	3	considered	consider	VERB
ejpam-1535	304	4	from	from	ADP
ejpam-1535	304	5	this	this	DET
ejpam-1535	304	6	point	point	NOUN
ejpam-1535	304	7	of	of	ADP
ejpam-1535	304	8	view	view	NOUN
ejpam-1535	304	9	(	(	PUNCT
ejpam-1535	304	10	i.e.	i.e.	X
ejpam-1535	304	11	,	,	PUNCT
ejpam-1535	304	12	in	in	ADP
ejpam-1535	304	13	sense	sense	NOUN
ejpam-1535	304	14	(	(	PUNCT
ejpam-1535	304	15	♣	♣	NOUN
ejpam-1535	304	16	)	)	PUNCT
ejpam-1535	304	17	)	)	PUNCT
ejpam-1535	304	18	will	will	AUX
ejpam-1535	304	19	be	be	AUX
ejpam-1535	304	20	small	small	ADJ
ejpam-1535	304	21	categories	category	NOUN
ejpam-1535	304	22	.	.	PUNCT
ejpam-1535	305	1	lemma	lemma	PROPN
ejpam-1535	305	2	2	2	NUM
ejpam-1535	305	3	(	(	PUNCT
ejpam-1535	305	4	[	[	X
ejpam-1535	305	5	f	f	X
ejpam-1535	305	6	]	]	X
ejpam-1535	305	7	)	)	PUNCT
ejpam-1535	305	8	.	.	PUNCT
ejpam-1535	306	1	let	let	AUX
ejpam-1535	306	2	(	(	PUNCT
ejpam-1535	306	3	c	c	NOUN
ejpam-1535	306	4	,	,	PUNCT
ejpam-1535	306	5	·	·	PUNCT
ejpam-1535	306	6	)	)	PUNCT
ejpam-1535	306	7	be	be	AUX
ejpam-1535	306	8	a	a	DET
ejpam-1535	306	9	category	category	NOUN
ejpam-1535	306	10	.	.	PUNCT
ejpam-1535	307	1	then	then	ADV
ejpam-1535	307	2	∃x	∃x	PROPN
ejpam-1535	307	3	·	·	PUNCT
ejpam-1535	307	4	y	y	SYM
ejpam-1535	307	5	⇐	⇐	PROPN
ejpam-1535	307	6	⇒	⇒	PROPN
ejpam-1535	307	7	r(x	r(x	PROPN
ejpam-1535	307	8	)	)	PUNCT
ejpam-1535	307	9	=	=	SYM
ejpam-1535	307	10	d(y	d(y	PROPN
ejpam-1535	307	11	)	)	PUNCT
ejpam-1535	307	12	.	.	PUNCT
ejpam-1535	308	1	lemma	lemma	PROPN
ejpam-1535	308	2	3	3	NUM
ejpam-1535	308	3	(	(	PUNCT
ejpam-1535	308	4	[	[	X
ejpam-1535	308	5	f	f	X
ejpam-1535	308	6	]	]	X
ejpam-1535	308	7	)	)	PUNCT
ejpam-1535	308	8	.	.	PUNCT
ejpam-1535	309	1	let	let	VERB
ejpam-1535	309	2	c	c	PRON
ejpam-1535	309	3	be	be	AUX
ejpam-1535	309	4	a	a	DET
ejpam-1535	309	5	category	category	NOUN
ejpam-1535	309	6	.	.	PUNCT
ejpam-1535	310	1	if	if	SCONJ
ejpam-1535	310	2	∃x	∃x	PROPN
ejpam-1535	310	3	·	·	PUNCT
ejpam-1535	310	4	y	y	NOUN
ejpam-1535	310	5	,	,	PUNCT
ejpam-1535	310	6	then	then	ADV
ejpam-1535	310	7	d(x	d(x	PROPN
ejpam-1535	310	8	·	·	PUNCT
ejpam-1535	310	9	y	y	X
ejpam-1535	310	10	)	)	PUNCT
ejpam-1535	310	11	=	=	SYM
ejpam-1535	310	12	d(x	d(x	PROPN
ejpam-1535	310	13	)	)	PUNCT
ejpam-1535	310	14	and	and	CCONJ
ejpam-1535	310	15	r(x	r(x	PROPN
ejpam-1535	310	16	·	·	PUNCT
ejpam-1535	310	17	y	y	X
ejpam-1535	310	18	)	)	PUNCT
ejpam-1535	310	19	=	=	PUNCT
ejpam-1535	310	20	r(y	r(y	VERB
ejpam-1535	310	21	)	)	PUNCT
ejpam-1535	310	22	.	.	PUNCT
ejpam-1535	311	1	let	let	AUX
ejpam-1535	311	2	(	(	PUNCT
ejpam-1535	311	3	c	c	NOUN
ejpam-1535	311	4	,	,	PUNCT
ejpam-1535	311	5	·	·	PUNCT
ejpam-1535	311	6	)	)	PUNCT
ejpam-1535	311	7	be	be	AUX
ejpam-1535	311	8	a	a	DET
ejpam-1535	311	9	category	category	NOUN
ejpam-1535	311	10	.	.	PUNCT
ejpam-1535	312	1	for	for	ADP
ejpam-1535	312	2	e	e	PROPN
ejpam-1535	312	3	,	,	PUNCT
ejpam-1535	312	4	f	f	PROPN
ejpam-1535	312	5	∈	∈	PROPN
ejpam-1535	312	6	co	co	NOUN
ejpam-1535	312	7	,	,	PUNCT
ejpam-1535	312	8	we	we	PRON
ejpam-1535	312	9	define	define	VERB
ejpam-1535	312	10	the	the	DET
ejpam-1535	312	11	set	set	ADJ
ejpam-1535	312	12	mor(e	mor(e	PROPN
ejpam-1535	312	13	,	,	PUNCT
ejpam-1535	312	14	f	f	PROPN
ejpam-1535	312	15	)	)	PUNCT
ejpam-1535	312	16	by	by	ADP
ejpam-1535	312	17	mor(e	mor(e	PROPN
ejpam-1535	312	18	,	,	PUNCT
ejpam-1535	312	19	f	f	PROPN
ejpam-1535	312	20	)	)	PUNCT
ejpam-1535	313	1	=	=	PRON
ejpam-1535	313	2	{	{	PUNCT
ejpam-1535	313	3	x	x	PUNCT
ejpam-1535	313	4	∈	∈	PROPN
ejpam-1535	313	5	c	c	NOUN
ejpam-1535	313	6	:	:	PUNCT
ejpam-1535	313	7	d(x	d(x	NOUN
ejpam-1535	313	8	)	)	PUNCT
ejpam-1535	313	9	=	=	SYM
ejpam-1535	314	1	e	e	NOUN
ejpam-1535	314	2	,	,	PUNCT
ejpam-1535	314	3	r(x	r(x	NOUN
ejpam-1535	314	4	)	)	PUNCT
ejpam-1535	314	5	=	=	SYM
ejpam-1535	314	6	f	f	PROPN
ejpam-1535	314	7	}	}	PUNCT
ejpam-1535	314	8	.	.	PUNCT
ejpam-1535	315	1	it	it	PRON
ejpam-1535	315	2	is	be	AUX
ejpam-1535	315	3	easy	easy	ADJ
ejpam-1535	315	4	to	to	PART
ejpam-1535	315	5	see	see	VERB
ejpam-1535	315	6	that	that	SCONJ
ejpam-1535	315	7	if	if	SCONJ
ejpam-1535	315	8	we	we	PRON
ejpam-1535	315	9	put	put	VERB
ejpam-1535	315	10	e	e	NOUN
ejpam-1535	315	11	=	=	NOUN
ejpam-1535	315	12	f	f	PROPN
ejpam-1535	315	13	,	,	PUNCT
ejpam-1535	315	14	then	then	ADV
ejpam-1535	315	15	we	we	PRON
ejpam-1535	315	16	have	have	VERB
ejpam-1535	315	17	a	a	DET
ejpam-1535	315	18	monoid	monoid	PROPN
ejpam-1535	315	19	mor(e	mor(e	PROPN
ejpam-1535	315	20	,	,	PUNCT
ejpam-1535	315	21	e	e	NOUN
ejpam-1535	315	22	)	)	PUNCT
ejpam-1535	315	23	with	with	ADP
ejpam-1535	315	24	identity	identity	NOUN
ejpam-1535	315	25	e	e	NOUN
ejpam-1535	315	26	:	:	PUNCT
ejpam-1535	315	27	since	since	SCONJ
ejpam-1535	315	28	d(x	d(x	PROPN
ejpam-1535	315	29	)	)	PUNCT
ejpam-1535	315	30	=	=	SYM
ejpam-1535	315	31	r(x	r(x	PROPN
ejpam-1535	315	32	)	)	PUNCT
ejpam-1535	315	33	=	=	SYM
ejpam-1535	316	1	e	e	NOUN
ejpam-1535	316	2	,	,	PUNCT
ejpam-1535	316	3	for	for	ADP
ejpam-1535	316	4	all	all	DET
ejpam-1535	316	5	elements	element	NOUN
ejpam-1535	316	6	x	x	PUNCT
ejpam-1535	316	7	,	,	PUNCT
ejpam-1535	316	8	it	it	PRON
ejpam-1535	316	9	follows	follow	VERB
ejpam-1535	316	10	that	that	SCONJ
ejpam-1535	316	11	all	all	DET
ejpam-1535	316	12	products	product	NOUN
ejpam-1535	316	13	are	be	AUX
ejpam-1535	316	14	defined	define	VERB
ejpam-1535	316	15	and	and	CCONJ
ejpam-1535	316	16	that	that	SCONJ
ejpam-1535	316	17	the	the	DET
ejpam-1535	316	18	multiplication	multiplication	NOUN
ejpam-1535	316	19	is	be	AUX
ejpam-1535	316	20	associative	associative	ADJ
ejpam-1535	316	21	,	,	PUNCT
ejpam-1535	316	22	thanks	thank	NOUN
ejpam-1535	316	23	to	to	ADP
ejpam-1535	316	24	(	(	PUNCT
ejpam-1535	316	25	ca1	ca1	NOUN
ejpam-1535	316	26	)	)	PUNCT
ejpam-1535	316	27	.	.	PUNCT
ejpam-1535	317	1	we	we	PRON
ejpam-1535	317	2	call	call	VERB
ejpam-1535	317	3	mor(e	mor(e	PROPN
ejpam-1535	317	4	,	,	PUNCT
ejpam-1535	317	5	e	e	X
ejpam-1535	317	6	)	)	PUNCT
ejpam-1535	317	7	the	the	DET
ejpam-1535	317	8	local	local	ADJ
ejpam-1535	317	9	submonoid	submonoid	NOUN
ejpam-1535	317	10	of	of	ADP
ejpam-1535	317	11	c	c	PROPN
ejpam-1535	317	12	at	at	ADP
ejpam-1535	317	13	e.	e.	PROPN
ejpam-1535	317	14	thus	thus	ADV
ejpam-1535	317	15	,	,	PUNCT
ejpam-1535	317	16	if	if	SCONJ
ejpam-1535	317	17	(	(	PUNCT
ejpam-1535	317	18	c	c	NOUN
ejpam-1535	317	19	,	,	PUNCT
ejpam-1535	317	20	·	·	PUNCT
ejpam-1535	317	21	)	)	PUNCT
ejpam-1535	317	22	is	be	AUX
ejpam-1535	317	23	a	a	DET
ejpam-1535	317	24	category	category	NOUN
ejpam-1535	317	25	with	with	ADP
ejpam-1535	317	26	precisely	precisely	ADV
ejpam-1535	317	27	one	one	NUM
ejpam-1535	317	28	identity	identity	NOUN
ejpam-1535	317	29	,	,	PUNCT
ejpam-1535	317	30	then	then	ADV
ejpam-1535	317	31	it	it	PRON
ejpam-1535	317	32	is	be	AUX
ejpam-1535	317	33	necessarily	necessarily	ADV
ejpam-1535	317	34	a	a	DET
ejpam-1535	317	35	monoid	monoid	NOUN
ejpam-1535	317	36	.	.	PUNCT
ejpam-1535	318	1	in	in	ADP
ejpam-1535	318	2	this	this	DET
ejpam-1535	318	3	way	way	NOUN
ejpam-1535	318	4	,	,	PUNCT
ejpam-1535	318	5	we	we	PRON
ejpam-1535	318	6	can	can	AUX
ejpam-1535	318	7	regard	regard	VERB
ejpam-1535	318	8	a	a	DET
ejpam-1535	318	9	category	category	NOUN
ejpam-1535	318	10	as	as	ADP
ejpam-1535	318	11	a	a	DET
ejpam-1535	318	12	generalisation	generalisation	NOUN
ejpam-1535	318	13	of	of	ADP
ejpam-1535	318	14	a	a	DET
ejpam-1535	318	15	monoid	monoid	NOUN
ejpam-1535	318	16	,	,	PUNCT
ejpam-1535	318	17	as	as	SCONJ
ejpam-1535	318	18	noted	note	VERB
ejpam-1535	318	19	in	in	ADP
ejpam-1535	318	20	the	the	DET
ejpam-1535	318	21	introduction	introduction	NOUN
ejpam-1535	318	22	.	.	PUNCT
ejpam-1535	319	1	using	use	VERB
ejpam-1535	319	2	the	the	DET
ejpam-1535	319	3	notion	notion	NOUN
ejpam-1535	319	4	of	of	ADP
ejpam-1535	319	5	a	a	DET
ejpam-1535	319	6	local	local	ADJ
ejpam-1535	319	7	submonoid	submonoid	NOUN
ejpam-1535	319	8	,	,	PUNCT
ejpam-1535	319	9	we	we	PRON
ejpam-1535	319	10	introduce	introduce	VERB
ejpam-1535	319	11	a	a	DET
ejpam-1535	319	12	special	special	ADJ
ejpam-1535	319	13	type	type	NOUN
ejpam-1535	319	14	of	of	ADP
ejpam-1535	319	15	category	category	NOUN
ejpam-1535	319	16	which	which	PRON
ejpam-1535	319	17	is	be	AUX
ejpam-1535	319	18	to	to	PART
ejpam-1535	319	19	appear	appear	VERB
ejpam-1535	319	20	in	in	ADP
ejpam-1535	319	21	the	the	DET
ejpam-1535	319	22	next	next	ADJ
ejpam-1535	319	23	section	section	NOUN
ejpam-1535	319	24	:	:	PUNCT
ejpam-1535	319	25	definition	definition	NOUN
ejpam-1535	319	26	9	9	NUM
ejpam-1535	319	27	(	(	PUNCT
ejpam-1535	319	28	[	[	X
ejpam-1535	319	29	26	26	NUM
ejpam-1535	319	30	]	]	NUM
ejpam-1535	319	31	)	)	PUNCT
ejpam-1535	319	32	.	.	PUNCT
ejpam-1535	320	1	a	a	DET
ejpam-1535	320	2	unipotent	unipotent	ADJ
ejpam-1535	320	3	category	category	NOUN
ejpam-1535	320	4	is	be	AUX
ejpam-1535	320	5	a	a	DET
ejpam-1535	320	6	category	category	NOUN
ejpam-1535	320	7	in	in	ADP
ejpam-1535	320	8	which	which	PRON
ejpam-1535	320	9	all	all	DET
ejpam-1535	320	10	local	local	ADJ
ejpam-1535	320	11	submonoids	submonoid	NOUN
ejpam-1535	320	12	are	be	AUX
ejpam-1535	320	13	unipotent	unipotent	ADJ
ejpam-1535	320	14	(	(	PUNCT
ejpam-1535	320	15	i.e.	i.e.	X
ejpam-1535	320	16	,	,	PUNCT
ejpam-1535	320	17	contain	contain	VERB
ejpam-1535	320	18	precisely	precisely	ADV
ejpam-1535	320	19	one	one	NUM
ejpam-1535	320	20	idempotent	idempotent	NOUN
ejpam-1535	320	21	)	)	PUNCT
ejpam-1535	320	22	.	.	PUNCT
ejpam-1535	321	1	in	in	ADP
ejpam-1535	321	2	other	other	ADJ
ejpam-1535	321	3	words	word	NOUN
ejpam-1535	321	4	,	,	PUNCT
ejpam-1535	321	5	a	a	DET
ejpam-1535	321	6	category	category	NOUN
ejpam-1535	321	7	is	be	AUX
ejpam-1535	321	8	unipotent	unipotent	ADJ
ejpam-1535	321	9	if	if	SCONJ
ejpam-1535	321	10	and	and	CCONJ
ejpam-1535	321	11	only	only	ADV
ejpam-1535	321	12	if	if	SCONJ
ejpam-1535	321	13	all	all	PRON
ejpam-1535	321	14	of	of	ADP
ejpam-1535	321	15	its	its	PRON
ejpam-1535	321	16	idempotents	idempotent	NOUN
ejpam-1535	321	17	are	be	AUX
ejpam-1535	321	18	identities	identity	NOUN
ejpam-1535	321	19	.	.	PUNCT
ejpam-1535	322	1	we	we	PRON
ejpam-1535	322	2	also	also	ADV
ejpam-1535	322	3	have	have	VERB
ejpam-1535	322	4	the	the	DET
ejpam-1535	322	5	following	follow	VERB
ejpam-1535	322	6	further	further	ADJ
ejpam-1535	322	7	special	special	ADJ
ejpam-1535	322	8	type	type	NOUN
ejpam-1535	322	9	of	of	ADP
ejpam-1535	322	10	category	category	NOUN
ejpam-1535	322	11	:	:	PUNCT
ejpam-1535	322	12	definition	definition	NOUN
ejpam-1535	322	13	10	10	NUM
ejpam-1535	322	14	(	(	PUNCT
ejpam-1535	322	15	[	[	X
ejpam-1535	322	16	1	1	NUM
ejpam-1535	322	17	]	]	NUM
ejpam-1535	322	18	)	)	PUNCT
ejpam-1535	322	19	.	.	PUNCT
ejpam-1535	323	1	a	a	DET
ejpam-1535	323	2	cancellative	cancellative	ADJ
ejpam-1535	323	3	category	category	NOUN
ejpam-1535	323	4	(	(	PUNCT
ejpam-1535	323	5	c	c	NOUN
ejpam-1535	323	6	,	,	PUNCT
ejpam-1535	323	7	·	·	PUNCT
ejpam-1535	323	8	)	)	PUNCT
ejpam-1535	323	9	is	be	AUX
ejpam-1535	323	10	a	a	DET
ejpam-1535	323	11	category	category	NOUN
ejpam-1535	323	12	in	in	ADP
ejpam-1535	323	13	which	which	PRON
ejpam-1535	323	14	the	the	DET
ejpam-1535	323	15	following	follow	VERB
ejpam-1535	323	16	additional	additional	ADJ
ejpam-1535	323	17	conditions	condition	NOUN
ejpam-1535	323	18	hold	hold	VERB
ejpam-1535	323	19	for	for	ADP
ejpam-1535	323	20	all	all	DET
ejpam-1535	323	21	x	x	SYM
ejpam-1535	323	22	,	,	PUNCT
ejpam-1535	323	23	y	y	PROPN
ejpam-1535	323	24	,	,	PUNCT
ejpam-1535	323	25	z	z	NOUN
ejpam-1535	323	26	∈	∈	PROPN
ejpam-1535	324	1	c	c	X
ejpam-1535	324	2	:	:	PUNCT
ejpam-1535	324	3	c.	c.	PROPN
ejpam-1535	324	4	hollings	hollings	PROPN
ejpam-1535	324	5	/	/	SYM
ejpam-1535	324	6	eur	eur	PROPN
ejpam-1535	324	7	.	.	PUNCT
ejpam-1535	325	1	j.	j.	PROPN
ejpam-1535	325	2	pure	pure	PROPN
ejpam-1535	325	3	appl	appl	PROPN
ejpam-1535	325	4	.	.	PROPN
ejpam-1535	325	5	math	math	PROPN
ejpam-1535	325	6	,	,	PUNCT
ejpam-1535	325	7	5	5	NUM
ejpam-1535	325	8	(	(	PUNCT
ejpam-1535	325	9	2012	2012	NUM
ejpam-1535	325	10	)	)	PUNCT
ejpam-1535	325	11	,	,	PUNCT
ejpam-1535	325	12	414	414	NUM
ejpam-1535	325	13	-	-	SYM
ejpam-1535	325	14	450	450	NUM
ejpam-1535	325	15	428	428	NUM
ejpam-1535	325	16	(	(	PUNCT
ejpam-1535	325	17	ca4	ca4	NOUN
ejpam-1535	325	18	)	)	PUNCT
ejpam-1535	325	19	(	(	PUNCT
ejpam-1535	325	20	i	i	NOUN
ejpam-1535	325	21	)	)	PUNCT
ejpam-1535	325	22	if	if	SCONJ
ejpam-1535	325	23	∃x	∃x	PROPN
ejpam-1535	325	24	·	·	PUNCT
ejpam-1535	326	1	z	z	X
ejpam-1535	326	2	,	,	PUNCT
ejpam-1535	326	3	∃y	∃y	PROPN
ejpam-1535	326	4	·	·	PUNCT
ejpam-1535	326	5	z	z	PROPN
ejpam-1535	327	1	and	and	CCONJ
ejpam-1535	327	2	x	x	SYM
ejpam-1535	327	3	·	·	PUNCT
ejpam-1535	327	4	z	z	X
ejpam-1535	327	5	=	=	SYM
ejpam-1535	327	6	y	y	PROPN
ejpam-1535	327	7	·	·	PUNCT
ejpam-1535	328	1	z	z	X
ejpam-1535	328	2	,	,	PUNCT
ejpam-1535	328	3	then	then	ADV
ejpam-1535	328	4	x	x	X
ejpam-1535	328	5	=	=	SYM
ejpam-1535	328	6	y	y	PROPN
ejpam-1535	328	7	;	;	PUNCT
ejpam-1535	328	8	(	(	PUNCT
ejpam-1535	328	9	ii	ii	NOUN
ejpam-1535	328	10	)	)	PUNCT
ejpam-1535	328	11	if	if	SCONJ
ejpam-1535	328	12	∃z	∃z	PROPN
ejpam-1535	328	13	·	·	PUNCT
ejpam-1535	328	14	x	x	X
ejpam-1535	328	15	,	,	PUNCT
ejpam-1535	328	16	∃z	∃z	PROPN
ejpam-1535	328	17	·	·	PUNCT
ejpam-1535	328	18	y	y	PROPN
ejpam-1535	328	19	and	and	CCONJ
ejpam-1535	328	20	z	z	NOUN
ejpam-1535	328	21	·	·	PUNCT
ejpam-1535	328	22	x	x	PUNCT
ejpam-1535	329	1	=	=	PUNCT
ejpam-1535	329	2	z	z	X
ejpam-1535	329	3	·	·	PUNCT
ejpam-1535	329	4	y	y	X
ejpam-1535	329	5	,	,	PUNCT
ejpam-1535	329	6	then	then	ADV
ejpam-1535	329	7	x	x	X
ejpam-1535	329	8	=	=	PUNCT
ejpam-1535	329	9	y.	y.	PROPN
ejpam-1535	329	10	lemma	lemma	PROPN
ejpam-1535	329	11	4	4	NUM
ejpam-1535	329	12	(	(	PUNCT
ejpam-1535	329	13	[	[	X
ejpam-1535	329	14	f	f	X
ejpam-1535	329	15	]	]	X
ejpam-1535	329	16	)	)	PUNCT
ejpam-1535	329	17	.	.	PUNCT
ejpam-1535	330	1	any	any	DET
ejpam-1535	330	2	cancellative	cancellative	ADJ
ejpam-1535	330	3	category	category	NOUN
ejpam-1535	330	4	is	be	AUX
ejpam-1535	330	5	unipotent	unipotent	ADJ
ejpam-1535	330	6	.	.	PUNCT
ejpam-1535	331	1	as	as	SCONJ
ejpam-1535	331	2	we	we	PRON
ejpam-1535	331	3	have	have	AUX
ejpam-1535	331	4	already	already	ADV
ejpam-1535	331	5	observed	observe	VERB
ejpam-1535	331	6	in	in	ADP
ejpam-1535	331	7	section	section	NOUN
ejpam-1535	331	8	2	2	NUM
ejpam-1535	331	9	,	,	PUNCT
ejpam-1535	331	10	ehresmann	ehresmann	PROPN
ejpam-1535	331	11	demonstrated	demonstrate	VERB
ejpam-1535	331	12	the	the	DET
ejpam-1535	331	13	usefulness	usefulness	NOUN
ejpam-1535	331	14	of	of	ADP
ejpam-1535	331	15	an	an	DET
ejpam-1535	331	16	order	order	NOUN
ejpam-1535	331	17	structure	structure	NOUN
ejpam-1535	331	18	on	on	ADP
ejpam-1535	331	19	a	a	DET
ejpam-1535	331	20	category	category	NOUN
ejpam-1535	331	21	,	,	PUNCT
ejpam-1535	331	22	so	so	ADV
ejpam-1535	331	23	,	,	PUNCT
ejpam-1535	331	24	returning	return	VERB
ejpam-1535	331	25	to	to	ADP
ejpam-1535	331	26	the	the	DET
ejpam-1535	331	27	general	general	ADJ
ejpam-1535	331	28	case	case	NOUN
ejpam-1535	331	29	of	of	ADP
ejpam-1535	331	30	an	an	DET
ejpam-1535	331	31	arbitrary	arbitrary	ADJ
ejpam-1535	331	32	category	category	NOUN
ejpam-1535	331	33	(	(	PUNCT
ejpam-1535	331	34	c	c	NOUN
ejpam-1535	331	35	,	,	PUNCT
ejpam-1535	331	36	·	·	PUNCT
ejpam-1535	331	37	)	)	PUNCT
ejpam-1535	331	38	,	,	PUNCT
ejpam-1535	331	39	we	we	PRON
ejpam-1535	331	40	now	now	ADV
ejpam-1535	331	41	introduce	introduce	VERB
ejpam-1535	331	42	an	an	DET
ejpam-1535	331	43	ordering	ordering	NOUN
ejpam-1535	331	44	on	on	ADP
ejpam-1535	331	45	c	c	NOUN
ejpam-1535	331	46	:	:	PUNCT
ejpam-1535	331	47	definition	definition	NOUN
ejpam-1535	331	48	11	11	NUM
ejpam-1535	331	49	.	.	PUNCT
ejpam-1535	332	1	let	let	AUX
ejpam-1535	332	2	(	(	PUNCT
ejpam-1535	332	3	c	c	NOUN
ejpam-1535	332	4	,	,	PUNCT
ejpam-1535	332	5	·	·	PUNCT
ejpam-1535	332	6	)	)	PUNCT
ejpam-1535	332	7	be	be	AUX
ejpam-1535	332	8	a	a	DET
ejpam-1535	332	9	category	category	NOUN
ejpam-1535	332	10	and	and	CCONJ
ejpam-1535	332	11	let	let	VERB
ejpam-1535	332	12	c	c	PRON
ejpam-1535	332	13	be	be	AUX
ejpam-1535	332	14	partially	partially	ADV
ejpam-1535	332	15	ordered	order	VERB
ejpam-1535	332	16	by	by	ADP
ejpam-1535	332	17	≤.	≤.	NOUN
ejpam-1535	332	18	the	the	DET
ejpam-1535	332	19	triple	triple	ADJ
ejpam-1535	332	20	(	(	PUNCT
ejpam-1535	332	21	c	c	NOUN
ejpam-1535	332	22	,	,	PUNCT
ejpam-1535	332	23	·	·	PUNCT
ejpam-1535	332	24	,	,	PUNCT
ejpam-1535	332	25	≤	≤	NUM
ejpam-1535	332	26	)	)	PUNCT
ejpam-1535	332	27	is	be	AUX
ejpam-1535	332	28	an	an	DET
ejpam-1535	332	29	ordered	order	VERB
ejpam-1535	332	30	category	category	NOUN
ejpam-1535	332	31	if	if	SCONJ
ejpam-1535	332	32	the	the	DET
ejpam-1535	332	33	following	follow	VERB
ejpam-1535	332	34	conditions	condition	NOUN
ejpam-1535	332	35	hold	hold	VERB
ejpam-1535	332	36	:	:	PUNCT
ejpam-1535	332	37	(	(	PUNCT
ejpam-1535	332	38	or1	or1	NOUN
ejpam-1535	332	39	)	)	PUNCT
ejpam-1535	332	40	if	if	SCONJ
ejpam-1535	332	41	a	a	DET
ejpam-1535	332	42	≤	≤	NUM
ejpam-1535	332	43	c	c	NOUN
ejpam-1535	332	44	,	,	PUNCT
ejpam-1535	332	45	b	b	PROPN
ejpam-1535	332	46	≤	≤	NUM
ejpam-1535	332	47	d	d	NOUN
ejpam-1535	332	48	,	,	PUNCT
ejpam-1535	332	49	∃a	∃a	NOUN
ejpam-1535	332	50	·	·	SYM
ejpam-1535	332	51	b	b	NOUN
ejpam-1535	332	52	and	and	CCONJ
ejpam-1535	332	53	∃c	∃c	PROPN
ejpam-1535	332	54	·	·	PUNCT
ejpam-1535	333	1	d	d	X
ejpam-1535	333	2	,	,	PUNCT
ejpam-1535	333	3	then	then	ADV
ejpam-1535	333	4	a	a	DET
ejpam-1535	333	5	·	·	PUNCT
ejpam-1535	333	6	b	b	X
ejpam-1535	333	7	≤	≤	NUM
ejpam-1535	333	8	c	c	X
ejpam-1535	333	9	·	·	PUNCT
ejpam-1535	334	1	d	d	X
ejpam-1535	334	2	;	;	PUNCT
ejpam-1535	334	3	(	(	PUNCT
ejpam-1535	334	4	or2	or2	NOUN
ejpam-1535	334	5	)	)	PUNCT
ejpam-1535	334	6	if	if	SCONJ
ejpam-1535	334	7	a	a	DET
ejpam-1535	334	8	≤	≤	NUM
ejpam-1535	334	9	b	b	NOUN
ejpam-1535	334	10	,	,	PUNCT
ejpam-1535	334	11	then	then	ADV
ejpam-1535	334	12	r(a)≤	r(a)≤	PROPN
ejpam-1535	334	13	r(b	r(b	PROPN
ejpam-1535	334	14	)	)	PUNCT
ejpam-1535	334	15	and	and	CCONJ
ejpam-1535	334	16	d(a)≤	d(a)≤	PROPN
ejpam-1535	334	17	d(b	d(b	PROPN
ejpam-1535	334	18	)	)	PUNCT
ejpam-1535	334	19	;	;	PUNCT
ejpam-1535	334	20	(	(	PUNCT
ejpam-1535	334	21	or3	or3	PROPN
ejpam-1535	334	22	)	)	PUNCT
ejpam-1535	334	23	(	(	PUNCT
ejpam-1535	334	24	i	i	NOUN
ejpam-1535	334	25	)	)	PUNCT
ejpam-1535	334	26	for	for	ADP
ejpam-1535	334	27	each	each	DET
ejpam-1535	334	28	f	f	PROPN
ejpam-1535	334	29	∈	∈	PROPN
ejpam-1535	334	30	co	co	NOUN
ejpam-1535	334	31	and	and	CCONJ
ejpam-1535	334	32	a	a	DET
ejpam-1535	334	33	∈	∈	NOUN
ejpam-1535	334	34	c	c	NOUN
ejpam-1535	334	35	with	with	ADP
ejpam-1535	334	36	f	f	PROPN
ejpam-1535	334	37	≤	≤	PROPN
ejpam-1535	334	38	r(a	r(a	PROPN
ejpam-1535	334	39	)	)	PUNCT
ejpam-1535	334	40	,	,	PUNCT
ejpam-1535	334	41	there	there	PRON
ejpam-1535	334	42	exists	exist	VERB
ejpam-1535	334	43	an	an	DET
ejpam-1535	334	44	element	element	NOUN
ejpam-1535	334	45	of	of	ADP
ejpam-1535	334	46	c	c	PROPN
ejpam-1535	334	47	,	,	PUNCT
ejpam-1535	334	48	denoted	denote	VERB
ejpam-1535	334	49	by	by	ADP
ejpam-1535	334	50	a|	a|	PROPN
ejpam-1535	334	51	f	f	PROPN
ejpam-1535	334	52	,	,	PUNCT
ejpam-1535	334	53	which	which	PRON
ejpam-1535	334	54	is	be	AUX
ejpam-1535	334	55	the	the	DET
ejpam-1535	334	56	unique	unique	ADJ
ejpam-1535	334	57	element	element	NOUN
ejpam-1535	334	58	with	with	ADP
ejpam-1535	334	59	the	the	DET
ejpam-1535	334	60	properties	property	NOUN
ejpam-1535	334	61	a|	a|	PROPN
ejpam-1535	334	62	f	f	PROPN
ejpam-1535	334	63	≤	≤	ADV
ejpam-1535	334	64	a	a	PRON
ejpam-1535	334	65	and	and	CCONJ
ejpam-1535	334	66	r(a|	r(a|	NOUN
ejpam-1535	334	67	f	f	PROPN
ejpam-1535	334	68	)	)	PUNCT
ejpam-1535	335	1	=	=	SYM
ejpam-1535	335	2	f	f	PROPN
ejpam-1535	335	3	;	;	PUNCT
ejpam-1535	335	4	(	(	PUNCT
ejpam-1535	335	5	ii	ii	NOUN
ejpam-1535	335	6	)	)	PUNCT
ejpam-1535	335	7	for	for	ADP
ejpam-1535	335	8	each	each	DET
ejpam-1535	335	9	f	f	PROPN
ejpam-1535	335	10	∈	∈	PROPN
ejpam-1535	335	11	co	co	NOUN
ejpam-1535	335	12	and	and	CCONJ
ejpam-1535	335	13	a	a	DET
ejpam-1535	335	14	∈	∈	NOUN
ejpam-1535	335	15	c	c	NOUN
ejpam-1535	335	16	with	with	ADP
ejpam-1535	335	17	f	f	PROPN
ejpam-1535	335	18	≤	≤	PROPN
ejpam-1535	335	19	d(a	d(a	PROPN
ejpam-1535	335	20	)	)	PUNCT
ejpam-1535	335	21	,	,	PUNCT
ejpam-1535	335	22	there	there	PRON
ejpam-1535	335	23	exists	exist	VERB
ejpam-1535	335	24	an	an	DET
ejpam-1535	335	25	element	element	NOUN
ejpam-1535	335	26	of	of	ADP
ejpam-1535	335	27	c	c	PROPN
ejpam-1535	335	28	,	,	PUNCT
ejpam-1535	335	29	denoted	denote	VERB
ejpam-1535	335	30	by	by	ADP
ejpam-1535	335	31	f	f	PROPN
ejpam-1535	335	32	|a	|a	PROPN
ejpam-1535	335	33	,	,	PUNCT
ejpam-1535	335	34	which	which	PRON
ejpam-1535	335	35	is	be	AUX
ejpam-1535	335	36	the	the	DET
ejpam-1535	335	37	unique	unique	ADJ
ejpam-1535	335	38	element	element	NOUN
ejpam-1535	335	39	with	with	ADP
ejpam-1535	335	40	the	the	DET
ejpam-1535	335	41	properties	property	NOUN
ejpam-1535	335	42	f	f	PROPN
ejpam-1535	335	43	|a	|a	VERB
ejpam-1535	335	44	≤	≤	NOUN
ejpam-1535	335	45	a	a	PRON
ejpam-1535	335	46	and	and	CCONJ
ejpam-1535	335	47	d	d	PROPN
ejpam-1535	335	48	(	(	PUNCT
ejpam-1535	335	49	f	f	PROPN
ejpam-1535	335	50	|a	|a	NOUN
ejpam-1535	335	51	)	)	PUNCT
ejpam-1535	335	52	=	=	SYM
ejpam-1535	335	53	f	f	PROPN
ejpam-1535	335	54	.	.	PUNCT
ejpam-1535	336	1	an	an	DET
ejpam-1535	336	2	ordered	order	VERB
ejpam-1535	336	3	unipotent	unipotent	ADJ
ejpam-1535	336	4	(	(	PUNCT
ejpam-1535	336	5	cancellative	cancellative	ADJ
ejpam-1535	336	6	)	)	PUNCT
ejpam-1535	336	7	category	category	NOUN
ejpam-1535	336	8	is	be	AUX
ejpam-1535	336	9	a	a	DET
ejpam-1535	336	10	unipotent	unipotent	ADJ
ejpam-1535	336	11	(	(	PUNCT
ejpam-1535	336	12	cancellative	cancellative	ADJ
ejpam-1535	336	13	)	)	PUNCT
ejpam-1535	336	14	category	category	NOUN
ejpam-1535	336	15	which	which	PRON
ejpam-1535	336	16	is	be	AUX
ejpam-1535	336	17	also	also	ADV
ejpam-1535	336	18	an	an	DET
ejpam-1535	336	19	ordered	order	VERB
ejpam-1535	336	20	category	category	NOUN
ejpam-1535	336	21	in	in	ADP
ejpam-1535	336	22	the	the	DET
ejpam-1535	336	23	sense	sense	NOUN
ejpam-1535	336	24	of	of	ADP
ejpam-1535	336	25	definition	definition	NOUN
ejpam-1535	336	26	11	11	NUM
ejpam-1535	336	27	.	.	PUNCT
ejpam-1535	337	1	the	the	DET
ejpam-1535	337	2	element	element	NOUN
ejpam-1535	337	3	a|	a|	PROPN
ejpam-1535	337	4	f	f	PROPN
ejpam-1535	337	5	of	of	ADP
ejpam-1535	337	6	condition	condition	NOUN
ejpam-1535	337	7	(	(	PUNCT
ejpam-1535	337	8	or3)(i	or3)(i	PROPN
ejpam-1535	337	9	)	)	PUNCT
ejpam-1535	337	10	is	be	AUX
ejpam-1535	337	11	called	call	VERB
ejpam-1535	337	12	the	the	DET
ejpam-1535	337	13	corestriction	corestriction	NOUN
ejpam-1535	337	14	(	(	PUNCT
ejpam-1535	337	15	of	of	ADP
ejpam-1535	337	16	a	a	PRON
ejpam-1535	337	17	to	to	ADP
ejpam-1535	337	18	f	f	PROPN
ejpam-1535	337	19	)	)	PUNCT
ejpam-1535	337	20	,	,	PUNCT
ejpam-1535	337	21	whilst	whilst	SCONJ
ejpam-1535	337	22	the	the	DET
ejpam-1535	337	23	element	element	NOUN
ejpam-1535	337	24	f	f	PROPN
ejpam-1535	337	25	|a	|a	X
ejpam-1535	337	26	of	of	ADP
ejpam-1535	337	27	condition	condition	NOUN
ejpam-1535	337	28	(	(	PUNCT
ejpam-1535	337	29	or3)(ii	or3)(ii	NOUN
ejpam-1535	337	30	)	)	PUNCT
ejpam-1535	337	31	is	be	AUX
ejpam-1535	337	32	called	call	VERB
ejpam-1535	337	33	the	the	DET
ejpam-1535	337	34	restriction	restriction	NOUN
ejpam-1535	337	35	(	(	PUNCT
ejpam-1535	337	36	of	of	ADP
ejpam-1535	337	37	f	f	PROPN
ejpam-1535	337	38	to	to	ADP
ejpam-1535	337	39	a	a	PRON
ejpam-1535	337	40	)	)	PUNCT
ejpam-1535	337	41	.	.	PUNCT
ejpam-1535	338	1	note	note	VERB
ejpam-1535	338	2	that	that	SCONJ
ejpam-1535	338	3	whenever	whenever	SCONJ
ejpam-1535	338	4	e|	e|	PROPN
ejpam-1535	338	5	f	f	PROPN
ejpam-1535	338	6	is	be	AUX
ejpam-1535	338	7	defined	define	VERB
ejpam-1535	338	8	both	both	PRON
ejpam-1535	338	9	as	as	ADP
ejpam-1535	338	10	a	a	DET
ejpam-1535	338	11	restriction	restriction	NOUN
ejpam-1535	338	12	and	and	CCONJ
ejpam-1535	338	13	as	as	ADP
ejpam-1535	338	14	a	a	DET
ejpam-1535	338	15	corestriction	corestriction	NOUN
ejpam-1535	338	16	,	,	PUNCT
ejpam-1535	338	17	for	for	ADP
ejpam-1535	338	18	e	e	NOUN
ejpam-1535	338	19	,	,	PUNCT
ejpam-1535	338	20	f	f	PROPN
ejpam-1535	338	21	∈	∈	PROPN
ejpam-1535	339	1	co	co	NOUN
ejpam-1535	339	2	,	,	PUNCT
ejpam-1535	339	3	it	it	PRON
ejpam-1535	339	4	follows	follow	VERB
ejpam-1535	339	5	that	that	SCONJ
ejpam-1535	339	6	we	we	PRON
ejpam-1535	339	7	must	must	AUX
ejpam-1535	339	8	have	have	VERB
ejpam-1535	339	9	e	e	NOUN
ejpam-1535	339	10	=	=	SYM
ejpam-1535	339	11	f	f	PROPN
ejpam-1535	339	12	,	,	PUNCT
ejpam-1535	339	13	since	since	SCONJ
ejpam-1535	339	14	we	we	PRON
ejpam-1535	339	15	require	require	VERB
ejpam-1535	339	16	e	e	X
ejpam-1535	339	17	≤	≤	ADJ
ejpam-1535	339	18	f	f	NOUN
ejpam-1535	339	19	for	for	SCONJ
ejpam-1535	339	20	the	the	DET
ejpam-1535	339	21	restriction	restriction	NOUN
ejpam-1535	339	22	to	to	PART
ejpam-1535	339	23	be	be	AUX
ejpam-1535	339	24	defined	define	VERB
ejpam-1535	339	25	,	,	PUNCT
ejpam-1535	339	26	and	and	CCONJ
ejpam-1535	339	27	f	f	PROPN
ejpam-1535	339	28	≤	≤	NUM
ejpam-1535	339	29	e	e	X
ejpam-1535	339	30	for	for	ADP
ejpam-1535	339	31	the	the	DET
ejpam-1535	339	32	corestriction	corestriction	NOUN
ejpam-1535	339	33	to	to	PART
ejpam-1535	339	34	be	be	AUX
ejpam-1535	339	35	defined	define	VERB
ejpam-1535	339	36	.	.	PUNCT
ejpam-1535	340	1	the	the	DET
ejpam-1535	340	2	introduction	introduction	NOUN
ejpam-1535	340	3	of	of	ADP
ejpam-1535	340	4	such	such	DET
ejpam-1535	340	5	an	an	DET
ejpam-1535	340	6	ordering	ordering	NOUN
ejpam-1535	340	7	on	on	ADP
ejpam-1535	340	8	our	our	PRON
ejpam-1535	340	9	category	category	NOUN
ejpam-1535	340	10	has	have	VERB
ejpam-1535	340	11	many	many	ADJ
ejpam-1535	340	12	useful	useful	ADJ
ejpam-1535	340	13	consequences	consequence	NOUN
ejpam-1535	340	14	:	:	PUNCT
ejpam-1535	340	15	lemma	lemma	PROPN
ejpam-1535	340	16	5	5	NUM
ejpam-1535	340	17	(	(	PUNCT
ejpam-1535	340	18	[	[	X
ejpam-1535	340	19	1	1	NUM
ejpam-1535	340	20	,	,	PUNCT
ejpam-1535	340	21	lemma	lemma	PROPN
ejpam-1535	340	22	3.4	3.4	NUM
ejpam-1535	340	23	]	]	NOUN
ejpam-1535	340	24	*	*	PUNCT
ejpam-1535	340	25	and	and	CCONJ
ejpam-1535	340	26	[	[	X
ejpam-1535	340	27	29	29	NUM
ejpam-1535	340	28	,	,	PUNCT
ejpam-1535	340	29	theorem	theorem	VERB
ejpam-1535	340	30	4.1.3	4.1.3	NUM
ejpam-1535	340	31	]	]	NOUN
ejpam-1535	340	32	*	*	NUM
ejpam-1535	340	33	)	)	PUNCT
ejpam-1535	340	34	.	.	PUNCT
ejpam-1535	341	1	let	let	AUX
ejpam-1535	341	2	(	(	PUNCT
ejpam-1535	341	3	c	c	NOUN
ejpam-1535	341	4	,	,	PUNCT
ejpam-1535	341	5	·	·	PUNCT
ejpam-1535	341	6	,	,	PUNCT
ejpam-1535	341	7	≤	≤	NUM
ejpam-1535	341	8	)	)	PUNCT
ejpam-1535	341	9	be	be	VERB
ejpam-1535	341	10	an	an	DET
ejpam-1535	341	11	ordered	order	VERB
ejpam-1535	341	12	category	category	NOUN
ejpam-1535	341	13	.	.	PUNCT
ejpam-1535	342	1	let	let	VERB
ejpam-1535	342	2	a	a	DET
ejpam-1535	342	3	,	,	PUNCT
ejpam-1535	342	4	b	b	NOUN
ejpam-1535	342	5	,	,	PUNCT
ejpam-1535	342	6	x	x	INTJ
ejpam-1535	342	7	,	,	PUNCT
ejpam-1535	342	8	y	y	PROPN
ejpam-1535	342	9	,	,	PUNCT
ejpam-1535	342	10	z	z	PROPN
ejpam-1535	342	11	∈	∈	PROPN
ejpam-1535	342	12	c	c	PROPN
ejpam-1535	342	13	and	and	CCONJ
ejpam-1535	342	14	e	e	NOUN
ejpam-1535	342	15	,	,	PUNCT
ejpam-1535	342	16	f	f	PROPN
ejpam-1535	342	17	∈	∈	PROPN
ejpam-1535	342	18	co.	co.	PROPN
ejpam-1535	343	1	then	then	ADV
ejpam-1535	343	2	(	(	PUNCT
ejpam-1535	343	3	a	a	X
ejpam-1535	343	4	)	)	PUNCT
ejpam-1535	343	5	if	if	SCONJ
ejpam-1535	343	6	a	a	DET
ejpam-1535	343	7	≤	≤	NUM
ejpam-1535	343	8	b	b	NOUN
ejpam-1535	343	9	,	,	PUNCT
ejpam-1535	343	10	then	then	ADV
ejpam-1535	343	11	d(a)|b	d(a)|b	PROPN
ejpam-1535	343	12	=	=	PUNCT
ejpam-1535	343	13	a	a	DET
ejpam-1535	343	14	=	=	PUNCT
ejpam-1535	343	15	b|r(a	b|r(a	PROPN
ejpam-1535	343	16	)	)	PUNCT
ejpam-1535	343	17	;	;	PUNCT
ejpam-1535	343	18	(	(	PUNCT
ejpam-1535	343	19	b	b	X
ejpam-1535	343	20	)	)	PUNCT
ejpam-1535	343	21	for	for	ADP
ejpam-1535	343	22	f	f	PROPN
ejpam-1535	343	23	≤	≤	PROPN
ejpam-1535	343	24	r(a	r(a	PROPN
ejpam-1535	343	25	)	)	PUNCT
ejpam-1535	343	26	,	,	PUNCT
ejpam-1535	344	1	∃(a|	∃(a|	PROPN
ejpam-1535	344	2	f	f	PROPN
ejpam-1535	344	3	)	)	PUNCT
ejpam-1535	344	4	·	·	PUNCT
ejpam-1535	344	5	f	f	X
ejpam-1535	344	6	with	with	ADP
ejpam-1535	344	7	(	(	PUNCT
ejpam-1535	344	8	a|	a|	PROPN
ejpam-1535	344	9	f	f	PROPN
ejpam-1535	344	10	)	)	PUNCT
ejpam-1535	344	11	·	·	PUNCT
ejpam-1535	345	1	f	f	X
ejpam-1535	345	2	=	=	PUNCT
ejpam-1535	345	3	a|	a|	PROPN
ejpam-1535	345	4	f	f	X
ejpam-1535	345	5	,	,	PUNCT
ejpam-1535	345	6	and	and	CCONJ
ejpam-1535	345	7	for	for	ADP
ejpam-1535	345	8	f	f	PROPN
ejpam-1535	345	9	≤	≤	PROPN
ejpam-1535	345	10	d(a	d(a	PROPN
ejpam-1535	345	11	)	)	PUNCT
ejpam-1535	345	12	,	,	PUNCT
ejpam-1535	345	13	∃	∃	PROPN
ejpam-1535	345	14	f	f	PROPN
ejpam-1535	345	15	·	·	PUNCT
ejpam-1535	345	16	(	(	PUNCT
ejpam-1535	345	17	f	f	X
ejpam-1535	345	18	|a	|a	NOUN
ejpam-1535	345	19	)	)	PUNCT
ejpam-1535	345	20	with	with	ADP
ejpam-1535	345	21	f	f	PROPN
ejpam-1535	345	22	·	·	PUNCT
ejpam-1535	345	23	(	(	PUNCT
ejpam-1535	345	24	f	f	X
ejpam-1535	345	25	|a	|a	NOUN
ejpam-1535	345	26	)	)	PUNCT
ejpam-1535	345	27	=	=	SYM
ejpam-1535	345	28	f	f	PROPN
ejpam-1535	345	29	|a	|a	NOUN
ejpam-1535	345	30	;	;	PUNCT
ejpam-1535	345	31	(	(	PUNCT
ejpam-1535	345	32	c	c	X
ejpam-1535	345	33	)	)	PUNCT
ejpam-1535	345	34	if	if	SCONJ
ejpam-1535	345	35	there	there	PRON
ejpam-1535	345	36	exists	exist	VERB
ejpam-1535	345	37	c	c	NOUN
ejpam-1535	345	38	∈	∈	PROPN
ejpam-1535	345	39	c	c	NOUN
ejpam-1535	345	40	such	such	ADJ
ejpam-1535	345	41	that	that	SCONJ
ejpam-1535	345	42	a	a	DET
ejpam-1535	345	43	≤	≤	PROPN
ejpam-1535	345	44	c	c	NOUN
ejpam-1535	345	45	and	and	CCONJ
ejpam-1535	345	46	b	b	NOUN
ejpam-1535	345	47	≤	≤	NOUN
ejpam-1535	345	48	c	c	NOUN
ejpam-1535	345	49	,	,	PUNCT
ejpam-1535	345	50	and	and	CCONJ
ejpam-1535	345	51	either	either	DET
ejpam-1535	345	52	r(a	r(a	PROPN
ejpam-1535	345	53	)	)	PUNCT
ejpam-1535	345	54	=	=	SYM
ejpam-1535	345	55	r(b	r(b	PROPN
ejpam-1535	345	56	)	)	PUNCT
ejpam-1535	345	57	or	or	CCONJ
ejpam-1535	345	58	d(a	d(a	PROPN
ejpam-1535	345	59	)	)	PUNCT
ejpam-1535	345	60	=	=	PUNCT
ejpam-1535	345	61	d(b	d(b	PROPN
ejpam-1535	345	62	)	)	PUNCT
ejpam-1535	345	63	,	,	PUNCT
ejpam-1535	345	64	then	then	ADV
ejpam-1535	345	65	a	a	DET
ejpam-1535	345	66	=	=	SYM
ejpam-1535	345	67	b	b	NOUN
ejpam-1535	345	68	;	;	PUNCT
ejpam-1535	345	69	(	(	PUNCT
ejpam-1535	345	70	d	d	X
ejpam-1535	345	71	)	)	PUNCT
ejpam-1535	345	72	if	if	SCONJ
ejpam-1535	345	73	e	e	NOUN
ejpam-1535	345	74	≤	≤	X
ejpam-1535	345	75	f	f	PROPN
ejpam-1535	345	76	≤	≤	PROPN
ejpam-1535	345	77	r(a	r(a	PROPN
ejpam-1535	345	78	)	)	PUNCT
ejpam-1535	345	79	,	,	PUNCT
ejpam-1535	345	80	then	then	ADV
ejpam-1535	345	81	(	(	PUNCT
ejpam-1535	345	82	a|	a|	PROPN
ejpam-1535	345	83	f	f	PROPN
ejpam-1535	345	84	)	)	PUNCT
ejpam-1535	345	85	|e	|e	PROPN
ejpam-1535	345	86	=	=	SYM
ejpam-1535	346	1	a|e	a|e	X
ejpam-1535	346	2	,	,	PUNCT
ejpam-1535	346	3	hence	hence	ADV
ejpam-1535	346	4	a|e	a|e	PUNCT
ejpam-1535	346	5	≤	≤	NUM
ejpam-1535	346	6	a|	a|	PROPN
ejpam-1535	346	7	f	f	X
ejpam-1535	346	8	;	;	PUNCT
ejpam-1535	346	9	similarly	similarly	ADV
ejpam-1535	346	10	,	,	PUNCT
ejpam-1535	346	11	if	if	SCONJ
ejpam-1535	346	12	e	e	ADP
ejpam-1535	346	13	≤	≤	X
ejpam-1535	346	14	f	f	PROPN
ejpam-1535	346	15	≤	≤	PROPN
ejpam-1535	346	16	d(a	d(a	PROPN
ejpam-1535	346	17	)	)	PUNCT
ejpam-1535	346	18	,	,	PUNCT
ejpam-1535	346	19	then	then	ADV
ejpam-1535	346	20	e|	e|	PROPN
ejpam-1535	346	21	(	(	PUNCT
ejpam-1535	346	22	f	f	PROPN
ejpam-1535	346	23	|a	|a	NOUN
ejpam-1535	346	24	)	)	PUNCT
ejpam-1535	346	25	=	=	SYM
ejpam-1535	346	26	e|a	e|a	NOUN
ejpam-1535	346	27	,	,	PUNCT
ejpam-1535	346	28	hence	hence	ADV
ejpam-1535	346	29	e|a	e|a	X
ejpam-1535	346	30	≤	≤	ADJ
ejpam-1535	346	31	f	f	NOUN
ejpam-1535	346	32	|a	|a	NOUN
ejpam-1535	346	33	;	;	PUNCT
ejpam-1535	346	34	(	(	PUNCT
ejpam-1535	346	35	e	e	X
ejpam-1535	346	36	)	)	PUNCT
ejpam-1535	346	37	if	if	SCONJ
ejpam-1535	346	38	∃x	∃x	PROPN
ejpam-1535	346	39	·	·	PUNCT
ejpam-1535	346	40	y	y	PROPN
ejpam-1535	346	41	and	and	CCONJ
ejpam-1535	346	42	e	e	X
ejpam-1535	346	43	≤	≤	NUM
ejpam-1535	346	44	r(x	r(x	PROPN
ejpam-1535	346	45	·	·	PUNCT
ejpam-1535	346	46	y	y	X
ejpam-1535	346	47	)	)	PUNCT
ejpam-1535	346	48	=	=	SYM
ejpam-1535	346	49	r(y	r(y	VERB
ejpam-1535	346	50	)	)	PUNCT
ejpam-1535	346	51	,	,	PUNCT
ejpam-1535	346	52	then	then	ADV
ejpam-1535	346	53	(	(	PUNCT
ejpam-1535	346	54	x	x	X
ejpam-1535	346	55	·	·	PUNCT
ejpam-1535	346	56	y)|e	y)|e	NOUN
ejpam-1535	346	57	=	=	SYM
ejpam-1535	346	58	�	�	PROPN
ejpam-1535	346	59	x	x	SYM
ejpam-1535	346	60	|d(y|e	|d(y|e	NOUN
ejpam-1535	346	61	)	)	PUNCT
ejpam-1535	346	62	�	�	PROPN
ejpam-1535	346	63	·	·	PUNCT
ejpam-1535	346	64	(	(	PUNCT
ejpam-1535	346	65	y|e	y|e	PROPN
ejpam-1535	346	66	)	)	PUNCT
ejpam-1535	346	67	;	;	PUNCT
ejpam-1535	346	68	similarly	similarly	ADV
ejpam-1535	346	69	,	,	PUNCT
ejpam-1535	346	70	if	if	SCONJ
ejpam-1535	346	71	∃x	∃x	PROPN
ejpam-1535	346	72	·	·	PUNCT
ejpam-1535	346	73	y	y	PROPN
ejpam-1535	346	74	and	and	CCONJ
ejpam-1535	346	75	e	e	X
ejpam-1535	346	76	≤	≤	X
ejpam-1535	346	77	d(x	d(x	NOUN
ejpam-1535	346	78	·	·	PUNCT
ejpam-1535	346	79	y	y	X
ejpam-1535	346	80	)	)	PUNCT
ejpam-1535	346	81	=	=	SYM
ejpam-1535	346	82	d(x	d(x	PROPN
ejpam-1535	346	83	)	)	PUNCT
ejpam-1535	346	84	,	,	PUNCT
ejpam-1535	346	85	then	then	ADV
ejpam-1535	346	86	e|(x	e|(x	ADV
ejpam-1535	346	87	·	·	PUNCT
ejpam-1535	346	88	y	y	X
ejpam-1535	346	89	)	)	PUNCT
ejpam-1535	346	90	=	=	SYM
ejpam-1535	346	91	(	(	PUNCT
ejpam-1535	346	92	e|x	e|x	PROPN
ejpam-1535	346	93	)	)	PUNCT
ejpam-1535	346	94	·	·	PUNCT
ejpam-1535	346	95	�	�	PROPN
ejpam-1535	346	96	r(e|x)|y	r(e|x)|y	NOUN
ejpam-1535	346	97	�	�	PROPN
ejpam-1535	346	98	.	.	PUNCT
ejpam-1535	347	1	c.	c.	PROPN
ejpam-1535	347	2	hollings	holling	NOUN
ejpam-1535	347	3	/	/	SYM
ejpam-1535	347	4	eur	eur	PROPN
ejpam-1535	347	5	.	.	PUNCT
ejpam-1535	348	1	j.	j.	PROPN
ejpam-1535	348	2	pure	pure	PROPN
ejpam-1535	348	3	appl	appl	PROPN
ejpam-1535	348	4	.	.	PROPN
ejpam-1535	348	5	math	math	PROPN
ejpam-1535	348	6	,	,	PUNCT
ejpam-1535	348	7	5	5	NUM
ejpam-1535	348	8	(	(	PUNCT
ejpam-1535	348	9	2012	2012	NUM
ejpam-1535	348	10	)	)	PUNCT
ejpam-1535	348	11	,	,	PUNCT
ejpam-1535	348	12	414	414	NUM
ejpam-1535	348	13	-	-	SYM
ejpam-1535	348	14	450	450	NUM
ejpam-1535	348	15	429	429	NUM
ejpam-1535	348	16	proof	proof	NOUN
ejpam-1535	348	17	.	.	PUNCT
ejpam-1535	349	1	(	(	PUNCT
ejpam-1535	349	2	a	a	X
ejpam-1535	349	3	)	)	PUNCT
ejpam-1535	349	4	if	if	SCONJ
ejpam-1535	349	5	a	a	DET
ejpam-1535	349	6	≤	≤	NUM
ejpam-1535	349	7	b	b	NOUN
ejpam-1535	349	8	,	,	PUNCT
ejpam-1535	349	9	then	then	ADV
ejpam-1535	349	10	r(a	r(a	PROPN
ejpam-1535	349	11	)	)	PUNCT
ejpam-1535	349	12	≤	≤	NOUN
ejpam-1535	349	13	r(b	r(b	PROPN
ejpam-1535	349	14	)	)	PUNCT
ejpam-1535	349	15	and	and	CCONJ
ejpam-1535	349	16	d(a	d(a	PROPN
ejpam-1535	349	17	)	)	PUNCT
ejpam-1535	349	18	≤	≤	NOUN
ejpam-1535	349	19	d(b	d(b	PROPN
ejpam-1535	349	20	)	)	PUNCT
ejpam-1535	349	21	,	,	PUNCT
ejpam-1535	349	22	by	by	ADP
ejpam-1535	349	23	(	(	PUNCT
ejpam-1535	349	24	or2	or2	PROPN
ejpam-1535	349	25	)	)	PUNCT
ejpam-1535	349	26	.	.	PUNCT
ejpam-1535	350	1	therefore	therefore	ADV
ejpam-1535	350	2	the	the	DET
ejpam-1535	350	3	restriction	restriction	NOUN
ejpam-1535	350	4	d(a)|b	d(a)|b	PROPN
ejpam-1535	350	5	and	and	CCONJ
ejpam-1535	350	6	the	the	DET
ejpam-1535	350	7	corestriction	corestriction	NOUN
ejpam-1535	350	8	b|r(a	b|r(a	PROPN
ejpam-1535	350	9	)	)	PUNCT
ejpam-1535	350	10	are	be	AUX
ejpam-1535	350	11	both	both	PRON
ejpam-1535	350	12	defined	define	VERB
ejpam-1535	350	13	.	.	PUNCT
ejpam-1535	351	1	the	the	DET
ejpam-1535	351	2	first	first	ADJ
ejpam-1535	351	3	of	of	ADP
ejpam-1535	351	4	these	these	PRON
ejpam-1535	351	5	is	be	AUX
ejpam-1535	351	6	defined	define	VERB
ejpam-1535	351	7	to	to	PART
ejpam-1535	351	8	be	be	AUX
ejpam-1535	351	9	the	the	DET
ejpam-1535	351	10	unique	unique	ADJ
ejpam-1535	351	11	element	element	NOUN
ejpam-1535	351	12	x	x	PUNCT
ejpam-1535	352	1	such	such	ADJ
ejpam-1535	352	2	that	that	SCONJ
ejpam-1535	352	3	x	x	SYM
ejpam-1535	352	4	≤	≤	NUM
ejpam-1535	352	5	b	b	NOUN
ejpam-1535	352	6	and	and	CCONJ
ejpam-1535	352	7	d(x	d(x	PROPN
ejpam-1535	352	8	)	)	PUNCT
ejpam-1535	353	1	=	=	SYM
ejpam-1535	353	2	d(a	d(a	PROPN
ejpam-1535	353	3	)	)	PUNCT
ejpam-1535	353	4	.	.	PUNCT
ejpam-1535	354	1	notice	notice	NOUN
ejpam-1535	354	2	,	,	PUNCT
ejpam-1535	354	3	however	however	ADV
ejpam-1535	354	4	,	,	PUNCT
ejpam-1535	354	5	that	that	SCONJ
ejpam-1535	354	6	a	a	PRON
ejpam-1535	354	7	also	also	ADV
ejpam-1535	354	8	satisfies	satisfy	VERB
ejpam-1535	354	9	these	these	DET
ejpam-1535	354	10	conditions	condition	NOUN
ejpam-1535	354	11	.	.	PUNCT
ejpam-1535	355	1	thus	thus	ADV
ejpam-1535	355	2	,	,	PUNCT
ejpam-1535	355	3	by	by	ADP
ejpam-1535	355	4	uniqueness	uniqueness	NOUN
ejpam-1535	355	5	,	,	PUNCT
ejpam-1535	355	6	a	a	DET
ejpam-1535	355	7	=	=	PROPN
ejpam-1535	355	8	d(a)|b	d(a)|b	PROPN
ejpam-1535	355	9	.	.	PUNCT
ejpam-1535	356	1	similarly	similarly	ADV
ejpam-1535	356	2	,	,	PUNCT
ejpam-1535	356	3	b|r(a	b|r(a	NOUN
ejpam-1535	356	4	)	)	PUNCT
ejpam-1535	356	5	=	=	SYM
ejpam-1535	356	6	a.	a.	NOUN
ejpam-1535	356	7	(	(	PUNCT
ejpam-1535	356	8	b	b	NOUN
ejpam-1535	356	9	)	)	PUNCT
ejpam-1535	356	10	by	by	ADP
ejpam-1535	356	11	definition	definition	NOUN
ejpam-1535	356	12	of	of	ADP
ejpam-1535	356	13	a|	a|	PROPN
ejpam-1535	356	14	f	f	PROPN
ejpam-1535	356	15	,	,	PUNCT
ejpam-1535	356	16	we	we	PRON
ejpam-1535	356	17	have	have	VERB
ejpam-1535	356	18	r(a|	r(a|	PROPN
ejpam-1535	356	19	f	f	PROPN
ejpam-1535	356	20	)	)	PUNCT
ejpam-1535	357	1	=	=	SYM
ejpam-1535	357	2	f	f	PROPN
ejpam-1535	357	3	,	,	PUNCT
ejpam-1535	357	4	and	and	CCONJ
ejpam-1535	357	5	so	so	ADV
ejpam-1535	357	6	a|	a|	PROPN
ejpam-1535	357	7	f	f	PROPN
ejpam-1535	357	8	=	=	PUNCT
ejpam-1535	357	9	(	(	PUNCT
ejpam-1535	357	10	a|	a|	PROPN
ejpam-1535	357	11	f	f	PROPN
ejpam-1535	357	12	)	)	PUNCT
ejpam-1535	357	13	·	·	PUNCT
ejpam-1535	358	1	r(a|	r(a|	NOUN
ejpam-1535	358	2	f	f	PROPN
ejpam-1535	358	3	)	)	PUNCT
ejpam-1535	358	4	=	=	PUNCT
ejpam-1535	358	5	(	(	PUNCT
ejpam-1535	358	6	a|	a|	PROPN
ejpam-1535	358	7	f	f	PROPN
ejpam-1535	358	8	)	)	PUNCT
ejpam-1535	358	9	·	·	PUNCT
ejpam-1535	359	1	f	f	X
ejpam-1535	359	2	.	.	PUNCT
ejpam-1535	360	1	similarly	similarly	ADV
ejpam-1535	360	2	,	,	PUNCT
ejpam-1535	360	3	f	f	PROPN
ejpam-1535	360	4	·	·	PUNCT
ejpam-1535	360	5	(	(	PUNCT
ejpam-1535	360	6	f	f	X
ejpam-1535	360	7	|a	|a	NOUN
ejpam-1535	360	8	)	)	PUNCT
ejpam-1535	360	9	=	=	SYM
ejpam-1535	360	10	f	f	PROPN
ejpam-1535	360	11	|a	|a	NOUN
ejpam-1535	360	12	.	.	PUNCT
ejpam-1535	361	1	(	(	PUNCT
ejpam-1535	361	2	c	c	X
ejpam-1535	361	3	)	)	PUNCT
ejpam-1535	361	4	suppose	suppose	VERB
ejpam-1535	361	5	that	that	SCONJ
ejpam-1535	361	6	r(a	r(a	PROPN
ejpam-1535	361	7	)	)	PUNCT
ejpam-1535	361	8	=	=	SYM
ejpam-1535	361	9	r(b	r(b	PROPN
ejpam-1535	361	10	)	)	PUNCT
ejpam-1535	361	11	.	.	PUNCT
ejpam-1535	362	1	then	then	ADV
ejpam-1535	362	2	,	,	PUNCT
ejpam-1535	362	3	since	since	SCONJ
ejpam-1535	362	4	a	a	DET
ejpam-1535	362	5	≤	≤	NOUN
ejpam-1535	362	6	c	c	NOUN
ejpam-1535	362	7	,	,	PUNCT
ejpam-1535	362	8	we	we	PRON
ejpam-1535	362	9	have	have	VERB
ejpam-1535	362	10	a	a	DET
ejpam-1535	362	11	=	=	SYM
ejpam-1535	362	12	c|r(a	c|r(a	NOUN
ejpam-1535	362	13	)	)	PUNCT
ejpam-1535	362	14	,	,	PUNCT
ejpam-1535	362	15	by	by	ADP
ejpam-1535	362	16	(	(	PUNCT
ejpam-1535	362	17	a	a	NOUN
ejpam-1535	362	18	)	)	PUNCT
ejpam-1535	362	19	.	.	PUNCT
ejpam-1535	363	1	also	also	ADV
ejpam-1535	363	2	by	by	ADP
ejpam-1535	363	3	(	(	PUNCT
ejpam-1535	363	4	a	a	NOUN
ejpam-1535	363	5	)	)	PUNCT
ejpam-1535	363	6	,	,	PUNCT
ejpam-1535	363	7	b	b	X
ejpam-1535	363	8	=	=	SYM
ejpam-1535	363	9	c|r(b	c|r(b	PROPN
ejpam-1535	363	10	)	)	PUNCT
ejpam-1535	363	11	.	.	PUNCT
ejpam-1535	364	1	thus	thus	ADV
ejpam-1535	364	2	a	a	DET
ejpam-1535	364	3	=	=	SYM
ejpam-1535	364	4	c|r(a	c|r(a	VERB
ejpam-1535	364	5	)	)	PUNCT
ejpam-1535	364	6	=	=	SYM
ejpam-1535	364	7	c|r(b	c|r(b	PROPN
ejpam-1535	364	8	)	)	PUNCT
ejpam-1535	364	9	=	=	SYM
ejpam-1535	364	10	b.	b.	PROPN
ejpam-1535	364	11	similarly	similarly	ADV
ejpam-1535	364	12	if	if	SCONJ
ejpam-1535	364	13	d(a	d(a	PROPN
ejpam-1535	364	14	)	)	PUNCT
ejpam-1535	364	15	=	=	PUNCT
ejpam-1535	364	16	d(b	d(b	PROPN
ejpam-1535	364	17	)	)	PUNCT
ejpam-1535	364	18	.	.	PUNCT
ejpam-1535	365	1	(	(	PUNCT
ejpam-1535	365	2	d	d	X
ejpam-1535	365	3	)	)	PUNCT
ejpam-1535	365	4	suppose	suppose	VERB
ejpam-1535	365	5	that	that	SCONJ
ejpam-1535	365	6	e	e	PROPN
ejpam-1535	365	7	≤	≤	X
ejpam-1535	365	8	f	f	PROPN
ejpam-1535	365	9	≤	≤	X
ejpam-1535	365	10	r(a	r(a	PROPN
ejpam-1535	365	11	)	)	PUNCT
ejpam-1535	365	12	.	.	PUNCT
ejpam-1535	366	1	then	then	ADV
ejpam-1535	366	2	,	,	PUNCT
ejpam-1535	366	3	by	by	ADP
ejpam-1535	366	4	definition	definition	NOUN
ejpam-1535	366	5	of	of	ADP
ejpam-1535	366	6	corestrictions	corestriction	NOUN
ejpam-1535	366	7	,	,	PUNCT
ejpam-1535	366	8	a|e	a|e	X
ejpam-1535	366	9	≤	≤	NOUN
ejpam-1535	367	1	a	a	PRON
ejpam-1535	367	2	and	and	CCONJ
ejpam-1535	367	3	(	(	PUNCT
ejpam-1535	367	4	a|	a|	PROPN
ejpam-1535	367	5	f	f	PROPN
ejpam-1535	367	6	)	)	PUNCT
ejpam-1535	367	7	|e	|e	PROPN
ejpam-1535	367	8	≤	≤	PUNCT
ejpam-1535	367	9	a|	a|	PROPN
ejpam-1535	367	10	f	f	PROPN
ejpam-1535	367	11	≤	≤	NUM
ejpam-1535	367	12	a.	a.	NOUN
ejpam-1535	367	13	also	also	ADV
ejpam-1535	367	14	,	,	PUNCT
ejpam-1535	367	15	r(a|e	r(a|e	NUM
ejpam-1535	367	16	)	)	PUNCT
ejpam-1535	367	17	=	=	SYM
ejpam-1535	367	18	e	e	NOUN
ejpam-1535	367	19	and	and	CCONJ
ejpam-1535	367	20	r[(a|	r[(a|	PROPN
ejpam-1535	367	21	f	f	PROPN
ejpam-1535	367	22	)	)	PUNCT
ejpam-1535	367	23	|e	|e	PROPN
ejpam-1535	367	24	]	]	X
ejpam-1535	368	1	=	=	SYM
ejpam-1535	368	2	e.	e.	PROPN
ejpam-1535	368	3	therefore	therefore	ADV
ejpam-1535	368	4	,	,	PUNCT
ejpam-1535	368	5	by	by	ADP
ejpam-1535	368	6	(	(	PUNCT
ejpam-1535	368	7	c	c	NOUN
ejpam-1535	368	8	)	)	PUNCT
ejpam-1535	368	9	,	,	PUNCT
ejpam-1535	368	10	a|e	a|e	PUNCT
ejpam-1535	368	11	=	=	PUNCT
ejpam-1535	369	1	(	(	PUNCT
ejpam-1535	369	2	a|	a|	PROPN
ejpam-1535	369	3	f	f	PROPN
ejpam-1535	369	4	)	)	PUNCT
ejpam-1535	369	5	|e	|e	PROPN
ejpam-1535	369	6	≤	≤	PUNCT
ejpam-1535	369	7	a|	a|	PROPN
ejpam-1535	369	8	f	f	X
ejpam-1535	369	9	.	.	PUNCT
ejpam-1535	370	1	similarly	similarly	ADV
ejpam-1535	370	2	,	,	PUNCT
ejpam-1535	370	3	e|a	e|a	PROPN
ejpam-1535	370	4	=	=	SYM
ejpam-1535	370	5	e|	e|	PROPN
ejpam-1535	370	6	(	(	PUNCT
ejpam-1535	370	7	f	f	PROPN
ejpam-1535	370	8	|a)≤	|a)≤	PROPN
ejpam-1535	370	9	f	f	PROPN
ejpam-1535	370	10	|a	|a	X
ejpam-1535	370	11	.	.	PUNCT
ejpam-1535	371	1	(	(	PUNCT
ejpam-1535	371	2	e	e	X
ejpam-1535	371	3	)	)	PUNCT
ejpam-1535	371	4	suppose	suppose	VERB
ejpam-1535	371	5	that	that	SCONJ
ejpam-1535	371	6	∃x	∃x	PROPN
ejpam-1535	371	7	·	·	PUNCT
ejpam-1535	371	8	y	y	NOUN
ejpam-1535	371	9	and	and	CCONJ
ejpam-1535	371	10	e	e	X
ejpam-1535	371	11	≤	≤	NUM
ejpam-1535	371	12	r(x	r(x	PROPN
ejpam-1535	371	13	·	·	PUNCT
ejpam-1535	371	14	y	y	X
ejpam-1535	371	15	)	)	PUNCT
ejpam-1535	371	16	=	=	PUNCT
ejpam-1535	371	17	r(y	r(y	VERB
ejpam-1535	371	18	)	)	PUNCT
ejpam-1535	371	19	.	.	PUNCT
ejpam-1535	372	1	then	then	ADV
ejpam-1535	372	2	the	the	DET
ejpam-1535	372	3	corestrictions	corestriction	NOUN
ejpam-1535	372	4	(	(	PUNCT
ejpam-1535	372	5	x	x	X
ejpam-1535	372	6	·	·	PUNCT
ejpam-1535	372	7	y)|e	y)|e	NOUN
ejpam-1535	372	8	and	and	CCONJ
ejpam-1535	372	9	y|e	y|e	NOUN
ejpam-1535	372	10	are	be	AUX
ejpam-1535	372	11	both	both	PRON
ejpam-1535	372	12	defined	define	VERB
ejpam-1535	372	13	.	.	PUNCT
ejpam-1535	373	1	note	note	VERB
ejpam-1535	373	2	that	that	SCONJ
ejpam-1535	373	3	the	the	DET
ejpam-1535	373	4	corestriction	corestriction	NOUN
ejpam-1535	373	5	x	x	PUNCT
ejpam-1535	373	6	|d(y|e	|d(y|e	NOUN
ejpam-1535	373	7	)	)	PUNCT
ejpam-1535	373	8	is	be	AUX
ejpam-1535	373	9	also	also	ADV
ejpam-1535	373	10	defined	define	VERB
ejpam-1535	373	11	,	,	PUNCT
ejpam-1535	373	12	since	since	SCONJ
ejpam-1535	373	13	d(y|e)≤	d(y|e)≤	NOUN
ejpam-1535	373	14	d(y	d(y	PROPN
ejpam-1535	373	15	)	)	PUNCT
ejpam-1535	373	16	=	=	SYM
ejpam-1535	374	1	r(x	r(x	PROPN
ejpam-1535	374	2	)	)	PUNCT
ejpam-1535	374	3	,	,	PUNCT
ejpam-1535	374	4	using	use	VERB
ejpam-1535	374	5	(	(	PUNCT
ejpam-1535	374	6	or2	or2	PROPN
ejpam-1535	374	7	)	)	PUNCT
ejpam-1535	374	8	,	,	PUNCT
ejpam-1535	374	9	together	together	ADV
ejpam-1535	374	10	with	with	ADP
ejpam-1535	374	11	lemma	lemma	PROPN
ejpam-1535	374	12	2	2	NUM
ejpam-1535	374	13	.	.	PUNCT
ejpam-1535	375	1	the	the	DET
ejpam-1535	375	2	product	product	NOUN
ejpam-1535	375	3	�	�	PROPN
ejpam-1535	375	4	x	x	SYM
ejpam-1535	375	5	|d(y|e	|d(y|e	NOUN
ejpam-1535	375	6	)	)	PUNCT
ejpam-1535	375	7	�	�	PROPN
ejpam-1535	375	8	·	·	PUNCT
ejpam-1535	375	9	(	(	PUNCT
ejpam-1535	375	10	y|e	y|e	NOUN
ejpam-1535	375	11	)	)	PUNCT
ejpam-1535	375	12	is	be	AUX
ejpam-1535	375	13	certainly	certainly	ADV
ejpam-1535	375	14	defined	define	VERB
ejpam-1535	375	15	.	.	PUNCT
ejpam-1535	376	1	observe	observe	VERB
ejpam-1535	376	2	that	that	SCONJ
ejpam-1535	376	3	x	x	PUNCT
ejpam-1535	376	4	|d(y|e	|d(y|e	NOUN
ejpam-1535	376	5	)	)	PUNCT
ejpam-1535	376	6	≤	≤	NUM
ejpam-1535	376	7	x	x	PUNCT
ejpam-1535	376	8	and	and	CCONJ
ejpam-1535	376	9	that	that	SCONJ
ejpam-1535	376	10	y|e	y|e	PROPN
ejpam-1535	376	11	≤	≤	PROPN
ejpam-1535	376	12	y	y	PROPN
ejpam-1535	376	13	,	,	PUNCT
ejpam-1535	376	14	so	so	ADV
ejpam-1535	376	15	�	�	PROPN
ejpam-1535	376	16	x	x	SYM
ejpam-1535	376	17	|d(y|e	|d(y|e	NOUN
ejpam-1535	376	18	)	)	PUNCT
ejpam-1535	376	19	�	�	PROPN
ejpam-1535	376	20	·	·	PUNCT
ejpam-1535	376	21	(	(	PUNCT
ejpam-1535	376	22	y|e	y|e	NOUN
ejpam-1535	376	23	)	)	PUNCT
ejpam-1535	376	24	≤	≤	NUM
ejpam-1535	376	25	x	x	X
ejpam-1535	376	26	·	·	PUNCT
ejpam-1535	376	27	y	y	X
ejpam-1535	376	28	,	,	PUNCT
ejpam-1535	376	29	by	by	ADP
ejpam-1535	376	30	(	(	PUNCT
ejpam-1535	376	31	or1	or1	NOUN
ejpam-1535	376	32	)	)	PUNCT
ejpam-1535	376	33	.	.	PUNCT
ejpam-1535	377	1	we	we	PRON
ejpam-1535	377	2	also	also	ADV
ejpam-1535	377	3	have	have	VERB
ejpam-1535	377	4	(	(	PUNCT
ejpam-1535	377	5	x	x	PART
ejpam-1535	377	6	·	·	PUNCT
ejpam-1535	377	7	y)|e	y)|e	NOUN
ejpam-1535	377	8	≤	≤	NUM
ejpam-1535	377	9	x	x	PUNCT
ejpam-1535	378	1	·	·	PUNCT
ejpam-1535	378	2	y.	y.	PROPN
ejpam-1535	378	3	moreover	moreover	ADV
ejpam-1535	378	4	,	,	PUNCT
ejpam-1535	378	5	r	r	PROPN
ejpam-1535	378	6	�	�	PROPN
ejpam-1535	378	7	(	(	PUNCT
ejpam-1535	378	8	x	x	SYM
ejpam-1535	378	9	·	·	PUNCT
ejpam-1535	378	10	y)|e	y)|e	X
ejpam-1535	378	11	�	�	PROPN
ejpam-1535	378	12	=	=	SYM
ejpam-1535	378	13	e	e	X
ejpam-1535	378	14	=	=	SYM
ejpam-1535	378	15	r	r	NOUN
ejpam-1535	378	16	�	�	PROPN
ejpam-1535	378	17	�	�	PROPN
ejpam-1535	378	18	x	x	SYM
ejpam-1535	378	19	|d(y|e	|d(y|e	NOUN
ejpam-1535	378	20	)	)	PUNCT
ejpam-1535	378	21	�	�	PROPN
ejpam-1535	378	22	·	·	PUNCT
ejpam-1535	378	23	(	(	PUNCT
ejpam-1535	378	24	y|e	y|e	PROPN
ejpam-1535	378	25	)	)	PUNCT
ejpam-1535	378	26	�	�	PROPN
ejpam-1535	378	27	.	.	PUNCT
ejpam-1535	379	1	it	it	PRON
ejpam-1535	379	2	therefore	therefore	ADV
ejpam-1535	379	3	follows	follow	VERB
ejpam-1535	379	4	from	from	ADP
ejpam-1535	379	5	(	(	PUNCT
ejpam-1535	379	6	c	c	NOUN
ejpam-1535	379	7	)	)	PUNCT
ejpam-1535	379	8	that	that	SCONJ
ejpam-1535	379	9	(	(	PUNCT
ejpam-1535	379	10	x	x	X
ejpam-1535	379	11	·	·	PUNCT
ejpam-1535	379	12	y)|e	y)|e	NOUN
ejpam-1535	379	13	=	=	SYM
ejpam-1535	379	14	�	�	PROPN
ejpam-1535	379	15	x	x	SYM
ejpam-1535	379	16	|d(y|e	|d(y|e	NOUN
ejpam-1535	379	17	)	)	PUNCT
ejpam-1535	379	18	�	�	PROPN
ejpam-1535	379	19	·	·	PUNCT
ejpam-1535	379	20	(	(	PUNCT
ejpam-1535	379	21	y|e	y|e	PROPN
ejpam-1535	379	22	)	)	PUNCT
ejpam-1535	379	23	.	.	PUNCT
ejpam-1535	380	1	the	the	DET
ejpam-1535	380	2	second	second	ADJ
ejpam-1535	380	3	part	part	NOUN
ejpam-1535	380	4	is	be	AUX
ejpam-1535	380	5	similar	similar	ADJ
ejpam-1535	380	6	.	.	PUNCT
ejpam-1535	381	1	we	we	PRON
ejpam-1535	381	2	note	note	VERB
ejpam-1535	381	3	two	two	NUM
ejpam-1535	381	4	important	important	ADJ
ejpam-1535	381	5	consequences	consequence	NOUN
ejpam-1535	381	6	of	of	ADP
ejpam-1535	381	7	lemma	lemma	PROPN
ejpam-1535	381	8	5(a	5(a	NUM
ejpam-1535	381	9	):	):	PUNCT
ejpam-1535	381	10	corollary	corollary	ADJ
ejpam-1535	381	11	1	1	NUM
ejpam-1535	381	12	.	.	PUNCT
ejpam-1535	382	1	let	let	AUX
ejpam-1535	382	2	(	(	PUNCT
ejpam-1535	382	3	c	c	NOUN
ejpam-1535	382	4	,	,	PUNCT
ejpam-1535	382	5	·	·	PUNCT
ejpam-1535	382	6	,	,	PUNCT
ejpam-1535	382	7	≤	≤	NUM
ejpam-1535	382	8	)	)	PUNCT
ejpam-1535	382	9	be	be	VERB
ejpam-1535	382	10	an	an	DET
ejpam-1535	382	11	ordered	order	VERB
ejpam-1535	382	12	category	category	NOUN
ejpam-1535	382	13	.	.	PUNCT
ejpam-1535	383	1	let	let	VERB
ejpam-1535	383	2	a	a	DET
ejpam-1535	383	3	∈	∈	PROPN
ejpam-1535	383	4	c	c	NOUN
ejpam-1535	383	5	and	and	CCONJ
ejpam-1535	383	6	e	e	NOUN
ejpam-1535	383	7	,	,	PUNCT
ejpam-1535	383	8	f	f	PROPN
ejpam-1535	383	9	∈	∈	PROPN
ejpam-1535	383	10	co.	co.	PROPN
ejpam-1535	383	11	then	then	ADV
ejpam-1535	383	12	(	(	PUNCT
ejpam-1535	383	13	a	a	X
ejpam-1535	383	14	)	)	PUNCT
ejpam-1535	383	15	a|r(a	a|r(a	PROPN
ejpam-1535	383	16	)	)	PUNCT
ejpam-1535	383	17	=	=	SYM
ejpam-1535	384	1	a	a	DET
ejpam-1535	384	2	=	=	SYM
ejpam-1535	384	3	d(a)|a	d(a)|a	PROPN
ejpam-1535	384	4	;	;	PUNCT
ejpam-1535	384	5	(	(	PUNCT
ejpam-1535	384	6	b	b	X
ejpam-1535	384	7	)	)	PUNCT
ejpam-1535	384	8	if	if	SCONJ
ejpam-1535	384	9	e	e	PROPN
ejpam-1535	384	10	≤	≤	X
ejpam-1535	384	11	f	f	NOUN
ejpam-1535	384	12	,	,	PUNCT
ejpam-1535	384	13	then	then	ADV
ejpam-1535	384	14	e|	e|	PROPN
ejpam-1535	384	15	f	f	PROPN
ejpam-1535	384	16	=	=	PUNCT
ejpam-1535	384	17	e	e	PROPN
ejpam-1535	384	18	=	=	SYM
ejpam-1535	384	19	f	f	PROPN
ejpam-1535	384	20	|e	|e	PROPN
ejpam-1535	384	21	,	,	PUNCT
ejpam-1535	384	22	where	where	SCONJ
ejpam-1535	384	23	e|	e|	PROPN
ejpam-1535	384	24	f	f	PROPN
ejpam-1535	384	25	is	be	AUX
ejpam-1535	384	26	regarded	regard	VERB
ejpam-1535	384	27	as	as	ADP
ejpam-1535	384	28	a	a	DET
ejpam-1535	384	29	restriction	restriction	NOUN
ejpam-1535	384	30	and	and	CCONJ
ejpam-1535	384	31	f	f	PROPN
ejpam-1535	384	32	|e	|e	PROPN
ejpam-1535	384	33	as	as	ADP
ejpam-1535	384	34	a	a	DET
ejpam-1535	384	35	corestriction	corestriction	NOUN
ejpam-1535	384	36	.	.	PUNCT
ejpam-1535	385	1	proof	proof	NOUN
ejpam-1535	385	2	.	.	PUNCT
ejpam-1535	386	1	(	(	PUNCT
ejpam-1535	386	2	a	a	X
ejpam-1535	386	3	)	)	PUNCT
ejpam-1535	386	4	put	put	VERB
ejpam-1535	386	5	a	a	DET
ejpam-1535	386	6	=	=	SYM
ejpam-1535	386	7	b	b	PROPN
ejpam-1535	386	8	in	in	ADP
ejpam-1535	386	9	lemma	lemma	PROPN
ejpam-1535	386	10	5(a	5(a	NUM
ejpam-1535	386	11	)	)	PUNCT
ejpam-1535	386	12	.	.	PUNCT
ejpam-1535	387	1	(	(	PUNCT
ejpam-1535	387	2	b	b	X
ejpam-1535	387	3	)	)	PUNCT
ejpam-1535	387	4	if	if	SCONJ
ejpam-1535	387	5	e	e	PROPN
ejpam-1535	387	6	≤	≤	X
ejpam-1535	387	7	f	f	NOUN
ejpam-1535	387	8	,	,	PUNCT
ejpam-1535	387	9	then	then	ADV
ejpam-1535	387	10	,	,	PUNCT
ejpam-1535	387	11	since	since	SCONJ
ejpam-1535	387	12	e	e	NOUN
ejpam-1535	387	13	=	=	SYM
ejpam-1535	387	14	d(e	d(e	PROPN
ejpam-1535	387	15	)	)	PUNCT
ejpam-1535	387	16	=	=	SYM
ejpam-1535	387	17	r(e	r(e	NOUN
ejpam-1535	387	18	)	)	PUNCT
ejpam-1535	387	19	,	,	PUNCT
ejpam-1535	387	20	we	we	PRON
ejpam-1535	387	21	have	have	VERB
ejpam-1535	387	22	e|	e|	PROPN
ejpam-1535	387	23	f	f	PROPN
ejpam-1535	388	1	=	=	PUNCT
ejpam-1535	388	2	d(e)|	d(e)|	NOUN
ejpam-1535	388	3	f	f	NOUN
ejpam-1535	388	4	=	=	SYM
ejpam-1535	388	5	e	e	PROPN
ejpam-1535	388	6	=	=	SYM
ejpam-1535	388	7	f	f	PROPN
ejpam-1535	388	8	|r(e	|r(e	PROPN
ejpam-1535	388	9	)	)	PUNCT
ejpam-1535	388	10	=	=	SYM
ejpam-1535	388	11	f	f	PROPN
ejpam-1535	388	12	|e	|e	PROPN
ejpam-1535	388	13	,	,	PUNCT
ejpam-1535	388	14	by	by	ADP
ejpam-1535	388	15	lemma	lemma	PROPN
ejpam-1535	388	16	5(a	5(a	NUM
ejpam-1535	388	17	)	)	PUNCT
ejpam-1535	388	18	.	.	PUNCT
ejpam-1535	389	1	we	we	PRON
ejpam-1535	389	2	also	also	ADV
ejpam-1535	389	3	record	record	VERB
ejpam-1535	389	4	the	the	DET
ejpam-1535	389	5	following	following	NOUN
ejpam-1535	389	6	for	for	ADP
ejpam-1535	389	7	future	future	ADJ
ejpam-1535	389	8	use	use	NOUN
ejpam-1535	389	9	:	:	PUNCT
ejpam-1535	389	10	lemma	lemma	PROPN
ejpam-1535	389	11	6	6	NUM
ejpam-1535	389	12	(	(	PUNCT
ejpam-1535	389	13	[	[	X
ejpam-1535	389	14	29	29	NUM
ejpam-1535	389	15	,	,	PUNCT
ejpam-1535	389	16	proposition	proposition	NOUN
ejpam-1535	389	17	4.1.3(5	4.1.3(5	NUM
ejpam-1535	389	18	)	)	PUNCT
ejpam-1535	389	19	]	]	PUNCT
ejpam-1535	389	20	*	*	PUNCT
ejpam-1535	389	21	)	)	PUNCT
ejpam-1535	389	22	.	.	PUNCT
ejpam-1535	390	1	let	let	AUX
ejpam-1535	390	2	(	(	PUNCT
ejpam-1535	390	3	c	c	NOUN
ejpam-1535	390	4	,	,	PUNCT
ejpam-1535	390	5	·	·	PUNCT
ejpam-1535	390	6	,	,	PUNCT
ejpam-1535	390	7	≤	≤	NUM
ejpam-1535	390	8	)	)	PUNCT
ejpam-1535	390	9	be	be	VERB
ejpam-1535	390	10	an	an	DET
ejpam-1535	390	11	ordered	order	VERB
ejpam-1535	390	12	category	category	NOUN
ejpam-1535	390	13	,	,	PUNCT
ejpam-1535	390	14	and	and	CCONJ
ejpam-1535	390	15	suppose	suppose	VERB
ejpam-1535	390	16	that	that	SCONJ
ejpam-1535	390	17	x	x	SYM
ejpam-1535	390	18	,	,	PUNCT
ejpam-1535	390	19	y	y	PROPN
ejpam-1535	390	20	,	,	PUNCT
ejpam-1535	390	21	z	z	PROPN
ejpam-1535	390	22	∈	∈	PROPN
ejpam-1535	390	23	c.	c.	NOUN
ejpam-1535	390	24	if	if	SCONJ
ejpam-1535	390	25	∃x	∃x	PROPN
ejpam-1535	390	26	·	·	PUNCT
ejpam-1535	390	27	y	y	PROPN
ejpam-1535	390	28	and	and	CCONJ
ejpam-1535	390	29	z	z	NOUN
ejpam-1535	390	30	≤	≤	NUM
ejpam-1535	390	31	x	x	X
ejpam-1535	390	32	·	·	PUNCT
ejpam-1535	390	33	y	y	X
ejpam-1535	390	34	,	,	PUNCT
ejpam-1535	390	35	then	then	ADV
ejpam-1535	390	36	there	there	PRON
ejpam-1535	390	37	exist	exist	VERB
ejpam-1535	390	38	x	x	NOUN
ejpam-1535	390	39	′	′	NUM
ejpam-1535	390	40	,	,	PUNCT
ejpam-1535	390	41	y	y	PROPN
ejpam-1535	390	42	′	′	NUM
ejpam-1535	390	43	∈	∈	PROPN
ejpam-1535	390	44	c	c	NOUN
ejpam-1535	390	45	with	with	ADP
ejpam-1535	390	46	x	x	PROPN
ejpam-1535	390	47	′	′	NOUN
ejpam-1535	390	48	≤	≤	NUM
ejpam-1535	390	49	x	x	PUNCT
ejpam-1535	390	50	and	and	CCONJ
ejpam-1535	390	51	y	y	PROPN
ejpam-1535	391	1	′	′	NOUN
ejpam-1535	391	2	≤	≤	NUM
ejpam-1535	392	1	y	y	NOUN
ejpam-1535	392	2	such	such	ADJ
ejpam-1535	392	3	that	that	PRON
ejpam-1535	392	4	∃x	∃x	ADJ
ejpam-1535	392	5	′	′	NUM
ejpam-1535	392	6	·	·	PUNCT
ejpam-1535	393	1	y	y	X
ejpam-1535	393	2	′	′	NOUN
ejpam-1535	393	3	and	and	CCONJ
ejpam-1535	393	4	z	z	NOUN
ejpam-1535	394	1	=	=	PUNCT
ejpam-1535	394	2	x	x	NOUN
ejpam-1535	394	3	′	′	NUM
ejpam-1535	394	4	·	·	PUNCT
ejpam-1535	394	5	y	y	NOUN
ejpam-1535	394	6	′.	′.	NOUN
ejpam-1535	394	7	proof	proof	NOUN
ejpam-1535	394	8	.	.	PUNCT
ejpam-1535	395	1	by	by	ADP
ejpam-1535	395	2	(	(	PUNCT
ejpam-1535	395	3	or2	or2	PROPN
ejpam-1535	395	4	)	)	PUNCT
ejpam-1535	395	5	,	,	PUNCT
ejpam-1535	395	6	we	we	PRON
ejpam-1535	395	7	have	have	VERB
ejpam-1535	395	8	r(z	r(z	NOUN
ejpam-1535	395	9	)	)	PUNCT
ejpam-1535	395	10	≤	≤	NOUN
ejpam-1535	396	1	r(x	r(x	PROPN
ejpam-1535	396	2	·	·	PUNCT
ejpam-1535	396	3	y	y	X
ejpam-1535	396	4	)	)	PUNCT
ejpam-1535	396	5	,	,	PUNCT
ejpam-1535	396	6	so	so	CCONJ
ejpam-1535	396	7	the	the	DET
ejpam-1535	396	8	corestriction	corestriction	NOUN
ejpam-1535	396	9	(	(	PUNCT
ejpam-1535	396	10	x	x	SYM
ejpam-1535	396	11	·	·	PUNCT
ejpam-1535	396	12	y)|r(z	y)|r(z	NOUN
ejpam-1535	396	13	)	)	PUNCT
ejpam-1535	396	14	is	be	AUX
ejpam-1535	396	15	defined	define	VERB
ejpam-1535	396	16	.	.	PUNCT
ejpam-1535	397	1	moreover	moreover	ADV
ejpam-1535	397	2	,	,	PUNCT
ejpam-1535	397	3	z	z	NOUN
ejpam-1535	397	4	=	=	SYM
ejpam-1535	397	5	(	(	PUNCT
ejpam-1535	397	6	x	x	X
ejpam-1535	397	7	·	·	PUNCT
ejpam-1535	397	8	y)|r(z	y)|r(z	NOUN
ejpam-1535	397	9	)	)	PUNCT
ejpam-1535	397	10	,	,	PUNCT
ejpam-1535	397	11	by	by	ADP
ejpam-1535	397	12	uniqueness	uniqueness	NOUN
ejpam-1535	397	13	of	of	ADP
ejpam-1535	397	14	corestrictions	corestriction	NOUN
ejpam-1535	397	15	.	.	PUNCT
ejpam-1535	398	1	then	then	ADV
ejpam-1535	398	2	z	z	X
ejpam-1535	398	3	=	=	SYM
ejpam-1535	398	4	(	(	PUNCT
ejpam-1535	398	5	x	x	X
ejpam-1535	398	6	·	·	PUNCT
ejpam-1535	398	7	y)|r(z	y)|r(z	NOUN
ejpam-1535	398	8	)	)	PUNCT
ejpam-1535	398	9	=	=	SYM
ejpam-1535	398	10	�	�	PROPN
ejpam-1535	398	11	x	x	SYM
ejpam-1535	398	12	|d(y|r(z	|d(y|r(z	NOUN
ejpam-1535	398	13	)	)	PUNCT
ejpam-1535	398	14	)	)	PUNCT
ejpam-1535	398	15	�	�	PROPN
ejpam-1535	398	16	·	·	PUNCT
ejpam-1535	398	17	(	(	PUNCT
ejpam-1535	398	18	y|r(z	y|r(z	PROPN
ejpam-1535	398	19	)	)	PUNCT
ejpam-1535	398	20	)	)	PUNCT
ejpam-1535	398	21	,	,	PUNCT
ejpam-1535	398	22	by	by	ADP
ejpam-1535	398	23	lemma	lemma	PROPN
ejpam-1535	398	24	5(e	5(e	NUM
ejpam-1535	398	25	)	)	PUNCT
ejpam-1535	398	26	.	.	PUNCT
ejpam-1535	399	1	we	we	PRON
ejpam-1535	399	2	put	put	VERB
ejpam-1535	399	3	x	x	PUNCT
ejpam-1535	399	4	′	′	NUM
ejpam-1535	399	5	=	=	NOUN
ejpam-1535	399	6	x	x	SYM
ejpam-1535	399	7	|d(y|r(z	|d(y|r(z	NOUN
ejpam-1535	399	8	)	)	PUNCT
ejpam-1535	399	9	)	)	PUNCT
ejpam-1535	400	1	and	and	CCONJ
ejpam-1535	400	2	y	y	PROPN
ejpam-1535	400	3	′	′	NUM
ejpam-1535	400	4	=	=	SYM
ejpam-1535	400	5	y|r(z	y|r(z	PROPN
ejpam-1535	400	6	)	)	PUNCT
ejpam-1535	400	7	.	.	PUNCT
ejpam-1535	401	1	we	we	PRON
ejpam-1535	401	2	now	now	ADV
ejpam-1535	401	3	turn	turn	VERB
ejpam-1535	401	4	our	our	PRON
ejpam-1535	401	5	attention	attention	NOUN
ejpam-1535	401	6	specifically	specifically	ADV
ejpam-1535	401	7	to	to	ADP
ejpam-1535	401	8	the	the	DET
ejpam-1535	401	9	ordering	ordering	NOUN
ejpam-1535	401	10	of	of	ADP
ejpam-1535	401	11	identities	identity	NOUN
ejpam-1535	401	12	in	in	ADP
ejpam-1535	401	13	an	an	DET
ejpam-1535	401	14	ordered	order	VERB
ejpam-1535	401	15	category	category	NOUN
ejpam-1535	401	16	:	:	PUNCT
ejpam-1535	401	17	c.	c.	PROPN
ejpam-1535	401	18	hollings	holling	NOUN
ejpam-1535	401	19	/	/	SYM
ejpam-1535	401	20	eur	eur	PROPN
ejpam-1535	401	21	.	.	PUNCT
ejpam-1535	402	1	j.	j.	PROPN
ejpam-1535	402	2	pure	pure	PROPN
ejpam-1535	402	3	appl	appl	PROPN
ejpam-1535	402	4	.	.	PROPN
ejpam-1535	402	5	math	math	PROPN
ejpam-1535	402	6	,	,	PUNCT
ejpam-1535	402	7	5	5	NUM
ejpam-1535	402	8	(	(	PUNCT
ejpam-1535	402	9	2012	2012	NUM
ejpam-1535	402	10	)	)	PUNCT
ejpam-1535	402	11	,	,	PUNCT
ejpam-1535	402	12	414	414	NUM
ejpam-1535	402	13	-	-	SYM
ejpam-1535	402	14	450	450	NUM
ejpam-1535	402	15	430	430	NUM
ejpam-1535	402	16	lemma	lemma	PROPN
ejpam-1535	402	17	7	7	NUM
ejpam-1535	402	18	(	(	PUNCT
ejpam-1535	402	19	[	[	X
ejpam-1535	402	20	1	1	NUM
ejpam-1535	402	21	,	,	PUNCT
ejpam-1535	402	22	lemma	lemma	PROPN
ejpam-1535	402	23	3.5	3.5	NUM
ejpam-1535	402	24	]	]	SYM
ejpam-1535	402	25	*	*	PUNCT
ejpam-1535	402	26	)	)	PUNCT
ejpam-1535	402	27	.	.	PUNCT
ejpam-1535	403	1	let	let	AUX
ejpam-1535	403	2	(	(	PUNCT
ejpam-1535	403	3	c	c	NOUN
ejpam-1535	403	4	,	,	PUNCT
ejpam-1535	403	5	·	·	PUNCT
ejpam-1535	403	6	,	,	PUNCT
ejpam-1535	403	7	≤	≤	NUM
ejpam-1535	403	8	)	)	PUNCT
ejpam-1535	403	9	be	be	VERB
ejpam-1535	403	10	an	an	DET
ejpam-1535	403	11	ordered	order	VERB
ejpam-1535	403	12	category	category	NOUN
ejpam-1535	403	13	,	,	PUNCT
ejpam-1535	403	14	and	and	CCONJ
ejpam-1535	403	15	suppose	suppose	VERB
ejpam-1535	403	16	that	that	SCONJ
ejpam-1535	403	17	a	a	DET
ejpam-1535	403	18	∈	∈	PROPN
ejpam-1535	403	19	c	c	X
ejpam-1535	403	20	and	and	CCONJ
ejpam-1535	403	21	e	e	PROPN
ejpam-1535	403	22	∈	∈	PROPN
ejpam-1535	403	23	co.	co.	PROPN
ejpam-1535	403	24	if	if	SCONJ
ejpam-1535	403	25	a	a	DET
ejpam-1535	403	26	≤	≤	X
ejpam-1535	403	27	e	e	NOUN
ejpam-1535	403	28	,	,	PUNCT
ejpam-1535	403	29	then	then	ADV
ejpam-1535	403	30	a	a	PRON
ejpam-1535	403	31	is	be	AUX
ejpam-1535	403	32	an	an	DET
ejpam-1535	403	33	identity	identity	NOUN
ejpam-1535	403	34	.	.	PUNCT
ejpam-1535	404	1	proof	proof	NOUN
ejpam-1535	404	2	.	.	PUNCT
ejpam-1535	405	1	if	if	SCONJ
ejpam-1535	405	2	a	a	PRON
ejpam-1535	405	3	and	and	CCONJ
ejpam-1535	405	4	e	e	NOUN
ejpam-1535	405	5	are	be	AUX
ejpam-1535	405	6	such	such	ADJ
ejpam-1535	405	7	that	that	SCONJ
ejpam-1535	405	8	a	a	DET
ejpam-1535	405	9	≤	≤	ADJ
ejpam-1535	405	10	e	e	NOUN
ejpam-1535	405	11	,	,	PUNCT
ejpam-1535	405	12	then	then	ADV
ejpam-1535	405	13	a	a	DET
ejpam-1535	405	14	=	=	SYM
ejpam-1535	405	15	e|r(a	e|r(a	NOUN
ejpam-1535	405	16	)	)	PUNCT
ejpam-1535	405	17	,	,	PUNCT
ejpam-1535	405	18	by	by	ADP
ejpam-1535	405	19	lemma	lemma	PROPN
ejpam-1535	405	20	5(a	5(a	NUM
ejpam-1535	405	21	)	)	PUNCT
ejpam-1535	405	22	.	.	PUNCT
ejpam-1535	406	1	by	by	ADP
ejpam-1535	406	2	uniqueness	uniqueness	NOUN
ejpam-1535	406	3	of	of	ADP
ejpam-1535	406	4	restrictions	restriction	NOUN
ejpam-1535	406	5	,	,	PUNCT
ejpam-1535	406	6	a	a	DET
ejpam-1535	406	7	=	=	SYM
ejpam-1535	406	8	r(a	r(a	PROPN
ejpam-1535	406	9	)	)	PUNCT
ejpam-1535	406	10	,	,	PUNCT
ejpam-1535	406	11	i.e.	i.e.	X
ejpam-1535	406	12	,	,	PUNCT
ejpam-1535	406	13	a	a	PRON
ejpam-1535	406	14	is	be	AUX
ejpam-1535	406	15	an	an	DET
ejpam-1535	406	16	identity	identity	NOUN
ejpam-1535	406	17	.	.	PUNCT
ejpam-1535	407	1	in	in	ADP
ejpam-1535	407	2	an	an	DET
ejpam-1535	407	3	ordered	order	VERB
ejpam-1535	407	4	category	category	NOUN
ejpam-1535	407	5	(	(	PUNCT
ejpam-1535	407	6	c	c	NOUN
ejpam-1535	407	7	,	,	PUNCT
ejpam-1535	407	8	·	·	PUNCT
ejpam-1535	407	9	,	,	PUNCT
ejpam-1535	407	10	≤	≤	NUM
ejpam-1535	407	11	)	)	PUNCT
ejpam-1535	407	12	,	,	PUNCT
ejpam-1535	407	13	if	if	SCONJ
ejpam-1535	407	14	the	the	DET
ejpam-1535	407	15	greatest	greatest	ADV
ejpam-1535	407	16	lower	low	ADJ
ejpam-1535	407	17	bound	bind	VERB
ejpam-1535	407	18	of	of	ADP
ejpam-1535	407	19	two	two	NUM
ejpam-1535	407	20	identities	identity	NOUN
ejpam-1535	407	21	e	e	NOUN
ejpam-1535	407	22	,	,	PUNCT
ejpam-1535	407	23	f	f	PROPN
ejpam-1535	407	24	exists	exist	VERB
ejpam-1535	407	25	(	(	PUNCT
ejpam-1535	407	26	with	with	ADP
ejpam-1535	407	27	respect	respect	NOUN
ejpam-1535	407	28	to	to	ADP
ejpam-1535	407	29	≤	≤	NUM
ejpam-1535	407	30	)	)	PUNCT
ejpam-1535	407	31	,	,	PUNCT
ejpam-1535	407	32	then	then	ADV
ejpam-1535	407	33	we	we	PRON
ejpam-1535	407	34	denote	denote	VERB
ejpam-1535	407	35	it	it	PRON
ejpam-1535	407	36	by	by	ADP
ejpam-1535	407	37	e	e	PROPN
ejpam-1535	407	38	∧	∧	PROPN
ejpam-1535	407	39	f	f	PROPN
ejpam-1535	407	40	.	.	PUNCT
ejpam-1535	408	1	it	it	PRON
ejpam-1535	408	2	follows	follow	VERB
ejpam-1535	408	3	from	from	ADP
ejpam-1535	408	4	lemma	lemma	PROPN
ejpam-1535	408	5	7	7	NUM
ejpam-1535	408	6	that	that	SCONJ
ejpam-1535	408	7	if	if	SCONJ
ejpam-1535	408	8	e	e	PROPN
ejpam-1535	408	9	∧	∧	PROPN
ejpam-1535	408	10	f	f	PROPN
ejpam-1535	408	11	exists	exist	VERB
ejpam-1535	408	12	,	,	PUNCT
ejpam-1535	408	13	then	then	ADV
ejpam-1535	408	14	it	it	PRON
ejpam-1535	408	15	is	be	AUX
ejpam-1535	408	16	an	an	DET
ejpam-1535	408	17	identity	identity	NOUN
ejpam-1535	408	18	.	.	PUNCT
ejpam-1535	409	1	definition	definition	NOUN
ejpam-1535	409	2	12	12	NUM
ejpam-1535	409	3	.	.	PUNCT
ejpam-1535	410	1	an	an	DET
ejpam-1535	410	2	inductive	inductive	ADJ
ejpam-1535	410	3	category	category	NOUN
ejpam-1535	410	4	(	(	PUNCT
ejpam-1535	410	5	c	c	NOUN
ejpam-1535	410	6	,	,	PUNCT
ejpam-1535	410	7	·	·	PUNCT
ejpam-1535	410	8	,	,	PUNCT
ejpam-1535	410	9	≤	≤	NUM
ejpam-1535	410	10	)	)	PUNCT
ejpam-1535	410	11	is	be	AUX
ejpam-1535	410	12	an	an	DET
ejpam-1535	410	13	ordered	order	VERB
ejpam-1535	410	14	category	category	NOUN
ejpam-1535	410	15	in	in	ADP
ejpam-1535	410	16	which	which	PRON
ejpam-1535	410	17	the	the	DET
ejpam-1535	410	18	following	follow	VERB
ejpam-1535	410	19	additional	additional	ADJ
ejpam-1535	410	20	condition	condition	NOUN
ejpam-1535	410	21	holds	hold	VERB
ejpam-1535	410	22	:	:	PUNCT
ejpam-1535	410	23	(	(	PUNCT
ejpam-1535	410	24	in	in	ADP
ejpam-1535	410	25	)	)	PUNCT
ejpam-1535	410	26	if	if	SCONJ
ejpam-1535	410	27	e	e	NOUN
ejpam-1535	410	28	,	,	PUNCT
ejpam-1535	410	29	f	f	PROPN
ejpam-1535	410	30	∈	∈	PROPN
ejpam-1535	410	31	co	co	NOUN
ejpam-1535	410	32	,	,	PUNCT
ejpam-1535	410	33	then	then	ADV
ejpam-1535	410	34	e	e	PROPN
ejpam-1535	410	35	∧	∧	PROPN
ejpam-1535	410	36	f	f	PROPN
ejpam-1535	410	37	exists	exist	VERB
ejpam-1535	410	38	in	in	ADP
ejpam-1535	410	39	co.	co.	PROPN
ejpam-1535	410	40	an	an	DET
ejpam-1535	410	41	inductive	inductive	ADJ
ejpam-1535	410	42	unipotent	unipotent	ADJ
ejpam-1535	410	43	(	(	PUNCT
ejpam-1535	410	44	cancellative	cancellative	ADJ
ejpam-1535	410	45	)	)	PUNCT
ejpam-1535	410	46	category	category	NOUN
ejpam-1535	410	47	is	be	AUX
ejpam-1535	410	48	a	a	DET
ejpam-1535	410	49	unipotent	unipotent	ADJ
ejpam-1535	410	50	(	(	PUNCT
ejpam-1535	410	51	cancellative	cancellative	ADJ
ejpam-1535	410	52	)	)	PUNCT
ejpam-1535	410	53	category	category	NOUN
ejpam-1535	410	54	which	which	PRON
ejpam-1535	410	55	is	be	AUX
ejpam-1535	410	56	also	also	ADV
ejpam-1535	410	57	an	an	DET
ejpam-1535	410	58	inductive	inductive	ADJ
ejpam-1535	410	59	category	category	NOUN
ejpam-1535	410	60	in	in	ADP
ejpam-1535	410	61	the	the	DET
ejpam-1535	410	62	sense	sense	NOUN
ejpam-1535	410	63	of	of	ADP
ejpam-1535	410	64	definition	definition	NOUN
ejpam-1535	410	65	12	12	NUM
ejpam-1535	410	66	.	.	PUNCT
ejpam-1535	411	1	as	as	SCONJ
ejpam-1535	411	2	we	we	PRON
ejpam-1535	411	3	already	already	ADV
ejpam-1535	411	4	know	know	VERB
ejpam-1535	411	5	from	from	ADP
ejpam-1535	411	6	the	the	DET
ejpam-1535	411	7	historical	historical	ADJ
ejpam-1535	411	8	comments	comment	NOUN
ejpam-1535	411	9	made	make	VERB
ejpam-1535	411	10	earlier	early	ADV
ejpam-1535	411	11	,	,	PUNCT
ejpam-1535	411	12	it	it	PRON
ejpam-1535	411	13	is	be	AUX
ejpam-1535	411	14	inductive	inductive	ADJ
ejpam-1535	411	15	categories	category	NOUN
ejpam-1535	411	16	which	which	PRON
ejpam-1535	411	17	will	will	AUX
ejpam-1535	411	18	be	be	AUX
ejpam-1535	411	19	of	of	ADP
ejpam-1535	411	20	the	the	DET
ejpam-1535	411	21	greatest	great	ADJ
ejpam-1535	411	22	interest	interest	NOUN
ejpam-1535	411	23	in	in	ADP
ejpam-1535	411	24	the	the	DET
ejpam-1535	411	25	sequel	sequel	NOUN
ejpam-1535	411	26	,	,	PUNCT
ejpam-1535	411	27	since	since	SCONJ
ejpam-1535	411	28	it	it	PRON
ejpam-1535	411	29	is	be	AUX
ejpam-1535	411	30	these	these	PRON
ejpam-1535	411	31	which	which	PRON
ejpam-1535	411	32	correspond	correspond	VERB
ejpam-1535	411	33	to	to	ADP
ejpam-1535	411	34	restriction	restriction	NOUN
ejpam-1535	411	35	semigroups	semigroup	NOUN
ejpam-1535	411	36	in	in	ADP
ejpam-1535	411	37	the	the	DET
ejpam-1535	411	38	appropriate	appropriate	ADJ
ejpam-1535	411	39	manner	manner	NOUN
ejpam-1535	411	40	.	.	PUNCT
ejpam-1535	412	1	however	however	ADV
ejpam-1535	412	2	,	,	PUNCT
ejpam-1535	412	3	for	for	ADP
ejpam-1535	412	4	the	the	DET
ejpam-1535	412	5	final	final	ADJ
ejpam-1535	412	6	few	few	ADJ
ejpam-1535	412	7	paragraphs	paragraph	NOUN
ejpam-1535	412	8	of	of	ADP
ejpam-1535	412	9	this	this	DET
ejpam-1535	412	10	section	section	NOUN
ejpam-1535	412	11	,	,	PUNCT
ejpam-1535	412	12	we	we	PRON
ejpam-1535	412	13	will	will	AUX
ejpam-1535	412	14	continue	continue	VERB
ejpam-1535	412	15	to	to	PART
ejpam-1535	412	16	work	work	VERB
ejpam-1535	412	17	with	with	ADP
ejpam-1535	412	18	the	the	DET
ejpam-1535	412	19	notion	notion	NOUN
ejpam-1535	412	20	of	of	ADP
ejpam-1535	412	21	an	an	DET
ejpam-1535	412	22	ordered	order	VERB
ejpam-1535	412	23	category	category	NOUN
ejpam-1535	412	24	,	,	PUNCT
ejpam-1535	412	25	since	since	SCONJ
ejpam-1535	412	26	almost	almost	ADV
ejpam-1535	412	27	everything	everything	PRON
ejpam-1535	412	28	we	we	PRON
ejpam-1535	412	29	have	have	VERB
ejpam-1535	412	30	to	to	PART
ejpam-1535	412	31	say	say	VERB
ejpam-1535	412	32	is	be	AUX
ejpam-1535	412	33	applicable	applicable	ADJ
ejpam-1535	412	34	in	in	ADP
ejpam-1535	412	35	this	this	DET
ejpam-1535	412	36	more	more	ADV
ejpam-1535	412	37	general	general	ADJ
ejpam-1535	412	38	case	case	NOUN
ejpam-1535	412	39	.	.	PUNCT
ejpam-1535	413	1	we	we	PRON
ejpam-1535	413	2	use	use	VERB
ejpam-1535	413	3	the	the	DET
ejpam-1535	413	4	order	order	NOUN
ejpam-1535	413	5	structure	structure	NOUN
ejpam-1535	413	6	of	of	ADP
ejpam-1535	413	7	an	an	DET
ejpam-1535	413	8	ordered	order	VERB
ejpam-1535	413	9	category	category	NOUN
ejpam-1535	413	10	to	to	PART
ejpam-1535	413	11	define	define	VERB
ejpam-1535	413	12	a	a	DET
ejpam-1535	413	13	notion	notion	NOUN
ejpam-1535	413	14	which	which	PRON
ejpam-1535	413	15	will	will	AUX
ejpam-1535	413	16	be	be	AUX
ejpam-1535	413	17	of	of	ADP
ejpam-1535	413	18	great	great	ADJ
ejpam-1535	413	19	significance	significance	NOUN
ejpam-1535	413	20	in	in	ADP
ejpam-1535	413	21	the	the	DET
ejpam-1535	413	22	following	follow	VERB
ejpam-1535	413	23	section	section	NOUN
ejpam-1535	413	24	.	.	PUNCT
ejpam-1535	414	1	let	let	AUX
ejpam-1535	414	2	(	(	PUNCT
ejpam-1535	414	3	c	c	NOUN
ejpam-1535	414	4	,	,	PUNCT
ejpam-1535	414	5	·	·	PUNCT
ejpam-1535	414	6	,	,	PUNCT
ejpam-1535	414	7	≤	≤	NUM
ejpam-1535	414	8	)	)	PUNCT
ejpam-1535	414	9	be	be	VERB
ejpam-1535	414	10	an	an	DET
ejpam-1535	414	11	ordered	order	VERB
ejpam-1535	414	12	category	category	NOUN
ejpam-1535	414	13	.	.	PUNCT
ejpam-1535	415	1	the	the	DET
ejpam-1535	415	2	pseudoproduct	pseudoproduct	NOUN
ejpam-1535	415	3	⊗	⊗	PROPN
ejpam-1535	415	4	in	in	ADP
ejpam-1535	415	5	(	(	PUNCT
ejpam-1535	415	6	c	c	NOUN
ejpam-1535	415	7	,	,	PUNCT
ejpam-1535	415	8	·	·	PUNCT
ejpam-1535	415	9	,	,	PUNCT
ejpam-1535	415	10	≤	≤	NUM
ejpam-1535	415	11	)	)	PUNCT
ejpam-1535	415	12	is	be	AUX
ejpam-1535	415	13	the	the	DET
ejpam-1535	415	14	binary	binary	ADJ
ejpam-1535	415	15	operation	operation	NOUN
ejpam-1535	415	16	given	give	VERB
ejpam-1535	415	17	by‖	by‖	PROPN
ejpam-1535	415	18	a⊗	a⊗	PROPN
ejpam-1535	415	19	b	b	NOUN
ejpam-1535	416	1	=	=	SYM
ejpam-1535	417	1	[	[	X
ejpam-1535	417	2	a|r(a)∧	a|r(a)∧	PROPN
ejpam-1535	417	3	d(b	d(b	PROPN
ejpam-1535	417	4	)	)	PUNCT
ejpam-1535	417	5	]	]	PUNCT
ejpam-1535	417	6	·	·	PUNCT
ejpam-1535	418	1	[	[	X
ejpam-1535	418	2	r(a)∧	r(a)∧	PROPN
ejpam-1535	418	3	d(b)|b	d(b)|b	PROPN
ejpam-1535	418	4	]	]	PUNCT
ejpam-1535	418	5	.	.	PUNCT
ejpam-1535	419	1	(	(	PUNCT
ejpam-1535	419	2	6	6	X
ejpam-1535	419	3	)	)	PUNCT
ejpam-1535	419	4	notice	notice	NOUN
ejpam-1535	419	5	that	that	SCONJ
ejpam-1535	419	6	if	if	SCONJ
ejpam-1535	419	7	r(a	r(a	PROPN
ejpam-1535	419	8	)	)	PUNCT
ejpam-1535	419	9	∧	∧	PROPN
ejpam-1535	419	10	d(b	d(b	PROPN
ejpam-1535	419	11	)	)	PUNCT
ejpam-1535	419	12	is	be	AUX
ejpam-1535	419	13	defined	define	VERB
ejpam-1535	419	14	,	,	PUNCT
ejpam-1535	419	15	then	then	ADV
ejpam-1535	419	16	r(a	r(a	PROPN
ejpam-1535	419	17	)	)	PUNCT
ejpam-1535	419	18	∧	∧	PROPN
ejpam-1535	419	19	d(b	d(b	NOUN
ejpam-1535	419	20	)	)	PUNCT
ejpam-1535	419	21	≤	≤	NOUN
ejpam-1535	419	22	r(a	r(a	X
ejpam-1535	419	23	)	)	PUNCT
ejpam-1535	419	24	and	and	CCONJ
ejpam-1535	419	25	r(a	r(a	ADJ
ejpam-1535	419	26	)	)	PUNCT
ejpam-1535	419	27	∧	∧	PROPN
ejpam-1535	419	28	d(b	d(b	NOUN
ejpam-1535	419	29	)	)	PUNCT
ejpam-1535	419	30	≤	≤	NOUN
ejpam-1535	419	31	d(b	d(b	PROPN
ejpam-1535	419	32	)	)	PUNCT
ejpam-1535	419	33	,	,	PUNCT
ejpam-1535	419	34	so	so	SCONJ
ejpam-1535	419	35	it	it	PRON
ejpam-1535	419	36	makes	make	VERB
ejpam-1535	419	37	sense	sense	NOUN
ejpam-1535	419	38	to	to	PART
ejpam-1535	419	39	write	write	VERB
ejpam-1535	419	40	“	"	PUNCT
ejpam-1535	419	41	a|r(a	a|r(a	PROPN
ejpam-1535	419	42	)	)	PUNCT
ejpam-1535	419	43	∧	∧	PROPN
ejpam-1535	419	44	d(b	d(b	PROPN
ejpam-1535	419	45	)	)	PUNCT
ejpam-1535	419	46	”	"	PUNCT
ejpam-1535	419	47	and	and	CCONJ
ejpam-1535	419	48	“	"	PUNCT
ejpam-1535	419	49	r(a	r(a	ADJ
ejpam-1535	419	50	)	)	PUNCT
ejpam-1535	419	51	∧	∧	PROPN
ejpam-1535	419	52	d(b)|b	d(b)|b	PROPN
ejpam-1535	419	53	”	"	PUNCT
ejpam-1535	419	54	.	.	PUNCT
ejpam-1535	420	1	the	the	DET
ejpam-1535	420	2	product	product	NOUN
ejpam-1535	420	3	of	of	ADP
ejpam-1535	420	4	these	these	DET
ejpam-1535	420	5	latter	latter	ADJ
ejpam-1535	420	6	two	two	NUM
ejpam-1535	420	7	clearly	clearly	ADV
ejpam-1535	420	8	exists	exist	VERB
ejpam-1535	420	9	.	.	PUNCT
ejpam-1535	421	1	moreover	moreover	ADV
ejpam-1535	421	2	:	:	PUNCT
ejpam-1535	421	3	lemma	lemma	PROPN
ejpam-1535	421	4	8	8	NUM
ejpam-1535	421	5	(	(	PUNCT
ejpam-1535	421	6	[	[	X
ejpam-1535	421	7	1	1	NUM
ejpam-1535	421	8	,	,	PUNCT
ejpam-1535	421	9	p.	p.	NOUN
ejpam-1535	421	10	327	327	NUM
ejpam-1535	421	11	]	]	X
ejpam-1535	421	12	*	*	PUNCT
ejpam-1535	421	13	)	)	PUNCT
ejpam-1535	421	14	.	.	PUNCT
ejpam-1535	422	1	if	if	SCONJ
ejpam-1535	422	2	both	both	DET
ejpam-1535	422	3	a⊗	a⊗	PROPN
ejpam-1535	422	4	b	b	PROPN
ejpam-1535	422	5	and	and	CCONJ
ejpam-1535	422	6	a	a	DET
ejpam-1535	422	7	·	·	PUNCT
ejpam-1535	422	8	b	b	X
ejpam-1535	422	9	are	be	AUX
ejpam-1535	422	10	defined	define	VERB
ejpam-1535	422	11	in	in	ADP
ejpam-1535	422	12	c	c	NOUN
ejpam-1535	422	13	,	,	PUNCT
ejpam-1535	422	14	then	then	ADV
ejpam-1535	422	15	they	they	PRON
ejpam-1535	422	16	are	be	AUX
ejpam-1535	422	17	equal	equal	ADJ
ejpam-1535	422	18	.	.	PUNCT
ejpam-1535	423	1	proof	proof	NOUN
ejpam-1535	423	2	.	.	PUNCT
ejpam-1535	424	1	if	if	SCONJ
ejpam-1535	424	2	∃a	∃a	PRON
ejpam-1535	424	3	·	·	SYM
ejpam-1535	424	4	b	b	X
ejpam-1535	424	5	,	,	PUNCT
ejpam-1535	424	6	then	then	ADV
ejpam-1535	424	7	r(a	r(a	PROPN
ejpam-1535	424	8	)	)	PUNCT
ejpam-1535	424	9	=	=	PUNCT
ejpam-1535	425	1	d(b	d(b	PROPN
ejpam-1535	425	2	)	)	PUNCT
ejpam-1535	425	3	,	,	PUNCT
ejpam-1535	425	4	by	by	ADP
ejpam-1535	425	5	lemma	lemma	PROPN
ejpam-1535	425	6	2	2	NUM
ejpam-1535	425	7	,	,	PUNCT
ejpam-1535	425	8	so	so	ADV
ejpam-1535	425	9	a	a	DET
ejpam-1535	425	10	⊗	⊗	PROPN
ejpam-1535	425	11	b	b	PROPN
ejpam-1535	425	12	=	=	SYM
ejpam-1535	425	13	(	(	PUNCT
ejpam-1535	425	14	a|r(a	a|r(a	NUM
ejpam-1535	425	15	)	)	PUNCT
ejpam-1535	425	16	)	)	PUNCT
ejpam-1535	425	17	·	·	PUNCT
ejpam-1535	425	18	(	(	PUNCT
ejpam-1535	425	19	d(b)|b	d(b)|b	PROPN
ejpam-1535	425	20	)	)	PUNCT
ejpam-1535	425	21	=	=	PUNCT
ejpam-1535	426	1	a	a	DET
ejpam-1535	426	2	·	·	PUNCT
ejpam-1535	426	3	b	b	NOUN
ejpam-1535	426	4	,	,	PUNCT
ejpam-1535	426	5	by	by	ADP
ejpam-1535	426	6	corollary	corollary	NOUN
ejpam-1535	426	7	1(a	1(a	NUM
ejpam-1535	426	8	)	)	PUNCT
ejpam-1535	426	9	.	.	PUNCT
ejpam-1535	427	1	the	the	DET
ejpam-1535	427	2	only	only	ADJ
ejpam-1535	427	3	bar	bar	NOUN
ejpam-1535	427	4	to	to	ADP
ejpam-1535	427	5	⊗	⊗	PROPN
ejpam-1535	427	6	being	be	AUX
ejpam-1535	427	7	an	an	DET
ejpam-1535	427	8	everywhere	everywhere	ADV
ejpam-1535	427	9	-	-	PUNCT
ejpam-1535	427	10	defined	define	VERB
ejpam-1535	427	11	operation	operation	NOUN
ejpam-1535	427	12	in	in	ADP
ejpam-1535	427	13	c	c	PROPN
ejpam-1535	427	14	is	be	AUX
ejpam-1535	427	15	the	the	DET
ejpam-1535	427	16	fact	fact	NOUN
ejpam-1535	427	17	that	that	SCONJ
ejpam-1535	427	18	r(a)∧	r(a)∧	PROPN
ejpam-1535	427	19	d(b	d(b	PROPN
ejpam-1535	427	20	)	)	PUNCT
ejpam-1535	427	21	may	may	AUX
ejpam-1535	427	22	not	not	PART
ejpam-1535	427	23	be	be	AUX
ejpam-1535	427	24	defined	define	VERB
ejpam-1535	427	25	.	.	PUNCT
ejpam-1535	428	1	indeed	indeed	ADV
ejpam-1535	428	2	,	,	PUNCT
ejpam-1535	428	3	a⊗	a⊗	PROPN
ejpam-1535	428	4	b	b	PROPN
ejpam-1535	428	5	exists	exist	VERB
ejpam-1535	428	6	if	if	SCONJ
ejpam-1535	428	7	and	and	CCONJ
ejpam-1535	428	8	only	only	ADV
ejpam-1535	428	9	if	if	SCONJ
ejpam-1535	428	10	r(a)∧d(b	r(a)∧d(b	PRON
ejpam-1535	428	11	)	)	PUNCT
ejpam-1535	428	12	does	do	VERB
ejpam-1535	428	13	.	.	PUNCT
ejpam-1535	429	1	we	we	PRON
ejpam-1535	429	2	see	see	VERB
ejpam-1535	429	3	therefore	therefore	ADV
ejpam-1535	429	4	that	that	SCONJ
ejpam-1535	429	5	in	in	ADP
ejpam-1535	429	6	an	an	DET
ejpam-1535	429	7	inductive	inductive	ADJ
ejpam-1535	429	8	category	category	NOUN
ejpam-1535	429	9	,	,	PUNCT
ejpam-1535	429	10	⊗	⊗	PROPN
ejpam-1535	429	11	is	be	AUX
ejpam-1535	429	12	fully	fully	ADV
ejpam-1535	429	13	defined	define	VERB
ejpam-1535	429	14	.	.	PUNCT
ejpam-1535	430	1	remaining	remain	VERB
ejpam-1535	430	2	for	for	ADP
ejpam-1535	430	3	the	the	DET
ejpam-1535	430	4	time	time	NOUN
ejpam-1535	430	5	being	be	AUX
ejpam-1535	430	6	in	in	ADP
ejpam-1535	430	7	the	the	DET
ejpam-1535	430	8	more	more	ADV
ejpam-1535	430	9	general	general	ADJ
ejpam-1535	430	10	case	case	NOUN
ejpam-1535	430	11	of	of	ADP
ejpam-1535	430	12	an	an	DET
ejpam-1535	430	13	ordered	order	VERB
ejpam-1535	430	14	category	category	NOUN
ejpam-1535	430	15	,	,	PUNCT
ejpam-1535	430	16	we	we	PRON
ejpam-1535	430	17	note	note	VERB
ejpam-1535	430	18	the	the	DET
ejpam-1535	430	19	following	follow	VERB
ejpam-1535	430	20	pair	pair	NOUN
ejpam-1535	430	21	of	of	ADP
ejpam-1535	430	22	propositions	proposition	NOUN
ejpam-1535	430	23	:	:	PUNCT
ejpam-1535	430	24	proposition	proposition	NOUN
ejpam-1535	430	25	1	1	NUM
ejpam-1535	430	26	(	(	PUNCT
ejpam-1535	430	27	[	[	X
ejpam-1535	430	28	29	29	NUM
ejpam-1535	430	29	,	,	PUNCT
ejpam-1535	430	30	lemma	lemma	PROPN
ejpam-1535	430	31	4.1.5	4.1.5	X
ejpam-1535	430	32	]	]	X
ejpam-1535	430	33	*	*	NUM
ejpam-1535	430	34	)	)	PUNCT
ejpam-1535	430	35	.	.	PUNCT
ejpam-1535	431	1	let	let	AUX
ejpam-1535	431	2	(	(	PUNCT
ejpam-1535	431	3	c	c	NOUN
ejpam-1535	431	4	,	,	PUNCT
ejpam-1535	431	5	·	·	PUNCT
ejpam-1535	431	6	,	,	PUNCT
ejpam-1535	431	7	≤	≤	NUM
ejpam-1535	431	8	)	)	PUNCT
ejpam-1535	431	9	be	be	VERB
ejpam-1535	431	10	an	an	DET
ejpam-1535	431	11	ordered	order	VERB
ejpam-1535	431	12	category	category	NOUN
ejpam-1535	431	13	and	and	CCONJ
ejpam-1535	431	14	define	define	VERB
ejpam-1535	431	15	the	the	DET
ejpam-1535	431	16	following	following	NOUN
ejpam-1535	431	17	subset	subset	NOUN
ejpam-1535	431	18	of	of	ADP
ejpam-1535	431	19	c	c	PROPN
ejpam-1535	431	20	×	×	PROPN
ejpam-1535	431	21	c	c	NOUN
ejpam-1535	431	22	:	:	PUNCT
ejpam-1535	431	23	〈	〈	PROPN
ejpam-1535	431	24	x	x	SYM
ejpam-1535	431	25	,	,	PUNCT
ejpam-1535	431	26	y	y	NUM
ejpam-1535	431	27	〉	〉	NOUN
ejpam-1535	431	28	=	=	SYM
ejpam-1535	431	29	{	{	PUNCT
ejpam-1535	431	30	(	(	PUNCT
ejpam-1535	431	31	x	x	SYM
ejpam-1535	431	32	′	′	NOUN
ejpam-1535	431	33	,	,	PUNCT
ejpam-1535	431	34	y	y	PROPN
ejpam-1535	431	35	′	′	NOUN
ejpam-1535	431	36	)	)	PUNCT
ejpam-1535	431	37	∈	∈	PROPN
ejpam-1535	432	1	c	c	AUX
ejpam-1535	432	2	×	×	NOUN
ejpam-1535	432	3	c	c	NOUN
ejpam-1535	432	4	:	:	PUNCT
ejpam-1535	432	5	r(x	r(x	PROPN
ejpam-1535	432	6	′	′	NOUN
ejpam-1535	432	7	)	)	PUNCT
ejpam-1535	432	8	=	=	PUNCT
ejpam-1535	433	1	d(y	d(y	PROPN
ejpam-1535	433	2	′	′	NUM
ejpam-1535	433	3	)	)	PUNCT
ejpam-1535	433	4	,	,	PUNCT
ejpam-1535	433	5	x	x	X
ejpam-1535	433	6	′	′	NOUN
ejpam-1535	433	7	≤	≤	NUM
ejpam-1535	434	1	x	x	X
ejpam-1535	434	2	,	,	PUNCT
ejpam-1535	434	3	y	y	PROPN
ejpam-1535	434	4	′	′	NOUN
ejpam-1535	434	5	≤	≤	NUM
ejpam-1535	435	1	y	y	X
ejpam-1535	435	2	}	}	PUNCT
ejpam-1535	435	3	.	.	PUNCT
ejpam-1535	436	1	‖note	‖note	NOUN
ejpam-1535	436	2	that	that	SCONJ
ejpam-1535	436	3	we	we	PRON
ejpam-1535	436	4	are	be	AUX
ejpam-1535	436	5	omitting	omit	VERB
ejpam-1535	436	6	brackets	bracket	NOUN
ejpam-1535	436	7	here	here	ADV
ejpam-1535	436	8	and	and	CCONJ
ejpam-1535	436	9	writing	write	VERB
ejpam-1535	436	10	“	"	PUNCT
ejpam-1535	436	11	a|r(a)∧	a|r(a)∧	PROPN
ejpam-1535	436	12	d(b	d(b	PROPN
ejpam-1535	436	13	)	)	PUNCT
ejpam-1535	436	14	”	"	PUNCT
ejpam-1535	436	15	for	for	ADP
ejpam-1535	436	16	“	"	PUNCT
ejpam-1535	436	17	a|(r(a)∧	a|(r(a)∧	PROPN
ejpam-1535	436	18	d(b	d(b	PROPN
ejpam-1535	436	19	)	)	PUNCT
ejpam-1535	436	20	)	)	PUNCT
ejpam-1535	436	21	”	"	PUNCT
ejpam-1535	436	22	;	;	PUNCT
ejpam-1535	436	23	“	"	PUNCT
ejpam-1535	436	24	a|r(a)∧	a|r(a)∧	X
ejpam-1535	436	25	d(b	d(b	PROPN
ejpam-1535	436	26	)	)	PUNCT
ejpam-1535	436	27	”	"	PUNCT
ejpam-1535	436	28	should	should	AUX
ejpam-1535	436	29	not	not	PART
ejpam-1535	436	30	be	be	AUX
ejpam-1535	436	31	read	read	VERB
ejpam-1535	436	32	as	as	ADP
ejpam-1535	436	33	“	"	PUNCT
ejpam-1535	436	34	(	(	PUNCT
ejpam-1535	436	35	a|r(a))∧	a|r(a))∧	PROPN
ejpam-1535	436	36	d(b	d(b	PROPN
ejpam-1535	436	37	)	)	PUNCT
ejpam-1535	436	38	”	"	PUNCT
ejpam-1535	436	39	.	.	PUNCT
ejpam-1535	437	1	c.	c.	PROPN
ejpam-1535	437	2	hollings	holling	NOUN
ejpam-1535	437	3	/	/	SYM
ejpam-1535	437	4	eur	eur	PROPN
ejpam-1535	437	5	.	.	PUNCT
ejpam-1535	438	1	j.	j.	PROPN
ejpam-1535	438	2	pure	pure	PROPN
ejpam-1535	438	3	appl	appl	PROPN
ejpam-1535	438	4	.	.	PROPN
ejpam-1535	438	5	math	math	PROPN
ejpam-1535	438	6	,	,	PUNCT
ejpam-1535	438	7	5	5	NUM
ejpam-1535	438	8	(	(	PUNCT
ejpam-1535	438	9	2012	2012	NUM
ejpam-1535	438	10	)	)	PUNCT
ejpam-1535	438	11	,	,	PUNCT
ejpam-1535	438	12	414	414	NUM
ejpam-1535	438	13	-	-	SYM
ejpam-1535	438	14	450	450	NUM
ejpam-1535	438	15	431	431	NUM
ejpam-1535	438	16	we	we	PRON
ejpam-1535	438	17	specify	specify	VERB
ejpam-1535	438	18	an	an	DET
ejpam-1535	438	19	ordering	ordering	NOUN
ejpam-1535	438	20	on	on	ADP
ejpam-1535	438	21	〈	〈	PROPN
ejpam-1535	438	22	x	x	SYM
ejpam-1535	438	23	,	,	PUNCT
ejpam-1535	438	24	y	y	PROPN
ejpam-1535	438	25	〉	〉	NOUN
ejpam-1535	438	26	by	by	ADP
ejpam-1535	438	27	(	(	PUNCT
ejpam-1535	438	28	a	a	DET
ejpam-1535	438	29	,	,	PUNCT
ejpam-1535	438	30	b	b	NOUN
ejpam-1535	438	31	)	)	PUNCT
ejpam-1535	438	32	ã	ã	X
ejpam-1535	439	1	(	(	PUNCT
ejpam-1535	439	2	c	c	X
ejpam-1535	439	3	,	,	PUNCT
ejpam-1535	439	4	d)	d)	NOUN
ejpam-1535	439	5	⇐	⇐	ADJ
ejpam-1535	439	6	⇒	⇒	NOUN
ejpam-1535	439	7	a	a	DET
ejpam-1535	439	8	≤	≤	NOUN
ejpam-1535	439	9	c	c	NOUN
ejpam-1535	439	10	and	and	CCONJ
ejpam-1535	439	11	b	b	NOUN
ejpam-1535	439	12	≤	≤	NUM
ejpam-1535	439	13	d	d	NOUN
ejpam-1535	439	14	in	in	ADP
ejpam-1535	439	15	c	c	PROPN
ejpam-1535	439	16	.	.	PUNCT
ejpam-1535	440	1	then	then	ADV
ejpam-1535	440	2	∃x	∃x	PROPN
ejpam-1535	440	3	⊗	⊗	ADJ
ejpam-1535	440	4	y	y	PROPN
ejpam-1535	440	5	if	if	SCONJ
ejpam-1535	440	6	and	and	CCONJ
ejpam-1535	440	7	only	only	ADV
ejpam-1535	440	8	if	if	SCONJ
ejpam-1535	440	9	〈	〈	PROPN
ejpam-1535	440	10	x	x	SYM
ejpam-1535	440	11	,	,	PUNCT
ejpam-1535	440	12	y	y	NUM
ejpam-1535	440	13	〉	〉	NOUN
ejpam-1535	440	14	has	have	VERB
ejpam-1535	440	15	a	a	DET
ejpam-1535	440	16	maximum	maximum	ADJ
ejpam-1535	440	17	element	element	NOUN
ejpam-1535	440	18	(	(	PUNCT
ejpam-1535	440	19	x	x	SYM
ejpam-1535	440	20	′	′	NUM
ejpam-1535	440	21	,	,	PUNCT
ejpam-1535	440	22	y	y	PROPN
ejpam-1535	440	23	′	′	NOUN
ejpam-1535	440	24	)	)	PUNCT
ejpam-1535	440	25	with	with	ADP
ejpam-1535	440	26	respect	respect	NOUN
ejpam-1535	440	27	to	to	ADP
ejpam-1535	440	28	ã	ã	NOUN
ejpam-1535	440	29	,	,	PUNCT
ejpam-1535	440	30	and	and	CCONJ
ejpam-1535	440	31	in	in	ADP
ejpam-1535	440	32	this	this	DET
ejpam-1535	440	33	case	case	NOUN
ejpam-1535	440	34	x	x	PUNCT
ejpam-1535	441	1	⊗	⊗	NOUN
ejpam-1535	441	2	y	y	PROPN
ejpam-1535	441	3	=	=	PUNCT
ejpam-1535	441	4	x	x	NOUN
ejpam-1535	441	5	′	′	NUM
ejpam-1535	441	6	·	·	PUNCT
ejpam-1535	441	7	y	y	PROPN
ejpam-1535	441	8	′.	′.	NOUN
ejpam-1535	441	9	proof	proof	NOUN
ejpam-1535	441	10	.	.	PUNCT
ejpam-1535	442	1	(	(	PUNCT
ejpam-1535	442	2	⇒	⇒	PROPN
ejpam-1535	442	3	)	)	PUNCT
ejpam-1535	442	4	suppose	suppose	VERB
ejpam-1535	442	5	that	that	SCONJ
ejpam-1535	442	6	∃x	∃x	PROPN
ejpam-1535	442	7	⊗	⊗	PROPN
ejpam-1535	442	8	y.	y.	PROPN
ejpam-1535	442	9	then	then	ADV
ejpam-1535	442	10	r(x)∧	r(x)∧	PROPN
ejpam-1535	442	11	d(y	d(y	PROPN
ejpam-1535	442	12	)	)	PUNCT
ejpam-1535	443	1	=	=	NOUN
ejpam-1535	443	2	:	:	PUNCT
ejpam-1535	443	3	e	e	NOUN
ejpam-1535	443	4	exists	exist	VERB
ejpam-1535	443	5	and	and	CCONJ
ejpam-1535	443	6	x	x	PART
ejpam-1535	443	7	|e	|e	VERB
ejpam-1535	443	8	≤	≤	PUNCT
ejpam-1535	443	9	x	x	X
ejpam-1535	443	10	,	,	PUNCT
ejpam-1535	443	11	e|y	e|y	VERB
ejpam-1535	443	12	≤	≤	ADJ
ejpam-1535	443	13	y	y	PROPN
ejpam-1535	443	14	and	and	CCONJ
ejpam-1535	443	15	r(x	r(x	PROPN
ejpam-1535	443	16	|e	|e	PROPN
ejpam-1535	443	17	)	)	PUNCT
ejpam-1535	443	18	=	=	SYM
ejpam-1535	443	19	e	e	X
ejpam-1535	443	20	=	=	PUNCT
ejpam-1535	443	21	d(e|y	d(e|y	NUM
ejpam-1535	443	22	)	)	PUNCT
ejpam-1535	443	23	,	,	PUNCT
ejpam-1535	443	24	so	so	CCONJ
ejpam-1535	443	25	(	(	PUNCT
ejpam-1535	443	26	x	x	SYM
ejpam-1535	443	27	|e	|e	PROPN
ejpam-1535	443	28	,	,	PUNCT
ejpam-1535	443	29	e|y	e|y	X
ejpam-1535	443	30	)	)	PUNCT
ejpam-1535	443	31	∈	∈	PROPN
ejpam-1535	443	32	〈	〈	PROPN
ejpam-1535	443	33	x	x	PROPN
ejpam-1535	443	34	,	,	PUNCT
ejpam-1535	443	35	y	y	PROPN
ejpam-1535	443	36	〉	〉	NOUN
ejpam-1535	443	37	.	.	PUNCT
ejpam-1535	444	1	now	now	ADV
ejpam-1535	444	2	let	let	VERB
ejpam-1535	444	3	(	(	PUNCT
ejpam-1535	444	4	u	u	NOUN
ejpam-1535	444	5	,	,	PUNCT
ejpam-1535	444	6	v	v	NOUN
ejpam-1535	444	7	)	)	PUNCT
ejpam-1535	444	8	∈	∈	PROPN
ejpam-1535	444	9	〈	〈	PROPN
ejpam-1535	444	10	x	x	PROPN
ejpam-1535	444	11	,	,	PUNCT
ejpam-1535	444	12	y	y	PROPN
ejpam-1535	444	13	〉	〉	NOUN
ejpam-1535	444	14	.	.	PUNCT
ejpam-1535	445	1	then	then	ADV
ejpam-1535	445	2	u	u	X
ejpam-1535	445	3	≤	≤	X
ejpam-1535	445	4	x	x	PUNCT
ejpam-1535	445	5	,	,	PUNCT
ejpam-1535	445	6	v	v	X
ejpam-1535	445	7	≤	≤	ADJ
ejpam-1535	445	8	y	y	PROPN
ejpam-1535	445	9	and	and	CCONJ
ejpam-1535	445	10	r(u	r(u	PROPN
ejpam-1535	445	11	)	)	PUNCT
ejpam-1535	445	12	=	=	SYM
ejpam-1535	445	13	d(v	d(v	ADJ
ejpam-1535	445	14	)	)	PUNCT
ejpam-1535	446	1	=	=	NOUN
ejpam-1535	446	2	:	:	PUNCT
ejpam-1535	446	3	f	f	X
ejpam-1535	446	4	,	,	PUNCT
ejpam-1535	446	5	so	so	ADV
ejpam-1535	446	6	,	,	PUNCT
ejpam-1535	446	7	by	by	ADP
ejpam-1535	446	8	uniqueness	uniqueness	NOUN
ejpam-1535	446	9	of	of	ADP
ejpam-1535	446	10	restrictions	restriction	NOUN
ejpam-1535	446	11	and	and	CCONJ
ejpam-1535	446	12	corestrictions	corestriction	NOUN
ejpam-1535	446	13	,	,	PUNCT
ejpam-1535	446	14	we	we	PRON
ejpam-1535	446	15	have	have	VERB
ejpam-1535	446	16	u	u	NOUN
ejpam-1535	446	17	=	=	NOUN
ejpam-1535	446	18	x	x	PROPN
ejpam-1535	447	1	|	|	ADV
ejpam-1535	447	2	f	f	PROPN
ejpam-1535	447	3	and	and	CCONJ
ejpam-1535	447	4	v	v	ADP
ejpam-1535	447	5	=	=	SYM
ejpam-1535	447	6	f	f	PROPN
ejpam-1535	447	7	|y	|y	NOUN
ejpam-1535	447	8	.	.	PUNCT
ejpam-1535	448	1	it	it	PRON
ejpam-1535	448	2	follows	follow	VERB
ejpam-1535	448	3	from	from	ADP
ejpam-1535	448	4	(	(	PUNCT
ejpam-1535	448	5	or2	or2	NOUN
ejpam-1535	448	6	)	)	PUNCT
ejpam-1535	448	7	that	that	PRON
ejpam-1535	448	8	r(u)≤	r(u)≤	VERB
ejpam-1535	448	9	r(x	r(x	PROPN
ejpam-1535	448	10	)	)	PUNCT
ejpam-1535	448	11	and	and	CCONJ
ejpam-1535	448	12	d(v)≤	d(v)≤	NOUN
ejpam-1535	448	13	d(y	d(y	PROPN
ejpam-1535	448	14	)	)	PUNCT
ejpam-1535	448	15	.	.	PUNCT
ejpam-1535	449	1	thus	thus	ADV
ejpam-1535	449	2	f	f	X
ejpam-1535	449	3	=	=	SYM
ejpam-1535	449	4	r(u	r(u	PROPN
ejpam-1535	449	5	)	)	PUNCT
ejpam-1535	449	6	=	=	SYM
ejpam-1535	450	1	d(v	d(v	PROPN
ejpam-1535	450	2	)	)	PUNCT
ejpam-1535	450	3	is	be	AUX
ejpam-1535	450	4	a	a	DET
ejpam-1535	450	5	lower	lower	ADV
ejpam-1535	450	6	bound	bind	VERB
ejpam-1535	450	7	for	for	ADP
ejpam-1535	450	8	r(x	r(x	PROPN
ejpam-1535	450	9	)	)	PUNCT
ejpam-1535	450	10	and	and	CCONJ
ejpam-1535	450	11	d(y	d(y	PROPN
ejpam-1535	450	12	)	)	PUNCT
ejpam-1535	450	13	,	,	PUNCT
ejpam-1535	450	14	in	in	ADP
ejpam-1535	450	15	which	which	DET
ejpam-1535	450	16	case	case	NOUN
ejpam-1535	450	17	,	,	PUNCT
ejpam-1535	450	18	f	f	PROPN
ejpam-1535	450	19	≤	≤	PROPN
ejpam-1535	450	20	e.	e.	PROPN
ejpam-1535	450	21	then	then	ADV
ejpam-1535	450	22	u	u	VERB
ejpam-1535	451	1	=	=	NOUN
ejpam-1535	451	2	x	x	SYM
ejpam-1535	451	3	|	|	NOUN
ejpam-1535	451	4	f	f	NOUN
ejpam-1535	451	5	≤	≤	NUM
ejpam-1535	451	6	x	x	PUNCT
ejpam-1535	451	7	|e	|e	NOUN
ejpam-1535	451	8	and	and	CCONJ
ejpam-1535	451	9	v	v	X
ejpam-1535	451	10	=	=	SYM
ejpam-1535	451	11	f	f	PROPN
ejpam-1535	451	12	|y	|y	NOUN
ejpam-1535	451	13	≤	≤	ADV
ejpam-1535	451	14	e|y	e|y	NOUN
ejpam-1535	451	15	,	,	PUNCT
ejpam-1535	451	16	by	by	ADP
ejpam-1535	451	17	lemma	lemma	PROPN
ejpam-1535	451	18	5(d	5(d	NUM
ejpam-1535	451	19	)	)	PUNCT
ejpam-1535	451	20	.	.	PUNCT
ejpam-1535	452	1	it	it	PRON
ejpam-1535	452	2	follows	follow	VERB
ejpam-1535	452	3	that	that	SCONJ
ejpam-1535	452	4	(	(	PUNCT
ejpam-1535	452	5	x	x	SYM
ejpam-1535	452	6	|e	|e	PROPN
ejpam-1535	452	7	,	,	PUNCT
ejpam-1535	452	8	e|y	e|y	NOUN
ejpam-1535	452	9	)	)	PUNCT
ejpam-1535	452	10	is	be	AUX
ejpam-1535	452	11	a	a	DET
ejpam-1535	452	12	maximum	maximum	ADJ
ejpam-1535	452	13	element	element	NOUN
ejpam-1535	452	14	in	in	ADP
ejpam-1535	452	15	〈	〈	PROPN
ejpam-1535	452	16	x	x	SYM
ejpam-1535	452	17	,	,	PUNCT
ejpam-1535	452	18	y	y	NOUN
ejpam-1535	452	19	〉	〉	NOUN
ejpam-1535	452	20	and	and	CCONJ
ejpam-1535	452	21	x	x	NOUN
ejpam-1535	453	1	⊗	⊗	PROPN
ejpam-1535	453	2	y	y	PROPN
ejpam-1535	453	3	=	=	PRON
ejpam-1535	453	4	(	(	PUNCT
ejpam-1535	453	5	x	x	SYM
ejpam-1535	453	6	|e	|e	PROPN
ejpam-1535	453	7	)	)	PUNCT
ejpam-1535	453	8	·	·	PUNCT
ejpam-1535	453	9	(	(	PUNCT
ejpam-1535	453	10	e|y	e|y	NOUN
ejpam-1535	453	11	)	)	PUNCT
ejpam-1535	453	12	.	.	PUNCT
ejpam-1535	454	1	(	(	PUNCT
ejpam-1535	454	2	⇐	⇐	NOUN
ejpam-1535	454	3	)	)	PUNCT
ejpam-1535	454	4	suppose	suppose	VERB
ejpam-1535	454	5	that	that	SCONJ
ejpam-1535	454	6	〈	〈	PROPN
ejpam-1535	454	7	x	x	SYM
ejpam-1535	454	8	,	,	PUNCT
ejpam-1535	454	9	y	y	NUM
ejpam-1535	454	10	〉	〉	NOUN
ejpam-1535	454	11	has	have	VERB
ejpam-1535	454	12	a	a	DET
ejpam-1535	454	13	maximum	maximum	ADJ
ejpam-1535	454	14	element	element	NOUN
ejpam-1535	454	15	(	(	PUNCT
ejpam-1535	454	16	x	x	SYM
ejpam-1535	454	17	′	′	NUM
ejpam-1535	454	18	,	,	PUNCT
ejpam-1535	454	19	y	y	PROPN
ejpam-1535	454	20	′	′	NUM
ejpam-1535	454	21	)	)	PUNCT
ejpam-1535	454	22	.	.	PUNCT
ejpam-1535	455	1	we	we	PRON
ejpam-1535	455	2	put	put	VERB
ejpam-1535	455	3	e	e	NOUN
ejpam-1535	455	4	=	=	SYM
ejpam-1535	455	5	r(x	r(x	PROPN
ejpam-1535	455	6	′	′	NOUN
ejpam-1535	455	7	)	)	PUNCT
ejpam-1535	456	1	=	=	PUNCT
ejpam-1535	456	2	d(y	d(y	PROPN
ejpam-1535	456	3	′	′	NUM
ejpam-1535	456	4	)	)	PUNCT
ejpam-1535	457	1	so	so	SCONJ
ejpam-1535	457	2	that	that	SCONJ
ejpam-1535	457	3	e	e	VERB
ejpam-1535	457	4	≤	≤	ADJ
ejpam-1535	457	5	r(x),d(y	r(x),d(y	NOUN
ejpam-1535	457	6	)	)	PUNCT
ejpam-1535	457	7	.	.	PUNCT
ejpam-1535	458	1	let	let	VERB
ejpam-1535	458	2	f	f	PROPN
ejpam-1535	458	3	∈	∈	PROPN
ejpam-1535	458	4	co	co	NOUN
ejpam-1535	458	5	be	be	AUX
ejpam-1535	458	6	such	such	ADJ
ejpam-1535	458	7	that	that	SCONJ
ejpam-1535	458	8	f	f	PROPN
ejpam-1535	458	9	≤	≤	ADJ
ejpam-1535	458	10	r(x),d(y	r(x),d(y	NUM
ejpam-1535	458	11	)	)	PUNCT
ejpam-1535	458	12	.	.	PUNCT
ejpam-1535	459	1	then	then	ADV
ejpam-1535	459	2	x	x	X
ejpam-1535	459	3	|	|	ADV
ejpam-1535	459	4	f	f	PROPN
ejpam-1535	459	5	and	and	CCONJ
ejpam-1535	459	6	f	f	PROPN
ejpam-1535	459	7	|y	|y	NOUN
ejpam-1535	459	8	are	be	AUX
ejpam-1535	459	9	defined	define	VERB
ejpam-1535	459	10	,	,	PUNCT
ejpam-1535	459	11	with	with	ADP
ejpam-1535	459	12	x	x	SYM
ejpam-1535	459	13	|e	|e	PROPN
ejpam-1535	459	14	≤	≤	PUNCT
ejpam-1535	459	15	x	x	X
ejpam-1535	459	16	,	,	PUNCT
ejpam-1535	459	17	f	f	PROPN
ejpam-1535	459	18	|y	|y	NOUN
ejpam-1535	459	19	≤	≤	NUM
ejpam-1535	459	20	y	y	PROPN
ejpam-1535	459	21	and	and	CCONJ
ejpam-1535	459	22	r(x	r(x	PROPN
ejpam-1535	460	1	|	|	NOUN
ejpam-1535	460	2	f	f	NOUN
ejpam-1535	460	3	)	)	PUNCT
ejpam-1535	461	1	=	=	PUNCT
ejpam-1535	462	1	f	f	X
ejpam-1535	463	1	=	=	SYM
ejpam-1535	463	2	d	d	PROPN
ejpam-1535	463	3	(	(	PUNCT
ejpam-1535	463	4	f	f	NOUN
ejpam-1535	463	5	|y	|y	NOUN
ejpam-1535	463	6	)	)	PUNCT
ejpam-1535	463	7	.	.	PUNCT
ejpam-1535	464	1	thus	thus	ADV
ejpam-1535	464	2	(	(	PUNCT
ejpam-1535	464	3	x	x	X
ejpam-1535	464	4	|	|	NOUN
ejpam-1535	464	5	f	f	NOUN
ejpam-1535	464	6	,	,	PUNCT
ejpam-1535	464	7	f	f	PROPN
ejpam-1535	464	8	|y	|y	NOUN
ejpam-1535	464	9	)	)	PUNCT
ejpam-1535	464	10	∈	∈	PROPN
ejpam-1535	464	11	〈	〈	PROPN
ejpam-1535	464	12	x	x	SYM
ejpam-1535	464	13	,	,	PUNCT
ejpam-1535	464	14	y	y	NOUN
ejpam-1535	464	15	〉	〉	NOUN
ejpam-1535	464	16	and	and	CCONJ
ejpam-1535	464	17	so	so	ADV
ejpam-1535	464	18	(	(	PUNCT
ejpam-1535	464	19	x	x	X
ejpam-1535	464	20	|	|	ADV
ejpam-1535	464	21	f	f	PROPN
ejpam-1535	464	22	,	,	PUNCT
ejpam-1535	464	23	f	f	PROPN
ejpam-1535	464	24	|y)ã	|y)ã	PROPN
ejpam-1535	464	25	(	(	PUNCT
ejpam-1535	464	26	x	x	PROPN
ejpam-1535	464	27	′	′	PROPN
ejpam-1535	464	28	,	,	PUNCT
ejpam-1535	464	29	y	y	PROPN
ejpam-1535	464	30	′	′	NUM
ejpam-1535	464	31	)	)	PUNCT
ejpam-1535	464	32	.	.	PUNCT
ejpam-1535	465	1	it	it	PRON
ejpam-1535	465	2	follows	follow	VERB
ejpam-1535	465	3	that	that	SCONJ
ejpam-1535	465	4	f	f	PROPN
ejpam-1535	465	5	≤	≤	X
ejpam-1535	465	6	e	e	X
ejpam-1535	465	7	,	,	PUNCT
ejpam-1535	465	8	hence	hence	ADV
ejpam-1535	465	9	e	e	NOUN
ejpam-1535	465	10	=	=	SYM
ejpam-1535	465	11	r(x)∧	r(x)∧	PROPN
ejpam-1535	465	12	d(y	d(y	PROPN
ejpam-1535	465	13	)	)	PUNCT
ejpam-1535	465	14	and	and	CCONJ
ejpam-1535	465	15	∃x	∃x	PROPN
ejpam-1535	465	16	⊗	⊗	PROPN
ejpam-1535	465	17	y.	y.	PROPN
ejpam-1535	465	18	proposition	proposition	NOUN
ejpam-1535	465	19	2	2	NUM
ejpam-1535	465	20	(	(	PUNCT
ejpam-1535	465	21	[	[	X
ejpam-1535	465	22	29	29	NUM
ejpam-1535	465	23	,	,	PUNCT
ejpam-1535	465	24	lemma	lemma	PROPN
ejpam-1535	465	25	4.1.6	4.1.6	PROPN
ejpam-1535	465	26	]	]	X
ejpam-1535	465	27	*	*	NUM
ejpam-1535	465	28	)	)	PUNCT
ejpam-1535	465	29	.	.	PUNCT
ejpam-1535	466	1	let	let	AUX
ejpam-1535	466	2	(	(	PUNCT
ejpam-1535	466	3	c	c	NOUN
ejpam-1535	466	4	,	,	PUNCT
ejpam-1535	466	5	·	·	PUNCT
ejpam-1535	466	6	,	,	PUNCT
ejpam-1535	466	7	≤	≤	NUM
ejpam-1535	466	8	)	)	PUNCT
ejpam-1535	466	9	be	be	VERB
ejpam-1535	466	10	an	an	DET
ejpam-1535	466	11	ordered	order	VERB
ejpam-1535	466	12	category	category	NOUN
ejpam-1535	466	13	.	.	PUNCT
ejpam-1535	467	1	if	if	SCONJ
ejpam-1535	467	2	both	both	DET
ejpam-1535	467	3	x	x	PROPN
ejpam-1535	467	4	⊗	⊗	PROPN
ejpam-1535	467	5	(	(	PUNCT
ejpam-1535	467	6	y	y	PROPN
ejpam-1535	467	7	⊗	⊗	PROPN
ejpam-1535	467	8	z	z	PROPN
ejpam-1535	467	9	)	)	PUNCT
ejpam-1535	467	10	and	and	CCONJ
ejpam-1535	467	11	(	(	PUNCT
ejpam-1535	467	12	x	x	SYM
ejpam-1535	467	13	⊗	⊗	NOUN
ejpam-1535	467	14	y)⊗	y)⊗	PROPN
ejpam-1535	467	15	z	z	NOUN
ejpam-1535	467	16	are	be	AUX
ejpam-1535	467	17	defined	define	VERB
ejpam-1535	467	18	,	,	PUNCT
ejpam-1535	467	19	then	then	ADV
ejpam-1535	467	20	they	they	PRON
ejpam-1535	467	21	are	be	AUX
ejpam-1535	467	22	equal	equal	ADJ
ejpam-1535	467	23	.	.	PUNCT
ejpam-1535	468	1	proof	proof	NOUN
ejpam-1535	468	2	.	.	PUNCT
ejpam-1535	469	1	we	we	PRON
ejpam-1535	469	2	put	put	VERB
ejpam-1535	469	3	(	(	PUNCT
ejpam-1535	469	4	x	x	PROPN
ejpam-1535	469	5	⊗	⊗	NOUN
ejpam-1535	469	6	y)⊗	y)⊗	PROPN
ejpam-1535	469	7	z	z	NOUN
ejpam-1535	470	1	=	=	PUNCT
ejpam-1535	470	2	a	a	PRON
ejpam-1535	470	3	·	·	PUNCT
ejpam-1535	470	4	z′	z′	NOUN
ejpam-1535	470	5	,	,	PUNCT
ejpam-1535	470	6	where	where	SCONJ
ejpam-1535	470	7	(	(	PUNCT
ejpam-1535	470	8	a	a	PRON
ejpam-1535	470	9	,	,	PUNCT
ejpam-1535	470	10	z′	z′	NUM
ejpam-1535	470	11	)	)	PUNCT
ejpam-1535	471	1	=	=	NOUN
ejpam-1535	471	2	max〈x	max〈x	NOUN
ejpam-1535	471	3	⊗	⊗	NUM
ejpam-1535	471	4	y	y	PROPN
ejpam-1535	471	5	,	,	PUNCT
ejpam-1535	471	6	z	z	NOUN
ejpam-1535	471	7	〉	〉	NOUN
ejpam-1535	471	8	,	,	PUNCT
ejpam-1535	471	9	and	and	CCONJ
ejpam-1535	471	10	also	also	ADV
ejpam-1535	471	11	x	x	PROPN
ejpam-1535	472	1	⊗	⊗	ADJ
ejpam-1535	472	2	y	y	PROPN
ejpam-1535	472	3	=	=	PUNCT
ejpam-1535	472	4	x	x	NOUN
ejpam-1535	472	5	′	′	NUM
ejpam-1535	472	6	·	·	PUNCT
ejpam-1535	472	7	y	y	PROPN
ejpam-1535	472	8	′	′	NOUN
ejpam-1535	472	9	,	,	PUNCT
ejpam-1535	472	10	where	where	SCONJ
ejpam-1535	472	11	(	(	PUNCT
ejpam-1535	472	12	x	x	SYM
ejpam-1535	472	13	′	′	NOUN
ejpam-1535	472	14	,	,	PUNCT
ejpam-1535	472	15	y	y	PROPN
ejpam-1535	472	16	′	′	NOUN
ejpam-1535	472	17	)	)	PUNCT
ejpam-1535	473	1	=	=	NOUN
ejpam-1535	473	2	max〈x	max〈x	NOUN
ejpam-1535	473	3	,	,	PUNCT
ejpam-1535	473	4	y	y	PROPN
ejpam-1535	473	5	〉	〉	NOUN
ejpam-1535	473	6	.	.	PUNCT
ejpam-1535	474	1	then	then	ADV
ejpam-1535	474	2	a	a	DET
ejpam-1535	474	3	≤	≤	NOUN
ejpam-1535	474	4	x	x	PUNCT
ejpam-1535	474	5	⊗	⊗	PROPN
ejpam-1535	474	6	y	y	PROPN
ejpam-1535	474	7	,	,	PUNCT
ejpam-1535	474	8	z′	z′	NOUN
ejpam-1535	474	9	≤	≤	NOUN
ejpam-1535	475	1	z	z	NUM
ejpam-1535	475	2	,	,	PUNCT
ejpam-1535	475	3	x	x	NOUN
ejpam-1535	475	4	′	′	NOUN
ejpam-1535	475	5	≤	≤	NUM
ejpam-1535	475	6	x	x	PUNCT
ejpam-1535	475	7	and	and	CCONJ
ejpam-1535	475	8	y	y	PROPN
ejpam-1535	475	9	′	′	NOUN
ejpam-1535	475	10	≤	≤	NOUN
ejpam-1535	476	1	y.	y.	NOUN
ejpam-1535	476	2	by	by	ADP
ejpam-1535	476	3	lemma	lemma	PROPN
ejpam-1535	476	4	6	6	NUM
ejpam-1535	476	5	,	,	PUNCT
ejpam-1535	476	6	since	since	SCONJ
ejpam-1535	476	7	a	a	DET
ejpam-1535	476	8	≤	≤	NOUN
ejpam-1535	476	9	x	x	SYM
ejpam-1535	476	10	′	′	NUM
ejpam-1535	476	11	·	·	PUNCT
ejpam-1535	476	12	y	y	PROPN
ejpam-1535	476	13	′	′	NOUN
ejpam-1535	476	14	,	,	PUNCT
ejpam-1535	476	15	there	there	PRON
ejpam-1535	476	16	exist	exist	VERB
ejpam-1535	476	17	elements	element	NOUN
ejpam-1535	476	18	x	x	PUNCT
ejpam-1535	476	19	′′	′′	NOUN
ejpam-1535	476	20	≤	≤	NOUN
ejpam-1535	476	21	x	x	PUNCT
ejpam-1535	477	1	′	′	NUM
ejpam-1535	477	2	and	and	CCONJ
ejpam-1535	477	3	y	y	PROPN
ejpam-1535	477	4	′′	′′	PROPN
ejpam-1535	477	5	≤	≤	PUNCT
ejpam-1535	478	1	y	y	PROPN
ejpam-1535	478	2	′	′	NUM
ejpam-1535	478	3	such	such	ADJ
ejpam-1535	478	4	that	that	SCONJ
ejpam-1535	478	5	a	a	DET
ejpam-1535	478	6	=	=	SYM
ejpam-1535	478	7	x	x	PART
ejpam-1535	478	8	′′	′′	PROPN
ejpam-1535	478	9	·	·	PUNCT
ejpam-1535	478	10	y	y	PROPN
ejpam-1535	478	11	′′.	′′.	PROPN
ejpam-1535	478	12	thus	thus	ADV
ejpam-1535	478	13	(	(	PUNCT
ejpam-1535	478	14	x	x	SYM
ejpam-1535	478	15	⊗	⊗	NOUN
ejpam-1535	478	16	y)⊗	y)⊗	X
ejpam-1535	478	17	z	z	NOUN
ejpam-1535	479	1	=	=	SYM
ejpam-1535	479	2	(	(	PUNCT
ejpam-1535	479	3	x	x	PUNCT
ejpam-1535	479	4	′′	′′	PROPN
ejpam-1535	479	5	·	·	PUNCT
ejpam-1535	479	6	y	y	PROPN
ejpam-1535	479	7	′′	′′	PROPN
ejpam-1535	479	8	)	)	PUNCT
ejpam-1535	479	9	·	·	PUNCT
ejpam-1535	479	10	z′	z′	NUM
ejpam-1535	480	1	=	=	PUNCT
ejpam-1535	480	2	x	x	PART
ejpam-1535	480	3	′′	′′	PROPN
ejpam-1535	480	4	·	·	PUNCT
ejpam-1535	480	5	(	(	PUNCT
ejpam-1535	480	6	y	y	PROPN
ejpam-1535	480	7	′′	′′	PROPN
ejpam-1535	480	8	·	·	PUNCT
ejpam-1535	480	9	z′	z′	NUM
ejpam-1535	480	10	)	)	PUNCT
ejpam-1535	480	11	.	.	PUNCT
ejpam-1535	481	1	since	since	SCONJ
ejpam-1535	481	2	∃y	∃y	PROPN
ejpam-1535	481	3	′′	′′	PROPN
ejpam-1535	481	4	·	·	PUNCT
ejpam-1535	481	5	z′	z′	NUM
ejpam-1535	481	6	,	,	PUNCT
ejpam-1535	481	7	we	we	PRON
ejpam-1535	481	8	have	have	VERB
ejpam-1535	481	9	r(y	r(y	VERB
ejpam-1535	481	10	′′	′′	PROPN
ejpam-1535	481	11	)	)	PUNCT
ejpam-1535	481	12	=	=	PUNCT
ejpam-1535	481	13	d(z′	d(z′	PROPN
ejpam-1535	481	14	)	)	PUNCT
ejpam-1535	481	15	.	.	PUNCT
ejpam-1535	482	1	moreover	moreover	ADV
ejpam-1535	482	2	,	,	PUNCT
ejpam-1535	482	3	y	y	PROPN
ejpam-1535	482	4	′′	′′	PROPN
ejpam-1535	482	5	≤	≤	PUNCT
ejpam-1535	482	6	y	y	PROPN
ejpam-1535	482	7	′	′	NOUN
ejpam-1535	482	8	≤	≤	NUM
ejpam-1535	482	9	y	y	PROPN
ejpam-1535	482	10	and	and	CCONJ
ejpam-1535	482	11	z′	z′	NUM
ejpam-1535	482	12	≤	≤	NUM
ejpam-1535	483	1	z	z	X
ejpam-1535	483	2	,	,	PUNCT
ejpam-1535	483	3	so	so	CCONJ
ejpam-1535	483	4	(	(	PUNCT
ejpam-1535	483	5	y	y	PROPN
ejpam-1535	483	6	′′	′′	PROPN
ejpam-1535	483	7	,	,	PUNCT
ejpam-1535	483	8	z′	z′	NUM
ejpam-1535	483	9	)	)	PUNCT
ejpam-1535	483	10	∈	∈	PROPN
ejpam-1535	483	11	〈	〈	PROPN
ejpam-1535	483	12	y	y	PROPN
ejpam-1535	483	13	,	,	PUNCT
ejpam-1535	483	14	z	z	NOUN
ejpam-1535	483	15	〉	〉	NOUN
ejpam-1535	483	16	.	.	PUNCT
ejpam-1535	484	1	let	let	VERB
ejpam-1535	484	2	(	(	PUNCT
ejpam-1535	484	3	b	b	X
ejpam-1535	484	4	,	,	PUNCT
ejpam-1535	484	5	c	c	NOUN
ejpam-1535	484	6	)	)	PUNCT
ejpam-1535	484	7	=	=	SYM
ejpam-1535	485	1	max〈y	max〈y	VERB
ejpam-1535	485	2	,	,	PUNCT
ejpam-1535	485	3	z	z	NOUN
ejpam-1535	485	4	〉	〉	NOUN
ejpam-1535	485	5	,	,	PUNCT
ejpam-1535	485	6	so	so	SCONJ
ejpam-1535	485	7	that	that	SCONJ
ejpam-1535	485	8	y	y	PRON
ejpam-1535	485	9	′′	′′	PROPN
ejpam-1535	485	10	≤	≤	NOUN
ejpam-1535	485	11	b	b	PROPN
ejpam-1535	485	12	and	and	CCONJ
ejpam-1535	485	13	z′	z′	NUM
ejpam-1535	485	14	≤	≤	NUM
ejpam-1535	486	1	c	c	X
ejpam-1535	486	2	,	,	PUNCT
ejpam-1535	486	3	whence	whence	ADP
ejpam-1535	486	4	y	y	PROPN
ejpam-1535	486	5	′′	′′	PROPN
ejpam-1535	486	6	·	·	PUNCT
ejpam-1535	486	7	z′	z′	NUM
ejpam-1535	486	8	≤	≤	NUM
ejpam-1535	486	9	b	b	X
ejpam-1535	486	10	·	·	PUNCT
ejpam-1535	486	11	c	c	X
ejpam-1535	486	12	=	=	SYM
ejpam-1535	486	13	y	y	PROPN
ejpam-1535	486	14	⊗	⊗	PROPN
ejpam-1535	486	15	z.	z.	PROPN
ejpam-1535	486	16	similarly	similarly	ADV
ejpam-1535	486	17	,	,	PUNCT
ejpam-1535	486	18	(	(	PUNCT
ejpam-1535	486	19	x	x	PART
ejpam-1535	486	20	′′	′′	PROPN
ejpam-1535	486	21	,	,	PUNCT
ejpam-1535	486	22	y	y	PROPN
ejpam-1535	486	23	′′	′′	PROPN
ejpam-1535	486	24	·	·	PUNCT
ejpam-1535	486	25	z′	z′	X
ejpam-1535	486	26	)	)	PUNCT
ejpam-1535	486	27	∈	∈	PROPN
ejpam-1535	486	28	〈	〈	PROPN
ejpam-1535	486	29	x	x	SYM
ejpam-1535	486	30	,	,	PUNCT
ejpam-1535	486	31	y⊗	y⊗	NOUN
ejpam-1535	486	32	z	z	NOUN
ejpam-1535	486	33	〉	〉	NOUN
ejpam-1535	486	34	and	and	CCONJ
ejpam-1535	486	35	so	so	ADV
ejpam-1535	486	36	(	(	PUNCT
ejpam-1535	486	37	x⊗	x⊗	PROPN
ejpam-1535	486	38	y)⊗	y)⊗	X
ejpam-1535	486	39	z	z	NOUN
ejpam-1535	487	1	=	=	PUNCT
ejpam-1535	487	2	x	x	SYM
ejpam-1535	487	3	′′	′′	PROPN
ejpam-1535	487	4	·	·	PUNCT
ejpam-1535	487	5	(	(	PUNCT
ejpam-1535	487	6	y	y	PROPN
ejpam-1535	487	7	′′	′′	PROPN
ejpam-1535	487	8	·	·	PUNCT
ejpam-1535	487	9	z′)≤	z′)≤	PROPN
ejpam-1535	487	10	x⊗	x⊗	PROPN
ejpam-1535	487	11	(	(	PUNCT
ejpam-1535	487	12	y⊗	y⊗	NOUN
ejpam-1535	487	13	z	z	NOUN
ejpam-1535	487	14	)	)	PUNCT
ejpam-1535	487	15	.	.	PUNCT
ejpam-1535	488	1	the	the	DET
ejpam-1535	488	2	reverse	reverse	ADJ
ejpam-1535	488	3	inequality	inequality	NOUN
ejpam-1535	488	4	is	be	AUX
ejpam-1535	488	5	similar	similar	ADJ
ejpam-1535	488	6	.	.	PUNCT
ejpam-1535	489	1	corollary	corollary	ADJ
ejpam-1535	489	2	2	2	NUM
ejpam-1535	489	3	.	.	PUNCT
ejpam-1535	490	1	in	in	ADP
ejpam-1535	490	2	an	an	DET
ejpam-1535	490	3	inductive	inductive	ADJ
ejpam-1535	490	4	category	category	NOUN
ejpam-1535	490	5	(	(	PUNCT
ejpam-1535	490	6	c	c	NOUN
ejpam-1535	490	7	,	,	PUNCT
ejpam-1535	490	8	·	·	PUNCT
ejpam-1535	490	9	,	,	PUNCT
ejpam-1535	490	10	≤	≤	NUM
ejpam-1535	490	11	)	)	PUNCT
ejpam-1535	490	12	,	,	PUNCT
ejpam-1535	490	13	⊗	⊗	PROPN
ejpam-1535	490	14	is	be	AUX
ejpam-1535	490	15	an	an	DET
ejpam-1535	490	16	everywhere	everywhere	ADV
ejpam-1535	490	17	-	-	PUNCT
ejpam-1535	490	18	defined	define	VERB
ejpam-1535	490	19	,	,	PUNCT
ejpam-1535	490	20	associative	associative	ADJ
ejpam-1535	490	21	binary	binary	ADJ
ejpam-1535	490	22	operation	operation	NOUN
ejpam-1535	490	23	.	.	PUNCT
ejpam-1535	491	1	c.	c.	PROPN
ejpam-1535	491	2	hollings	holling	NOUN
ejpam-1535	491	3	/	/	SYM
ejpam-1535	491	4	eur	eur	PROPN
ejpam-1535	491	5	.	.	PUNCT
ejpam-1535	492	1	j.	j.	PROPN
ejpam-1535	492	2	pure	pure	PROPN
ejpam-1535	492	3	appl	appl	PROPN
ejpam-1535	492	4	.	.	PROPN
ejpam-1535	492	5	math	math	PROPN
ejpam-1535	492	6	,	,	PUNCT
ejpam-1535	492	7	5	5	NUM
ejpam-1535	492	8	(	(	PUNCT
ejpam-1535	492	9	2012	2012	NUM
ejpam-1535	492	10	)	)	PUNCT
ejpam-1535	492	11	,	,	PUNCT
ejpam-1535	492	12	414	414	NUM
ejpam-1535	492	13	-	-	SYM
ejpam-1535	492	14	450	450	NUM
ejpam-1535	492	15	432	432	NUM
ejpam-1535	492	16	by	by	ADP
ejpam-1535	492	17	way	way	NOUN
ejpam-1535	492	18	of	of	ADP
ejpam-1535	492	19	concluding	conclude	VERB
ejpam-1535	492	20	this	this	DET
ejpam-1535	492	21	section	section	NOUN
ejpam-1535	492	22	,	,	PUNCT
ejpam-1535	492	23	we	we	PRON
ejpam-1535	492	24	record	record	VERB
ejpam-1535	492	25	the	the	DET
ejpam-1535	492	26	following	follow	VERB
ejpam-1535	492	27	properties	property	NOUN
ejpam-1535	492	28	of	of	ADP
ejpam-1535	492	29	the	the	DET
ejpam-1535	492	30	pseudoproduct	pseudoproduct	NOUN
ejpam-1535	492	31	for	for	ADP
ejpam-1535	492	32	later	later	ADJ
ejpam-1535	492	33	use	use	NOUN
ejpam-1535	492	34	:	:	PUNCT
ejpam-1535	492	35	lemma	lemma	PROPN
ejpam-1535	492	36	9	9	NUM
ejpam-1535	492	37	(	(	PUNCT
ejpam-1535	492	38	[	[	X
ejpam-1535	492	39	1	1	NUM
ejpam-1535	492	40	,	,	PUNCT
ejpam-1535	492	41	lemma	lemma	PROPN
ejpam-1535	492	42	3.8	3.8	NUM
ejpam-1535	492	43	]	]	NOUN
ejpam-1535	492	44	*	*	PUNCT
ejpam-1535	492	45	)	)	PUNCT
ejpam-1535	492	46	.	.	PUNCT
ejpam-1535	493	1	let	let	AUX
ejpam-1535	493	2	(	(	PUNCT
ejpam-1535	493	3	c	c	NOUN
ejpam-1535	493	4	,	,	PUNCT
ejpam-1535	493	5	·	·	PUNCT
ejpam-1535	493	6	,	,	PUNCT
ejpam-1535	493	7	≤	≤	NUM
ejpam-1535	493	8	)	)	PUNCT
ejpam-1535	493	9	be	be	VERB
ejpam-1535	493	10	an	an	DET
ejpam-1535	493	11	inductive	inductive	ADJ
ejpam-1535	493	12	category	category	NOUN
ejpam-1535	493	13	and	and	CCONJ
ejpam-1535	493	14	let	let	VERB
ejpam-1535	493	15	a	a	DET
ejpam-1535	493	16	∈	∈	PROPN
ejpam-1535	493	17	c	c	X
ejpam-1535	493	18	and	and	CCONJ
ejpam-1535	493	19	e	e	PROPN
ejpam-1535	493	20	∈	∈	PROPN
ejpam-1535	493	21	co.	co.	PROPN
ejpam-1535	493	22	then	then	ADV
ejpam-1535	493	23	e⊗	e⊗	VERB
ejpam-1535	493	24	a	a	DET
ejpam-1535	493	25	=	=	SYM
ejpam-1535	493	26	e	e	PROPN
ejpam-1535	493	27	∧	∧	PROPN
ejpam-1535	493	28	d(a)|a	d(a)|a	PROPN
ejpam-1535	493	29	and	and	CCONJ
ejpam-1535	493	30	a⊗	a⊗	NOUN
ejpam-1535	493	31	e	e	PROPN
ejpam-1535	493	32	=	=	PROPN
ejpam-1535	493	33	a|r(a)∧	a|r(a)∧	PROPN
ejpam-1535	493	34	e.	e.	PROPN
ejpam-1535	493	35	proof	proof	PROPN
ejpam-1535	493	36	.	.	PUNCT
ejpam-1535	494	1	we	we	PRON
ejpam-1535	494	2	demonstrate	demonstrate	VERB
ejpam-1535	494	3	the	the	DET
ejpam-1535	494	4	first	first	ADJ
ejpam-1535	494	5	equality	equality	NOUN
ejpam-1535	494	6	;	;	PUNCT
ejpam-1535	494	7	the	the	DET
ejpam-1535	494	8	second	second	NOUN
ejpam-1535	494	9	is	be	AUX
ejpam-1535	494	10	similar	similar	ADJ
ejpam-1535	494	11	.	.	PUNCT
ejpam-1535	495	1	by	by	ADP
ejpam-1535	495	2	definition	definition	NOUN
ejpam-1535	495	3	,	,	PUNCT
ejpam-1535	495	4	we	we	PRON
ejpam-1535	495	5	have	have	VERB
ejpam-1535	495	6	:	:	PUNCT
ejpam-1535	495	7	e⊗	e⊗	VERB
ejpam-1535	495	8	a	a	PRON
ejpam-1535	495	9	=	=	X
ejpam-1535	496	1	[	[	X
ejpam-1535	496	2	e|e	e|e	X
ejpam-1535	496	3	∧	∧	PROPN
ejpam-1535	496	4	d(a	d(a	PROPN
ejpam-1535	496	5	)	)	PUNCT
ejpam-1535	496	6	]	]	PUNCT
ejpam-1535	496	7	·	·	PUNCT
ejpam-1535	497	1	[	[	X
ejpam-1535	497	2	e	e	X
ejpam-1535	497	3	∧	∧	PROPN
ejpam-1535	497	4	d(a)|a	d(a)|a	PROPN
ejpam-1535	497	5	]	]	X
ejpam-1535	497	6	=	=	SYM
ejpam-1535	497	7	e	e	X
ejpam-1535	497	8	∧	∧	PROPN
ejpam-1535	497	9	d(a	d(a	PROPN
ejpam-1535	497	10	)	)	PUNCT
ejpam-1535	497	11	·	·	PUNCT
ejpam-1535	498	1	[	[	X
ejpam-1535	498	2	e	e	X
ejpam-1535	498	3	∧	∧	PROPN
ejpam-1535	498	4	d(a)|a	d(a)|a	PROPN
ejpam-1535	498	5	]	]	PUNCT
ejpam-1535	498	6	(	(	PUNCT
ejpam-1535	498	7	by	by	ADP
ejpam-1535	498	8	corollary	corollary	ADJ
ejpam-1535	498	9	1(b	1(b	NUM
ejpam-1535	498	10	)	)	PUNCT
ejpam-1535	498	11	,	,	PUNCT
ejpam-1535	498	12	since	since	SCONJ
ejpam-1535	498	13	e	e	PROPN
ejpam-1535	498	14	∧	∧	PROPN
ejpam-1535	498	15	d(a)≤	d(a)≤	PROPN
ejpam-1535	498	16	e	e	X
ejpam-1535	498	17	)	)	PUNCT
ejpam-1535	498	18	=	=	SYM
ejpam-1535	498	19	e	e	X
ejpam-1535	498	20	∧	∧	PROPN
ejpam-1535	498	21	d(a)|a	d(a)|a	PROPN
ejpam-1535	498	22	,	,	PUNCT
ejpam-1535	498	23	by	by	ADP
ejpam-1535	498	24	lemma	lemma	PROPN
ejpam-1535	498	25	5(b	5(b	NUM
ejpam-1535	498	26	)	)	PUNCT
ejpam-1535	498	27	,	,	PUNCT
ejpam-1535	498	28	as	as	SCONJ
ejpam-1535	498	29	required	require	VERB
ejpam-1535	498	30	.	.	PUNCT
ejpam-1535	499	1	5	5	X
ejpam-1535	499	2	.	.	NUM
ejpam-1535	499	3	inductive	inductive	ADJ
ejpam-1535	499	4	categories	category	NOUN
ejpam-1535	499	5	and	and	CCONJ
ejpam-1535	499	6	restriction	restriction	NOUN
ejpam-1535	499	7	semigroups	semigroup	NOUN
ejpam-1535	499	8	in	in	ADP
ejpam-1535	499	9	this	this	DET
ejpam-1535	499	10	section	section	NOUN
ejpam-1535	500	1	,	,	PUNCT
ejpam-1535	500	2	we	we	PRON
ejpam-1535	500	3	show	show	VERB
ejpam-1535	500	4	that	that	SCONJ
ejpam-1535	500	5	an	an	DET
ejpam-1535	500	6	inductive	inductive	ADJ
ejpam-1535	500	7	category	category	NOUN
ejpam-1535	500	8	may	may	AUX
ejpam-1535	500	9	be	be	AUX
ejpam-1535	500	10	constructed	construct	VERB
ejpam-1535	500	11	from	from	ADP
ejpam-1535	500	12	a	a	DET
ejpam-1535	500	13	restriction	restriction	NOUN
ejpam-1535	500	14	semigroup	semigroup	NOUN
ejpam-1535	500	15	,	,	PUNCT
ejpam-1535	500	16	and	and	CCONJ
ejpam-1535	500	17	vice	vice	ADV
ejpam-1535	500	18	versa	versa	ADV
ejpam-1535	500	19	.	.	PUNCT
ejpam-1535	501	1	given	give	VERB
ejpam-1535	501	2	a	a	DET
ejpam-1535	501	3	restriction	restriction	NOUN
ejpam-1535	501	4	semigroup	semigroup	NOUN
ejpam-1535	501	5	s	s	PROPN
ejpam-1535	501	6	,	,	PUNCT
ejpam-1535	501	7	we	we	PRON
ejpam-1535	501	8	define	define	VERB
ejpam-1535	501	9	the	the	DET
ejpam-1535	501	10	restricted	restricted	ADJ
ejpam-1535	501	11	product	product	NOUN
ejpam-1535	501	12	in	in	ADP
ejpam-1535	501	13	s	s	PRON
ejpam-1535	501	14	by	by	ADP
ejpam-1535	501	15	a	a	DET
ejpam-1535	501	16	·	·	PUNCT
ejpam-1535	501	17	b	b	X
ejpam-1535	501	18	=	=	SYM
ejpam-1535	501	19	(	(	PUNCT
ejpam-1535	501	20	ab	ab	NOUN
ejpam-1535	501	21	if	if	SCONJ
ejpam-1535	501	22	a∗	a∗	PROPN
ejpam-1535	501	23	=	=	SYM
ejpam-1535	501	24	b+	b+	X
ejpam-1535	501	25	;	;	PUNCT
ejpam-1535	501	26	undefined	undefined	ADJ
ejpam-1535	501	27	otherwise	otherwise	ADV
ejpam-1535	501	28	.	.	PUNCT
ejpam-1535	502	1	(	(	PUNCT
ejpam-1535	502	2	7	7	X
ejpam-1535	502	3	)	)	PUNCT
ejpam-1535	502	4	we	we	PRON
ejpam-1535	502	5	then	then	ADV
ejpam-1535	502	6	have	have	VERB
ejpam-1535	502	7	the	the	DET
ejpam-1535	502	8	following	follow	VERB
ejpam-1535	502	9	result	result	NOUN
ejpam-1535	502	10	,	,	PUNCT
ejpam-1535	502	11	originally	originally	ADV
ejpam-1535	502	12	proved	prove	VERB
ejpam-1535	502	13	by	by	ADP
ejpam-1535	502	14	lawson	lawson	PROPN
ejpam-1535	503	1	[	[	X
ejpam-1535	503	2	28	28	NUM
ejpam-1535	503	3	,	,	PUNCT
ejpam-1535	503	4	theorem	theorem	VERB
ejpam-1535	503	5	5.7	5.7	NUM
ejpam-1535	503	6	]	]	PUNCT
ejpam-1535	503	7	:	:	PUNCT
ejpam-1535	503	8	theorem	theorem	NOUN
ejpam-1535	503	9	2	2	X
ejpam-1535	503	10	.	.	PUNCT
ejpam-1535	504	1	let	let	VERB
ejpam-1535	504	2	s	s	PRON
ejpam-1535	504	3	be	be	AUX
ejpam-1535	504	4	a	a	DET
ejpam-1535	504	5	restriction	restriction	NOUN
ejpam-1535	504	6	semigroup	semigroup	NOUN
ejpam-1535	504	7	with	with	ADP
ejpam-1535	504	8	respect	respect	NOUN
ejpam-1535	504	9	to	to	ADP
ejpam-1535	504	10	some	some	DET
ejpam-1535	504	11	subsemilattice	subsemilattice	NOUN
ejpam-1535	504	12	e	e	NOUN
ejpam-1535	504	13	and	and	CCONJ
ejpam-1535	504	14	with	with	ADP
ejpam-1535	504	15	natural	natural	ADJ
ejpam-1535	504	16	partial	partial	ADJ
ejpam-1535	504	17	order	order	NOUN
ejpam-1535	504	18	≤.	≤.	NOUN
ejpam-1535	504	19	then	then	ADV
ejpam-1535	504	20	(	(	PUNCT
ejpam-1535	504	21	s	s	X
ejpam-1535	504	22	,	,	PUNCT
ejpam-1535	504	23	·	·	PUNCT
ejpam-1535	504	24	,	,	PUNCT
ejpam-1535	504	25	≤	≤	NUM
ejpam-1535	504	26	)	)	PUNCT
ejpam-1535	504	27	is	be	AUX
ejpam-1535	504	28	an	an	DET
ejpam-1535	504	29	inductive	inductive	ADJ
ejpam-1535	504	30	category	category	NOUN
ejpam-1535	504	31	with	with	ADP
ejpam-1535	504	32	so	so	ADV
ejpam-1535	504	33	=	=	SYM
ejpam-1535	504	34	e	e	NOUN
ejpam-1535	504	35	,	,	PUNCT
ejpam-1535	504	36	d(x	d(x	PROPN
ejpam-1535	504	37	)	)	PUNCT
ejpam-1535	505	1	=	=	SYM
ejpam-1535	505	2	x+	x+	X
ejpam-1535	505	3	and	and	CCONJ
ejpam-1535	505	4	r(x	r(x	PROPN
ejpam-1535	505	5	)	)	PUNCT
ejpam-1535	505	6	=	=	SYM
ejpam-1535	505	7	x∗	x∗	NOUN
ejpam-1535	505	8	,	,	PUNCT
ejpam-1535	505	9	where	where	SCONJ
ejpam-1535	505	10	·	·	PUNCT
ejpam-1535	505	11	is	be	AUX
ejpam-1535	505	12	the	the	DET
ejpam-1535	505	13	restricted	restricted	ADJ
ejpam-1535	505	14	product	product	NOUN
ejpam-1535	505	15	of	of	ADP
ejpam-1535	505	16	(	(	PUNCT
ejpam-1535	505	17	7	7	NUM
ejpam-1535	505	18	)	)	PUNCT
ejpam-1535	505	19	.	.	PUNCT
ejpam-1535	506	1	restrictions	restriction	NOUN
ejpam-1535	506	2	,	,	PUNCT
ejpam-1535	506	3	corestrictions	corestriction	NOUN
ejpam-1535	506	4	and	and	CCONJ
ejpam-1535	506	5	meets	meet	VERB
ejpam-1535	506	6	in	in	ADP
ejpam-1535	506	7	(	(	PUNCT
ejpam-1535	506	8	s	s	X
ejpam-1535	506	9	,	,	PUNCT
ejpam-1535	506	10	·	·	PUNCT
ejpam-1535	506	11	,	,	PUNCT
ejpam-1535	506	12	≤	≤	NUM
ejpam-1535	506	13	)	)	PUNCT
ejpam-1535	506	14	are	be	AUX
ejpam-1535	506	15	equal	equal	ADJ
ejpam-1535	506	16	to	to	ADP
ejpam-1535	506	17	the	the	DET
ejpam-1535	506	18	corresponding	correspond	VERB
ejpam-1535	506	19	products	product	NOUN
ejpam-1535	506	20	in	in	ADP
ejpam-1535	506	21	s.	s.	PROPN
ejpam-1535	506	22	proof	proof	PROPN
ejpam-1535	506	23	.	.	PUNCT
ejpam-1535	507	1	we	we	PRON
ejpam-1535	507	2	begin	begin	VERB
ejpam-1535	507	3	by	by	ADP
ejpam-1535	507	4	showing	show	VERB
ejpam-1535	507	5	that	that	SCONJ
ejpam-1535	507	6	the	the	DET
ejpam-1535	507	7	idempotents	idempotent	NOUN
ejpam-1535	507	8	in	in	ADP
ejpam-1535	507	9	e	e	NOUN
ejpam-1535	507	10	are	be	AUX
ejpam-1535	507	11	the	the	DET
ejpam-1535	507	12	identities	identity	NOUN
ejpam-1535	507	13	of	of	ADP
ejpam-1535	507	14	(	(	PUNCT
ejpam-1535	507	15	s	s	X
ejpam-1535	507	16	,	,	PUNCT
ejpam-1535	507	17	·	·	PUNCT
ejpam-1535	507	18	)	)	PUNCT
ejpam-1535	507	19	.	.	PUNCT
ejpam-1535	508	1	let	let	VERB
ejpam-1535	508	2	e	e	NOUN
ejpam-1535	508	3	∈	∈	NOUN
ejpam-1535	508	4	e	e	X
ejpam-1535	508	5	and	and	CCONJ
ejpam-1535	508	6	suppose	suppose	VERB
ejpam-1535	508	7	that	that	SCONJ
ejpam-1535	508	8	∃e	∃e	NUM
ejpam-1535	508	9	·	·	PUNCT
ejpam-1535	508	10	x	x	X
ejpam-1535	508	11	.	.	PUNCT
ejpam-1535	508	12	then	then	ADV
ejpam-1535	508	13	e∗	e∗	PROPN
ejpam-1535	508	14	=	=	SYM
ejpam-1535	508	15	e	e	PROPN
ejpam-1535	508	16	=	=	PUNCT
ejpam-1535	508	17	x+	x+	X
ejpam-1535	508	18	and	and	CCONJ
ejpam-1535	508	19	e	e	X
ejpam-1535	508	20	·	·	PUNCT
ejpam-1535	508	21	x	x	PUNCT
ejpam-1535	509	1	=	=	PUNCT
ejpam-1535	509	2	ex	ex	X
ejpam-1535	509	3	=	=	PUNCT
ejpam-1535	509	4	x+x	x+x	PUNCT
ejpam-1535	509	5	=	=	PUNCT
ejpam-1535	509	6	x	x	X
ejpam-1535	509	7	.	.	PUNCT
ejpam-1535	510	1	similarly	similarly	ADV
ejpam-1535	510	2	,	,	PUNCT
ejpam-1535	510	3	if	if	SCONJ
ejpam-1535	510	4	∃x	∃x	PROPN
ejpam-1535	510	5	·	·	PUNCT
ejpam-1535	510	6	e	e	X
ejpam-1535	510	7	,	,	PUNCT
ejpam-1535	510	8	then	then	ADV
ejpam-1535	510	9	x∗	x∗	PROPN
ejpam-1535	510	10	=	=	SYM
ejpam-1535	510	11	e	e	PROPN
ejpam-1535	510	12	and	and	CCONJ
ejpam-1535	510	13	x	x	PUNCT
ejpam-1535	510	14	·	·	PUNCT
ejpam-1535	510	15	e	e	X
ejpam-1535	510	16	=	=	PUNCT
ejpam-1535	510	17	xe	xe	PROPN
ejpam-1535	510	18	=	=	PROPN
ejpam-1535	510	19	x	x	X
ejpam-1535	510	20	x∗	x∗	X
ejpam-1535	510	21	=	=	PUNCT
ejpam-1535	511	1	x	x	X
ejpam-1535	511	2	.	.	PUNCT
ejpam-1535	512	1	it	it	PRON
ejpam-1535	512	2	is	be	AUX
ejpam-1535	512	3	easy	easy	ADJ
ejpam-1535	512	4	to	to	PART
ejpam-1535	512	5	see	see	VERB
ejpam-1535	512	6	that	that	DET
ejpam-1535	512	7	∃x+·x	∃x+·x	NOUN
ejpam-1535	512	8	,	,	PUNCT
ejpam-1535	512	9	since	since	SCONJ
ejpam-1535	512	10	(	(	PUNCT
ejpam-1535	512	11	x+)∗	x+)∗	PROPN
ejpam-1535	512	12	=	=	PUNCT
ejpam-1535	512	13	x+	x+	ADJ
ejpam-1535	512	14	.	.	PUNCT
ejpam-1535	513	1	in	in	ADP
ejpam-1535	513	2	this	this	DET
ejpam-1535	513	3	case	case	NOUN
ejpam-1535	513	4	,	,	PUNCT
ejpam-1535	513	5	x+·x	x+·x	NOUN
ejpam-1535	513	6	=	=	SYM
ejpam-1535	513	7	x+x	x+x	PUNCT
ejpam-1535	513	8	=	=	PUNCT
ejpam-1535	513	9	x	x	INTJ
ejpam-1535	513	10	,	,	PUNCT
ejpam-1535	513	11	so	so	ADV
ejpam-1535	513	12	d(x	d(x	NOUN
ejpam-1535	513	13	)	)	PUNCT
ejpam-1535	513	14	=	=	PUNCT
ejpam-1535	514	1	x+	x+	X
ejpam-1535	514	2	.	.	PUNCT
ejpam-1535	515	1	similarly	similarly	ADV
ejpam-1535	515	2	,	,	PUNCT
ejpam-1535	515	3	∃x	∃x	PROPN
ejpam-1535	515	4	·	·	PUNCT
ejpam-1535	515	5	x∗	x∗	PROPN
ejpam-1535	515	6	and	and	CCONJ
ejpam-1535	515	7	x	x	PRON
ejpam-1535	515	8	·	·	PUNCT
ejpam-1535	515	9	x∗	x∗	X
ejpam-1535	516	1	=	=	PUNCT
ejpam-1535	516	2	x	x	X
ejpam-1535	516	3	,	,	PUNCT
ejpam-1535	516	4	so	so	ADV
ejpam-1535	516	5	r(x	r(x	NOUN
ejpam-1535	516	6	)	)	PUNCT
ejpam-1535	516	7	=	=	SYM
ejpam-1535	516	8	x∗.	x∗.	PROPN
ejpam-1535	516	9	(	(	PUNCT
ejpam-1535	516	10	ca1	ca1	NOUN
ejpam-1535	516	11	)	)	PUNCT
ejpam-1535	516	12	suppose	suppose	VERB
ejpam-1535	516	13	that	that	SCONJ
ejpam-1535	516	14	∃x	∃x	NOUN
ejpam-1535	516	15	·	·	PUNCT
ejpam-1535	516	16	(	(	PUNCT
ejpam-1535	516	17	y	y	PROPN
ejpam-1535	516	18	·	·	PUNCT
ejpam-1535	516	19	z	z	X
ejpam-1535	516	20	)	)	PUNCT
ejpam-1535	516	21	,	,	PUNCT
ejpam-1535	516	22	i.e.	i.e.	X
ejpam-1535	516	23	,	,	PUNCT
ejpam-1535	516	24	x∗	x∗	PROPN
ejpam-1535	516	25	=	=	SYM
ejpam-1535	516	26	(	(	PUNCT
ejpam-1535	516	27	yz)+	yz)+	NOUN
ejpam-1535	516	28	and	and	CCONJ
ejpam-1535	516	29	y∗	y∗	NOUN
ejpam-1535	516	30	=	=	SYM
ejpam-1535	516	31	z+	z+	X
ejpam-1535	516	32	.	.	PUNCT
ejpam-1535	516	33	then	then	ADV
ejpam-1535	516	34	x∗	x∗	PROPN
ejpam-1535	516	35	=	=	PUNCT
ejpam-1535	516	36	(	(	PUNCT
ejpam-1535	516	37	yz)+	yz)+	NOUN
ejpam-1535	516	38	=	=	SYM
ejpam-1535	516	39	(	(	PUNCT
ejpam-1535	516	40	yz+)+	yz+)+	NOUN
ejpam-1535	516	41	=	=	SYM
ejpam-1535	516	42	(	(	PUNCT
ejpam-1535	516	43	y	y	PROPN
ejpam-1535	516	44	y∗)+	y∗)+	NOUN
ejpam-1535	516	45	=	=	SYM
ejpam-1535	516	46	y+	y+	PROPN
ejpam-1535	516	47	,	,	PUNCT
ejpam-1535	516	48	by	by	ADP
ejpam-1535	516	49	lemma	lemma	PROPN
ejpam-1535	516	50	1	1	NUM
ejpam-1535	516	51	,	,	PUNCT
ejpam-1535	516	52	so	so	ADV
ejpam-1535	516	53	∃x	∃x	PROPN
ejpam-1535	516	54	·	·	PUNCT
ejpam-1535	516	55	y.	y.	NOUN
ejpam-1535	516	56	also	also	ADV
ejpam-1535	516	57	by	by	ADP
ejpam-1535	516	58	lemma	lemma	PROPN
ejpam-1535	516	59	1	1	NUM
ejpam-1535	516	60	,	,	PUNCT
ejpam-1535	516	61	(	(	PUNCT
ejpam-1535	516	62	x	x	X
ejpam-1535	516	63	y)∗	y)∗	NOUN
ejpam-1535	516	64	=	=	PUNCT
ejpam-1535	516	65	(	(	PUNCT
ejpam-1535	516	66	x∗	x∗	PROPN
ejpam-1535	516	67	y)∗	y)∗	NOUN
ejpam-1535	516	68	=	=	PUNCT
ejpam-1535	516	69	(	(	PUNCT
ejpam-1535	516	70	y+	y+	NUM
ejpam-1535	516	71	y)∗	y)∗	NOUN
ejpam-1535	516	72	=	=	PUNCT
ejpam-1535	516	73	y∗	y∗	PROPN
ejpam-1535	516	74	=	=	SYM
ejpam-1535	516	75	z+	z+	X
ejpam-1535	516	76	,	,	PUNCT
ejpam-1535	516	77	so	so	ADV
ejpam-1535	516	78	∃(x	∃(x	PROPN
ejpam-1535	516	79	·	·	PUNCT
ejpam-1535	516	80	y	y	X
ejpam-1535	516	81	)	)	PUNCT
ejpam-1535	516	82	·	·	PUNCT
ejpam-1535	517	1	z.	z.	PROPN
ejpam-1535	518	1	it	it	PRON
ejpam-1535	518	2	is	be	AUX
ejpam-1535	518	3	easy	easy	ADJ
ejpam-1535	518	4	to	to	PART
ejpam-1535	518	5	see	see	VERB
ejpam-1535	518	6	that	that	SCONJ
ejpam-1535	518	7	x	x	X
ejpam-1535	518	8	·	·	PUNCT
ejpam-1535	518	9	(	(	PUNCT
ejpam-1535	518	10	y	y	PROPN
ejpam-1535	518	11	·	·	PUNCT
ejpam-1535	518	12	z	z	X
ejpam-1535	518	13	)	)	PUNCT
ejpam-1535	518	14	=	=	SYM
ejpam-1535	518	15	(	(	PUNCT
ejpam-1535	518	16	x	x	X
ejpam-1535	518	17	·	·	PUNCT
ejpam-1535	518	18	y	y	X
ejpam-1535	518	19	)	)	PUNCT
ejpam-1535	518	20	·	·	PUNCT
ejpam-1535	519	1	z.	z.	PROPN
ejpam-1535	520	1	the	the	DET
ejpam-1535	520	2	converse	converse	NOUN
ejpam-1535	520	3	is	be	AUX
ejpam-1535	520	4	similar	similar	ADJ
ejpam-1535	520	5	.	.	PUNCT
ejpam-1535	521	1	c.	c.	NOUN
ejpam-1535	521	2	hollings	holling	NOUN
ejpam-1535	521	3	/	/	SYM
ejpam-1535	521	4	eur	eur	PROPN
ejpam-1535	521	5	.	.	PUNCT
ejpam-1535	522	1	j.	j.	PROPN
ejpam-1535	522	2	pure	pure	PROPN
ejpam-1535	522	3	appl	appl	PROPN
ejpam-1535	522	4	.	.	PROPN
ejpam-1535	522	5	math	math	PROPN
ejpam-1535	522	6	,	,	PUNCT
ejpam-1535	522	7	5	5	NUM
ejpam-1535	522	8	(	(	PUNCT
ejpam-1535	522	9	2012	2012	NUM
ejpam-1535	522	10	)	)	PUNCT
ejpam-1535	522	11	,	,	PUNCT
ejpam-1535	522	12	414	414	NUM
ejpam-1535	522	13	-	-	SYM
ejpam-1535	522	14	450	450	NUM
ejpam-1535	522	15	433	433	NUM
ejpam-1535	522	16	(	(	PUNCT
ejpam-1535	522	17	ca2	ca2	PROPN
ejpam-1535	522	18	)	)	PUNCT
ejpam-1535	522	19	this	this	DET
ejpam-1535	522	20	part	part	NOUN
ejpam-1535	522	21	is	be	AUX
ejpam-1535	522	22	proved	prove	VERB
ejpam-1535	522	23	in	in	ADP
ejpam-1535	522	24	much	much	ADV
ejpam-1535	522	25	the	the	DET
ejpam-1535	522	26	same	same	ADJ
ejpam-1535	522	27	way	way	NOUN
ejpam-1535	522	28	as	as	ADP
ejpam-1535	522	29	(	(	PUNCT
ejpam-1535	522	30	ca1	ca1	NOUN
ejpam-1535	522	31	):	):	PUNCT
ejpam-1535	522	32	suppose	suppose	VERB
ejpam-1535	522	33	that	that	SCONJ
ejpam-1535	522	34	∃x	∃x	PROPN
ejpam-1535	522	35	·	·	PUNCT
ejpam-1535	522	36	y	y	PROPN
ejpam-1535	522	37	and	and	CCONJ
ejpam-1535	522	38	∃y	∃y	PROPN
ejpam-1535	522	39	·	·	PUNCT
ejpam-1535	523	1	z	z	X
ejpam-1535	523	2	,	,	PUNCT
ejpam-1535	523	3	i.e.	i.e.	X
ejpam-1535	523	4	,	,	PUNCT
ejpam-1535	523	5	x∗	x∗	PROPN
ejpam-1535	523	6	=	=	SYM
ejpam-1535	523	7	y+	y+	PROPN
ejpam-1535	523	8	and	and	CCONJ
ejpam-1535	523	9	y∗	y∗	PROPN
ejpam-1535	523	10	=	=	SYM
ejpam-1535	523	11	z+	z+	X
ejpam-1535	523	12	.	.	PUNCT
ejpam-1535	524	1	then	then	ADV
ejpam-1535	524	2	(	(	PUNCT
ejpam-1535	524	3	yz)+	yz)+	NOUN
ejpam-1535	524	4	=	=	X
ejpam-1535	524	5	y+	y+	PROPN
ejpam-1535	524	6	=	=	SYM
ejpam-1535	524	7	x∗	x∗	PROPN
ejpam-1535	524	8	,	,	PUNCT
ejpam-1535	524	9	again	again	ADV
ejpam-1535	524	10	by	by	ADP
ejpam-1535	524	11	lemma	lemma	PROPN
ejpam-1535	524	12	3	3	NUM
ejpam-1535	524	13	,	,	PUNCT
ejpam-1535	524	14	so	so	ADV
ejpam-1535	524	15	∃x	∃x	ADJ
ejpam-1535	524	16	·	·	PUNCT
ejpam-1535	524	17	(	(	PUNCT
ejpam-1535	524	18	y	y	PROPN
ejpam-1535	524	19	·	·	PUNCT
ejpam-1535	524	20	z	z	X
ejpam-1535	524	21	)	)	PUNCT
ejpam-1535	524	22	.	.	PUNCT
ejpam-1535	525	1	conversely	conversely	ADV
ejpam-1535	525	2	,	,	PUNCT
ejpam-1535	525	3	suppose	suppose	VERB
ejpam-1535	525	4	that	that	SCONJ
ejpam-1535	525	5	∃x	∃x	NOUN
ejpam-1535	525	6	·	·	PUNCT
ejpam-1535	525	7	(	(	PUNCT
ejpam-1535	525	8	y	y	PROPN
ejpam-1535	525	9	·	·	PROPN
ejpam-1535	525	10	z	z	NOUN
ejpam-1535	525	11	)	)	PUNCT
ejpam-1535	525	12	.	.	PUNCT
ejpam-1535	526	1	this	this	PRON
ejpam-1535	526	2	tells	tell	VERB
ejpam-1535	526	3	us	we	PRON
ejpam-1535	526	4	implicitly	implicitly	ADV
ejpam-1535	526	5	that	that	SCONJ
ejpam-1535	526	6	∃y	∃y	PROPN
ejpam-1535	526	7	·	·	PUNCT
ejpam-1535	526	8	z.	z.	PROPN
ejpam-1535	526	9	by	by	ADP
ejpam-1535	526	10	(	(	PUNCT
ejpam-1535	526	11	ca1	ca1	PROPN
ejpam-1535	526	12	)	)	PUNCT
ejpam-1535	526	13	,	,	PUNCT
ejpam-1535	526	14	∃(x	∃(x	PROPN
ejpam-1535	526	15	·	·	PUNCT
ejpam-1535	526	16	y	y	X
ejpam-1535	526	17	)	)	PUNCT
ejpam-1535	526	18	·	·	PUNCT
ejpam-1535	526	19	z	z	X
ejpam-1535	526	20	,	,	PUNCT
ejpam-1535	526	21	in	in	ADP
ejpam-1535	526	22	which	which	DET
ejpam-1535	526	23	case	case	NOUN
ejpam-1535	526	24	∃x	∃x	X
ejpam-1535	526	25	·	·	PUNCT
ejpam-1535	526	26	y	y	PROPN
ejpam-1535	526	27	also	also	ADV
ejpam-1535	526	28	.	.	PUNCT
ejpam-1535	527	1	(	(	PUNCT
ejpam-1535	527	2	ca3	ca3	NOUN
ejpam-1535	527	3	)	)	PUNCT
ejpam-1535	527	4	as	as	SCONJ
ejpam-1535	527	5	already	already	ADV
ejpam-1535	527	6	observed	observe	VERB
ejpam-1535	527	7	,	,	PUNCT
ejpam-1535	527	8	d(x	d(x	PROPN
ejpam-1535	527	9	)	)	PUNCT
ejpam-1535	528	1	=	=	SYM
ejpam-1535	528	2	x+	x+	X
ejpam-1535	528	3	and	and	CCONJ
ejpam-1535	528	4	r(x	r(x	PROPN
ejpam-1535	528	5	)	)	PUNCT
ejpam-1535	529	1	=	=	PUNCT
ejpam-1535	529	2	x∗.	x∗.	INTJ
ejpam-1535	530	1	we	we	PRON
ejpam-1535	530	2	have	have	AUX
ejpam-1535	530	3	shown	show	VERB
ejpam-1535	530	4	that	that	SCONJ
ejpam-1535	530	5	(	(	PUNCT
ejpam-1535	530	6	s	s	X
ejpam-1535	530	7	,	,	PUNCT
ejpam-1535	530	8	·	·	PUNCT
ejpam-1535	530	9	)	)	PUNCT
ejpam-1535	530	10	is	be	AUX
ejpam-1535	530	11	a	a	DET
ejpam-1535	530	12	category	category	NOUN
ejpam-1535	530	13	.	.	PUNCT
ejpam-1535	531	1	we	we	PRON
ejpam-1535	531	2	must	must	AUX
ejpam-1535	531	3	now	now	ADV
ejpam-1535	531	4	deal	deal	VERB
ejpam-1535	531	5	with	with	ADP
ejpam-1535	531	6	the	the	DET
ejpam-1535	531	7	“	"	PUNCT
ejpam-1535	531	8	ordered	order	VERB
ejpam-1535	531	9	”	"	PUNCT
ejpam-1535	531	10	and	and	CCONJ
ejpam-1535	531	11	“	"	PUNCT
ejpam-1535	531	12	inductive	inductive	ADJ
ejpam-1535	531	13	”	"	PUNCT
ejpam-1535	531	14	parts	part	NOUN
ejpam-1535	531	15	.	.	PUNCT
ejpam-1535	532	1	(	(	PUNCT
ejpam-1535	532	2	or1	or1	NOUN
ejpam-1535	532	3	)	)	PUNCT
ejpam-1535	532	4	suppose	suppose	VERB
ejpam-1535	532	5	that	that	SCONJ
ejpam-1535	532	6	∃a	∃a	NOUN
ejpam-1535	532	7	·	·	PUNCT
ejpam-1535	532	8	b	b	X
ejpam-1535	532	9	=	=	PUNCT
ejpam-1535	532	10	ab	ab	PROPN
ejpam-1535	532	11	and	and	CCONJ
ejpam-1535	532	12	∃c	∃c	PROPN
ejpam-1535	532	13	·	·	PUNCT
ejpam-1535	532	14	d	d	X
ejpam-1535	532	15	=	=	PUNCT
ejpam-1535	532	16	cd	cd	PROPN
ejpam-1535	532	17	,	,	PUNCT
ejpam-1535	532	18	and	and	CCONJ
ejpam-1535	532	19	that	that	SCONJ
ejpam-1535	532	20	a	a	DET
ejpam-1535	532	21	≤	≤	NUM
ejpam-1535	532	22	c	c	NOUN
ejpam-1535	532	23	and	and	CCONJ
ejpam-1535	532	24	b	b	NOUN
ejpam-1535	532	25	≤	≤	NUM
ejpam-1535	532	26	d	d	NOUN
ejpam-1535	532	27	.	.	PUNCT
ejpam-1535	533	1	we	we	PRON
ejpam-1535	533	2	have	have	VERB
ejpam-1535	533	3	a	a	DET
ejpam-1535	533	4	=	=	SYM
ejpam-1535	533	5	ec	ec	PROPN
ejpam-1535	533	6	and	and	CCONJ
ejpam-1535	533	7	b	b	X
ejpam-1535	533	8	=	=	SYM
ejpam-1535	533	9	f	f	PROPN
ejpam-1535	533	10	d	d	NOUN
ejpam-1535	533	11	,	,	PUNCT
ejpam-1535	533	12	for	for	ADP
ejpam-1535	533	13	some	some	DET
ejpam-1535	533	14	e	e	NOUN
ejpam-1535	533	15	,	,	PUNCT
ejpam-1535	533	16	f	f	PROPN
ejpam-1535	533	17	∈	∈	PROPN
ejpam-1535	533	18	e.	e.	PROPN
ejpam-1535	533	19	then	then	ADV
ejpam-1535	533	20	ab	ab	PROPN
ejpam-1535	534	1	=	=	PUNCT
ejpam-1535	534	2	ec	ec	PROPN
ejpam-1535	534	3	f	f	PROPN
ejpam-1535	535	1	d	d	PROPN
ejpam-1535	535	2	=	=	SYM
ejpam-1535	535	3	e(c	e(c	PROPN
ejpam-1535	535	4	f	f	PROPN
ejpam-1535	535	5	)	)	PUNCT
ejpam-1535	536	1	+	+	ADJ
ejpam-1535	536	2	cd	cd	PROPN
ejpam-1535	536	3	≤	≤	PROPN
ejpam-1535	536	4	cd	cd	PROPN
ejpam-1535	536	5	,	,	PUNCT
ejpam-1535	536	6	using	use	VERB
ejpam-1535	536	7	the	the	DET
ejpam-1535	536	8	left	left	ADJ
ejpam-1535	536	9	ample	ample	ADJ
ejpam-1535	536	10	identity	identity	NOUN
ejpam-1535	536	11	,	,	PUNCT
ejpam-1535	536	12	so	so	SCONJ
ejpam-1535	537	1	a	a	DET
ejpam-1535	537	2	·	·	PUNCT
ejpam-1535	537	3	b	b	X
ejpam-1535	537	4	≤	≤	NUM
ejpam-1535	537	5	c	c	X
ejpam-1535	537	6	·	·	PUNCT
ejpam-1535	538	1	d	d	X
ejpam-1535	538	2	.	.	PUNCT
ejpam-1535	539	1	(	(	PUNCT
ejpam-1535	539	2	or2	or2	NOUN
ejpam-1535	539	3	)	)	PUNCT
ejpam-1535	539	4	suppose	suppose	VERB
ejpam-1535	539	5	that	that	SCONJ
ejpam-1535	539	6	a	a	DET
ejpam-1535	539	7	≤	≤	PROPN
ejpam-1535	539	8	b.	b.	NOUN
ejpam-1535	539	9	we	we	PRON
ejpam-1535	539	10	apply	apply	VERB
ejpam-1535	539	11	+	+	CCONJ
ejpam-1535	539	12	to	to	ADP
ejpam-1535	539	13	a	a	DET
ejpam-1535	539	14	=	=	X
ejpam-1535	539	15	eb	eb	PROPN
ejpam-1535	539	16	to	to	PART
ejpam-1535	539	17	obtain	obtain	VERB
ejpam-1535	539	18	a+	a+	PRON
ejpam-1535	539	19	=	=	SYM
ejpam-1535	539	20	(	(	PUNCT
ejpam-1535	539	21	eb)+	eb)+	NOUN
ejpam-1535	539	22	=	=	SYM
ejpam-1535	539	23	(	(	PUNCT
ejpam-1535	539	24	eb+)+	eb+)+	ADJ
ejpam-1535	539	25	=	=	SYM
ejpam-1535	539	26	eb+	eb+	ADJ
ejpam-1535	539	27	≤	≤	NUM
ejpam-1535	539	28	b+	b+	NOUN
ejpam-1535	539	29	,	,	PUNCT
ejpam-1535	539	30	using	use	VERB
ejpam-1535	539	31	lemma	lemma	PROPN
ejpam-1535	539	32	1	1	NUM
ejpam-1535	539	33	,	,	PUNCT
ejpam-1535	539	34	whence	whence	ADP
ejpam-1535	539	35	d(a	d(a	PROPN
ejpam-1535	539	36	)	)	PUNCT
ejpam-1535	539	37	≤	≤	NOUN
ejpam-1535	539	38	d(b	d(b	PROPN
ejpam-1535	539	39	)	)	PUNCT
ejpam-1535	539	40	.	.	PUNCT
ejpam-1535	540	1	similarly	similarly	ADV
ejpam-1535	540	2	,	,	PUNCT
ejpam-1535	540	3	applying	apply	VERB
ejpam-1535	540	4	∗	∗	NOUN
ejpam-1535	540	5	to	to	ADP
ejpam-1535	540	6	a	a	PRON
ejpam-1535	540	7	=	=	SYM
ejpam-1535	540	8	b	b	X
ejpam-1535	540	9	f	f	X
ejpam-1535	540	10	(	(	PUNCT
ejpam-1535	540	11	f	f	PROPN
ejpam-1535	540	12	∈	∈	PROPN
ejpam-1535	540	13	e	e	X
ejpam-1535	540	14	)	)	PUNCT
ejpam-1535	540	15	gives	give	VERB
ejpam-1535	540	16	a∗	a∗	ADJ
ejpam-1535	540	17	≤	≤	NOUN
ejpam-1535	540	18	b∗	b∗	ADJ
ejpam-1535	540	19	and	and	CCONJ
ejpam-1535	540	20	so	so	ADV
ejpam-1535	540	21	r(a)≤	r(a)≤	PROPN
ejpam-1535	540	22	r(b	r(b	PROPN
ejpam-1535	540	23	)	)	PUNCT
ejpam-1535	540	24	.	.	PUNCT
ejpam-1535	541	1	(	(	PUNCT
ejpam-1535	541	2	or3)(i	or3)(i	PROPN
ejpam-1535	541	3	)	)	PUNCT
ejpam-1535	541	4	we	we	PRON
ejpam-1535	541	5	note	note	VERB
ejpam-1535	541	6	that	that	SCONJ
ejpam-1535	541	7	a|	a|	PROPN
ejpam-1535	541	8	f	f	PROPN
ejpam-1535	542	1	=	=	PUNCT
ejpam-1535	542	2	a	a	DET
ejpam-1535	542	3	f	f	PROPN
ejpam-1535	542	4	has	have	VERB
ejpam-1535	542	5	the	the	DET
ejpam-1535	542	6	desired	desire	VERB
ejpam-1535	542	7	properties	property	NOUN
ejpam-1535	542	8	:	:	PUNCT
ejpam-1535	542	9	a	a	DET
ejpam-1535	542	10	f	f	PROPN
ejpam-1535	542	11	≤	≤	NOUN
ejpam-1535	542	12	a	a	PRON
ejpam-1535	542	13	and	and	CCONJ
ejpam-1535	542	14	(	(	PUNCT
ejpam-1535	542	15	a	a	DET
ejpam-1535	542	16	f	f	NOUN
ejpam-1535	542	17	)	)	PUNCT
ejpam-1535	542	18	∗	∗	NOUN
ejpam-1535	542	19	=	=	SYM
ejpam-1535	542	20	(	(	PUNCT
ejpam-1535	542	21	a∗	a∗	PROPN
ejpam-1535	542	22	f	f	PROPN
ejpam-1535	542	23	)	)	PUNCT
ejpam-1535	542	24	∗	∗	NOUN
ejpam-1535	542	25	=	=	PUNCT
ejpam-1535	542	26	a∗	a∗	PROPN
ejpam-1535	542	27	f	f	PROPN
ejpam-1535	542	28	=	=	SYM
ejpam-1535	542	29	f	f	PROPN
ejpam-1535	542	30	,	,	PUNCT
ejpam-1535	542	31	since	since	SCONJ
ejpam-1535	542	32	f	f	PROPN
ejpam-1535	542	33	≤	≤	ADV
ejpam-1535	542	34	a∗	a∗	NOUN
ejpam-1535	542	35	=	=	SYM
ejpam-1535	542	36	r(a	r(a	PROPN
ejpam-1535	542	37	)	)	PUNCT
ejpam-1535	542	38	.	.	PUNCT
ejpam-1535	543	1	to	to	PART
ejpam-1535	543	2	show	show	VERB
ejpam-1535	543	3	uniqueness	uniqueness	NOUN
ejpam-1535	543	4	,	,	PUNCT
ejpam-1535	543	5	suppose	suppose	VERB
ejpam-1535	543	6	that	that	SCONJ
ejpam-1535	543	7	there	there	PRON
ejpam-1535	543	8	is	be	VERB
ejpam-1535	543	9	another	another	DET
ejpam-1535	543	10	element	element	NOUN
ejpam-1535	543	11	g	g	NOUN
ejpam-1535	543	12	which	which	PRON
ejpam-1535	543	13	satisfies	satisfy	VERB
ejpam-1535	543	14	the	the	DET
ejpam-1535	543	15	conditions	condition	NOUN
ejpam-1535	543	16	of	of	ADP
ejpam-1535	543	17	(	(	PUNCT
ejpam-1535	543	18	o3)(i	o3)(i	PROPN
ejpam-1535	543	19	)	)	PUNCT
ejpam-1535	543	20	,	,	PUNCT
ejpam-1535	543	21	i.e.	i.e.	X
ejpam-1535	543	22	,	,	PUNCT
ejpam-1535	543	23	g	g	PROPN
ejpam-1535	543	24	≤	≤	PROPN
ejpam-1535	543	25	a	a	PRON
ejpam-1535	543	26	and	and	CCONJ
ejpam-1535	543	27	g∗	g∗	VERB
ejpam-1535	543	28	=	=	SYM
ejpam-1535	543	29	f	f	PROPN
ejpam-1535	543	30	.	.	PUNCT
ejpam-1535	544	1	then	then	ADV
ejpam-1535	544	2	g	g	PROPN
ejpam-1535	544	3	=	=	PUNCT
ejpam-1535	544	4	ag∗	ag∗	NOUN
ejpam-1535	544	5	=	=	PUNCT
ejpam-1535	544	6	a	a	DET
ejpam-1535	544	7	f	f	X
ejpam-1535	544	8	.	.	PUNCT
ejpam-1535	545	1	hence	hence	ADV
ejpam-1535	545	2	a|	a|	PROPN
ejpam-1535	545	3	f	f	PROPN
ejpam-1535	545	4	is	be	AUX
ejpam-1535	545	5	uniquely	uniquely	ADV
ejpam-1535	545	6	defined	define	VERB
ejpam-1535	545	7	.	.	PUNCT
ejpam-1535	546	1	similarly	similarly	ADV
ejpam-1535	546	2	,	,	PUNCT
ejpam-1535	546	3	put	put	VERB
ejpam-1535	546	4	f	f	PRON
ejpam-1535	546	5	|a	|a	X
ejpam-1535	546	6	=	=	SYM
ejpam-1535	546	7	f	f	PROPN
ejpam-1535	546	8	a	a	PRON
ejpam-1535	546	9	for	for	ADP
ejpam-1535	546	10	part	part	NOUN
ejpam-1535	546	11	(	(	PUNCT
ejpam-1535	546	12	ii	ii	NOUN
ejpam-1535	546	13	)	)	PUNCT
ejpam-1535	546	14	.	.	PUNCT
ejpam-1535	547	1	(	(	PUNCT
ejpam-1535	547	2	in	in	ADP
ejpam-1535	547	3	)	)	PUNCT
ejpam-1535	547	4	note	note	NOUN
ejpam-1535	547	5	that	that	SCONJ
ejpam-1535	547	6	e	e	PROPN
ejpam-1535	547	7	f	f	NOUN
ejpam-1535	547	8	≤	≤	PROPN
ejpam-1535	547	9	e	e	NOUN
ejpam-1535	547	10	and	and	CCONJ
ejpam-1535	547	11	e	e	X
ejpam-1535	547	12	f	f	PROPN
ejpam-1535	547	13	≤	≤	PROPN
ejpam-1535	547	14	f	f	PROPN
ejpam-1535	547	15	,	,	PUNCT
ejpam-1535	547	16	so	so	CCONJ
ejpam-1535	547	17	e	e	X
ejpam-1535	547	18	f	f	PROPN
ejpam-1535	547	19	≤	≤	PROPN
ejpam-1535	547	20	e	e	PROPN
ejpam-1535	547	21	∧	∧	PROPN
ejpam-1535	547	22	f	f	PROPN
ejpam-1535	547	23	.	.	PUNCT
ejpam-1535	548	1	now	now	ADV
ejpam-1535	548	2	suppose	suppose	VERB
ejpam-1535	548	3	that	that	SCONJ
ejpam-1535	548	4	g	g	PROPN
ejpam-1535	548	5	is	be	AUX
ejpam-1535	548	6	an	an	DET
ejpam-1535	548	7	idempotent	idempotent	NOUN
ejpam-1535	548	8	lower	lower	ADV
ejpam-1535	548	9	bound	bind	VERB
ejpam-1535	548	10	for	for	ADP
ejpam-1535	548	11	e	e	PROPN
ejpam-1535	548	12	and	and	CCONJ
ejpam-1535	548	13	f	f	PROPN
ejpam-1535	548	14	.	.	PUNCT
ejpam-1535	549	1	then	then	ADV
ejpam-1535	549	2	g	g	PROPN
ejpam-1535	549	3	=	=	PROPN
ejpam-1535	549	4	g2	g2	PROPN
ejpam-1535	549	5	≤	≤	NUM
ejpam-1535	550	1	e	e	X
ejpam-1535	550	2	f	f	PROPN
ejpam-1535	550	3	,	,	PUNCT
ejpam-1535	550	4	by	by	ADP
ejpam-1535	550	5	compatibility	compatibility	NOUN
ejpam-1535	550	6	of	of	ADP
ejpam-1535	550	7	≤.	≤.	NOUN
ejpam-1535	550	8	thus	thus	ADV
ejpam-1535	550	9	e	e	X
ejpam-1535	550	10	f	f	PROPN
ejpam-1535	550	11	=	=	SYM
ejpam-1535	550	12	e	e	PROPN
ejpam-1535	550	13	∧	∧	PROPN
ejpam-1535	550	14	f	f	X
ejpam-1535	550	15	.	.	PUNCT
ejpam-1535	551	1	we	we	PRON
ejpam-1535	551	2	deduce	deduce	VERB
ejpam-1535	551	3	some	some	DET
ejpam-1535	551	4	corollaries	corollary	NOUN
ejpam-1535	551	5	in	in	ADP
ejpam-1535	551	6	the	the	DET
ejpam-1535	551	7	full	full	ADJ
ejpam-1535	551	8	restriction	restriction	NOUN
ejpam-1535	551	9	and	and	CCONJ
ejpam-1535	551	10	ample	ample	ADJ
ejpam-1535	551	11	cases	case	NOUN
ejpam-1535	551	12	:	:	PUNCT
ejpam-1535	551	13	corollary	corollary	ADJ
ejpam-1535	551	14	3	3	NUM
ejpam-1535	551	15	(	(	PUNCT
ejpam-1535	551	16	[	[	X
ejpam-1535	551	17	26	26	NUM
ejpam-1535	551	18	,	,	PUNCT
ejpam-1535	551	19	theorem	theorem	ADJ
ejpam-1535	551	20	3.15(i	3.15(i	NUM
ejpam-1535	551	21	)	)	PUNCT
ejpam-1535	551	22	]	]	PUNCT
ejpam-1535	551	23	)	)	PUNCT
ejpam-1535	551	24	.	.	PUNCT
ejpam-1535	552	1	let	let	VERB
ejpam-1535	552	2	s	s	PRON
ejpam-1535	552	3	be	be	AUX
ejpam-1535	552	4	a	a	DET
ejpam-1535	552	5	full	full	ADJ
ejpam-1535	552	6	restriction	restriction	NOUN
ejpam-1535	552	7	semigroup	semigroup	NOUN
ejpam-1535	552	8	with	with	ADP
ejpam-1535	552	9	natural	natural	ADJ
ejpam-1535	552	10	partial	partial	ADJ
ejpam-1535	552	11	order	order	NOUN
ejpam-1535	552	12	≤.	≤.	NOUN
ejpam-1535	552	13	then	then	ADV
ejpam-1535	552	14	(	(	PUNCT
ejpam-1535	552	15	s	s	X
ejpam-1535	552	16	,	,	PUNCT
ejpam-1535	552	17	·	·	PUNCT
ejpam-1535	552	18	,	,	PUNCT
ejpam-1535	552	19	≤	≤	NUM
ejpam-1535	552	20	)	)	PUNCT
ejpam-1535	552	21	is	be	AUX
ejpam-1535	552	22	an	an	DET
ejpam-1535	552	23	inductive	inductive	ADJ
ejpam-1535	552	24	unipotent	unipotent	ADJ
ejpam-1535	552	25	category	category	NOUN
ejpam-1535	552	26	with	with	ADP
ejpam-1535	552	27	so	so	ADV
ejpam-1535	552	28	=	=	SYM
ejpam-1535	552	29	e(s	e(s	PROPN
ejpam-1535	552	30	)	)	PUNCT
ejpam-1535	552	31	,	,	PUNCT
ejpam-1535	552	32	d(x	d(x	PROPN
ejpam-1535	552	33	)	)	PUNCT
ejpam-1535	553	1	=	=	SYM
ejpam-1535	553	2	x+	x+	X
ejpam-1535	553	3	and	and	CCONJ
ejpam-1535	553	4	r(x	r(x	PROPN
ejpam-1535	553	5	)	)	PUNCT
ejpam-1535	553	6	=	=	SYM
ejpam-1535	553	7	x∗	x∗	NOUN
ejpam-1535	553	8	,	,	PUNCT
ejpam-1535	553	9	where	where	SCONJ
ejpam-1535	553	10	·	·	PUNCT
ejpam-1535	553	11	is	be	AUX
ejpam-1535	553	12	the	the	DET
ejpam-1535	553	13	restricted	restricted	ADJ
ejpam-1535	553	14	product	product	NOUN
ejpam-1535	553	15	of	of	ADP
ejpam-1535	553	16	(	(	PUNCT
ejpam-1535	553	17	7	7	NUM
ejpam-1535	553	18	)	)	PUNCT
ejpam-1535	553	19	.	.	PUNCT
ejpam-1535	554	1	proof	proof	NOUN
ejpam-1535	554	2	.	.	PUNCT
ejpam-1535	555	1	by	by	ADP
ejpam-1535	555	2	theorem	theorem	NOUN
ejpam-1535	555	3	2	2	NUM
ejpam-1535	555	4	,	,	PUNCT
ejpam-1535	555	5	(	(	PUNCT
ejpam-1535	555	6	s	s	X
ejpam-1535	555	7	,	,	PUNCT
ejpam-1535	555	8	·	·	PUNCT
ejpam-1535	555	9	,	,	PUNCT
ejpam-1535	555	10	≤	≤	NUM
ejpam-1535	555	11	)	)	PUNCT
ejpam-1535	555	12	is	be	AUX
ejpam-1535	555	13	an	an	DET
ejpam-1535	555	14	inductive	inductive	ADJ
ejpam-1535	555	15	category	category	NOUN
ejpam-1535	555	16	with	with	ADP
ejpam-1535	555	17	so	so	ADV
ejpam-1535	555	18	=	=	SYM
ejpam-1535	555	19	e(s	e(s	PROPN
ejpam-1535	555	20	)	)	PUNCT
ejpam-1535	555	21	.	.	PUNCT
ejpam-1535	556	1	if	if	SCONJ
ejpam-1535	556	2	e	e	PROPN
ejpam-1535	556	3	is	be	AUX
ejpam-1535	556	4	idempotent	idempotent	ADJ
ejpam-1535	556	5	with	with	ADP
ejpam-1535	556	6	respect	respect	NOUN
ejpam-1535	556	7	to	to	ADP
ejpam-1535	556	8	·	·	PUNCT
ejpam-1535	556	9	,	,	PUNCT
ejpam-1535	556	10	then	then	ADV
ejpam-1535	556	11	it	it	PRON
ejpam-1535	556	12	is	be	AUX
ejpam-1535	556	13	also	also	ADV
ejpam-1535	556	14	idempotent	idempotent	ADJ
ejpam-1535	556	15	with	with	ADP
ejpam-1535	556	16	respect	respect	NOUN
ejpam-1535	556	17	to	to	ADP
ejpam-1535	556	18	multiplication	multiplication	NOUN
ejpam-1535	556	19	in	in	ADP
ejpam-1535	556	20	s	s	PROPN
ejpam-1535	556	21	,	,	PUNCT
ejpam-1535	556	22	so	so	ADV
ejpam-1535	556	23	e	e	PROPN
ejpam-1535	556	24	∈	∈	PROPN
ejpam-1535	556	25	e(s	e(s	PROPN
ejpam-1535	556	26	)	)	PUNCT
ejpam-1535	556	27	.	.	PUNCT
ejpam-1535	557	1	but	but	CCONJ
ejpam-1535	557	2	e(s	e(s	NUM
ejpam-1535	557	3	)	)	PUNCT
ejpam-1535	558	1	=	=	PUNCT
ejpam-1535	559	1	so	so	ADV
ejpam-1535	559	2	,	,	PUNCT
ejpam-1535	559	3	so	so	CCONJ
ejpam-1535	559	4	e	e	NOUN
ejpam-1535	559	5	is	be	AUX
ejpam-1535	559	6	an	an	DET
ejpam-1535	559	7	identity	identity	NOUN
ejpam-1535	559	8	,	,	PUNCT
ejpam-1535	559	9	and	and	CCONJ
ejpam-1535	559	10	(	(	PUNCT
ejpam-1535	559	11	s	s	X
ejpam-1535	559	12	,	,	PUNCT
ejpam-1535	559	13	·	·	PUNCT
ejpam-1535	559	14	,	,	PUNCT
ejpam-1535	559	15	≤	≤	NUM
ejpam-1535	559	16	)	)	PUNCT
ejpam-1535	559	17	is	be	AUX
ejpam-1535	559	18	unipotent	unipotent	ADJ
ejpam-1535	559	19	.	.	PUNCT
ejpam-1535	560	1	corollary	corollary	ADJ
ejpam-1535	560	2	4	4	NUM
ejpam-1535	560	3	(	(	PUNCT
ejpam-1535	560	4	[	[	X
ejpam-1535	560	5	1	1	NUM
ejpam-1535	560	6	,	,	PUNCT
ejpam-1535	560	7	theorem	theorem	VERB
ejpam-1535	560	8	3.9	3.9	NUM
ejpam-1535	560	9	]	]	PUNCT
ejpam-1535	560	10	)	)	PUNCT
ejpam-1535	560	11	.	.	PUNCT
ejpam-1535	561	1	let	let	VERB
ejpam-1535	561	2	s	s	PRON
ejpam-1535	561	3	be	be	AUX
ejpam-1535	561	4	an	an	DET
ejpam-1535	561	5	ample	ample	ADJ
ejpam-1535	561	6	semigroup	semigroup	NOUN
ejpam-1535	561	7	with	with	ADP
ejpam-1535	561	8	natural	natural	ADJ
ejpam-1535	561	9	partial	partial	ADJ
ejpam-1535	561	10	order	order	NOUN
ejpam-1535	561	11	≤.	≤.	NOUN
ejpam-1535	561	12	then	then	ADV
ejpam-1535	561	13	(	(	PUNCT
ejpam-1535	561	14	s	s	X
ejpam-1535	561	15	,	,	PUNCT
ejpam-1535	561	16	·	·	PUNCT
ejpam-1535	561	17	,	,	PUNCT
ejpam-1535	561	18	≤	≤	NUM
ejpam-1535	561	19	)	)	PUNCT
ejpam-1535	561	20	is	be	AUX
ejpam-1535	561	21	an	an	DET
ejpam-1535	561	22	inductive	inductive	ADJ
ejpam-1535	561	23	cancellative	cancellative	ADJ
ejpam-1535	561	24	category	category	NOUN
ejpam-1535	561	25	with	with	ADP
ejpam-1535	561	26	so	so	ADV
ejpam-1535	561	27	=	=	SYM
ejpam-1535	561	28	e(s	e(s	PROPN
ejpam-1535	561	29	)	)	PUNCT
ejpam-1535	561	30	,	,	PUNCT
ejpam-1535	561	31	d(x	d(x	PROPN
ejpam-1535	561	32	)	)	PUNCT
ejpam-1535	562	1	=	=	SYM
ejpam-1535	562	2	x+	x+	X
ejpam-1535	562	3	and	and	CCONJ
ejpam-1535	562	4	r(x	r(x	PROPN
ejpam-1535	562	5	)	)	PUNCT
ejpam-1535	562	6	=	=	SYM
ejpam-1535	562	7	x∗	x∗	NOUN
ejpam-1535	562	8	,	,	PUNCT
ejpam-1535	562	9	where	where	SCONJ
ejpam-1535	562	10	·	·	PUNCT
ejpam-1535	562	11	is	be	AUX
ejpam-1535	562	12	the	the	DET
ejpam-1535	562	13	restricted	restricted	ADJ
ejpam-1535	562	14	product	product	NOUN
ejpam-1535	562	15	of	of	ADP
ejpam-1535	562	16	(	(	PUNCT
ejpam-1535	562	17	7	7	NUM
ejpam-1535	562	18	)	)	PUNCT
ejpam-1535	562	19	.	.	PUNCT
ejpam-1535	563	1	proof	proof	NOUN
ejpam-1535	563	2	.	.	PUNCT
ejpam-1535	564	1	by	by	ADP
ejpam-1535	564	2	corollary	corollary	ADJ
ejpam-1535	564	3	3	3	NUM
ejpam-1535	564	4	,	,	PUNCT
ejpam-1535	564	5	(	(	PUNCT
ejpam-1535	564	6	s	s	X
ejpam-1535	564	7	,	,	PUNCT
ejpam-1535	564	8	·	·	PUNCT
ejpam-1535	564	9	,	,	PUNCT
ejpam-1535	564	10	≤	≤	NUM
ejpam-1535	564	11	)	)	PUNCT
ejpam-1535	564	12	is	be	AUX
ejpam-1535	564	13	an	an	DET
ejpam-1535	564	14	inductive	inductive	ADJ
ejpam-1535	564	15	unipotent	unipotent	ADJ
ejpam-1535	564	16	category	category	NOUN
ejpam-1535	564	17	.	.	PUNCT
ejpam-1535	565	1	suppose	suppose	VERB
ejpam-1535	565	2	that	that	SCONJ
ejpam-1535	565	3	∃x	∃x	ADJ
ejpam-1535	565	4	·	·	SYM
ejpam-1535	565	5	z	z	NOUN
ejpam-1535	565	6	,	,	PUNCT
ejpam-1535	565	7	∃y	∃y	PROPN
ejpam-1535	565	8	·	·	PUNCT
ejpam-1535	565	9	z	z	PROPN
ejpam-1535	565	10	and	and	CCONJ
ejpam-1535	565	11	that	that	SCONJ
ejpam-1535	565	12	x	x	X
ejpam-1535	565	13	·	·	PUNCT
ejpam-1535	565	14	z	z	X
ejpam-1535	566	1	=	=	SYM
ejpam-1535	566	2	y	y	PROPN
ejpam-1535	566	3	·	·	PUNCT
ejpam-1535	566	4	z.	z.	PROPN
ejpam-1535	567	1	then	then	ADV
ejpam-1535	567	2	x∗	x∗	PROPN
ejpam-1535	567	3	=	=	PUNCT
ejpam-1535	567	4	z+	z+	NUM
ejpam-1535	567	5	=	=	SYM
ejpam-1535	567	6	y∗.	y∗.	PROPN
ejpam-1535	567	7	since	since	SCONJ
ejpam-1535	567	8	zr∗	zr∗	PROPN
ejpam-1535	567	9	z+	z+	X
ejpam-1535	567	10	,	,	PUNCT
ejpam-1535	567	11	we	we	PRON
ejpam-1535	567	12	can	can	AUX
ejpam-1535	567	13	take	take	VERB
ejpam-1535	567	14	the	the	DET
ejpam-1535	567	15	equality	equality	NOUN
ejpam-1535	567	16	xz	xz	PROPN
ejpam-1535	567	17	=	=	SYM
ejpam-1535	567	18	yz	yz	PROPN
ejpam-1535	567	19	and	and	CCONJ
ejpam-1535	567	20	replace	replace	VERB
ejpam-1535	567	21	z	z	NOUN
ejpam-1535	567	22	by	by	ADP
ejpam-1535	567	23	z+	z+	NOUN
ejpam-1535	567	24	:	:	PUNCT
ejpam-1535	567	25	xz+	xz+	PROPN
ejpam-1535	567	26	=	=	SYM
ejpam-1535	567	27	yz+	yz+	PROPN
ejpam-1535	567	28	.	.	PUNCT
ejpam-1535	568	1	but	but	CCONJ
ejpam-1535	568	2	x∗	x∗	PROPN
ejpam-1535	568	3	=	=	SYM
ejpam-1535	569	1	z+	z+	NUM
ejpam-1535	569	2	=	=	SYM
ejpam-1535	569	3	y∗	y∗	PROPN
ejpam-1535	569	4	,	,	PUNCT
ejpam-1535	569	5	so	so	ADV
ejpam-1535	569	6	x	x	X
ejpam-1535	569	7	x∗	x∗	PROPN
ejpam-1535	569	8	=	=	SYM
ejpam-1535	569	9	y	y	PROPN
ejpam-1535	569	10	y∗	y∗	ADV
ejpam-1535	569	11	,	,	PUNCT
ejpam-1535	569	12	hence	hence	ADV
ejpam-1535	569	13	x	x	PUNCT
ejpam-1535	569	14	=	=	PUNCT
ejpam-1535	569	15	y.	y.	NOUN
ejpam-1535	569	16	we	we	PRON
ejpam-1535	569	17	have	have	AUX
ejpam-1535	569	18	shown	show	VERB
ejpam-1535	569	19	that	that	SCONJ
ejpam-1535	569	20	(	(	PUNCT
ejpam-1535	569	21	ca4)(i	ca4)(i	NOUN
ejpam-1535	569	22	)	)	PUNCT
ejpam-1535	569	23	holds	hold	VERB
ejpam-1535	569	24	;	;	PUNCT
ejpam-1535	569	25	part	part	NOUN
ejpam-1535	569	26	(	(	PUNCT
ejpam-1535	569	27	ii	ii	NOUN
ejpam-1535	569	28	)	)	PUNCT
ejpam-1535	569	29	is	be	AUX
ejpam-1535	569	30	similar	similar	ADJ
ejpam-1535	569	31	.	.	PUNCT
ejpam-1535	570	1	c.	c.	NOUN
ejpam-1535	570	2	hollings	holling	NOUN
ejpam-1535	570	3	/	/	SYM
ejpam-1535	570	4	eur	eur	PROPN
ejpam-1535	570	5	.	.	PUNCT
ejpam-1535	571	1	j.	j.	PROPN
ejpam-1535	571	2	pure	pure	PROPN
ejpam-1535	571	3	appl	appl	PROPN
ejpam-1535	571	4	.	.	PROPN
ejpam-1535	571	5	math	math	PROPN
ejpam-1535	571	6	,	,	PUNCT
ejpam-1535	571	7	5	5	NUM
ejpam-1535	571	8	(	(	PUNCT
ejpam-1535	571	9	2012	2012	NUM
ejpam-1535	571	10	)	)	PUNCT
ejpam-1535	571	11	,	,	PUNCT
ejpam-1535	571	12	414	414	NUM
ejpam-1535	571	13	-	-	SYM
ejpam-1535	571	14	450	450	NUM
ejpam-1535	571	15	434	434	NUM
ejpam-1535	571	16	we	we	PRON
ejpam-1535	571	17	now	now	ADV
ejpam-1535	571	18	turn	turn	VERB
ejpam-1535	571	19	our	our	PRON
ejpam-1535	571	20	attention	attention	NOUN
ejpam-1535	571	21	to	to	ADP
ejpam-1535	571	22	the	the	DET
ejpam-1535	571	23	converse	converse	NOUN
ejpam-1535	571	24	construction	construction	NOUN
ejpam-1535	571	25	whereby	whereby	SCONJ
ejpam-1535	571	26	we	we	PRON
ejpam-1535	571	27	obtain	obtain	VERB
ejpam-1535	571	28	a	a	DET
ejpam-1535	571	29	restriction	restriction	NOUN
ejpam-1535	571	30	semigroup	semigroup	NOUN
ejpam-1535	571	31	from	from	ADP
ejpam-1535	571	32	an	an	DET
ejpam-1535	571	33	inductive	inductive	ADJ
ejpam-1535	571	34	category	category	NOUN
ejpam-1535	571	35	;	;	PUNCT
ejpam-1535	571	36	the	the	DET
ejpam-1535	571	37	construction	construction	NOUN
ejpam-1535	571	38	makes	make	VERB
ejpam-1535	571	39	use	use	NOUN
ejpam-1535	571	40	of	of	ADP
ejpam-1535	571	41	the	the	DET
ejpam-1535	571	42	pseudoproduct	pseudoproduct	NOUN
ejpam-1535	571	43	⊗	⊗	PROPN
ejpam-1535	571	44	introduced	introduce	VERB
ejpam-1535	571	45	in	in	ADP
ejpam-1535	571	46	(	(	PUNCT
ejpam-1535	571	47	6	6	NUM
ejpam-1535	571	48	)	)	PUNCT
ejpam-1535	571	49	.	.	PUNCT
ejpam-1535	572	1	the	the	DET
ejpam-1535	572	2	result	result	NOUN
ejpam-1535	572	3	is	be	AUX
ejpam-1535	572	4	due	due	ADJ
ejpam-1535	572	5	originally	originally	ADV
ejpam-1535	572	6	to	to	ADP
ejpam-1535	572	7	lawson	lawson	PROPN
ejpam-1535	572	8	[	[	X
ejpam-1535	572	9	28	28	NUM
ejpam-1535	572	10	,	,	PUNCT
ejpam-1535	572	11	theorem	theorem	VERB
ejpam-1535	572	12	5.7	5.7	NUM
ejpam-1535	572	13	]	]	PUNCT
ejpam-1535	572	14	,	,	PUNCT
ejpam-1535	572	15	but	but	CCONJ
ejpam-1535	572	16	we	we	PRON
ejpam-1535	572	17	give	give	VERB
ejpam-1535	572	18	a	a	DET
ejpam-1535	572	19	slightly	slightly	ADV
ejpam-1535	572	20	shorter	short	ADJ
ejpam-1535	572	21	proof	proof	NOUN
ejpam-1535	572	22	,	,	PUNCT
ejpam-1535	572	23	using	use	VERB
ejpam-1535	572	24	propositions	proposition	NOUN
ejpam-1535	572	25	1	1	NUM
ejpam-1535	572	26	and	and	CCONJ
ejpam-1535	572	27	2	2	NUM
ejpam-1535	572	28	,	,	PUNCT
ejpam-1535	572	29	based	base	VERB
ejpam-1535	572	30	upon	upon	SCONJ
ejpam-1535	572	31	that	that	PRON
ejpam-1535	572	32	given	give	VERB
ejpam-1535	572	33	in	in	ADP
ejpam-1535	572	34	[	[	NOUN
ejpam-1535	572	35	29	29	NUM
ejpam-1535	572	36	,	,	PUNCT
ejpam-1535	572	37	proposition	proposition	NOUN
ejpam-1535	572	38	4.1.7	4.1.7	NUM
ejpam-1535	572	39	]	]	PUNCT
ejpam-1535	572	40	for	for	ADP
ejpam-1535	572	41	the	the	DET
ejpam-1535	572	42	inverse	inverse	NOUN
ejpam-1535	572	43	case	case	NOUN
ejpam-1535	572	44	.	.	PUNCT
ejpam-1535	573	1	theorem	theorem	NOUN
ejpam-1535	573	2	3	3	NUM
ejpam-1535	573	3	.	.	PUNCT
ejpam-1535	574	1	if	if	SCONJ
ejpam-1535	574	2	(	(	PUNCT
ejpam-1535	574	3	c	c	NOUN
ejpam-1535	574	4	,	,	PUNCT
ejpam-1535	574	5	·	·	PUNCT
ejpam-1535	574	6	,	,	PUNCT
ejpam-1535	574	7	≤	≤	NUM
ejpam-1535	574	8	)	)	PUNCT
ejpam-1535	574	9	is	be	AUX
ejpam-1535	574	10	an	an	DET
ejpam-1535	574	11	inductive	inductive	ADJ
ejpam-1535	574	12	category	category	NOUN
ejpam-1535	574	13	,	,	PUNCT
ejpam-1535	574	14	then	then	ADV
ejpam-1535	574	15	(	(	PUNCT
ejpam-1535	574	16	c	c	X
ejpam-1535	574	17	,	,	PUNCT
ejpam-1535	574	18	⊗	⊗	PROPN
ejpam-1535	574	19	)	)	PUNCT
ejpam-1535	574	20	is	be	AUX
ejpam-1535	574	21	a	a	DET
ejpam-1535	574	22	restriction	restriction	NOUN
ejpam-1535	574	23	semigroup	semigroup	NOUN
ejpam-1535	574	24	with	with	ADP
ejpam-1535	574	25	respect	respect	NOUN
ejpam-1535	574	26	to	to	ADP
ejpam-1535	574	27	co.	co.	NOUN
ejpam-1535	574	28	proof	proof	NOUN
ejpam-1535	574	29	.	.	PUNCT
ejpam-1535	575	1	we	we	PRON
ejpam-1535	575	2	first	first	ADV
ejpam-1535	575	3	note	note	VERB
ejpam-1535	575	4	that	that	SCONJ
ejpam-1535	575	5	(	(	PUNCT
ejpam-1535	575	6	c	c	X
ejpam-1535	575	7	,	,	PUNCT
ejpam-1535	575	8	⊗	⊗	PROPN
ejpam-1535	575	9	)	)	PUNCT
ejpam-1535	575	10	is	be	AUX
ejpam-1535	575	11	indeed	indeed	ADV
ejpam-1535	575	12	a	a	DET
ejpam-1535	575	13	semigroup	semigroup	NOUN
ejpam-1535	575	14	,	,	PUNCT
ejpam-1535	575	15	by	by	ADP
ejpam-1535	575	16	corollary	corollary	ADJ
ejpam-1535	575	17	2	2	NUM
ejpam-1535	575	18	.	.	PUNCT
ejpam-1535	576	1	we	we	PRON
ejpam-1535	576	2	aim	aim	VERB
ejpam-1535	576	3	to	to	PART
ejpam-1535	576	4	construct	construct	VERB
ejpam-1535	576	5	a	a	DET
ejpam-1535	576	6	restriction	restriction	NOUN
ejpam-1535	576	7	semigroup	semigroup	NOUN
ejpam-1535	576	8	,	,	PUNCT
ejpam-1535	576	9	so	so	SCONJ
ejpam-1535	576	10	we	we	PRON
ejpam-1535	576	11	must	must	AUX
ejpam-1535	576	12	define	define	VERB
ejpam-1535	576	13	a+	a+	PUNCT
ejpam-1535	576	14	and	and	CCONJ
ejpam-1535	576	15	a∗	a∗	PROPN
ejpam-1535	576	16	,	,	PUNCT
ejpam-1535	576	17	for	for	ADP
ejpam-1535	576	18	each	each	PRON
ejpam-1535	576	19	a	a	DET
ejpam-1535	576	20	∈	∈	PROPN
ejpam-1535	576	21	c	c	NOUN
ejpam-1535	576	22	.	.	PUNCT
ejpam-1535	577	1	let	let	VERB
ejpam-1535	577	2	us	we	PRON
ejpam-1535	577	3	put	put	VERB
ejpam-1535	577	4	a+	a+	PUNCT
ejpam-1535	577	5	=	=	SYM
ejpam-1535	577	6	d(a	d(a	PROPN
ejpam-1535	577	7	)	)	PUNCT
ejpam-1535	577	8	and	and	CCONJ
ejpam-1535	577	9	a∗	a∗	PROPN
ejpam-1535	577	10	=	=	SYM
ejpam-1535	577	11	r(a	r(a	PROPN
ejpam-1535	577	12	)	)	PUNCT
ejpam-1535	577	13	.	.	PUNCT
ejpam-1535	578	1	we	we	PRON
ejpam-1535	578	2	must	must	AUX
ejpam-1535	578	3	now	now	ADV
ejpam-1535	578	4	show	show	VERB
ejpam-1535	578	5	that	that	SCONJ
ejpam-1535	578	6	a∗	a∗	PROPN
ejpam-1535	578	7	is	be	AUX
ejpam-1535	578	8	in	in	ADP
ejpam-1535	578	9	fact	fact	NOUN
ejpam-1535	578	10	the	the	DET
ejpam-1535	578	11	unique	unique	ADJ
ejpam-1535	578	12	idempotent	idempotent	NOUN
ejpam-1535	578	13	in	in	ADP
ejpam-1535	578	14	the	the	DET
ejpam-1535	578	15	flco	flco	ADJ
ejpam-1535	578	16	-class	-class	NOUN
ejpam-1535	578	17	of	of	ADP
ejpam-1535	578	18	a	a	PRON
ejpam-1535	578	19	,	,	PUNCT
ejpam-1535	578	20	and	and	CCONJ
ejpam-1535	578	21	that	that	PRON
ejpam-1535	578	22	a+	a+	PUNCT
ejpam-1535	578	23	is	be	AUX
ejpam-1535	578	24	the	the	DET
ejpam-1535	578	25	unique	unique	ADJ
ejpam-1535	578	26	idempotent	idempotent	NOUN
ejpam-1535	578	27	in	in	ADP
ejpam-1535	578	28	the	the	DET
ejpam-1535	578	29	erco	erco	NOUN
ejpam-1535	578	30	-class	-class	PROPN
ejpam-1535	578	31	of	of	ADP
ejpam-1535	578	32	a.	a.	NOUN
ejpam-1535	578	33	we	we	PRON
ejpam-1535	578	34	have	have	VERB
ejpam-1535	578	35	a⊗	a⊗	NOUN
ejpam-1535	578	36	a∗	a∗	PROPN
ejpam-1535	578	37	=	=	SYM
ejpam-1535	578	38	a|a∗	a|a∗	ADJ
ejpam-1535	578	39	∧	∧	PROPN
ejpam-1535	578	40	a∗	a∗	NOUN
ejpam-1535	578	41	=	=	SYM
ejpam-1535	578	42	a|a∗	a|a∗	PROPN
ejpam-1535	578	43	=	=	SYM
ejpam-1535	578	44	a	a	PRON
ejpam-1535	578	45	,	,	PUNCT
ejpam-1535	578	46	by	by	ADP
ejpam-1535	578	47	lemmas	lemmas	PROPN
ejpam-1535	578	48	1(a	1(a	NUM
ejpam-1535	578	49	)	)	PUNCT
ejpam-1535	578	50	and	and	CCONJ
ejpam-1535	578	51	9	9	NUM
ejpam-1535	578	52	.	.	PUNCT
ejpam-1535	579	1	thus	thus	ADV
ejpam-1535	579	2	a∗	a∗	PROPN
ejpam-1535	579	3	is	be	AUX
ejpam-1535	579	4	a	a	DET
ejpam-1535	579	5	right	right	ADJ
ejpam-1535	579	6	identity	identity	NOUN
ejpam-1535	579	7	for	for	ADP
ejpam-1535	579	8	a.	a.	NOUN
ejpam-1535	579	9	suppose	suppose	VERB
ejpam-1535	579	10	now	now	ADV
ejpam-1535	579	11	that	that	SCONJ
ejpam-1535	579	12	a	a	DET
ejpam-1535	579	13	⊗	⊗	PROPN
ejpam-1535	579	14	e	e	NOUN
ejpam-1535	579	15	=	=	PUNCT
ejpam-1535	579	16	a	a	X
ejpam-1535	579	17	,	,	PUNCT
ejpam-1535	579	18	for	for	ADP
ejpam-1535	579	19	some	some	DET
ejpam-1535	579	20	e	e	NOUN
ejpam-1535	579	21	∈	∈	PROPN
ejpam-1535	579	22	so	so	ADV
ejpam-1535	579	23	.	.	PUNCT
ejpam-1535	580	1	we	we	PRON
ejpam-1535	580	2	need	need	VERB
ejpam-1535	580	3	to	to	PART
ejpam-1535	580	4	show	show	VERB
ejpam-1535	580	5	that	that	SCONJ
ejpam-1535	580	6	a∗	a∗	PROPN
ejpam-1535	580	7	⊗	⊗	PROPN
ejpam-1535	580	8	e	e	NOUN
ejpam-1535	580	9	=	=	NOUN
ejpam-1535	580	10	a∗.	a∗.	NOUN
ejpam-1535	580	11	by	by	ADP
ejpam-1535	580	12	lemma	lemma	PROPN
ejpam-1535	580	13	9	9	NUM
ejpam-1535	580	14	,	,	PUNCT
ejpam-1535	580	15	we	we	PRON
ejpam-1535	580	16	have	have	VERB
ejpam-1535	580	17	a⊗	a⊗	NOUN
ejpam-1535	580	18	e	e	NOUN
ejpam-1535	580	19	=	=	SYM
ejpam-1535	580	20	a|a∗	a|a∗	PROPN
ejpam-1535	580	21	∧	∧	PROPN
ejpam-1535	580	22	e	e	NOUN
ejpam-1535	580	23	=	=	NOUN
ejpam-1535	580	24	a.	a.	NOUN
ejpam-1535	580	25	by	by	ADP
ejpam-1535	580	26	applying	apply	VERB
ejpam-1535	580	27	∗	∗	NOUN
ejpam-1535	580	28	to	to	ADP
ejpam-1535	580	29	both	both	DET
ejpam-1535	580	30	sides	side	NOUN
ejpam-1535	580	31	,	,	PUNCT
ejpam-1535	580	32	we	we	PRON
ejpam-1535	580	33	obtain	obtain	VERB
ejpam-1535	580	34	[	[	PUNCT
ejpam-1535	580	35	a|a∗	a|a∗	ADJ
ejpam-1535	580	36	∧	∧	PROPN
ejpam-1535	580	37	e]∗	e]∗	NOUN
ejpam-1535	580	38	=	=	SYM
ejpam-1535	580	39	a∗	a∗	PROPN
ejpam-1535	580	40	,	,	PUNCT
ejpam-1535	580	41	whence	whence	ADP
ejpam-1535	580	42	a∗	a∗	PROPN
ejpam-1535	580	43	∧	∧	PROPN
ejpam-1535	580	44	e	e	NOUN
ejpam-1535	580	45	=	=	NOUN
ejpam-1535	580	46	a∗.	a∗.	NOUN
ejpam-1535	580	47	then	then	ADV
ejpam-1535	580	48	a∗	a∗	PROPN
ejpam-1535	580	49	⊗	⊗	PROPN
ejpam-1535	580	50	e	e	PROPN
ejpam-1535	580	51	=	=	SYM
ejpam-1535	580	52	a∗|a∗	a∗|a∗	PROPN
ejpam-1535	580	53	∧	∧	NOUN
ejpam-1535	580	54	e	e	NOUN
ejpam-1535	580	55	=	=	SYM
ejpam-1535	580	56	a∗|a∗	a∗|a∗	PROPN
ejpam-1535	580	57	=	=	SYM
ejpam-1535	580	58	a∗	a∗	NOUN
ejpam-1535	580	59	,	,	PUNCT
ejpam-1535	580	60	as	as	SCONJ
ejpam-1535	580	61	required	require	VERB
ejpam-1535	580	62	.	.	PUNCT
ejpam-1535	581	1	therefore	therefore	ADV
ejpam-1535	581	2	a∗	a∗	PROPN
ejpam-1535	581	3	flco	flco	VERB
ejpam-1535	581	4	a.	a.	NOUN
ejpam-1535	581	5	it	it	PRON
ejpam-1535	581	6	may	may	AUX
ejpam-1535	581	7	be	be	AUX
ejpam-1535	581	8	shown	show	VERB
ejpam-1535	581	9	in	in	ADP
ejpam-1535	581	10	a	a	DET
ejpam-1535	581	11	similar	similar	ADJ
ejpam-1535	581	12	way	way	NOUN
ejpam-1535	581	13	that	that	PRON
ejpam-1535	581	14	a+	a+	PUNCT
ejpam-1535	581	15	is	be	AUX
ejpam-1535	581	16	erco	erco	PROPN
ejpam-1535	581	17	-related	-relate	VERB
ejpam-1535	581	18	to	to	ADP
ejpam-1535	581	19	a.	a.	NOUN
ejpam-1535	581	20	we	we	PRON
ejpam-1535	581	21	now	now	ADV
ejpam-1535	581	22	show	show	VERB
ejpam-1535	581	23	that	that	SCONJ
ejpam-1535	581	24	idempotents	idempotent	NOUN
ejpam-1535	581	25	in	in	ADP
ejpam-1535	581	26	co	co	NOUN
ejpam-1535	581	27	commute	commute	NOUN
ejpam-1535	581	28	(	(	PUNCT
ejpam-1535	581	29	with	with	ADP
ejpam-1535	581	30	respect	respect	NOUN
ejpam-1535	581	31	to	to	ADP
ejpam-1535	581	32	⊗	⊗	PROPN
ejpam-1535	581	33	)	)	PUNCT
ejpam-1535	581	34	;	;	PUNCT
ejpam-1535	581	35	it	it	PRON
ejpam-1535	581	36	will	will	AUX
ejpam-1535	581	37	then	then	ADV
ejpam-1535	581	38	follow	follow	VERB
ejpam-1535	581	39	that	that	SCONJ
ejpam-1535	581	40	the	the	DET
ejpam-1535	581	41	idempotents	idempotent	NOUN
ejpam-1535	581	42	a+	a+	PUNCT
ejpam-1535	581	43	and	and	CCONJ
ejpam-1535	581	44	a∗	a∗	PROPN
ejpam-1535	581	45	are	be	AUX
ejpam-1535	581	46	the	the	DET
ejpam-1535	581	47	unique	unique	ADJ
ejpam-1535	581	48	idempotents	idempotent	NOUN
ejpam-1535	581	49	in	in	ADP
ejpam-1535	581	50	the	the	DET
ejpam-1535	581	51	erco	erco	NOUN
ejpam-1535	581	52	and	and	CCONJ
ejpam-1535	581	53	flco	flco	VERB
ejpam-1535	581	54	-classes	-classe	NOUN
ejpam-1535	581	55	of	of	ADP
ejpam-1535	581	56	a	a	PRON
ejpam-1535	581	57	,	,	PUNCT
ejpam-1535	581	58	respectively	respectively	ADV
ejpam-1535	581	59	.	.	PUNCT
ejpam-1535	582	1	let	let	VERB
ejpam-1535	582	2	e	e	NOUN
ejpam-1535	582	3	,	,	PUNCT
ejpam-1535	582	4	f	f	PROPN
ejpam-1535	582	5	∈	∈	PROPN
ejpam-1535	582	6	co.	co.	PROPN
ejpam-1535	582	7	then	then	ADV
ejpam-1535	582	8	e⊗	e⊗	PROPN
ejpam-1535	583	1	f	f	PROPN
ejpam-1535	584	1	=	=	PROPN
ejpam-1535	585	1	[	[	X
ejpam-1535	585	2	e|e	e|e	X
ejpam-1535	585	3	∧	∧	PROPN
ejpam-1535	585	4	f	f	X
ejpam-1535	585	5	]	]	PUNCT
ejpam-1535	585	6	·	·	PUNCT
ejpam-1535	586	1	[	[	X
ejpam-1535	586	2	e	e	X
ejpam-1535	586	3	∧	∧	NOUN
ejpam-1535	586	4	f	f	PROPN
ejpam-1535	587	1	|	|	NOUN
ejpam-1535	587	2	f	f	X
ejpam-1535	587	3	]	]	PUNCT
ejpam-1535	587	4	.	.	PUNCT
ejpam-1535	588	1	note	note	VERB
ejpam-1535	588	2	that	that	SCONJ
ejpam-1535	588	3	e|e	e|e	PROPN
ejpam-1535	588	4	∧	∧	PROPN
ejpam-1535	588	5	f	f	PROPN
ejpam-1535	588	6	=	=	SYM
ejpam-1535	588	7	e	e	PROPN
ejpam-1535	588	8	∧	∧	PROPN
ejpam-1535	588	9	f	f	PROPN
ejpam-1535	588	10	=	=	SYM
ejpam-1535	588	11	e	e	PROPN
ejpam-1535	588	12	∧	∧	PROPN
ejpam-1535	588	13	f	f	PROPN
ejpam-1535	589	1	|	|	ADV
ejpam-1535	589	2	f	f	PROPN
ejpam-1535	589	3	,	,	PUNCT
ejpam-1535	589	4	by	by	ADP
ejpam-1535	589	5	corollary	corollary	ADJ
ejpam-1535	589	6	1	1	NUM
ejpam-1535	589	7	.	.	PUNCT
ejpam-1535	590	1	thus	thus	ADV
ejpam-1535	590	2	e	e	X
ejpam-1535	590	3	⊗	⊗	PROPN
ejpam-1535	590	4	f	f	PROPN
ejpam-1535	590	5	=	=	PRON
ejpam-1535	591	1	(	(	PUNCT
ejpam-1535	591	2	e	e	X
ejpam-1535	591	3	∧	∧	PROPN
ejpam-1535	591	4	f	f	PROPN
ejpam-1535	591	5	)	)	PUNCT
ejpam-1535	591	6	·	·	PUNCT
ejpam-1535	592	1	(	(	PUNCT
ejpam-1535	592	2	e	e	X
ejpam-1535	592	3	∧	∧	PROPN
ejpam-1535	592	4	f	f	PROPN
ejpam-1535	592	5	)	)	PUNCT
ejpam-1535	592	6	=	=	PUNCT
ejpam-1535	592	7	e	e	X
ejpam-1535	592	8	∧	∧	PROPN
ejpam-1535	592	9	f	f	PROPN
ejpam-1535	592	10	.	.	PUNCT
ejpam-1535	593	1	similarly	similarly	ADV
ejpam-1535	593	2	,	,	PUNCT
ejpam-1535	593	3	f	f	PROPN
ejpam-1535	593	4	⊗	⊗	PROPN
ejpam-1535	593	5	e	e	PROPN
ejpam-1535	593	6	=	=	SYM
ejpam-1535	593	7	f	f	PROPN
ejpam-1535	593	8	∧	∧	PROPN
ejpam-1535	593	9	e	e	NOUN
ejpam-1535	593	10	=	=	SYM
ejpam-1535	593	11	e	e	PROPN
ejpam-1535	593	12	∧	∧	PROPN
ejpam-1535	593	13	f	f	PROPN
ejpam-1535	593	14	,	,	PUNCT
ejpam-1535	593	15	hence	hence	ADV
ejpam-1535	593	16	idempotents	idempotent	VERB
ejpam-1535	593	17	in	in	ADP
ejpam-1535	593	18	co	co	NOUN
ejpam-1535	593	19	commute	commute	VERB
ejpam-1535	593	20	with	with	ADP
ejpam-1535	593	21	respect	respect	NOUN
ejpam-1535	593	22	to	to	ADP
ejpam-1535	593	23	⊗.	⊗.	NOUN
ejpam-1535	593	24	we	we	PRON
ejpam-1535	593	25	show	show	VERB
ejpam-1535	593	26	that	that	SCONJ
ejpam-1535	593	27	erco	erco	NOUN
ejpam-1535	593	28	is	be	AUX
ejpam-1535	593	29	a	a	DET
ejpam-1535	593	30	left	left	ADJ
ejpam-1535	593	31	congruence	congruence	NOUN
ejpam-1535	593	32	.	.	PUNCT
ejpam-1535	594	1	first	first	ADV
ejpam-1535	594	2	note	note	VERB
ejpam-1535	594	3	that	that	SCONJ
ejpam-1535	594	4	a	a	DET
ejpam-1535	594	5	erco	erco	NOUN
ejpam-1535	594	6	b	b	PROPN
ejpam-1535	594	7	if	if	SCONJ
ejpam-1535	594	8	and	and	CCONJ
ejpam-1535	594	9	only	only	ADV
ejpam-1535	594	10	if	if	SCONJ
ejpam-1535	594	11	d(a	d(a	PROPN
ejpam-1535	594	12	)	)	PUNCT
ejpam-1535	594	13	=	=	PUNCT
ejpam-1535	594	14	d(b	d(b	PROPN
ejpam-1535	594	15	)	)	PUNCT
ejpam-1535	594	16	.	.	PUNCT
ejpam-1535	595	1	let	let	VERB
ejpam-1535	595	2	a	a	PRON
ejpam-1535	595	3	,	,	PUNCT
ejpam-1535	595	4	b	b	X
ejpam-1535	595	5	∈	∈	PROPN
ejpam-1535	595	6	c	c	AUX
ejpam-1535	595	7	be	be	AUX
ejpam-1535	595	8	such	such	ADJ
ejpam-1535	595	9	that	that	SCONJ
ejpam-1535	595	10	a	a	DET
ejpam-1535	595	11	erco	erco	PROPN
ejpam-1535	595	12	b.	b.	PROPN
ejpam-1535	595	13	for	for	ADP
ejpam-1535	595	14	any	any	DET
ejpam-1535	595	15	c	c	PROPN
ejpam-1535	595	16	∈	∈	PROPN
ejpam-1535	595	17	c	c	NOUN
ejpam-1535	595	18	,	,	PUNCT
ejpam-1535	595	19	we	we	PRON
ejpam-1535	595	20	have	have	VERB
ejpam-1535	595	21	d(c	d(c	PROPN
ejpam-1535	595	22	⊗	⊗	PROPN
ejpam-1535	595	23	a	a	NOUN
ejpam-1535	595	24	)	)	PUNCT
ejpam-1535	596	1	=	=	SYM
ejpam-1535	596	2	d	d	PROPN
ejpam-1535	596	3	(	(	PUNCT
ejpam-1535	596	4	c|r(c)∧	c|r(c)∧	PROPN
ejpam-1535	596	5	d(a	d(a	PROPN
ejpam-1535	596	6	)	)	PUNCT
ejpam-1535	596	7	)	)	PUNCT
ejpam-1535	597	1	=	=	PUNCT
ejpam-1535	597	2	d	d	PROPN
ejpam-1535	597	3	(	(	PUNCT
ejpam-1535	597	4	c|r(c)∧	c|r(c)∧	NUM
ejpam-1535	597	5	d(b	d(b	PROPN
ejpam-1535	597	6	)	)	PUNCT
ejpam-1535	597	7	)	)	PUNCT
ejpam-1535	598	1	=	=	SYM
ejpam-1535	599	1	d(c	d(c	PROPN
ejpam-1535	599	2	⊗	⊗	PROPN
ejpam-1535	599	3	b	b	PROPN
ejpam-1535	599	4	)	)	PUNCT
ejpam-1535	599	5	.	.	PUNCT
ejpam-1535	600	1	hence	hence	ADV
ejpam-1535	600	2	c	c	PROPN
ejpam-1535	600	3	⊗	⊗	PROPN
ejpam-1535	600	4	a	a	DET
ejpam-1535	600	5	erco	erco	NOUN
ejpam-1535	600	6	c	c	PROPN
ejpam-1535	600	7	⊗	⊗	PROPN
ejpam-1535	600	8	b	b	PROPN
ejpam-1535	600	9	,	,	PUNCT
ejpam-1535	600	10	i.e.	i.e.	X
ejpam-1535	600	11	,	,	PUNCT
ejpam-1535	600	12	erco	erco	NOUN
ejpam-1535	600	13	is	be	AUX
ejpam-1535	600	14	a	a	DET
ejpam-1535	600	15	left	left	ADJ
ejpam-1535	600	16	congruence	congruence	NOUN
ejpam-1535	600	17	.	.	PUNCT
ejpam-1535	601	1	it	it	PRON
ejpam-1535	601	2	may	may	AUX
ejpam-1535	601	3	be	be	AUX
ejpam-1535	601	4	shown	show	VERB
ejpam-1535	601	5	in	in	ADP
ejpam-1535	601	6	a	a	DET
ejpam-1535	601	7	similar	similar	ADJ
ejpam-1535	601	8	way	way	NOUN
ejpam-1535	601	9	that	that	PRON
ejpam-1535	601	10	flco	flco	VERB
ejpam-1535	601	11	is	be	AUX
ejpam-1535	601	12	a	a	DET
ejpam-1535	601	13	right	right	ADJ
ejpam-1535	601	14	congruence	congruence	NOUN
ejpam-1535	601	15	.	.	PUNCT
ejpam-1535	602	1	we	we	PRON
ejpam-1535	602	2	must	must	AUX
ejpam-1535	602	3	show	show	VERB
ejpam-1535	602	4	that	that	SCONJ
ejpam-1535	602	5	the	the	DET
ejpam-1535	602	6	ample	ample	ADJ
ejpam-1535	602	7	identities	identity	NOUN
ejpam-1535	602	8	hold	hold	VERB
ejpam-1535	602	9	:	:	PUNCT
ejpam-1535	602	10	a⊗	a⊗	NOUN
ejpam-1535	602	11	e	e	NOUN
ejpam-1535	603	1	=	=	PUNCT
ejpam-1535	603	2	(	(	PUNCT
ejpam-1535	603	3	a⊗	a⊗	NOUN
ejpam-1535	603	4	e)+⊗	e)+⊗	PROPN
ejpam-1535	603	5	a	a	PROPN
ejpam-1535	603	6	and	and	CCONJ
ejpam-1535	603	7	e⊗	e⊗	PROPN
ejpam-1535	603	8	a	a	DET
ejpam-1535	603	9	=	=	NOUN
ejpam-1535	603	10	a⊗	a⊗	NOUN
ejpam-1535	603	11	(	(	PUNCT
ejpam-1535	603	12	e⊗	e⊗	PROPN
ejpam-1535	603	13	a)∗.	a)∗.	PROPN
ejpam-1535	603	14	we	we	PRON
ejpam-1535	603	15	consider	consider	VERB
ejpam-1535	603	16	the	the	DET
ejpam-1535	603	17	+	+	NOUN
ejpam-1535	603	18	identity	identity	NOUN
ejpam-1535	603	19	.	.	PUNCT
ejpam-1535	604	1	by	by	ADP
ejpam-1535	604	2	lemma	lemma	PROPN
ejpam-1535	604	3	9	9	NUM
ejpam-1535	604	4	,	,	PUNCT
ejpam-1535	604	5	a⊗	a⊗	NOUN
ejpam-1535	604	6	e	e	NOUN
ejpam-1535	604	7	=	=	PUNCT
ejpam-1535	604	8	a|(a∗	a|(a∗	PUNCT
ejpam-1535	604	9	∧	∧	PROPN
ejpam-1535	604	10	e	e	NOUN
ejpam-1535	604	11	)	)	PUNCT
ejpam-1535	604	12	and	and	CCONJ
ejpam-1535	604	13	(	(	PUNCT
ejpam-1535	604	14	a⊗	a⊗	PROPN
ejpam-1535	604	15	e)+	e)+	PROPN
ejpam-1535	605	1	⊗	⊗	PROPN
ejpam-1535	606	1	a	a	PROPN
ejpam-1535	607	1	=	=	X
ejpam-1535	608	1	[	[	X
ejpam-1535	608	2	(	(	PUNCT
ejpam-1535	608	3	a⊗	a⊗	NOUN
ejpam-1535	608	4	e)+	e)+	PROPN
ejpam-1535	608	5	∧	∧	PROPN
ejpam-1535	608	6	a+]|a	a+]|a	PROPN
ejpam-1535	608	7	=	=	SYM
ejpam-1535	608	8	�	�	PROPN
ejpam-1535	608	9	(	(	PUNCT
ejpam-1535	608	10	a|a∗	a|a∗	PROPN
ejpam-1535	608	11	∧	∧	PROPN
ejpam-1535	608	12	e)+	e)+	NOUN
ejpam-1535	608	13	∧	∧	PROPN
ejpam-1535	608	14	a+	a+	PRON
ejpam-1535	608	15	�	�	PROPN
ejpam-1535	608	16	|a	|a	NOUN
ejpam-1535	608	17	.	.	PUNCT
ejpam-1535	609	1	c.	c.	PROPN
ejpam-1535	609	2	hollings	holling	NOUN
ejpam-1535	609	3	/	/	SYM
ejpam-1535	609	4	eur	eur	PROPN
ejpam-1535	609	5	.	.	PUNCT
ejpam-1535	610	1	j.	j.	PROPN
ejpam-1535	610	2	pure	pure	PROPN
ejpam-1535	610	3	appl	appl	PROPN
ejpam-1535	610	4	.	.	PROPN
ejpam-1535	610	5	math	math	PROPN
ejpam-1535	610	6	,	,	PUNCT
ejpam-1535	610	7	5	5	NUM
ejpam-1535	610	8	(	(	PUNCT
ejpam-1535	610	9	2012	2012	NUM
ejpam-1535	610	10	)	)	PUNCT
ejpam-1535	610	11	,	,	PUNCT
ejpam-1535	610	12	414	414	NUM
ejpam-1535	610	13	-	-	SYM
ejpam-1535	610	14	450	450	NUM
ejpam-1535	610	15	435	435	NUM
ejpam-1535	610	16	since	since	SCONJ
ejpam-1535	610	17	a|a∗	a|a∗	ADJ
ejpam-1535	610	18	∧	∧	PROPN
ejpam-1535	610	19	e	e	PROPN
ejpam-1535	610	20	≤	≤	NOUN
ejpam-1535	610	21	a	a	X
ejpam-1535	610	22	,	,	PUNCT
ejpam-1535	610	23	we	we	PRON
ejpam-1535	610	24	have	have	AUX
ejpam-1535	610	25	[	[	X
ejpam-1535	610	26	a|a∗	a|a∗	ADJ
ejpam-1535	610	27	∧	∧	PROPN
ejpam-1535	610	28	e]+	e]+	PROPN
ejpam-1535	610	29	≤	≤	NOUN
ejpam-1535	610	30	a+	a+	PUNCT
ejpam-1535	610	31	,	,	PUNCT
ejpam-1535	610	32	hence	hence	ADV
ejpam-1535	610	33	�	�	PROPN
ejpam-1535	610	34	(	(	PUNCT
ejpam-1535	610	35	a|a∗	a|a∗	PROPN
ejpam-1535	610	36	∧	∧	PROPN
ejpam-1535	610	37	e)+	e)+	NOUN
ejpam-1535	610	38	∧	∧	PROPN
ejpam-1535	610	39	a+	a+	PRON
ejpam-1535	610	40	�	�	PROPN
ejpam-1535	610	41	|a	|a	X
ejpam-1535	610	42	=	=	SYM
ejpam-1535	610	43	(	(	PUNCT
ejpam-1535	610	44	a|a∗	a|a∗	ADJ
ejpam-1535	610	45	∧	∧	PROPN
ejpam-1535	610	46	e)+|a	e)+|a	NOUN
ejpam-1535	610	47	.	.	PUNCT
ejpam-1535	611	1	so	so	ADV
ejpam-1535	611	2	a⊗	a⊗	NOUN
ejpam-1535	611	3	e	e	NOUN
ejpam-1535	611	4	=	=	SYM
ejpam-1535	611	5	a|a∗	a|a∗	PROPN
ejpam-1535	612	1	∧	∧	PROPN
ejpam-1535	612	2	e	e	NOUN
ejpam-1535	612	3	≤	≤	NOUN
ejpam-1535	612	4	a	a	PRON
ejpam-1535	612	5	and	and	CCONJ
ejpam-1535	612	6	(	(	PUNCT
ejpam-1535	612	7	a⊗	a⊗	NOUN
ejpam-1535	612	8	e)+	e)+	PROPN
ejpam-1535	613	1	⊗	⊗	PROPN
ejpam-1535	613	2	a	a	PROPN
ejpam-1535	613	3	=	=	X
ejpam-1535	613	4	(	(	PUNCT
ejpam-1535	613	5	a|a∗	a|a∗	ADJ
ejpam-1535	613	6	∧	∧	PROPN
ejpam-1535	613	7	e)+|a	e)+|a	NOUN
ejpam-1535	613	8	≤	≤	NUM
ejpam-1535	613	9	a.	a.	NOUN
ejpam-1535	613	10	also	also	ADV
ejpam-1535	613	11	,	,	PUNCT
ejpam-1535	613	12	[	[	X
ejpam-1535	613	13	(	(	PUNCT
ejpam-1535	613	14	a⊗	a⊗	PROPN
ejpam-1535	613	15	e)+	e)+	PROPN
ejpam-1535	614	1	⊗	⊗	PROPN
ejpam-1535	614	2	a]+	a]+	PROPN
ejpam-1535	614	3	=	=	SYM
ejpam-1535	614	4	�	�	PROPN
ejpam-1535	614	5	(	(	PUNCT
ejpam-1535	614	6	a|a∗	a|a∗	ADJ
ejpam-1535	614	7	∧	∧	PROPN
ejpam-1535	614	8	e)+|a	e)+|a	NOUN
ejpam-1535	614	9	�	�	PROPN
ejpam-1535	614	10	+	+	NOUN
ejpam-1535	614	11	=	=	SYM
ejpam-1535	615	1	[	[	X
ejpam-1535	615	2	a|a∗	a|a∗	ADJ
ejpam-1535	615	3	∧	∧	PROPN
ejpam-1535	615	4	e]+	e]+	NOUN
ejpam-1535	615	5	=	=	SYM
ejpam-1535	615	6	(	(	PUNCT
ejpam-1535	615	7	a⊗	a⊗	PROPN
ejpam-1535	615	8	e)+	e)+	PROPN
ejpam-1535	615	9	.	.	PUNCT
ejpam-1535	616	1	thus	thus	ADV
ejpam-1535	616	2	,	,	PUNCT
ejpam-1535	616	3	by	by	ADP
ejpam-1535	616	4	lemma	lemma	PROPN
ejpam-1535	616	5	5(c	5(c	NUM
ejpam-1535	616	6	)	)	PUNCT
ejpam-1535	616	7	,	,	PUNCT
ejpam-1535	616	8	a⊗	a⊗	NOUN
ejpam-1535	616	9	e	e	NOUN
ejpam-1535	616	10	=	=	PUNCT
ejpam-1535	616	11	(	(	PUNCT
ejpam-1535	616	12	a⊗	a⊗	PROPN
ejpam-1535	616	13	e)+	e)+	PROPN
ejpam-1535	616	14	⊗	⊗	PROPN
ejpam-1535	616	15	a	a	PROPN
ejpam-1535	616	16	,	,	PUNCT
ejpam-1535	616	17	hence	hence	ADV
ejpam-1535	616	18	(	(	PUNCT
ejpam-1535	616	19	c	c	NOUN
ejpam-1535	616	20	,	,	PUNCT
ejpam-1535	616	21	⊗	⊗	PROPN
ejpam-1535	616	22	)	)	PUNCT
ejpam-1535	616	23	is	be	AUX
ejpam-1535	616	24	a	a	DET
ejpam-1535	616	25	left	left	ADJ
ejpam-1535	616	26	restriction	restriction	NOUN
ejpam-1535	616	27	semigroup	semigroup	NOUN
ejpam-1535	616	28	with	with	ADP
ejpam-1535	616	29	respect	respect	NOUN
ejpam-1535	616	30	to	to	ADP
ejpam-1535	616	31	co.	co.	PROPN
ejpam-1535	616	32	the	the	DET
ejpam-1535	616	33	∗	∗	NOUN
ejpam-1535	616	34	identity	identity	NOUN
ejpam-1535	616	35	is	be	AUX
ejpam-1535	616	36	shown	show	VERB
ejpam-1535	616	37	in	in	ADP
ejpam-1535	616	38	a	a	DET
ejpam-1535	616	39	similar	similar	ADJ
ejpam-1535	616	40	way	way	NOUN
ejpam-1535	616	41	.	.	PUNCT
ejpam-1535	617	1	we	we	PRON
ejpam-1535	617	2	finally	finally	ADV
ejpam-1535	617	3	confirm	confirm	VERB
ejpam-1535	617	4	that	that	SCONJ
ejpam-1535	617	5	the	the	DET
ejpam-1535	617	6	ordering≤	ordering≤	PROPN
ejpam-1535	617	7	in	in	ADP
ejpam-1535	617	8	the	the	DET
ejpam-1535	617	9	original	original	ADJ
ejpam-1535	617	10	inductive	inductive	ADJ
ejpam-1535	617	11	category	category	NOUN
ejpam-1535	617	12	becomes	become	VERB
ejpam-1535	617	13	the	the	DET
ejpam-1535	617	14	usual	usual	ADJ
ejpam-1535	617	15	ordering	ordering	NOUN
ejpam-1535	617	16	(	(	PUNCT
ejpam-1535	617	17	4	4	NUM
ejpam-1535	617	18	)	)	PUNCT
ejpam-1535	617	19	of	of	ADP
ejpam-1535	617	20	a	a	DET
ejpam-1535	617	21	restriction	restriction	NOUN
ejpam-1535	617	22	semigroup	semigroup	NOUN
ejpam-1535	617	23	in	in	ADP
ejpam-1535	617	24	(	(	PUNCT
ejpam-1535	617	25	c	c	PROPN
ejpam-1535	617	26	,	,	PUNCT
ejpam-1535	617	27	⊗	⊗	PROPN
ejpam-1535	617	28	)	)	PUNCT
ejpam-1535	617	29	.	.	PUNCT
ejpam-1535	618	1	suppose	suppose	VERB
ejpam-1535	618	2	that	that	SCONJ
ejpam-1535	618	3	a	a	DET
ejpam-1535	618	4	≤	≤	PROPN
ejpam-1535	618	5	b.	b.	NOUN
ejpam-1535	618	6	then	then	ADV
ejpam-1535	618	7	d(a	d(a	PROPN
ejpam-1535	618	8	)	)	PUNCT
ejpam-1535	618	9	≤	≤	NOUN
ejpam-1535	618	10	d(b	d(b	PROPN
ejpam-1535	618	11	)	)	PUNCT
ejpam-1535	618	12	,	,	PUNCT
ejpam-1535	618	13	by	by	ADP
ejpam-1535	618	14	(	(	PUNCT
ejpam-1535	618	15	or2	or2	PROPN
ejpam-1535	618	16	)	)	PUNCT
ejpam-1535	618	17	.	.	PUNCT
ejpam-1535	619	1	also	also	ADV
ejpam-1535	619	2	,	,	PUNCT
ejpam-1535	619	3	by	by	ADP
ejpam-1535	619	4	lemma	lemma	PROPN
ejpam-1535	619	5	5(a	5(a	NUM
ejpam-1535	619	6	)	)	PUNCT
ejpam-1535	619	7	,	,	PUNCT
ejpam-1535	619	8	a	a	DET
ejpam-1535	619	9	=	=	X
ejpam-1535	619	10	d(a)|b	d(a)|b	PROPN
ejpam-1535	619	11	.	.	PUNCT
ejpam-1535	620	1	consider	consider	VERB
ejpam-1535	620	2	a+⊗	a+⊗	PROPN
ejpam-1535	620	3	b.	b.	PROPN
ejpam-1535	620	4	by	by	ADP
ejpam-1535	620	5	lemma	lemma	PROPN
ejpam-1535	620	6	9	9	NUM
ejpam-1535	620	7	,	,	PUNCT
ejpam-1535	620	8	we	we	PRON
ejpam-1535	620	9	have	have	VERB
ejpam-1535	620	10	a+	a+	PUNCT
ejpam-1535	621	1	⊗	⊗	PROPN
ejpam-1535	621	2	b	b	X
ejpam-1535	621	3	=	=	SYM
ejpam-1535	621	4	d(a)⊗	d(a)⊗	NOUN
ejpam-1535	621	5	b	b	NOUN
ejpam-1535	622	1	=	=	PUNCT
ejpam-1535	622	2	d(a)∧	d(a)∧	NOUN
ejpam-1535	622	3	d(b)|b	d(b)|b	PROPN
ejpam-1535	622	4	=	=	SYM
ejpam-1535	622	5	d(a)|b	d(a)|b	PROPN
ejpam-1535	622	6	,	,	PUNCT
ejpam-1535	622	7	so	so	ADV
ejpam-1535	622	8	a	a	DET
ejpam-1535	622	9	=	=	X
ejpam-1535	622	10	a+⊗	a+⊗	NOUN
ejpam-1535	622	11	b	b	NOUN
ejpam-1535	622	12	,	,	PUNCT
ejpam-1535	622	13	as	as	SCONJ
ejpam-1535	622	14	required	require	VERB
ejpam-1535	622	15	.	.	PUNCT
ejpam-1535	623	1	now	now	ADV
ejpam-1535	623	2	suppose	suppose	VERB
ejpam-1535	623	3	that	that	SCONJ
ejpam-1535	623	4	a	a	DET
ejpam-1535	623	5	≤	≤	PROPN
ejpam-1535	623	6	b	b	NOUN
ejpam-1535	623	7	in	in	X
ejpam-1535	623	8	(	(	PUNCT
ejpam-1535	623	9	c	c	NOUN
ejpam-1535	623	10	,	,	PUNCT
ejpam-1535	623	11	⊗	⊗	PROPN
ejpam-1535	623	12	)	)	PUNCT
ejpam-1535	623	13	,	,	PUNCT
ejpam-1535	623	14	so	so	SCONJ
ejpam-1535	623	15	that	that	SCONJ
ejpam-1535	623	16	a	a	DET
ejpam-1535	623	17	=	=	SYM
ejpam-1535	623	18	e	e	PROPN
ejpam-1535	623	19	⊗	⊗	PROPN
ejpam-1535	623	20	b	b	PROPN
ejpam-1535	623	21	,	,	PUNCT
ejpam-1535	623	22	for	for	ADP
ejpam-1535	623	23	some	some	DET
ejpam-1535	623	24	idempotent	idempotent	ADJ
ejpam-1535	623	25	e	e	NOUN
ejpam-1535	623	26	∈	∈	NOUN
ejpam-1535	623	27	e	e	X
ejpam-1535	623	28	=	=	PROPN
ejpam-1535	623	29	co.	co.	PROPN
ejpam-1535	623	30	then	then	ADV
ejpam-1535	623	31	,	,	PUNCT
ejpam-1535	623	32	using	use	VERB
ejpam-1535	623	33	lemma	lemma	PROPN
ejpam-1535	623	34	9	9	NUM
ejpam-1535	623	35	,	,	PUNCT
ejpam-1535	623	36	a	a	DET
ejpam-1535	623	37	=	=	PROPN
ejpam-1535	623	38	e⊗	e⊗	PROPN
ejpam-1535	623	39	b	b	PROPN
ejpam-1535	623	40	=	=	SYM
ejpam-1535	623	41	e	e	PROPN
ejpam-1535	623	42	∧	∧	PROPN
ejpam-1535	623	43	d(b)|b	d(b)|b	PROPN
ejpam-1535	623	44	≤	≤	PROPN
ejpam-1535	623	45	b	b	NOUN
ejpam-1535	623	46	,	,	PUNCT
ejpam-1535	623	47	in	in	ADP
ejpam-1535	623	48	(	(	PUNCT
ejpam-1535	623	49	c	c	NOUN
ejpam-1535	623	50	,	,	PUNCT
ejpam-1535	623	51	·	·	PUNCT
ejpam-1535	623	52	,	,	PUNCT
ejpam-1535	623	53	≤	≤	NUM
ejpam-1535	623	54	)	)	PUNCT
ejpam-1535	623	55	.	.	PUNCT
ejpam-1535	624	1	thus	thus	ADV
ejpam-1535	624	2	(	(	PUNCT
ejpam-1535	624	3	c	c	NOUN
ejpam-1535	624	4	,	,	PUNCT
ejpam-1535	624	5	·	·	PUNCT
ejpam-1535	624	6	,	,	PUNCT
ejpam-1535	624	7	≤	≤	NUM
ejpam-1535	624	8	)	)	PUNCT
ejpam-1535	624	9	and	and	CCONJ
ejpam-1535	624	10	(	(	PUNCT
ejpam-1535	624	11	c	c	PROPN
ejpam-1535	624	12	,	,	PUNCT
ejpam-1535	624	13	⊗	⊗	PROPN
ejpam-1535	624	14	)	)	PUNCT
ejpam-1535	624	15	have	have	VERB
ejpam-1535	624	16	the	the	DET
ejpam-1535	624	17	same	same	ADJ
ejpam-1535	624	18	ordering	ordering	NOUN
ejpam-1535	624	19	.	.	PUNCT
ejpam-1535	625	1	once	once	ADV
ejpam-1535	625	2	again	again	ADV
ejpam-1535	625	3	,	,	PUNCT
ejpam-1535	625	4	we	we	PRON
ejpam-1535	625	5	can	can	AUX
ejpam-1535	625	6	write	write	VERB
ejpam-1535	625	7	down	down	ADP
ejpam-1535	625	8	corollaries	corollary	NOUN
ejpam-1535	625	9	in	in	ADP
ejpam-1535	625	10	the	the	DET
ejpam-1535	625	11	full	full	ADJ
ejpam-1535	625	12	restriction	restriction	NOUN
ejpam-1535	625	13	and	and	CCONJ
ejpam-1535	625	14	ample	ample	ADJ
ejpam-1535	625	15	cases	case	NOUN
ejpam-1535	625	16	:	:	PUNCT
ejpam-1535	625	17	corollary	corollary	ADJ
ejpam-1535	625	18	5	5	NUM
ejpam-1535	625	19	(	(	PUNCT
ejpam-1535	625	20	[	[	X
ejpam-1535	625	21	26	26	NUM
ejpam-1535	625	22	,	,	PUNCT
ejpam-1535	625	23	theorem	theorem	ADJ
ejpam-1535	625	24	3.15(ii	3.15(ii	NUM
ejpam-1535	625	25	)	)	PUNCT
ejpam-1535	625	26	]	]	PUNCT
ejpam-1535	625	27	)	)	PUNCT
ejpam-1535	625	28	.	.	PUNCT
ejpam-1535	626	1	if	if	SCONJ
ejpam-1535	626	2	(	(	PUNCT
ejpam-1535	626	3	c	c	NOUN
ejpam-1535	626	4	,	,	PUNCT
ejpam-1535	626	5	·	·	PUNCT
ejpam-1535	626	6	,	,	PUNCT
ejpam-1535	626	7	≤	≤	NUM
ejpam-1535	626	8	)	)	PUNCT
ejpam-1535	626	9	is	be	AUX
ejpam-1535	626	10	an	an	DET
ejpam-1535	626	11	inductive	inductive	ADJ
ejpam-1535	626	12	unipotent	unipotent	ADJ
ejpam-1535	626	13	category	category	NOUN
ejpam-1535	626	14	,	,	PUNCT
ejpam-1535	626	15	then	then	ADV
ejpam-1535	626	16	(	(	PUNCT
ejpam-1535	626	17	c	c	X
ejpam-1535	626	18	,	,	PUNCT
ejpam-1535	626	19	⊗	⊗	PROPN
ejpam-1535	626	20	)	)	PUNCT
ejpam-1535	626	21	is	be	AUX
ejpam-1535	626	22	a	a	DET
ejpam-1535	626	23	full	full	ADJ
ejpam-1535	626	24	restriction	restriction	NOUN
ejpam-1535	626	25	semigroup	semigroup	NOUN
ejpam-1535	626	26	.	.	PUNCT
ejpam-1535	627	1	proof	proof	NOUN
ejpam-1535	627	2	.	.	PUNCT
ejpam-1535	628	1	this	this	PRON
ejpam-1535	628	2	follows	follow	VERB
ejpam-1535	628	3	easily	easily	ADV
ejpam-1535	628	4	from	from	ADP
ejpam-1535	628	5	the	the	DET
ejpam-1535	628	6	fact	fact	NOUN
ejpam-1535	628	7	that	that	SCONJ
ejpam-1535	628	8	the	the	DET
ejpam-1535	628	9	only	only	ADJ
ejpam-1535	628	10	idempotents	idempotent	NOUN
ejpam-1535	628	11	in	in	ADP
ejpam-1535	628	12	the	the	DET
ejpam-1535	628	13	category	category	NOUN
ejpam-1535	628	14	are	be	AUX
ejpam-1535	628	15	its	its	PRON
ejpam-1535	628	16	identities	identity	NOUN
ejpam-1535	628	17	.	.	PUNCT
ejpam-1535	629	1	corollary	corollary	ADJ
ejpam-1535	629	2	6	6	NUM
ejpam-1535	629	3	(	(	PUNCT
ejpam-1535	629	4	[	[	X
ejpam-1535	629	5	1	1	NUM
ejpam-1535	629	6	,	,	PUNCT
ejpam-1535	629	7	theorem	theorem	VERB
ejpam-1535	629	8	3.9	3.9	NUM
ejpam-1535	629	9	]	]	PUNCT
ejpam-1535	629	10	)	)	PUNCT
ejpam-1535	629	11	.	.	PUNCT
ejpam-1535	630	1	if	if	SCONJ
ejpam-1535	630	2	(	(	PUNCT
ejpam-1535	630	3	c	c	NOUN
ejpam-1535	630	4	,	,	PUNCT
ejpam-1535	630	5	·	·	PUNCT
ejpam-1535	630	6	,	,	PUNCT
ejpam-1535	630	7	≤	≤	NUM
ejpam-1535	630	8	)	)	PUNCT
ejpam-1535	630	9	is	be	AUX
ejpam-1535	630	10	an	an	DET
ejpam-1535	630	11	inductive	inductive	ADJ
ejpam-1535	630	12	cancellative	cancellative	ADJ
ejpam-1535	630	13	category	category	NOUN
ejpam-1535	630	14	,	,	PUNCT
ejpam-1535	630	15	then	then	ADV
ejpam-1535	630	16	(	(	PUNCT
ejpam-1535	630	17	c	c	X
ejpam-1535	630	18	,	,	PUNCT
ejpam-1535	630	19	⊗	⊗	PROPN
ejpam-1535	630	20	)	)	PUNCT
ejpam-1535	630	21	is	be	AUX
ejpam-1535	630	22	an	an	DET
ejpam-1535	630	23	ample	ample	ADJ
ejpam-1535	630	24	semigroup	semigroup	NOUN
ejpam-1535	630	25	.	.	PUNCT
ejpam-1535	631	1	proof	proof	NOUN
ejpam-1535	631	2	.	.	PUNCT
ejpam-1535	632	1	by	by	ADP
ejpam-1535	632	2	corollary	corollary	ADJ
ejpam-1535	632	3	5	5	NUM
ejpam-1535	632	4	,	,	PUNCT
ejpam-1535	632	5	(	(	PUNCT
ejpam-1535	632	6	c	c	X
ejpam-1535	632	7	,	,	PUNCT
ejpam-1535	632	8	⊗	⊗	PROPN
ejpam-1535	632	9	)	)	PUNCT
ejpam-1535	632	10	is	be	AUX
ejpam-1535	632	11	a	a	DET
ejpam-1535	632	12	full	full	ADJ
ejpam-1535	632	13	restriction	restriction	NOUN
ejpam-1535	632	14	semigroup	semigroup	NOUN
ejpam-1535	632	15	.	.	PUNCT
ejpam-1535	633	1	it	it	PRON
ejpam-1535	633	2	only	only	ADV
ejpam-1535	633	3	remains	remain	VERB
ejpam-1535	633	4	to	to	PART
ejpam-1535	633	5	prove	prove	VERB
ejpam-1535	633	6	that	that	SCONJ
ejpam-1535	633	7	a∗	a∗	PROPN
ejpam-1535	633	8	=	=	SYM
ejpam-1535	633	9	r(a	r(a	PROPN
ejpam-1535	633	10	)	)	PUNCT
ejpam-1535	633	11	is	be	AUX
ejpam-1535	633	12	the	the	DET
ejpam-1535	633	13	unique	unique	ADJ
ejpam-1535	633	14	idempotent	idempotent	NOUN
ejpam-1535	633	15	which	which	PRON
ejpam-1535	633	16	is	be	AUX
ejpam-1535	633	17	l	l	NOUN
ejpam-1535	633	18	∗-related	∗-relate	VERB
ejpam-1535	633	19	to	to	ADP
ejpam-1535	633	20	a	a	PRON
ejpam-1535	633	21	and	and	CCONJ
ejpam-1535	633	22	that	that	SCONJ
ejpam-1535	633	23	a+	a+	PUNCT
ejpam-1535	633	24	=	=	SYM
ejpam-1535	633	25	d(a	d(a	PROPN
ejpam-1535	633	26	)	)	PUNCT
ejpam-1535	633	27	is	be	AUX
ejpam-1535	633	28	the	the	DET
ejpam-1535	633	29	unique	unique	ADJ
ejpam-1535	633	30	idempotent	idempotent	NOUN
ejpam-1535	633	31	which	which	PRON
ejpam-1535	633	32	is	be	AUX
ejpam-1535	633	33	r∗-related	r∗-relate	VERB
ejpam-1535	633	34	to	to	ADP
ejpam-1535	633	35	a.	a.	NOUN
ejpam-1535	633	36	we	we	PRON
ejpam-1535	633	37	already	already	ADV
ejpam-1535	633	38	know	know	VERB
ejpam-1535	633	39	that	that	SCONJ
ejpam-1535	633	40	a∗	a∗	PROPN
ejpam-1535	633	41	is	be	AUX
ejpam-1535	633	42	a	a	DET
ejpam-1535	633	43	left	left	ADJ
ejpam-1535	633	44	identity	identity	NOUN
ejpam-1535	633	45	for	for	ADP
ejpam-1535	633	46	a	a	PRON
ejpam-1535	633	47	,	,	PUNCT
ejpam-1535	633	48	so	so	ADV
ejpam-1535	633	49	,	,	PUNCT
ejpam-1535	633	50	following	follow	VERB
ejpam-1535	633	51	(	(	PUNCT
ejpam-1535	633	52	5	5	NUM
ejpam-1535	633	53	)	)	PUNCT
ejpam-1535	633	54	,	,	PUNCT
ejpam-1535	633	55	we	we	PRON
ejpam-1535	633	56	need	need	VERB
ejpam-1535	633	57	to	to	PART
ejpam-1535	633	58	prove	prove	VERB
ejpam-1535	633	59	that	that	DET
ejpam-1535	633	60	a⊗	a⊗	NOUN
ejpam-1535	633	61	x	x	X
ejpam-1535	634	1	=	=	PUNCT
ejpam-1535	634	2	a⊗	a⊗	NOUN
ejpam-1535	634	3	y	y	PROPN
ejpam-1535	634	4	=	=	AUX
ejpam-1535	634	5	⇒	⇒	VERB
ejpam-1535	634	6	a∗	a∗	PROPN
ejpam-1535	634	7	⊗	⊗	PROPN
ejpam-1535	634	8	x	x	PUNCT
ejpam-1535	635	1	=	=	PUNCT
ejpam-1535	635	2	a∗⊗	a∗⊗	PROPN
ejpam-1535	635	3	y	y	PROPN
ejpam-1535	635	4	,	,	PUNCT
ejpam-1535	635	5	for	for	ADP
ejpam-1535	635	6	all	all	DET
ejpam-1535	635	7	x	x	SYM
ejpam-1535	635	8	,	,	PUNCT
ejpam-1535	635	9	y	y	PROPN
ejpam-1535	635	10	∈	∈	PROPN
ejpam-1535	635	11	(	(	PUNCT
ejpam-1535	635	12	c	c	NOUN
ejpam-1535	635	13	,	,	PUNCT
ejpam-1535	635	14	⊗)1	⊗)1	NOUN
ejpam-1535	635	15	(	(	PUNCT
ejpam-1535	635	16	that	that	PRON
ejpam-1535	635	17	is	is	ADV
ejpam-1535	635	18	,	,	PUNCT
ejpam-1535	635	19	(	(	PUNCT
ejpam-1535	635	20	c	c	X
ejpam-1535	635	21	,	,	PUNCT
ejpam-1535	635	22	⊗	⊗	PROPN
ejpam-1535	635	23	)	)	PUNCT
ejpam-1535	635	24	with	with	ADP
ejpam-1535	635	25	identity	identity	NOUN
ejpam-1535	635	26	adjoined	adjoin	VERB
ejpam-1535	635	27	)	)	PUNCT
ejpam-1535	635	28	.	.	PUNCT
ejpam-1535	636	1	in	in	ADP
ejpam-1535	636	2	fact	fact	NOUN
ejpam-1535	636	3	,	,	PUNCT
ejpam-1535	636	4	it	it	PRON
ejpam-1535	636	5	is	be	AUX
ejpam-1535	636	6	sufficient	sufficient	ADJ
ejpam-1535	636	7	to	to	PART
ejpam-1535	636	8	show	show	VERB
ejpam-1535	636	9	this	this	PRON
ejpam-1535	636	10	for	for	ADP
ejpam-1535	636	11	x	x	X
ejpam-1535	636	12	,	,	PUNCT
ejpam-1535	636	13	y	y	PROPN
ejpam-1535	636	14	∈	∈	PROPN
ejpam-1535	636	15	(	(	PUNCT
ejpam-1535	636	16	c	c	NOUN
ejpam-1535	636	17	,	,	PUNCT
ejpam-1535	636	18	⊗	⊗	PROPN
ejpam-1535	636	19	)	)	PUNCT
ejpam-1535	636	20	.	.	PUNCT
ejpam-1535	637	1	suppose	suppose	VERB
ejpam-1535	637	2	that	that	SCONJ
ejpam-1535	637	3	a⊗	a⊗	NOUN
ejpam-1535	637	4	x	x	X
ejpam-1535	638	1	=	=	PUNCT
ejpam-1535	638	2	a⊗	a⊗	PROPN
ejpam-1535	638	3	y.	y.	PROPN
ejpam-1535	638	4	then	then	ADV
ejpam-1535	638	5	(	(	PUNCT
ejpam-1535	638	6	a⊗	a⊗	PROPN
ejpam-1535	638	7	x)+	x)+	PROPN
ejpam-1535	638	8	=	=	PUNCT
ejpam-1535	638	9	(	(	PUNCT
ejpam-1535	638	10	a⊗	a⊗	NOUN
ejpam-1535	638	11	y)+	y)+	PROPN
ejpam-1535	638	12	,	,	PUNCT
ejpam-1535	638	13	i.e.	i.e.	X
ejpam-1535	638	14	,	,	PUNCT
ejpam-1535	638	15	�	�	PROPN
ejpam-1535	638	16	(	(	PUNCT
ejpam-1535	638	17	a|a∗	a|a∗	ADJ
ejpam-1535	638	18	∧	∧	PROPN
ejpam-1535	638	19	x+	x+	ADJ
ejpam-1535	638	20	)	)	PUNCT
ejpam-1535	638	21	·	·	PUNCT
ejpam-1535	638	22	(	(	PUNCT
ejpam-1535	638	23	a∗	a∗	PROPN
ejpam-1535	638	24	∧	∧	PROPN
ejpam-1535	638	25	x+|x	x+|x	NOUN
ejpam-1535	638	26	)	)	PUNCT
ejpam-1535	638	27	�	�	PROPN
ejpam-1535	638	28	+	+	SYM
ejpam-1535	638	29	=	=	SYM
ejpam-1535	638	30	�	�	PROPN
ejpam-1535	638	31	(	(	PUNCT
ejpam-1535	638	32	a|a∗	a|a∗	PROPN
ejpam-1535	638	33	∧	∧	PROPN
ejpam-1535	638	34	y+	y+	NOUN
ejpam-1535	638	35	)	)	PUNCT
ejpam-1535	638	36	·	·	PUNCT
ejpam-1535	638	37	(	(	PUNCT
ejpam-1535	638	38	a∗	a∗	PROPN
ejpam-1535	638	39	∧	∧	PROPN
ejpam-1535	638	40	y+|y	y+|y	NOUN
ejpam-1535	638	41	)	)	PUNCT
ejpam-1535	638	42	�	�	PROPN
ejpam-1535	638	43	+	+	NOUN
ejpam-1535	638	44	,	,	PUNCT
ejpam-1535	638	45	c.	c.	PROPN
ejpam-1535	638	46	hollings	holling	NOUN
ejpam-1535	638	47	/	/	SYM
ejpam-1535	638	48	eur	eur	PROPN
ejpam-1535	638	49	.	.	PUNCT
ejpam-1535	639	1	j.	j.	PROPN
ejpam-1535	639	2	pure	pure	PROPN
ejpam-1535	639	3	appl	appl	PROPN
ejpam-1535	639	4	.	.	PROPN
ejpam-1535	639	5	math	math	PROPN
ejpam-1535	639	6	,	,	PUNCT
ejpam-1535	639	7	5	5	NUM
ejpam-1535	639	8	(	(	PUNCT
ejpam-1535	639	9	2012	2012	NUM
ejpam-1535	639	10	)	)	PUNCT
ejpam-1535	639	11	,	,	PUNCT
ejpam-1535	639	12	414	414	NUM
ejpam-1535	639	13	-	-	SYM
ejpam-1535	639	14	450	450	NUM
ejpam-1535	639	15	436	436	NUM
ejpam-1535	639	16	whence	whence	PROPN
ejpam-1535	639	17	�	�	PROPN
ejpam-1535	639	18	a|a∗	a|a∗	PROPN
ejpam-1535	639	19	∧	∧	PROPN
ejpam-1535	639	20	x+	x+	X
ejpam-1535	639	21	�	�	PROPN
ejpam-1535	639	22	+	+	CCONJ
ejpam-1535	639	23	=	=	PUNCT
ejpam-1535	639	24	�	�	PROPN
ejpam-1535	639	25	a|a∗	a|a∗	ADJ
ejpam-1535	639	26	∧	∧	PROPN
ejpam-1535	639	27	y+	y+	NUM
ejpam-1535	639	28	�	�	PROPN
ejpam-1535	639	29	+	+	NUM
ejpam-1535	639	30	,	,	PUNCT
ejpam-1535	639	31	(	(	PUNCT
ejpam-1535	639	32	8)	8)	NUM
ejpam-1535	639	33	by	by	ADP
ejpam-1535	639	34	lemma	lemma	PROPN
ejpam-1535	639	35	3	3	NUM
ejpam-1535	639	36	.	.	PUNCT
ejpam-1535	639	37	notice	notice	VERB
ejpam-1535	639	38	that	that	SCONJ
ejpam-1535	639	39	a|a∗	a|a∗	ADJ
ejpam-1535	639	40	∧	∧	NOUN
ejpam-1535	639	41	x+	x+	PUNCT
ejpam-1535	639	42	≤	≤	PROPN
ejpam-1535	639	43	a	a	DET
ejpam-1535	639	44	and	and	CCONJ
ejpam-1535	639	45	a|a∗	a|a∗	ADJ
ejpam-1535	639	46	∧	∧	PROPN
ejpam-1535	639	47	y+	y+	NUM
ejpam-1535	639	48	≤	≤	NOUN
ejpam-1535	639	49	a	a	DET
ejpam-1535	639	50	so	so	ADV
ejpam-1535	639	51	,	,	PUNCT
ejpam-1535	639	52	using	use	VERB
ejpam-1535	639	53	(	(	PUNCT
ejpam-1535	639	54	8)	8)	NUM
ejpam-1535	639	55	,	,	PUNCT
ejpam-1535	639	56	we	we	PRON
ejpam-1535	639	57	deduce	deduce	VERB
ejpam-1535	639	58	that	that	SCONJ
ejpam-1535	639	59	a|a∗	a|a∗	ADJ
ejpam-1535	639	60	∧	∧	NOUN
ejpam-1535	639	61	x+	x+	X
ejpam-1535	639	62	=	=	SYM
ejpam-1535	639	63	a|a∗	a|a∗	PROPN
ejpam-1535	639	64	∧	∧	PROPN
ejpam-1535	639	65	y+	y+	NOUN
ejpam-1535	639	66	,	,	PUNCT
ejpam-1535	639	67	by	by	ADP
ejpam-1535	639	68	lemma	lemma	PROPN
ejpam-1535	639	69	5(c	5(c	NUM
ejpam-1535	639	70	)	)	PUNCT
ejpam-1535	639	71	.	.	PUNCT
ejpam-1535	640	1	then	then	ADV
ejpam-1535	640	2	a⊗	a⊗	NOUN
ejpam-1535	640	3	x	x	X
ejpam-1535	640	4	=	=	PUNCT
ejpam-1535	641	1	[	[	X
ejpam-1535	641	2	a|a∗	a|a∗	ADJ
ejpam-1535	641	3	∧	∧	NOUN
ejpam-1535	641	4	x+	x+	X
ejpam-1535	641	5	]	]	PUNCT
ejpam-1535	641	6	·	·	PUNCT
ejpam-1535	642	1	[	[	X
ejpam-1535	642	2	a∗	a∗	PROPN
ejpam-1535	642	3	∧	∧	PROPN
ejpam-1535	642	4	x+|x	x+|x	X
ejpam-1535	642	5	]	]	X
ejpam-1535	642	6	=	=	PUNCT
ejpam-1535	643	1	[	[	X
ejpam-1535	643	2	a|a∗	a|a∗	ADJ
ejpam-1535	643	3	∧	∧	NOUN
ejpam-1535	643	4	y+	y+	X
ejpam-1535	643	5	]	]	PUNCT
ejpam-1535	643	6	·	·	PUNCT
ejpam-1535	644	1	[	[	X
ejpam-1535	644	2	a∗	a∗	PROPN
ejpam-1535	644	3	∧	∧	PROPN
ejpam-1535	644	4	x+|x	x+|x	PROPN
ejpam-1535	644	5	]	]	PUNCT
ejpam-1535	644	6	.	.	PUNCT
ejpam-1535	645	1	but	but	CCONJ
ejpam-1535	645	2	a⊗	a⊗	NOUN
ejpam-1535	645	3	x	x	X
ejpam-1535	646	1	=	=	PUNCT
ejpam-1535	646	2	a⊗	a⊗	NOUN
ejpam-1535	646	3	y	y	PROPN
ejpam-1535	646	4	=	=	PUNCT
ejpam-1535	647	1	[	[	X
ejpam-1535	647	2	a|a∗	a|a∗	ADJ
ejpam-1535	647	3	∧	∧	NOUN
ejpam-1535	647	4	y+	y+	X
ejpam-1535	647	5	]	]	PUNCT
ejpam-1535	647	6	·	·	PUNCT
ejpam-1535	648	1	[	[	X
ejpam-1535	648	2	a∗	a∗	PROPN
ejpam-1535	648	3	∧	∧	PROPN
ejpam-1535	648	4	y+|y	y+|y	NOUN
ejpam-1535	648	5	]	]	PUNCT
ejpam-1535	648	6	,	,	PUNCT
ejpam-1535	648	7	by	by	ADP
ejpam-1535	648	8	assumption	assumption	NOUN
ejpam-1535	648	9	,	,	PUNCT
ejpam-1535	648	10	so	so	CCONJ
ejpam-1535	648	11	[	[	X
ejpam-1535	648	12	a|a∗	a|a∗	ADJ
ejpam-1535	648	13	∧	∧	NOUN
ejpam-1535	648	14	y+	y+	X
ejpam-1535	648	15	]	]	PUNCT
ejpam-1535	648	16	·	·	PUNCT
ejpam-1535	649	1	[	[	X
ejpam-1535	649	2	a∗	a∗	PROPN
ejpam-1535	649	3	∧	∧	PROPN
ejpam-1535	649	4	x+|x	x+|x	X
ejpam-1535	649	5	]	]	X
ejpam-1535	649	6	=	=	PUNCT
ejpam-1535	650	1	[	[	X
ejpam-1535	650	2	a|a∗	a|a∗	ADJ
ejpam-1535	650	3	∧	∧	NOUN
ejpam-1535	650	4	y+	y+	X
ejpam-1535	650	5	]	]	PUNCT
ejpam-1535	650	6	·	·	PUNCT
ejpam-1535	651	1	[	[	X
ejpam-1535	651	2	a∗	a∗	PROPN
ejpam-1535	651	3	∧	∧	PROPN
ejpam-1535	651	4	y+|y	y+|y	NOUN
ejpam-1535	651	5	]	]	PUNCT
ejpam-1535	651	6	,	,	PUNCT
ejpam-1535	651	7	whence	whence	ADP
ejpam-1535	651	8	a∗	a∗	PROPN
ejpam-1535	651	9	∧	∧	PROPN
ejpam-1535	651	10	x+|x	x+|x	X
ejpam-1535	651	11	=	=	SYM
ejpam-1535	651	12	a∗	a∗	PROPN
ejpam-1535	651	13	∧	∧	PROPN
ejpam-1535	651	14	y+|y	y+|y	NOUN
ejpam-1535	651	15	,	,	PUNCT
ejpam-1535	651	16	by	by	ADP
ejpam-1535	651	17	cancellation	cancellation	NOUN
ejpam-1535	651	18	.	.	PUNCT
ejpam-1535	652	1	thus	thus	ADV
ejpam-1535	652	2	,	,	PUNCT
ejpam-1535	652	3	using	use	VERB
ejpam-1535	652	4	lemma	lemma	PROPN
ejpam-1535	652	5	9	9	NUM
ejpam-1535	652	6	,	,	PUNCT
ejpam-1535	652	7	a∗	a∗	PROPN
ejpam-1535	652	8	⊗	⊗	PROPN
ejpam-1535	652	9	x	x	PUNCT
ejpam-1535	652	10	=	=	PUNCT
ejpam-1535	652	11	a∗	a∗	PROPN
ejpam-1535	652	12	∧	∧	PROPN
ejpam-1535	652	13	x+|x	x+|x	X
ejpam-1535	652	14	=	=	SYM
ejpam-1535	652	15	a∗	a∗	PROPN
ejpam-1535	652	16	∧	∧	PROPN
ejpam-1535	652	17	y+|y	y+|y	NOUN
ejpam-1535	652	18	=	=	PUNCT
ejpam-1535	652	19	a∗	a∗	PROPN
ejpam-1535	652	20	⊗	⊗	PROPN
ejpam-1535	652	21	y.	y.	PROPN
ejpam-1535	652	22	therefore	therefore	ADV
ejpam-1535	652	23	al	al	PROPN
ejpam-1535	652	24	∗	∗	PROPN
ejpam-1535	652	25	a∗	a∗	PROPN
ejpam-1535	652	26	in	in	ADP
ejpam-1535	652	27	(	(	PUNCT
ejpam-1535	652	28	s,⊗	s,⊗	NOUN
ejpam-1535	652	29	)	)	PUNCT
ejpam-1535	652	30	.	.	PUNCT
ejpam-1535	653	1	similarly	similarly	ADV
ejpam-1535	653	2	,	,	PUNCT
ejpam-1535	653	3	ar∗	ar∗	PROPN
ejpam-1535	653	4	a+	a+	PUNCT
ejpam-1535	653	5	in	in	ADP
ejpam-1535	653	6	(	(	PUNCT
ejpam-1535	653	7	s,⊗	s,⊗	NOUN
ejpam-1535	653	8	)	)	PUNCT
ejpam-1535	653	9	.	.	PUNCT
ejpam-1535	654	1	let	let	VERB
ejpam-1535	654	2	s	s	PRON
ejpam-1535	654	3	be	be	AUX
ejpam-1535	654	4	a	a	DET
ejpam-1535	654	5	restriction	restriction	NOUN
ejpam-1535	654	6	semigroup	semigroup	NOUN
ejpam-1535	654	7	.	.	PUNCT
ejpam-1535	655	1	we	we	PRON
ejpam-1535	655	2	will	will	AUX
ejpam-1535	655	3	denote	denote	VERB
ejpam-1535	655	4	the	the	DET
ejpam-1535	655	5	inductive	inductive	ADJ
ejpam-1535	655	6	category	category	NOUN
ejpam-1535	655	7	associated	associate	VERB
ejpam-1535	655	8	with	with	ADP
ejpam-1535	655	9	s	s	PRON
ejpam-1535	655	10	by	by	ADP
ejpam-1535	655	11	c(s	c(	NOUN
ejpam-1535	655	12	)	)	PUNCT
ejpam-1535	655	13	.	.	PUNCT
ejpam-1535	656	1	similarly	similarly	ADV
ejpam-1535	656	2	,	,	PUNCT
ejpam-1535	656	3	if	if	SCONJ
ejpam-1535	656	4	c	c	PROPN
ejpam-1535	656	5	is	be	AUX
ejpam-1535	656	6	an	an	DET
ejpam-1535	656	7	inductive	inductive	ADJ
ejpam-1535	656	8	category	category	NOUN
ejpam-1535	656	9	,	,	PUNCT
ejpam-1535	656	10	then	then	ADV
ejpam-1535	656	11	we	we	PRON
ejpam-1535	656	12	will	will	AUX
ejpam-1535	656	13	denote	denote	VERB
ejpam-1535	656	14	its	its	PRON
ejpam-1535	656	15	associated	associated	ADJ
ejpam-1535	656	16	restriction	restriction	NOUN
ejpam-1535	656	17	semigroup	semigroup	NOUN
ejpam-1535	656	18	by	by	ADP
ejpam-1535	656	19	s(c	s(c	PROPN
ejpam-1535	656	20	)	)	PUNCT
ejpam-1535	656	21	.	.	PUNCT
ejpam-1535	657	1	theorem	theorem	ADJ
ejpam-1535	657	2	4	4	NUM
ejpam-1535	657	3	(	(	PUNCT
ejpam-1535	657	4	implicit	implicit	ADJ
ejpam-1535	657	5	in	in	ADP
ejpam-1535	657	6	[	[	X
ejpam-1535	657	7	28	28	NUM
ejpam-1535	657	8	]	]	NUM
ejpam-1535	657	9	)	)	PUNCT
ejpam-1535	657	10	.	.	PUNCT
ejpam-1535	658	1	let	let	VERB
ejpam-1535	658	2	s	s	PRON
ejpam-1535	658	3	be	be	AUX
ejpam-1535	658	4	a	a	DET
ejpam-1535	658	5	restriction	restriction	NOUN
ejpam-1535	658	6	semigroup	semigroup	NOUN
ejpam-1535	658	7	and	and	CCONJ
ejpam-1535	658	8	c	c	PROPN
ejpam-1535	658	9	be	be	AUX
ejpam-1535	658	10	an	an	DET
ejpam-1535	658	11	inductive	inductive	ADJ
ejpam-1535	658	12	category	category	NOUN
ejpam-1535	658	13	.	.	PUNCT
ejpam-1535	659	1	then	then	ADV
ejpam-1535	659	2	s(c(s	s(c(	NOUN
ejpam-1535	659	3	)	)	PUNCT
ejpam-1535	659	4	)	)	PUNCT
ejpam-1535	660	1	=	=	SYM
ejpam-1535	660	2	s	s	X
ejpam-1535	660	3	and	and	CCONJ
ejpam-1535	660	4	c(s(c	c(s(c	ADJ
ejpam-1535	660	5	)	)	PUNCT
ejpam-1535	660	6	)	)	PUNCT
ejpam-1535	661	1	=	=	SYM
ejpam-1535	661	2	c.	c.	NOUN
ejpam-1535	661	3	proof	proof	NOUN
ejpam-1535	661	4	.	.	PUNCT
ejpam-1535	662	1	let	let	VERB
ejpam-1535	662	2	the	the	DET
ejpam-1535	662	3	operation	operation	NOUN
ejpam-1535	662	4	in	in	ADP
ejpam-1535	662	5	s	s	PRON
ejpam-1535	662	6	be	be	AUX
ejpam-1535	662	7	denoted	denote	VERB
ejpam-1535	662	8	by	by	ADP
ejpam-1535	662	9	juxtaposition	juxtaposition	NOUN
ejpam-1535	662	10	.	.	PUNCT
ejpam-1535	663	1	by	by	ADP
ejpam-1535	663	2	theorem	theorem	NOUN
ejpam-1535	663	3	2	2	NUM
ejpam-1535	663	4	,	,	PUNCT
ejpam-1535	663	5	c(s	c(	NOUN
ejpam-1535	663	6	)	)	PUNCT
ejpam-1535	663	7	is	be	AUX
ejpam-1535	663	8	an	an	DET
ejpam-1535	663	9	inductive	inductive	ADJ
ejpam-1535	663	10	category	category	NOUN
ejpam-1535	663	11	under	under	ADP
ejpam-1535	663	12	the	the	DET
ejpam-1535	663	13	restricted	restricted	ADJ
ejpam-1535	663	14	product	product	NOUN
ejpam-1535	663	15	·	·	PUNCT
ejpam-1535	663	16	of	of	ADP
ejpam-1535	663	17	(	(	PUNCT
ejpam-1535	663	18	7	7	NUM
ejpam-1535	663	19	)	)	PUNCT
ejpam-1535	663	20	.	.	PUNCT
ejpam-1535	664	1	further	far	ADV
ejpam-1535	664	2	,	,	PUNCT
ejpam-1535	664	3	in	in	ADP
ejpam-1535	664	4	c(s	c(	NOUN
ejpam-1535	664	5	)	)	PUNCT
ejpam-1535	664	6	,	,	PUNCT
ejpam-1535	664	7	we	we	PRON
ejpam-1535	664	8	have	have	VERB
ejpam-1535	664	9	e|a	e|a	X
ejpam-1535	664	10	=	=	SYM
ejpam-1535	664	11	ea	ea	PROPN
ejpam-1535	664	12	,	,	PUNCT
ejpam-1535	664	13	a|e	a|e	PUNCT
ejpam-1535	665	1	=	=	SYM
ejpam-1535	665	2	ae	ae	PROPN
ejpam-1535	665	3	and	and	CCONJ
ejpam-1535	665	4	e	e	PROPN
ejpam-1535	665	5	∧	∧	NOUN
ejpam-1535	665	6	f	f	X
ejpam-1535	665	7	=	=	SYM
ejpam-1535	665	8	e	e	PROPN
ejpam-1535	665	9	f	f	PROPN
ejpam-1535	665	10	.	.	PUNCT
ejpam-1535	666	1	we	we	PRON
ejpam-1535	666	2	now	now	ADV
ejpam-1535	666	3	construct	construct	VERB
ejpam-1535	666	4	s(c(s	s(c(	NOUN
ejpam-1535	666	5	)	)	PUNCT
ejpam-1535	666	6	)	)	PUNCT
ejpam-1535	666	7	by	by	ADP
ejpam-1535	666	8	defining	define	VERB
ejpam-1535	666	9	the	the	DET
ejpam-1535	666	10	pseudoproduct	pseudoproduct	NOUN
ejpam-1535	666	11	⊗	⊗	PROPN
ejpam-1535	666	12	of	of	ADP
ejpam-1535	666	13	(	(	PUNCT
ejpam-1535	666	14	6	6	NUM
ejpam-1535	666	15	)	)	PUNCT
ejpam-1535	666	16	.	.	PUNCT
ejpam-1535	667	1	by	by	ADP
ejpam-1535	667	2	theorem	theorem	ADJ
ejpam-1535	667	3	3	3	NUM
ejpam-1535	667	4	,	,	PUNCT
ejpam-1535	667	5	s(c(s	s(c(s	ADJ
ejpam-1535	667	6	)	)	PUNCT
ejpam-1535	667	7	)	)	PUNCT
ejpam-1535	667	8	is	be	AUX
ejpam-1535	667	9	a	a	DET
ejpam-1535	667	10	restriction	restriction	NOUN
ejpam-1535	667	11	semigroup	semigroup	NOUN
ejpam-1535	667	12	under	under	ADP
ejpam-1535	667	13	⊗.	⊗.	ADP
ejpam-1535	667	14	it	it	PRON
ejpam-1535	667	15	is	be	AUX
ejpam-1535	667	16	clear	clear	ADJ
ejpam-1535	667	17	that	that	SCONJ
ejpam-1535	667	18	s	s	VERB
ejpam-1535	667	19	and	and	CCONJ
ejpam-1535	667	20	s(c(s	s(c(	NOUN
ejpam-1535	667	21	)	)	PUNCT
ejpam-1535	667	22	)	)	PUNCT
ejpam-1535	667	23	share	share	VERB
ejpam-1535	667	24	the	the	DET
ejpam-1535	667	25	same	same	ADJ
ejpam-1535	667	26	underlying	underlying	ADJ
ejpam-1535	667	27	set	set	NOUN
ejpam-1535	667	28	.	.	PUNCT
ejpam-1535	668	1	observe	observe	VERB
ejpam-1535	668	2	further	far	ADV
ejpam-1535	668	3	that	that	DET
ejpam-1535	668	4	a⊗	a⊗	PROPN
ejpam-1535	668	5	b	b	PROPN
ejpam-1535	669	1	=	=	SYM
ejpam-1535	670	1	[	[	X
ejpam-1535	670	2	a|r(a)∧	a|r(a)∧	PROPN
ejpam-1535	670	3	d(b	d(b	PROPN
ejpam-1535	670	4	)	)	PUNCT
ejpam-1535	670	5	]	]	PUNCT
ejpam-1535	670	6	·	·	PUNCT
ejpam-1535	671	1	[	[	X
ejpam-1535	671	2	r(a)∧	r(a)∧	PROPN
ejpam-1535	671	3	d(b)|b	d(b)|b	PROPN
ejpam-1535	671	4	]	]	X
ejpam-1535	672	1	=	=	SYM
ejpam-1535	672	2	(	(	PUNCT
ejpam-1535	672	3	aa∗b+	aa∗b+	PROPN
ejpam-1535	672	4	)	)	PUNCT
ejpam-1535	672	5	·	·	PUNCT
ejpam-1535	672	6	(	(	PUNCT
ejpam-1535	672	7	a∗b+b	a∗b+b	NOUN
ejpam-1535	672	8	)	)	PUNCT
ejpam-1535	672	9	=	=	SYM
ejpam-1535	672	10	ab	ab	PROPN
ejpam-1535	672	11	,	,	PUNCT
ejpam-1535	672	12	so	so	SCONJ
ejpam-1535	672	13	the	the	DET
ejpam-1535	672	14	operations	operation	NOUN
ejpam-1535	672	15	in	in	ADP
ejpam-1535	672	16	s	s	PRON
ejpam-1535	672	17	and	and	CCONJ
ejpam-1535	672	18	s(c(s	s(c(	NOUN
ejpam-1535	672	19	)	)	PUNCT
ejpam-1535	672	20	)	)	PUNCT
ejpam-1535	672	21	are	be	AUX
ejpam-1535	672	22	the	the	DET
ejpam-1535	672	23	same	same	ADJ
ejpam-1535	672	24	.	.	PUNCT
ejpam-1535	673	1	hence	hence	ADV
ejpam-1535	673	2	s	s	X
ejpam-1535	673	3	=	=	SYM
ejpam-1535	673	4	s(c(s	s(c(s	ADJ
ejpam-1535	673	5	)	)	PUNCT
ejpam-1535	673	6	)	)	PUNCT
ejpam-1535	673	7	.	.	PUNCT
ejpam-1535	674	1	we	we	PRON
ejpam-1535	674	2	turn	turn	VERB
ejpam-1535	674	3	now	now	ADV
ejpam-1535	674	4	to	to	ADP
ejpam-1535	674	5	the	the	DET
ejpam-1535	674	6	second	second	ADJ
ejpam-1535	674	7	part	part	NOUN
ejpam-1535	674	8	of	of	ADP
ejpam-1535	674	9	the	the	DET
ejpam-1535	674	10	proposition	proposition	NOUN
ejpam-1535	674	11	.	.	PUNCT
ejpam-1535	675	1	let	let	VERB
ejpam-1535	675	2	·	·	PUNCT
ejpam-1535	675	3	denote	denote	VERB
ejpam-1535	675	4	the	the	DET
ejpam-1535	675	5	operation	operation	NOUN
ejpam-1535	675	6	in	in	ADP
ejpam-1535	675	7	c	c	PROPN
ejpam-1535	675	8	.	.	PUNCT
ejpam-1535	676	1	we	we	PRON
ejpam-1535	676	2	construct	construct	VERB
ejpam-1535	676	3	the	the	DET
ejpam-1535	676	4	restriction	restriction	NOUN
ejpam-1535	676	5	semigroup	semigroup	PROPN
ejpam-1535	676	6	s(c	s(c	PROPN
ejpam-1535	676	7	)	)	PUNCT
ejpam-1535	676	8	by	by	ADP
ejpam-1535	676	9	defining	define	VERB
ejpam-1535	676	10	the	the	DET
ejpam-1535	676	11	pseudoproduct	pseudoproduct	NOUN
ejpam-1535	676	12	⊗	⊗	PROPN
ejpam-1535	676	13	of	of	ADP
ejpam-1535	676	14	(	(	PUNCT
ejpam-1535	676	15	6	6	NUM
ejpam-1535	676	16	)	)	PUNCT
ejpam-1535	676	17	.	.	PUNCT
ejpam-1535	677	1	we	we	PRON
ejpam-1535	677	2	next	next	ADV
ejpam-1535	677	3	define	define	VERB
ejpam-1535	677	4	the	the	DET
ejpam-1535	677	5	restricted	restricted	ADJ
ejpam-1535	677	6	product	product	NOUN
ejpam-1535	677	7	:	:	PUNCT
ejpam-1535	677	8	a⊙	a⊙	PROPN
ejpam-1535	677	9	b	b	PROPN
ejpam-1535	677	10	=	=	PUNCT
ejpam-1535	677	11	(	(	PUNCT
ejpam-1535	677	12	a⊗	a⊗	PROPN
ejpam-1535	677	13	b	b	PROPN
ejpam-1535	677	14	if	if	SCONJ
ejpam-1535	677	15	a∗	a∗	PROPN
ejpam-1535	677	16	=	=	SYM
ejpam-1535	677	17	b+	b+	X
ejpam-1535	677	18	;	;	PUNCT
ejpam-1535	677	19	undefined	undefined	ADJ
ejpam-1535	677	20	otherwise	otherwise	ADV
ejpam-1535	677	21	.	.	PUNCT
ejpam-1535	678	1	=	=	PUNCT
ejpam-1535	679	1	(	(	PUNCT
ejpam-1535	679	2	[	[	X
ejpam-1535	679	3	a|r(a)∧	a|r(a)∧	X
ejpam-1535	679	4	d(b	d(b	NOUN
ejpam-1535	679	5	)	)	PUNCT
ejpam-1535	679	6	]	]	PUNCT
ejpam-1535	679	7	·	·	PUNCT
ejpam-1535	680	1	[	[	X
ejpam-1535	680	2	r(a)∧	r(a)∧	PROPN
ejpam-1535	680	3	d(b)|b	d(b)|b	PROPN
ejpam-1535	680	4	]	]	PUNCT
ejpam-1535	680	5	if	if	SCONJ
ejpam-1535	680	6	r(a	r(a	VERB
ejpam-1535	680	7	)	)	PUNCT
ejpam-1535	680	8	=	=	PUNCT
ejpam-1535	681	1	d(b	d(b	PROPN
ejpam-1535	681	2	)	)	PUNCT
ejpam-1535	681	3	;	;	PUNCT
ejpam-1535	681	4	undefined	undefined	ADJ
ejpam-1535	681	5	otherwise	otherwise	ADV
ejpam-1535	681	6	.	.	PUNCT
ejpam-1535	682	1	c.	c.	PROPN
ejpam-1535	682	2	hollings	holling	NOUN
ejpam-1535	682	3	/	/	SYM
ejpam-1535	682	4	eur	eur	PROPN
ejpam-1535	682	5	.	.	PUNCT
ejpam-1535	683	1	j.	j.	PROPN
ejpam-1535	683	2	pure	pure	PROPN
ejpam-1535	683	3	appl	appl	PROPN
ejpam-1535	683	4	.	.	PROPN
ejpam-1535	683	5	math	math	PROPN
ejpam-1535	683	6	,	,	PUNCT
ejpam-1535	683	7	5	5	NUM
ejpam-1535	683	8	(	(	PUNCT
ejpam-1535	683	9	2012	2012	NUM
ejpam-1535	683	10	)	)	PUNCT
ejpam-1535	683	11	,	,	PUNCT
ejpam-1535	683	12	414	414	NUM
ejpam-1535	683	13	-	-	SYM
ejpam-1535	683	14	450	450	NUM
ejpam-1535	683	15	437	437	NUM
ejpam-1535	683	16	=	=	SYM
ejpam-1535	683	17	(	(	PUNCT
ejpam-1535	683	18	(	(	PUNCT
ejpam-1535	683	19	a|r(a	a|r(a	NUM
ejpam-1535	683	20	)	)	PUNCT
ejpam-1535	683	21	)	)	PUNCT
ejpam-1535	683	22	·	·	PUNCT
ejpam-1535	684	1	(	(	PUNCT
ejpam-1535	684	2	d(b)|b	d(b)|b	PROPN
ejpam-1535	684	3	)	)	PUNCT
ejpam-1535	684	4	if	if	SCONJ
ejpam-1535	684	5	r(a	r(a	VERB
ejpam-1535	684	6	)	)	PUNCT
ejpam-1535	684	7	=	=	PUNCT
ejpam-1535	684	8	d(b	d(b	PROPN
ejpam-1535	684	9	)	)	PUNCT
ejpam-1535	684	10	;	;	PUNCT
ejpam-1535	684	11	undefined	undefined	ADJ
ejpam-1535	684	12	otherwise	otherwise	ADV
ejpam-1535	684	13	.	.	PUNCT
ejpam-1535	685	1	=	=	PUNCT
ejpam-1535	685	2	a	a	DET
ejpam-1535	685	3	·	·	SYM
ejpam-1535	685	4	b	b	NOUN
ejpam-1535	685	5	,	,	PUNCT
ejpam-1535	685	6	using	use	VERB
ejpam-1535	685	7	lemma	lemma	PROPN
ejpam-1535	685	8	5(a	5(a	NUM
ejpam-1535	685	9	)	)	PUNCT
ejpam-1535	685	10	.	.	PUNCT
ejpam-1535	686	1	we	we	PRON
ejpam-1535	686	2	know	know	VERB
ejpam-1535	686	3	that	that	SCONJ
ejpam-1535	686	4	c(s(c	c(s(c	NOUN
ejpam-1535	686	5	)	)	PUNCT
ejpam-1535	686	6	)	)	PUNCT
ejpam-1535	686	7	is	be	AUX
ejpam-1535	686	8	an	an	DET
ejpam-1535	686	9	inductive	inductive	ADJ
ejpam-1535	686	10	category	category	NOUN
ejpam-1535	686	11	under	under	ADP
ejpam-1535	686	12	⊙	⊙	PROPN
ejpam-1535	686	13	,	,	PUNCT
ejpam-1535	686	14	and	and	CCONJ
ejpam-1535	686	15	we	we	PRON
ejpam-1535	686	16	see	see	VERB
ejpam-1535	686	17	that	that	DET
ejpam-1535	686	18	⊙	⊙	PROPN
ejpam-1535	686	19	and	and	CCONJ
ejpam-1535	686	20	·	·	PUNCT
ejpam-1535	686	21	coincide	coincide	NOUN
ejpam-1535	686	22	.	.	PUNCT
ejpam-1535	687	1	it	it	PRON
ejpam-1535	687	2	is	be	AUX
ejpam-1535	687	3	again	again	ADV
ejpam-1535	687	4	clear	clear	ADJ
ejpam-1535	687	5	that	that	SCONJ
ejpam-1535	687	6	c	c	NOUN
ejpam-1535	687	7	and	and	CCONJ
ejpam-1535	687	8	c(s(c	c(s(c	NOUN
ejpam-1535	687	9	)	)	PUNCT
ejpam-1535	687	10	)	)	PUNCT
ejpam-1535	687	11	share	share	VERB
ejpam-1535	687	12	the	the	DET
ejpam-1535	687	13	same	same	ADJ
ejpam-1535	687	14	underlying	underlying	ADJ
ejpam-1535	687	15	set	set	NOUN
ejpam-1535	687	16	.	.	PUNCT
ejpam-1535	688	1	we	we	PRON
ejpam-1535	688	2	must	must	AUX
ejpam-1535	688	3	now	now	ADV
ejpam-1535	688	4	show	show	VERB
ejpam-1535	688	5	they	they	PRON
ejpam-1535	688	6	have	have	VERB
ejpam-1535	688	7	the	the	DET
ejpam-1535	688	8	same	same	ADJ
ejpam-1535	688	9	ordering	ordering	NOUN
ejpam-1535	688	10	,	,	PUNCT
ejpam-1535	688	11	restriction	restriction	NOUN
ejpam-1535	688	12	and	and	CCONJ
ejpam-1535	688	13	corestriction	corestriction	NOUN
ejpam-1535	688	14	.	.	PUNCT
ejpam-1535	689	1	we	we	PRON
ejpam-1535	689	2	first	first	ADV
ejpam-1535	689	3	consider	consider	VERB
ejpam-1535	689	4	the	the	DET
ejpam-1535	689	5	ordering	ordering	NOUN
ejpam-1535	689	6	.	.	PUNCT
ejpam-1535	690	1	by	by	ADP
ejpam-1535	690	2	definition	definition	NOUN
ejpam-1535	690	3	,	,	PUNCT
ejpam-1535	690	4	c(s(c	c(s(c	NOUN
ejpam-1535	690	5	)	)	PUNCT
ejpam-1535	690	6	)	)	PUNCT
ejpam-1535	690	7	has	have	VERB
ejpam-1535	690	8	the	the	DET
ejpam-1535	690	9	same	same	ADJ
ejpam-1535	690	10	ordering	ordering	NOUN
ejpam-1535	690	11	as	as	ADP
ejpam-1535	690	12	s(c	s(c	NOUN
ejpam-1535	690	13	)	)	PUNCT
ejpam-1535	690	14	.	.	PUNCT
ejpam-1535	691	1	we	we	PRON
ejpam-1535	691	2	know	know	VERB
ejpam-1535	691	3	from	from	ADP
ejpam-1535	691	4	theorem	theorem	ADJ
ejpam-1535	691	5	3	3	NUM
ejpam-1535	691	6	that	that	SCONJ
ejpam-1535	691	7	the	the	DET
ejpam-1535	691	8	ordering	ordering	NOUN
ejpam-1535	691	9	in	in	ADP
ejpam-1535	691	10	s(c	s(c	PROPN
ejpam-1535	691	11	)	)	PUNCT
ejpam-1535	691	12	is	be	AUX
ejpam-1535	691	13	the	the	DET
ejpam-1535	691	14	same	same	ADJ
ejpam-1535	691	15	as	as	ADP
ejpam-1535	691	16	the	the	DET
ejpam-1535	691	17	ordering	ordering	NOUN
ejpam-1535	691	18	in	in	ADP
ejpam-1535	691	19	c	c	PROPN
ejpam-1535	691	20	.	.	PUNCT
ejpam-1535	692	1	hence	hence	ADV
ejpam-1535	692	2	c(s(c	c(s(c	ADJ
ejpam-1535	692	3	)	)	PUNCT
ejpam-1535	692	4	)	)	PUNCT
ejpam-1535	693	1	and	and	CCONJ
ejpam-1535	693	2	c	c	PROPN
ejpam-1535	693	3	have	have	VERB
ejpam-1535	693	4	the	the	DET
ejpam-1535	693	5	same	same	ADJ
ejpam-1535	693	6	ordering	ordering	NOUN
ejpam-1535	693	7	.	.	PUNCT
ejpam-1535	694	1	let	let	VERB
ejpam-1535	694	2	|	|	ADV
ejpam-1535	694	3	denote	denote	VERB
ejpam-1535	694	4	restriction	restriction	NOUN
ejpam-1535	694	5	and	and	CCONJ
ejpam-1535	694	6	corestriction	corestriction	NOUN
ejpam-1535	694	7	in	in	ADP
ejpam-1535	694	8	c	c	PROPN
ejpam-1535	694	9	,	,	PUNCT
ejpam-1535	694	10	and	and	CCONJ
ejpam-1535	694	11	‖	‖	PROPN
ejpam-1535	694	12	denote	denote	VERB
ejpam-1535	694	13	the	the	DET
ejpam-1535	694	14	same	same	ADJ
ejpam-1535	694	15	in	in	ADP
ejpam-1535	694	16	c(s(c	c(s(c	NOUN
ejpam-1535	694	17	)	)	PUNCT
ejpam-1535	694	18	)	)	PUNCT
ejpam-1535	694	19	.	.	PUNCT
ejpam-1535	695	1	suppose	suppose	VERB
ejpam-1535	695	2	that	that	SCONJ
ejpam-1535	695	3	e	e	PROPN
ejpam-1535	695	4	≤	≤	X
ejpam-1535	695	5	r(a	r(a	PROPN
ejpam-1535	695	6	)	)	PUNCT
ejpam-1535	695	7	.	.	PUNCT
ejpam-1535	696	1	we	we	PRON
ejpam-1535	696	2	then	then	ADV
ejpam-1535	696	3	have	have	VERB
ejpam-1535	696	4	a‖e	a‖e	NOUN
ejpam-1535	696	5	=	=	PUNCT
ejpam-1535	696	6	a⊗	a⊗	NOUN
ejpam-1535	696	7	e	e	NOUN
ejpam-1535	696	8	=	=	PUNCT
ejpam-1535	696	9	a|r(a)∧	a|r(a)∧	PROPN
ejpam-1535	696	10	e	e	PROPN
ejpam-1535	696	11	=	=	PUNCT
ejpam-1535	696	12	a|e	a|e	PROPN
ejpam-1535	696	13	,	,	PUNCT
ejpam-1535	696	14	using	use	VERB
ejpam-1535	696	15	lemma	lemma	PROPN
ejpam-1535	696	16	9	9	NUM
ejpam-1535	696	17	.	.	PUNCT
ejpam-1535	697	1	similarly	similarly	ADV
ejpam-1535	697	2	,	,	PUNCT
ejpam-1535	697	3	if	if	SCONJ
ejpam-1535	697	4	e	e	PROPN
ejpam-1535	697	5	≤	≤	VERB
ejpam-1535	697	6	d(a	d(a	PROPN
ejpam-1535	697	7	)	)	PUNCT
ejpam-1535	697	8	,	,	PUNCT
ejpam-1535	697	9	then	then	ADV
ejpam-1535	697	10	e‖a	e‖a	ADV
ejpam-1535	697	11	=	=	SYM
ejpam-1535	697	12	e|a	e|a	X
ejpam-1535	697	13	.	.	PUNCT
ejpam-1535	698	1	thus	thus	ADV
ejpam-1535	698	2	c	c	X
ejpam-1535	698	3	=	=	SYM
ejpam-1535	698	4	c(s(c	c(s(c	ADJ
ejpam-1535	698	5	)	)	PUNCT
ejpam-1535	698	6	)	)	PUNCT
ejpam-1535	698	7	,	,	PUNCT
ejpam-1535	698	8	as	as	SCONJ
ejpam-1535	698	9	required	require	VERB
ejpam-1535	698	10	.	.	PUNCT
ejpam-1535	699	1	in	in	ADP
ejpam-1535	699	2	the	the	DET
ejpam-1535	699	3	following	follow	VERB
ejpam-1535	699	4	sections	section	NOUN
ejpam-1535	699	5	,	,	PUNCT
ejpam-1535	699	6	we	we	PRON
ejpam-1535	699	7	will	will	AUX
ejpam-1535	699	8	prove	prove	VERB
ejpam-1535	699	9	results	result	NOUN
ejpam-1535	699	10	which	which	PRON
ejpam-1535	699	11	establish	establish	VERB
ejpam-1535	699	12	the	the	DET
ejpam-1535	699	13	isomorphisms	isomorphism	NOUN
ejpam-1535	699	14	of	of	ADP
ejpam-1535	699	15	certain	certain	ADJ
ejpam-1535	699	16	categories	category	NOUN
ejpam-1535	699	17	(	(	PUNCT
ejpam-1535	699	18	in	in	ADP
ejpam-1535	699	19	sense	sense	NOUN
ejpam-1535	699	20	(	(	PUNCT
ejpam-1535	699	21	♠	♠	NOUN
ejpam-1535	699	22	)	)	PUNCT
ejpam-1535	699	23	)	)	PUNCT
ejpam-1535	699	24	of	of	ADP
ejpam-1535	699	25	restriction	restriction	NOUN
ejpam-1535	699	26	semigroups	semigroup	NOUN
ejpam-1535	699	27	and	and	CCONJ
ejpam-1535	699	28	certain	certain	ADJ
ejpam-1535	699	29	categories	category	NOUN
ejpam-1535	699	30	(	(	PUNCT
ejpam-1535	699	31	again	again	ADV
ejpam-1535	699	32	in	in	ADP
ejpam-1535	699	33	sense	sense	NOUN
ejpam-1535	699	34	(	(	PUNCT
ejpam-1535	699	35	♠	♠	NOUN
ejpam-1535	699	36	)	)	PUNCT
ejpam-1535	699	37	)	)	PUNCT
ejpam-1535	699	38	of	of	ADP
ejpam-1535	699	39	inductive	inductive	ADJ
ejpam-1535	699	40	categories	category	NOUN
ejpam-1535	699	41	(	(	PUNCT
ejpam-1535	699	42	now	now	ADV
ejpam-1535	699	43	in	in	ADP
ejpam-1535	699	44	sense	sense	NOUN
ejpam-1535	699	45	(	(	PUNCT
ejpam-1535	699	46	♣	♣	NOUN
ejpam-1535	699	47	)	)	PUNCT
ejpam-1535	699	48	)	)	PUNCT
ejpam-1535	699	49	.	.	PUNCT
ejpam-1535	700	1	the	the	DET
ejpam-1535	700	2	arrows	arrow	NOUN
ejpam-1535	700	3	of	of	ADP
ejpam-1535	700	4	these	these	DET
ejpam-1535	700	5	categories	category	NOUN
ejpam-1535	700	6	are	be	AUX
ejpam-1535	700	7	yet	yet	ADV
ejpam-1535	700	8	to	to	PART
ejpam-1535	700	9	be	be	AUX
ejpam-1535	700	10	defined	define	VERB
ejpam-1535	700	11	and	and	CCONJ
ejpam-1535	700	12	considered	consider	VERB
ejpam-1535	700	13	but	but	CCONJ
ejpam-1535	700	14	theorems	theorem	NOUN
ejpam-1535	700	15	2	2	NUM
ejpam-1535	700	16	,	,	PUNCT
ejpam-1535	700	17	3	3	NUM
ejpam-1535	700	18	and	and	CCONJ
ejpam-1535	700	19	4	4	NUM
ejpam-1535	700	20	provide	provide	VERB
ejpam-1535	700	21	us	we	PRON
ejpam-1535	700	22	with	with	ADP
ejpam-1535	700	23	the	the	DET
ejpam-1535	700	24	“	"	PUNCT
ejpam-1535	700	25	objects	object	NOUN
ejpam-1535	700	26	”	"	PUNCT
ejpam-1535	700	27	parts	part	NOUN
ejpam-1535	700	28	of	of	ADP
ejpam-1535	700	29	the	the	DET
ejpam-1535	700	30	upcoming	upcoming	ADJ
ejpam-1535	700	31	category	category	NOUN
ejpam-1535	700	32	isomorphisms	isomorphism	NOUN
ejpam-1535	700	33	.	.	PUNCT
ejpam-1535	701	1	6	6	NUM
ejpam-1535	701	2	.	.	PUNCT
ejpam-1535	701	3	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	701	4	and	and	CCONJ
ejpam-1535	701	5	ordered	order	VERB
ejpam-1535	701	6	functors	functor	NOUN
ejpam-1535	701	7	the	the	DET
ejpam-1535	701	8	first	first	ADJ
ejpam-1535	701	9	functions	function	NOUN
ejpam-1535	701	10	to	to	PART
ejpam-1535	701	11	be	be	AUX
ejpam-1535	701	12	considered	consider	VERB
ejpam-1535	701	13	as	as	ADP
ejpam-1535	701	14	the	the	DET
ejpam-1535	701	15	arrows	arrow	NOUN
ejpam-1535	701	16	of	of	ADP
ejpam-1535	701	17	a	a	DET
ejpam-1535	701	18	category	category	NOUN
ejpam-1535	701	19	of	of	ADP
ejpam-1535	701	20	restriction	restriction	NOUN
ejpam-1535	701	21	semigroups	semigroup	NOUN
ejpam-1535	701	22	are	be	AUX
ejpam-1535	701	23	so	so	ADV
ejpam-1535	701	24	-	-	PUNCT
ejpam-1535	701	25	called	call	VERB
ejpam-1535	701	26	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	701	27	,	,	PUNCT
ejpam-1535	701	28	which	which	PRON
ejpam-1535	701	29	generalise	generalise	VERB
ejpam-1535	701	30	morphisms	morphism	NOUN
ejpam-1535	701	31	.	.	PUNCT
ejpam-1535	702	1	these	these	DET
ejpam-1535	702	2	functions	function	NOUN
ejpam-1535	702	3	were	be	AUX
ejpam-1535	702	4	originally	originally	ADV
ejpam-1535	702	5	introduced	introduce	VERB
ejpam-1535	702	6	in	in	ADP
ejpam-1535	702	7	the	the	DET
ejpam-1535	702	8	inverse	inverse	NOUN
ejpam-1535	702	9	case	case	NOUN
ejpam-1535	702	10	;	;	PUNCT
ejpam-1535	702	11	we	we	PRON
ejpam-1535	702	12	will	will	AUX
ejpam-1535	702	13	see	see	VERB
ejpam-1535	702	14	their	their	PRON
ejpam-1535	702	15	“	"	PUNCT
ejpam-1535	702	16	inverse	inverse	ADJ
ejpam-1535	702	17	version	version	NOUN
ejpam-1535	702	18	”	"	PUNCT
ejpam-1535	702	19	in	in	ADP
ejpam-1535	702	20	section	section	NOUN
ejpam-1535	702	21	8.2	8.2	NUM
ejpam-1535	702	22	.	.	PUNCT
ejpam-1535	703	1	definition	definition	NOUN
ejpam-1535	703	2	13	13	NUM
ejpam-1535	703	3	.	.	PUNCT
ejpam-1535	704	1	let	let	VERB
ejpam-1535	704	2	s	s	PRON
ejpam-1535	704	3	and	and	CCONJ
ejpam-1535	704	4	t	t	PROPN
ejpam-1535	704	5	be	be	AUX
ejpam-1535	704	6	restriction	restriction	NOUN
ejpam-1535	704	7	semigroups	semigroup	NOUN
ejpam-1535	704	8	.	.	PUNCT
ejpam-1535	705	1	a	a	DET
ejpam-1535	705	2	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	705	3	is	be	AUX
ejpam-1535	705	4	a	a	DET
ejpam-1535	705	5	function	function	NOUN
ejpam-1535	705	6	θ	θ	NOUN
ejpam-1535	705	7	:	:	PUNCT
ejpam-1535	706	1	s→	s→	X
ejpam-1535	706	2	t	t	NOUN
ejpam-1535	706	3	such	such	ADJ
ejpam-1535	706	4	that	that	PRON
ejpam-1535	706	5	(	(	PUNCT
ejpam-1535	706	6	∨1	∨1	PROPN
ejpam-1535	706	7	)	)	PUNCT
ejpam-1535	706	8	(	(	PUNCT
ejpam-1535	706	9	st)θ	st)θ	PROPN
ejpam-1535	706	10	≤	≤	PROPN
ejpam-1535	706	11	(	(	PUNCT
ejpam-1535	706	12	sθ)(tθ	sθ)(tθ	PROPN
ejpam-1535	706	13	)	)	PUNCT
ejpam-1535	706	14	;	;	PUNCT
ejpam-1535	706	15	(	(	PUNCT
ejpam-1535	706	16	∨2	∨2	X
ejpam-1535	706	17	)	)	PUNCT
ejpam-1535	706	18	s+θ	s+θ	NUM
ejpam-1535	706	19	≤	≤	NUM
ejpam-1535	706	20	(	(	PUNCT
ejpam-1535	706	21	sθ)+	sθ)+	NOUN
ejpam-1535	706	22	and	and	CCONJ
ejpam-1535	706	23	s∗θ	s∗θ	ADJ
ejpam-1535	706	24	≤	≤	NUM
ejpam-1535	706	25	(	(	PUNCT
ejpam-1535	706	26	sθ)∗.	sθ)∗.	NOUN
ejpam-1535	706	27	we	we	PRON
ejpam-1535	706	28	note	note	VERB
ejpam-1535	706	29	some	some	DET
ejpam-1535	706	30	useful	useful	ADJ
ejpam-1535	706	31	properties	property	NOUN
ejpam-1535	706	32	of	of	ADP
ejpam-1535	706	33	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	706	34	:	:	PUNCT
ejpam-1535	706	35	lemma	lemma	PROPN
ejpam-1535	706	36	10	10	NUM
ejpam-1535	706	37	(	(	PUNCT
ejpam-1535	706	38	[	[	X
ejpam-1535	706	39	22	22	NUM
ejpam-1535	706	40	,	,	PUNCT
ejpam-1535	706	41	lemma	lemma	PROPN
ejpam-1535	706	42	4.5	4.5	NUM
ejpam-1535	706	43	]	]	PUNCT
ejpam-1535	706	44	)	)	PUNCT
ejpam-1535	706	45	.	.	PUNCT
ejpam-1535	707	1	let	let	VERB
ejpam-1535	707	2	s	s	PRON
ejpam-1535	707	3	and	and	CCONJ
ejpam-1535	707	4	t	t	PROPN
ejpam-1535	707	5	be	be	VERB
ejpam-1535	707	6	restriction	restriction	NOUN
ejpam-1535	707	7	semigroups	semigroup	NOUN
ejpam-1535	707	8	with	with	ADP
ejpam-1535	707	9	respect	respect	NOUN
ejpam-1535	707	10	to	to	ADP
ejpam-1535	707	11	semilattices	semilattice	NOUN
ejpam-1535	707	12	e	e	NOUN
ejpam-1535	707	13	and	and	CCONJ
ejpam-1535	707	14	f	f	PROPN
ejpam-1535	707	15	,	,	PUNCT
ejpam-1535	707	16	respectively	respectively	ADV
ejpam-1535	707	17	.	.	PUNCT
ejpam-1535	708	1	if	if	SCONJ
ejpam-1535	708	2	θ	θ	PROPN
ejpam-1535	708	3	:	:	PUNCT
ejpam-1535	708	4	s→	s→	PROPN
ejpam-1535	708	5	t	t	PROPN
ejpam-1535	708	6	is	be	AUX
ejpam-1535	708	7	a	a	DET
ejpam-1535	708	8	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	708	9	,	,	PUNCT
ejpam-1535	708	10	then	then	ADV
ejpam-1535	708	11	(	(	PUNCT
ejpam-1535	708	12	a	a	X
ejpam-1535	708	13	)	)	PUNCT
ejpam-1535	708	14	e	e	NOUN
ejpam-1535	708	15	∈	∈	PROPN
ejpam-1535	708	16	e(s)⇒	e(s)⇒	VERB
ejpam-1535	708	17	eθ	eθ	ADP
ejpam-1535	708	18	∈	∈	PROPN
ejpam-1535	708	19	e(t	e(t	PROPN
ejpam-1535	708	20	)	)	PUNCT
ejpam-1535	708	21	;	;	PUNCT
ejpam-1535	708	22	(	(	PUNCT
ejpam-1535	708	23	b	b	X
ejpam-1535	708	24	)	)	PUNCT
ejpam-1535	708	25	e	e	NOUN
ejpam-1535	708	26	∈	∈	PROPN
ejpam-1535	708	27	e⇒	e⇒	PROPN
ejpam-1535	708	28	eθ	eθ	ADP
ejpam-1535	708	29	∈	∈	PROPN
ejpam-1535	708	30	f	f	X
ejpam-1535	708	31	;	;	PUNCT
ejpam-1535	708	32	(	(	PUNCT
ejpam-1535	708	33	c	c	X
ejpam-1535	708	34	)	)	PUNCT
ejpam-1535	708	35	(	(	PUNCT
ejpam-1535	708	36	sθ)+	sθ)+	NOUN
ejpam-1535	708	37	=	=	SYM
ejpam-1535	708	38	s+θ	s+θ	NUM
ejpam-1535	708	39	and	and	CCONJ
ejpam-1535	708	40	(	(	PUNCT
ejpam-1535	708	41	sθ)∗	sθ)∗	X
ejpam-1535	708	42	=	=	PRON
ejpam-1535	708	43	s∗θ	s∗θ	PROPN
ejpam-1535	708	44	;	;	PUNCT
ejpam-1535	708	45	c.	c.	PROPN
ejpam-1535	708	46	hollings	holling	NOUN
ejpam-1535	708	47	/	/	SYM
ejpam-1535	708	48	eur	eur	PROPN
ejpam-1535	708	49	.	.	PUNCT
ejpam-1535	709	1	j.	j.	PROPN
ejpam-1535	709	2	pure	pure	PROPN
ejpam-1535	709	3	appl	appl	PROPN
ejpam-1535	709	4	.	.	PROPN
ejpam-1535	709	5	math	math	PROPN
ejpam-1535	709	6	,	,	PUNCT
ejpam-1535	709	7	5	5	NUM
ejpam-1535	709	8	(	(	PUNCT
ejpam-1535	709	9	2012	2012	NUM
ejpam-1535	709	10	)	)	PUNCT
ejpam-1535	709	11	,	,	PUNCT
ejpam-1535	709	12	414	414	NUM
ejpam-1535	709	13	-	-	SYM
ejpam-1535	709	14	450	450	NUM
ejpam-1535	709	15	438	438	NUM
ejpam-1535	709	16	(	(	PUNCT
ejpam-1535	709	17	d	d	NOUN
ejpam-1535	709	18	)	)	PUNCT
ejpam-1535	709	19	θ	θ	PROPN
ejpam-1535	709	20	is	be	AUX
ejpam-1535	709	21	order	order	NOUN
ejpam-1535	709	22	-	-	PUNCT
ejpam-1535	709	23	preserving	preserve	VERB
ejpam-1535	709	24	.	.	PUNCT
ejpam-1535	710	1	using	use	VERB
ejpam-1535	710	2	lemma	lemma	PROPN
ejpam-1535	710	3	10(d	10(d	NUM
ejpam-1535	710	4	)	)	PUNCT
ejpam-1535	710	5	,	,	PUNCT
ejpam-1535	710	6	the	the	DET
ejpam-1535	710	7	following	follow	VERB
ejpam-1535	710	8	is	be	AUX
ejpam-1535	710	9	easily	easily	ADV
ejpam-1535	710	10	verified	verify	VERB
ejpam-1535	710	11	:	:	PUNCT
ejpam-1535	710	12	proposition	proposition	NOUN
ejpam-1535	710	13	3	3	NUM
ejpam-1535	710	14	.	.	PUNCT
ejpam-1535	711	1	the	the	DET
ejpam-1535	711	2	composition	composition	NOUN
ejpam-1535	711	3	of	of	ADP
ejpam-1535	711	4	two	two	NUM
ejpam-1535	711	5	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	711	6	is	be	AUX
ejpam-1535	711	7	a	a	DET
ejpam-1535	711	8	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	711	9	,	,	PUNCT
ejpam-1535	711	10	hence	hence	ADV
ejpam-1535	711	11	restriction	restriction	NOUN
ejpam-1535	711	12	semigroups	semigroup	NOUN
ejpam-1535	711	13	and	and	CCONJ
ejpam-1535	711	14	∨-premorphisms	∨-premorphism	VERB
ejpam-1535	711	15	form	form	VERB
ejpam-1535	711	16	a	a	DET
ejpam-1535	711	17	category	category	NOUN
ejpam-1535	711	18	.	.	PUNCT
ejpam-1535	712	1	regarding	regard	VERB
ejpam-1535	712	2	restriction	restriction	NOUN
ejpam-1535	712	3	semigroups	semigroup	NOUN
ejpam-1535	712	4	as	as	ADP
ejpam-1535	712	5	algebras	algebra	NOUN
ejpam-1535	712	6	with	with	ADP
ejpam-1535	712	7	one	one	NUM
ejpam-1535	712	8	binary	binary	ADJ
ejpam-1535	712	9	operation	operation	NOUN
ejpam-1535	712	10	and	and	CCONJ
ejpam-1535	712	11	two	two	NUM
ejpam-1535	712	12	unary	unary	ADJ
ejpam-1535	712	13	operations	operation	NOUN
ejpam-1535	712	14	,	,	PUNCT
ejpam-1535	712	15	we	we	PRON
ejpam-1535	712	16	can	can	AUX
ejpam-1535	712	17	speak	speak	VERB
ejpam-1535	712	18	of	of	ADP
ejpam-1535	712	19	(	(	PUNCT
ejpam-1535	712	20	2,1,1)-morphisms	2,1,1)-morphism	NOUN
ejpam-1535	712	21	of	of	ADP
ejpam-1535	712	22	restriction	restriction	NOUN
ejpam-1535	712	23	semigroups	semigroup	NOUN
ejpam-1535	712	24	:	:	PUNCT
ejpam-1535	712	25	morphisms	morphism	NOUN
ejpam-1535	712	26	which	which	DET
ejpam-1535	712	27	respect	respect	VERB
ejpam-1535	712	28	+	+	CCONJ
ejpam-1535	712	29	and	and	CCONJ
ejpam-1535	712	30	∗.	∗.	PROPN
ejpam-1535	712	31	it	it	PRON
ejpam-1535	712	32	is	be	AUX
ejpam-1535	712	33	clear	clear	ADJ
ejpam-1535	712	34	that	that	SCONJ
ejpam-1535	712	35	any	any	DET
ejpam-1535	712	36	such	such	ADJ
ejpam-1535	712	37	morphism	morphism	NOUN
ejpam-1535	712	38	is	be	AUX
ejpam-1535	712	39	a	a	DET
ejpam-1535	712	40	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	712	41	.	.	PUNCT
ejpam-1535	713	1	the	the	DET
ejpam-1535	713	2	following	follow	VERB
ejpam-1535	713	3	results	result	NOUN
ejpam-1535	713	4	will	will	AUX
ejpam-1535	713	5	allow	allow	VERB
ejpam-1535	713	6	us	we	PRON
ejpam-1535	713	7	(	(	PUNCT
ejpam-1535	713	8	in	in	ADP
ejpam-1535	713	9	the	the	DET
ejpam-1535	713	10	next	next	ADJ
ejpam-1535	713	11	section	section	NOUN
ejpam-1535	713	12	)	)	PUNCT
ejpam-1535	713	13	to	to	PART
ejpam-1535	713	14	deduce	deduce	VERB
ejpam-1535	713	15	theorems	theorem	NOUN
ejpam-1535	713	16	on	on	ADP
ejpam-1535	713	17	(	(	PUNCT
ejpam-1535	713	18	2,1,1)-morphisms	2,1,1)-morphism	NOUN
ejpam-1535	713	19	from	from	ADP
ejpam-1535	713	20	those	those	PRON
ejpam-1535	713	21	proved	prove	VERB
ejpam-1535	713	22	here	here	ADV
ejpam-1535	713	23	for	for	ADP
ejpam-1535	713	24	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	713	25	.	.	PUNCT
ejpam-1535	714	1	lemma	lemma	PROPN
ejpam-1535	714	2	11	11	NUM
ejpam-1535	714	3	(	(	PUNCT
ejpam-1535	714	4	[	[	X
ejpam-1535	714	5	29	29	NUM
ejpam-1535	714	6	,	,	PUNCT
ejpam-1535	714	7	theorem	theorem	VERB
ejpam-1535	714	8	3.1.5	3.1.5	X
ejpam-1535	714	9	]	]	SYM
ejpam-1535	714	10	*	*	NUM
ejpam-1535	714	11	)	)	PUNCT
ejpam-1535	714	12	.	.	PUNCT
ejpam-1535	715	1	a	a	DET
ejpam-1535	715	2	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	715	3	of	of	ADP
ejpam-1535	715	4	restriction	restriction	NOUN
ejpam-1535	715	5	semigroups	semigroup	VERB
ejpam-1535	715	6	respects	respect	VERB
ejpam-1535	715	7	the	the	DET
ejpam-1535	715	8	restricted	restricted	ADJ
ejpam-1535	715	9	product	product	NOUN
ejpam-1535	715	10	(	(	PUNCT
ejpam-1535	715	11	7	7	NUM
ejpam-1535	715	12	)	)	PUNCT
ejpam-1535	715	13	.	.	PUNCT
ejpam-1535	716	1	proof	proof	NOUN
ejpam-1535	716	2	.	.	PUNCT
ejpam-1535	717	1	let	let	VERB
ejpam-1535	717	2	θ	θ	NOUN
ejpam-1535	717	3	:	:	PUNCT
ejpam-1535	717	4	s	s	X
ejpam-1535	717	5	→	→	SYM
ejpam-1535	717	6	t	t	PROPN
ejpam-1535	717	7	be	be	AUX
ejpam-1535	717	8	a	a	DET
ejpam-1535	717	9	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	717	10	of	of	ADP
ejpam-1535	717	11	restriction	restriction	NOUN
ejpam-1535	717	12	semigroups	semigroup	NOUN
ejpam-1535	717	13	,	,	PUNCT
ejpam-1535	717	14	and	and	CCONJ
ejpam-1535	717	15	suppose	suppose	VERB
ejpam-1535	717	16	that	that	SCONJ
ejpam-1535	717	17	∃s	∃s	PROPN
ejpam-1535	717	18	·	·	PUNCT
ejpam-1535	717	19	t	t	PROPN
ejpam-1535	717	20	in	in	ADP
ejpam-1535	717	21	s	s	PROPN
ejpam-1535	717	22	,	,	PUNCT
ejpam-1535	717	23	where	where	SCONJ
ejpam-1535	717	24	·	·	PUNCT
ejpam-1535	717	25	denotes	denote	VERB
ejpam-1535	717	26	the	the	DET
ejpam-1535	717	27	restricted	restricted	ADJ
ejpam-1535	717	28	product	product	NOUN
ejpam-1535	717	29	(	(	PUNCT
ejpam-1535	717	30	7	7	NUM
ejpam-1535	717	31	)	)	PUNCT
ejpam-1535	717	32	.	.	PUNCT
ejpam-1535	718	1	by	by	ADP
ejpam-1535	718	2	definition	definition	NOUN
ejpam-1535	718	3	of	of	ADP
ejpam-1535	718	4	·	·	PUNCT
ejpam-1535	718	5	,	,	PUNCT
ejpam-1535	718	6	we	we	PRON
ejpam-1535	718	7	have	have	AUX
ejpam-1535	718	8	s∗	s∗	PROPN
ejpam-1535	718	9	=	=	SYM
ejpam-1535	718	10	t+	t+	PUNCT
ejpam-1535	718	11	and	and	CCONJ
ejpam-1535	718	12	s	s	PROPN
ejpam-1535	718	13	·	·	PUNCT
ejpam-1535	718	14	t	t	PROPN
ejpam-1535	718	15	=	=	SYM
ejpam-1535	718	16	st	st	AUX
ejpam-1535	718	17	.	.	PROPN
ejpam-1535	718	18	observe	observe	VERB
ejpam-1535	718	19	further	far	ADV
ejpam-1535	718	20	that	that	PRON
ejpam-1535	718	21	s∗	s∗	PROPN
ejpam-1535	718	22	=	=	PUNCT
ejpam-1535	718	23	t+	t+	PUNCT
ejpam-1535	719	1	=	=	PRON
ejpam-1535	719	2	⇒	⇒	NOUN
ejpam-1535	719	3	s∗θ	s∗θ	NUM
ejpam-1535	719	4	=	=	SYM
ejpam-1535	719	5	t+θ	t+θ	NUM
ejpam-1535	719	6	=	=	NUM
ejpam-1535	719	7	⇒	⇒	NOUN
ejpam-1535	719	8	(	(	PUNCT
ejpam-1535	719	9	sθ)∗	sθ)∗	X
ejpam-1535	719	10	=	=	SYM
ejpam-1535	719	11	(	(	PUNCT
ejpam-1535	719	12	tθ)+	tθ)+	PROPN
ejpam-1535	719	13	,	,	PUNCT
ejpam-1535	719	14	using	use	VERB
ejpam-1535	719	15	lemma	lemma	PROPN
ejpam-1535	719	16	10(c	10(c	NUM
ejpam-1535	719	17	)	)	PUNCT
ejpam-1535	719	18	,	,	PUNCT
ejpam-1535	719	19	and	and	CCONJ
ejpam-1535	719	20	so	so	ADV
ejpam-1535	719	21	∃(sθ	∃(sθ	PROPN
ejpam-1535	719	22	)	)	PUNCT
ejpam-1535	719	23	·	·	PUNCT
ejpam-1535	719	24	(	(	PUNCT
ejpam-1535	719	25	tθ	tθ	NOUN
ejpam-1535	719	26	)	)	PUNCT
ejpam-1535	719	27	in	in	ADP
ejpam-1535	719	28	t	t	PROPN
ejpam-1535	719	29	.	.	PUNCT
ejpam-1535	720	1	it	it	PRON
ejpam-1535	720	2	follows	follow	VERB
ejpam-1535	720	3	further	far	ADV
ejpam-1535	720	4	from	from	ADP
ejpam-1535	720	5	the	the	DET
ejpam-1535	720	6	definition	definition	NOUN
ejpam-1535	720	7	of	of	ADP
ejpam-1535	720	8	θ	θ	PROPN
ejpam-1535	720	9	that	that	SCONJ
ejpam-1535	720	10	(	(	PUNCT
ejpam-1535	720	11	s	s	X
ejpam-1535	720	12	·	·	PUNCT
ejpam-1535	720	13	t)θ	t)θ	NOUN
ejpam-1535	720	14	≤	≤	NUM
ejpam-1535	720	15	(	(	PUNCT
ejpam-1535	720	16	sθ	sθ	NOUN
ejpam-1535	720	17	)	)	PUNCT
ejpam-1535	720	18	·	·	PUNCT
ejpam-1535	720	19	(	(	PUNCT
ejpam-1535	720	20	tθ	tθ	NOUN
ejpam-1535	720	21	)	)	PUNCT
ejpam-1535	720	22	=	=	SYM
ejpam-1535	720	23	(	(	PUNCT
ejpam-1535	720	24	sθ)(tθ	sθ)(tθ	PROPN
ejpam-1535	720	25	)	)	PUNCT
ejpam-1535	720	26	.	.	PUNCT
ejpam-1535	721	1	thus	thus	ADV
ejpam-1535	721	2	,	,	PUNCT
ejpam-1535	721	3	applying	apply	VERB
ejpam-1535	721	4	(	(	PUNCT
ejpam-1535	721	5	4	4	NUM
ejpam-1535	721	6	)	)	PUNCT
ejpam-1535	721	7	,	,	PUNCT
ejpam-1535	721	8	we	we	PRON
ejpam-1535	721	9	have	have	VERB
ejpam-1535	721	10	(	(	PUNCT
ejpam-1535	721	11	s	s	X
ejpam-1535	721	12	·	·	PUNCT
ejpam-1535	721	13	t)θ	t)θ	NOUN
ejpam-1535	722	1	=	=	PUNCT
ejpam-1535	723	1	[	[	X
ejpam-1535	723	2	(	(	PUNCT
ejpam-1535	723	3	s	s	X
ejpam-1535	723	4	·	·	PUNCT
ejpam-1535	723	5	t)θ]+	t)θ]+	X
ejpam-1535	723	6	(	(	PUNCT
ejpam-1535	723	7	sθ)(tθ	sθ)(tθ	PROPN
ejpam-1535	723	8	)	)	PUNCT
ejpam-1535	723	9	=	=	SYM
ejpam-1535	723	10	�	�	PROPN
ejpam-1535	723	11	(	(	PUNCT
ejpam-1535	723	12	s	s	PROPN
ejpam-1535	723	13	·	·	PUNCT
ejpam-1535	723	14	t)+θ	t)+θ	PROPN
ejpam-1535	723	15	�	�	PROPN
ejpam-1535	723	16	(	(	PUNCT
ejpam-1535	723	17	sθ)(tθ	sθ)(tθ	PROPN
ejpam-1535	723	18	)	)	PUNCT
ejpam-1535	723	19	=	=	SYM
ejpam-1535	723	20	�	�	PROPN
ejpam-1535	723	21	(	(	PUNCT
ejpam-1535	723	22	st)+θ	st)+θ	NOUN
ejpam-1535	723	23	�	�	PROPN
ejpam-1535	723	24	(	(	PUNCT
ejpam-1535	723	25	sθ)(tθ	sθ)(tθ	PROPN
ejpam-1535	723	26	)	)	PUNCT
ejpam-1535	723	27	=	=	SYM
ejpam-1535	723	28	�	�	PROPN
ejpam-1535	723	29	(	(	PUNCT
ejpam-1535	723	30	st+)+θ	st+)+θ	NOUN
ejpam-1535	723	31	�	�	PROPN
ejpam-1535	723	32	(	(	PUNCT
ejpam-1535	723	33	sθ)(tθ	sθ)(tθ	PROPN
ejpam-1535	723	34	)	)	PUNCT
ejpam-1535	723	35	=	=	SYM
ejpam-1535	723	36	�	�	PROPN
ejpam-1535	723	37	(	(	PUNCT
ejpam-1535	723	38	ss∗)+θ	ss∗)+θ	PROPN
ejpam-1535	723	39	�	�	PROPN
ejpam-1535	723	40	(	(	PUNCT
ejpam-1535	723	41	sθ)(tθ	sθ)(tθ	PROPN
ejpam-1535	723	42	)	)	PUNCT
ejpam-1535	723	43	=	=	SYM
ejpam-1535	723	44	�	�	PROPN
ejpam-1535	723	45	s+θ	s+θ	NUM
ejpam-1535	723	46	�	�	PROPN
ejpam-1535	723	47	(	(	PUNCT
ejpam-1535	723	48	sθ)(tθ	sθ)(tθ	PROPN
ejpam-1535	723	49	)	)	PUNCT
ejpam-1535	723	50	=	=	SYM
ejpam-1535	723	51	(	(	PUNCT
ejpam-1535	723	52	sθ)+	sθ)+	NOUN
ejpam-1535	723	53	(	(	PUNCT
ejpam-1535	723	54	sθ)(tθ	sθ)(tθ	PROPN
ejpam-1535	723	55	)	)	PUNCT
ejpam-1535	723	56	=	=	SYM
ejpam-1535	723	57	(	(	PUNCT
ejpam-1535	723	58	sθ)(tθ	sθ)(tθ	PROPN
ejpam-1535	723	59	)	)	PUNCT
ejpam-1535	723	60	=	=	SYM
ejpam-1535	723	61	(	(	PUNCT
ejpam-1535	723	62	sθ	sθ	NOUN
ejpam-1535	723	63	)	)	PUNCT
ejpam-1535	723	64	·	·	PUNCT
ejpam-1535	723	65	(	(	PUNCT
ejpam-1535	723	66	tθ	tθ	NOUN
ejpam-1535	723	67	)	)	PUNCT
ejpam-1535	723	68	.	.	PUNCT
ejpam-1535	724	1	hence	hence	ADV
ejpam-1535	724	2	θ	θ	PROPN
ejpam-1535	724	3	respects	respect	NOUN
ejpam-1535	724	4	restricted	restrict	VERB
ejpam-1535	724	5	products	product	NOUN
ejpam-1535	724	6	.	.	PUNCT
ejpam-1535	725	1	lemma	lemma	PROPN
ejpam-1535	725	2	12	12	NUM
ejpam-1535	725	3	(	(	PUNCT
ejpam-1535	725	4	[	[	X
ejpam-1535	725	5	29	29	NUM
ejpam-1535	725	6	,	,	PUNCT
ejpam-1535	725	7	theorem	theorem	VERB
ejpam-1535	725	8	3.1.5	3.1.5	X
ejpam-1535	725	9	]	]	SYM
ejpam-1535	725	10	*	*	NUM
ejpam-1535	725	11	)	)	PUNCT
ejpam-1535	725	12	.	.	PUNCT
ejpam-1535	726	1	let	let	VERB
ejpam-1535	726	2	s	s	PRON
ejpam-1535	726	3	and	and	CCONJ
ejpam-1535	726	4	t	t	PROPN
ejpam-1535	726	5	be	be	AUX
ejpam-1535	726	6	restriction	restriction	NOUN
ejpam-1535	726	7	semigroups	semigroup	NOUN
ejpam-1535	726	8	,	,	PUNCT
ejpam-1535	726	9	where	where	SCONJ
ejpam-1535	726	10	s	s	NOUN
ejpam-1535	726	11	has	have	AUX
ejpam-1535	726	12	distinguished	distinguish	VERB
ejpam-1535	726	13	subsemilattice	subsemilattice	NOUN
ejpam-1535	726	14	of	of	ADP
ejpam-1535	726	15	idempotents	idempotents	PROPN
ejpam-1535	726	16	e.	e.	PROPN
ejpam-1535	726	17	a	a	DET
ejpam-1535	726	18	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	726	19	θ	θ	PROPN
ejpam-1535	726	20	:	:	PUNCT
ejpam-1535	726	21	s	s	X
ejpam-1535	726	22	→	→	SYM
ejpam-1535	726	23	t	t	PROPN
ejpam-1535	726	24	is	be	AUX
ejpam-1535	726	25	a	a	DET
ejpam-1535	726	26	(	(	PUNCT
ejpam-1535	726	27	2,1,1)-morphism	2,1,1)-morphism	NUM
ejpam-1535	726	28	if	if	SCONJ
ejpam-1535	726	29	and	and	CCONJ
ejpam-1535	726	30	only	only	ADV
ejpam-1535	726	31	if	if	SCONJ
ejpam-1535	726	32	(	(	PUNCT
ejpam-1535	726	33	eθ	eθ	NOUN
ejpam-1535	726	34	)	)	PUNCT
ejpam-1535	726	35	(	(	PUNCT
ejpam-1535	726	36	f	f	PROPN
ejpam-1535	726	37	θ	θ	PROPN
ejpam-1535	726	38	)	)	PUNCT
ejpam-1535	726	39	=	=	SYM
ejpam-1535	727	1	(	(	PUNCT
ejpam-1535	727	2	e	e	NOUN
ejpam-1535	727	3	f	f	PROPN
ejpam-1535	727	4	)	)	PUNCT
ejpam-1535	727	5	θ	θ	PROPN
ejpam-1535	727	6	,	,	PUNCT
ejpam-1535	727	7	for	for	ADP
ejpam-1535	727	8	any	any	DET
ejpam-1535	727	9	e	e	NOUN
ejpam-1535	727	10	,	,	PUNCT
ejpam-1535	727	11	f	f	PROPN
ejpam-1535	727	12	∈	∈	PROPN
ejpam-1535	727	13	e.	e.	PROPN
ejpam-1535	727	14	proof	proof	PROPN
ejpam-1535	727	15	.	.	PUNCT
ejpam-1535	728	1	if	if	SCONJ
ejpam-1535	728	2	θ	θ	PROPN
ejpam-1535	728	3	is	be	AUX
ejpam-1535	728	4	a	a	DET
ejpam-1535	728	5	(	(	PUNCT
ejpam-1535	728	6	2,1,1)-morphism	2,1,1)-morphism	NUM
ejpam-1535	728	7	,	,	PUNCT
ejpam-1535	728	8	then	then	ADV
ejpam-1535	728	9	it	it	PRON
ejpam-1535	728	10	is	be	AUX
ejpam-1535	728	11	clear	clear	ADJ
ejpam-1535	728	12	that	that	SCONJ
ejpam-1535	728	13	(	(	PUNCT
ejpam-1535	728	14	eθ	eθ	X
ejpam-1535	728	15	)	)	PUNCT
ejpam-1535	728	16	(	(	PUNCT
ejpam-1535	728	17	f	f	PROPN
ejpam-1535	728	18	θ	θ	PROPN
ejpam-1535	728	19	)	)	PUNCT
ejpam-1535	728	20	=	=	SYM
ejpam-1535	729	1	(	(	PUNCT
ejpam-1535	729	2	e	e	NOUN
ejpam-1535	729	3	f	f	PROPN
ejpam-1535	729	4	)	)	PUNCT
ejpam-1535	729	5	θ	θ	PROPN
ejpam-1535	729	6	,	,	PUNCT
ejpam-1535	729	7	for	for	ADP
ejpam-1535	729	8	any	any	DET
ejpam-1535	729	9	e	e	NOUN
ejpam-1535	729	10	,	,	PUNCT
ejpam-1535	729	11	f	f	PROPN
ejpam-1535	729	12	∈	∈	PROPN
ejpam-1535	729	13	e	e	NOUN
ejpam-1535	729	14	,	,	PUNCT
ejpam-1535	729	15	so	so	SCONJ
ejpam-1535	729	16	we	we	PRON
ejpam-1535	729	17	move	move	VERB
ejpam-1535	729	18	straight	straight	ADV
ejpam-1535	729	19	to	to	ADP
ejpam-1535	729	20	the	the	DET
ejpam-1535	729	21	converse	converse	NOUN
ejpam-1535	729	22	.	.	PUNCT
ejpam-1535	730	1	we	we	PRON
ejpam-1535	730	2	need	need	VERB
ejpam-1535	730	3	only	only	ADV
ejpam-1535	730	4	deal	deal	VERB
ejpam-1535	730	5	with	with	ADP
ejpam-1535	730	6	the	the	DET
ejpam-1535	730	7	“	"	PUNCT
ejpam-1535	730	8	2	2	NUM
ejpam-1535	730	9	”	"	PUNCT
ejpam-1535	730	10	part	part	NOUN
ejpam-1535	730	11	of	of	ADP
ejpam-1535	730	12	“	"	PUNCT
ejpam-1535	730	13	(	(	PUNCT
ejpam-1535	730	14	2,1,1)morphism	2,1,1)morphism	NUM
ejpam-1535	730	15	”	"	PUNCT
ejpam-1535	730	16	,	,	PUNCT
ejpam-1535	730	17	since	since	SCONJ
ejpam-1535	730	18	both	both	DET
ejpam-1535	730	19	“	"	PUNCT
ejpam-1535	730	20	1	1	NUM
ejpam-1535	730	21	”	"	PUNCT
ejpam-1535	730	22	parts	part	NOUN
ejpam-1535	730	23	are	be	AUX
ejpam-1535	730	24	taken	take	VERB
ejpam-1535	730	25	care	care	NOUN
ejpam-1535	730	26	of	of	ADP
ejpam-1535	730	27	by	by	ADP
ejpam-1535	730	28	lemma	lemma	PROPN
ejpam-1535	730	29	10(c	10(c	NUM
ejpam-1535	730	30	)	)	PUNCT
ejpam-1535	730	31	.	.	PUNCT
ejpam-1535	731	1	c.	c.	PROPN
ejpam-1535	731	2	hollings	holling	NOUN
ejpam-1535	731	3	/	/	SYM
ejpam-1535	731	4	eur	eur	PROPN
ejpam-1535	731	5	.	.	PUNCT
ejpam-1535	732	1	j.	j.	PROPN
ejpam-1535	732	2	pure	pure	PROPN
ejpam-1535	732	3	appl	appl	PROPN
ejpam-1535	732	4	.	.	PROPN
ejpam-1535	732	5	math	math	PROPN
ejpam-1535	732	6	,	,	PUNCT
ejpam-1535	732	7	5	5	NUM
ejpam-1535	732	8	(	(	PUNCT
ejpam-1535	732	9	2012	2012	NUM
ejpam-1535	732	10	)	)	PUNCT
ejpam-1535	732	11	,	,	PUNCT
ejpam-1535	732	12	414	414	NUM
ejpam-1535	732	13	-	-	SYM
ejpam-1535	732	14	450	450	NUM
ejpam-1535	732	15	439	439	NUM
ejpam-1535	732	16	suppose	suppose	VERB
ejpam-1535	732	17	that	that	SCONJ
ejpam-1535	732	18	(	(	PUNCT
ejpam-1535	732	19	eθ	eθ	X
ejpam-1535	732	20	)	)	PUNCT
ejpam-1535	732	21	(	(	PUNCT
ejpam-1535	732	22	f	f	PROPN
ejpam-1535	732	23	θ	θ	PROPN
ejpam-1535	732	24	)	)	PUNCT
ejpam-1535	732	25	=	=	SYM
ejpam-1535	732	26	(	(	PUNCT
ejpam-1535	732	27	e	e	NOUN
ejpam-1535	732	28	f	f	PROPN
ejpam-1535	732	29	)	)	PUNCT
ejpam-1535	732	30	θ	θ	PROPN
ejpam-1535	732	31	,	,	PUNCT
ejpam-1535	732	32	for	for	ADP
ejpam-1535	732	33	any	any	DET
ejpam-1535	732	34	e	e	NOUN
ejpam-1535	732	35	,	,	PUNCT
ejpam-1535	732	36	f	f	PROPN
ejpam-1535	732	37	∈	∈	PROPN
ejpam-1535	732	38	e	e	NOUN
ejpam-1535	732	39	,	,	PUNCT
ejpam-1535	732	40	and	and	CCONJ
ejpam-1535	732	41	take	take	VERB
ejpam-1535	732	42	a	a	DET
ejpam-1535	732	43	(	(	PUNCT
ejpam-1535	732	44	semigroup	semigroup	NOUN
ejpam-1535	732	45	)	)	PUNCT
ejpam-1535	732	46	product	product	NOUN
ejpam-1535	732	47	st	st	PROPN
ejpam-1535	732	48	∈	∈	PROPN
ejpam-1535	732	49	s.	s.	PROPN
ejpam-1535	732	50	we	we	PRON
ejpam-1535	732	51	notice	notice	VERB
ejpam-1535	732	52	that	that	SCONJ
ejpam-1535	733	1	st	st	PROPN
ejpam-1535	733	2	=	=	SYM
ejpam-1535	733	3	(	(	PUNCT
ejpam-1535	733	4	se)(et	se)(et	NOUN
ejpam-1535	733	5	)	)	PUNCT
ejpam-1535	733	6	,	,	PUNCT
ejpam-1535	734	1	where	where	SCONJ
ejpam-1535	734	2	e	e	NOUN
ejpam-1535	734	3	=	=	PRON
ejpam-1535	734	4	s∗	s∗	PROPN
ejpam-1535	734	5	t+	t+	VERB
ejpam-1535	734	6	.	.	PUNCT
ejpam-1535	734	7	indeed	indeed	ADV
ejpam-1535	734	8	,	,	PUNCT
ejpam-1535	734	9	we	we	PRON
ejpam-1535	734	10	observe	observe	VERB
ejpam-1535	734	11	further	far	ADV
ejpam-1535	734	12	that	that	SCONJ
ejpam-1535	734	13	the	the	DET
ejpam-1535	734	14	restricted	restricted	ADJ
ejpam-1535	734	15	product	product	NOUN
ejpam-1535	734	16	(	(	PUNCT
ejpam-1535	734	17	se	se	X
ejpam-1535	734	18	)	)	PUNCT
ejpam-1535	734	19	·	·	PUNCT
ejpam-1535	734	20	(	(	PUNCT
ejpam-1535	734	21	et	et	NOUN
ejpam-1535	734	22	)	)	PUNCT
ejpam-1535	734	23	is	be	AUX
ejpam-1535	734	24	defined	define	VERB
ejpam-1535	734	25	,	,	PUNCT
ejpam-1535	734	26	since	since	SCONJ
ejpam-1535	734	27	(	(	PUNCT
ejpam-1535	734	28	se)∗	se)∗	PROPN
ejpam-1535	734	29	=	=	SYM
ejpam-1535	734	30	(	(	PUNCT
ejpam-1535	734	31	ss∗	ss∗	NOUN
ejpam-1535	734	32	t+)∗	t+)∗	NOUN
ejpam-1535	734	33	=	=	PUNCT
ejpam-1535	734	34	(	(	PUNCT
ejpam-1535	735	1	st+)∗	st+)∗	PROPN
ejpam-1535	735	2	=	=	PUNCT
ejpam-1535	735	3	(	(	PUNCT
ejpam-1535	735	4	s∗	s∗	PROPN
ejpam-1535	735	5	t+)∗	t+)∗	PROPN
ejpam-1535	735	6	=	=	PUNCT
ejpam-1535	735	7	(	(	PUNCT
ejpam-1535	735	8	s∗	s∗	PROPN
ejpam-1535	735	9	t+)+	t+)+	NOUN
ejpam-1535	735	10	=	=	SYM
ejpam-1535	735	11	(	(	PUNCT
ejpam-1535	735	12	s∗	s∗	PROPN
ejpam-1535	735	13	t)+	t)+	NOUN
ejpam-1535	735	14	=	=	PUNCT
ejpam-1535	735	15	(	(	PUNCT
ejpam-1535	735	16	s∗	s∗	PROPN
ejpam-1535	735	17	t+	t+	X
ejpam-1535	735	18	t)+	t)+	NOUN
ejpam-1535	735	19	=	=	SYM
ejpam-1535	735	20	(	(	PUNCT
ejpam-1535	735	21	et)+	et)+	NOUN
ejpam-1535	735	22	.	.	PUNCT
ejpam-1535	736	1	thus	thus	ADV
ejpam-1535	736	2	st	st	X
ejpam-1535	736	3	=	=	SYM
ejpam-1535	736	4	(	(	PUNCT
ejpam-1535	736	5	se	se	X
ejpam-1535	736	6	)	)	PUNCT
ejpam-1535	736	7	·	·	PUNCT
ejpam-1535	736	8	(	(	PUNCT
ejpam-1535	736	9	et	et	NOUN
ejpam-1535	736	10	)	)	PUNCT
ejpam-1535	736	11	.	.	PUNCT
ejpam-1535	737	1	then	then	ADV
ejpam-1535	737	2	,	,	PUNCT
ejpam-1535	737	3	since	since	SCONJ
ejpam-1535	737	4	θ	θ	PROPN
ejpam-1535	737	5	respects	respect	NOUN
ejpam-1535	737	6	restricted	restrict	VERB
ejpam-1535	737	7	products	product	NOUN
ejpam-1535	737	8	(	(	PUNCT
ejpam-1535	737	9	by	by	ADP
ejpam-1535	737	10	lemma	lemma	PROPN
ejpam-1535	737	11	11	11	NUM
ejpam-1535	737	12	)	)	PUNCT
ejpam-1535	737	13	,	,	PUNCT
ejpam-1535	737	14	we	we	PRON
ejpam-1535	737	15	have	have	VERB
ejpam-1535	737	16	(	(	PUNCT
ejpam-1535	737	17	st)θ	st)θ	PROPN
ejpam-1535	737	18	=	=	SYM
ejpam-1535	737	19	(	(	PUNCT
ejpam-1535	737	20	se)θ	se)θ	PROPN
ejpam-1535	737	21	·	·	PUNCT
ejpam-1535	737	22	(	(	PUNCT
ejpam-1535	737	23	et)θ	et)θ	NUM
ejpam-1535	737	24	=	=	SYM
ejpam-1535	737	25	(	(	PUNCT
ejpam-1535	737	26	se)θ(et)θ	se)θ(et)θ	PROPN
ejpam-1535	737	27	.	.	PUNCT
ejpam-1535	738	1	we	we	PRON
ejpam-1535	738	2	next	next	ADV
ejpam-1535	738	3	show	show	VERB
ejpam-1535	738	4	that	that	SCONJ
ejpam-1535	738	5	(	(	PUNCT
ejpam-1535	738	6	se)θ	se)θ	NOUN
ejpam-1535	738	7	=	=	SYM
ejpam-1535	738	8	(	(	PUNCT
ejpam-1535	738	9	sθ)(eθ	sθ)(eθ	PROPN
ejpam-1535	738	10	)	)	PUNCT
ejpam-1535	738	11	;	;	PUNCT
ejpam-1535	738	12	we	we	PRON
ejpam-1535	738	13	do	do	VERB
ejpam-1535	738	14	so	so	ADV
ejpam-1535	738	15	by	by	ADP
ejpam-1535	738	16	stepping	step	VERB
ejpam-1535	738	17	across	across	ADP
ejpam-1535	738	18	into	into	ADP
ejpam-1535	738	19	the	the	DET
ejpam-1535	738	20	inductive	inductive	ADJ
ejpam-1535	738	21	category	category	NOUN
ejpam-1535	738	22	c(t	c(t	PROPN
ejpam-1535	738	23	)	)	PUNCT
ejpam-1535	738	24	and	and	CCONJ
ejpam-1535	738	25	employing	employ	VERB
ejpam-1535	738	26	lemma	lemma	PROPN
ejpam-1535	738	27	5(c	5(c	NUM
ejpam-1535	738	28	)	)	PUNCT
ejpam-1535	738	29	.	.	PUNCT
ejpam-1535	739	1	notice	notice	VERB
ejpam-1535	739	2	first	first	ADV
ejpam-1535	739	3	of	of	ADP
ejpam-1535	739	4	all	all	PRON
ejpam-1535	739	5	that	that	PRON
ejpam-1535	739	6	(	(	PUNCT
ejpam-1535	739	7	se)θ	se)θ	NOUN
ejpam-1535	739	8	≤	≤	NOUN
ejpam-1535	739	9	(	(	PUNCT
ejpam-1535	739	10	sθ)(eθ	sθ)(eθ	PROPN
ejpam-1535	739	11	)	)	PUNCT
ejpam-1535	739	12	,	,	PUNCT
ejpam-1535	739	13	by	by	ADP
ejpam-1535	739	14	definition	definition	NOUN
ejpam-1535	739	15	of	of	ADP
ejpam-1535	739	16	θ	θ	PROPN
ejpam-1535	739	17	,	,	PUNCT
ejpam-1535	739	18	and	and	CCONJ
ejpam-1535	739	19	that	that	SCONJ
ejpam-1535	739	20	,	,	PUNCT
ejpam-1535	739	21	naturally	naturally	ADV
ejpam-1535	739	22	,	,	PUNCT
ejpam-1535	739	23	(	(	PUNCT
ejpam-1535	739	24	sθ)(eθ	sθ)(eθ	NOUN
ejpam-1535	739	25	)	)	PUNCT
ejpam-1535	739	26	≤	≤	NOUN
ejpam-1535	739	27	(	(	PUNCT
ejpam-1535	739	28	sθ)(eθ	sθ)(eθ	PROPN
ejpam-1535	739	29	)	)	PUNCT
ejpam-1535	739	30	.	.	PUNCT
ejpam-1535	740	1	we	we	PRON
ejpam-1535	740	2	now	now	ADV
ejpam-1535	740	3	observe	observe	VERB
ejpam-1535	740	4	that	that	SCONJ
ejpam-1535	740	5	,	,	PUNCT
ejpam-1535	740	6	on	on	ADP
ejpam-1535	740	7	the	the	DET
ejpam-1535	740	8	one	one	NUM
ejpam-1535	740	9	hand	hand	NOUN
ejpam-1535	740	10	,	,	PUNCT
ejpam-1535	740	11	r	r	NOUN
ejpam-1535	740	12	(	(	PUNCT
ejpam-1535	740	13	(	(	PUNCT
ejpam-1535	740	14	se)θ	se)θ	NOUN
ejpam-1535	740	15	)	)	PUNCT
ejpam-1535	740	16	=	=	SYM
ejpam-1535	740	17	(	(	PUNCT
ejpam-1535	740	18	(	(	PUNCT
ejpam-1535	740	19	se)θ)∗	se)θ)∗	X
ejpam-1535	740	20	=	=	SYM
ejpam-1535	740	21	(	(	PUNCT
ejpam-1535	740	22	se)∗θ	se)∗θ	NUM
ejpam-1535	740	23	=	=	SYM
ejpam-1535	740	24	(	(	PUNCT
ejpam-1535	740	25	s∗e)∗θ	s∗e)∗θ	NOUN
ejpam-1535	740	26	=	=	SYM
ejpam-1535	740	27	(	(	PUNCT
ejpam-1535	740	28	s∗e)θ	s∗e)θ	X
ejpam-1535	740	29	=	=	PUNCT
ejpam-1535	740	30	eθ	eθ	PROPN
ejpam-1535	740	31	(	(	PUNCT
ejpam-1535	740	32	since	since	SCONJ
ejpam-1535	740	33	e	e	PROPN
ejpam-1535	740	34	=	=	PRON
ejpam-1535	740	35	s∗	s∗	PROPN
ejpam-1535	740	36	t+	t+	PUNCT
ejpam-1535	740	37	≤	≤	NUM
ejpam-1535	740	38	s∗	s∗	PROPN
ejpam-1535	740	39	)	)	PUNCT
ejpam-1535	740	40	,	,	PUNCT
ejpam-1535	740	41	whilst	whilst	SCONJ
ejpam-1535	740	42	on	on	ADP
ejpam-1535	740	43	the	the	DET
ejpam-1535	740	44	other	other	ADJ
ejpam-1535	740	45	,	,	PUNCT
ejpam-1535	740	46	r	r	NOUN
ejpam-1535	740	47	(	(	PUNCT
ejpam-1535	740	48	(	(	PUNCT
ejpam-1535	740	49	sθ)(eθ	sθ)(eθ	ADJ
ejpam-1535	740	50	)	)	PUNCT
ejpam-1535	740	51	)	)	PUNCT
ejpam-1535	740	52	=	=	SYM
ejpam-1535	740	53	(	(	PUNCT
ejpam-1535	740	54	(	(	PUNCT
ejpam-1535	740	55	sθ)(eθ))∗	sθ)(eθ))∗	NOUN
ejpam-1535	740	56	=	=	SYM
ejpam-1535	740	57	�	�	PROPN
ejpam-1535	740	58	(	(	PUNCT
ejpam-1535	740	59	sθ)∗(eθ	sθ)∗(eθ	NOUN
ejpam-1535	740	60	)	)	PUNCT
ejpam-1535	740	61	�	�	PROPN
ejpam-1535	740	62	∗	∗	NOUN
ejpam-1535	740	63	=	=	SYM
ejpam-1535	740	64	�	�	PROPN
ejpam-1535	740	65	(	(	PUNCT
ejpam-1535	740	66	s∗θ)(eθ	s∗θ)(eθ	NOUN
ejpam-1535	740	67	)	)	PUNCT
ejpam-1535	740	68	�	�	PROPN
ejpam-1535	740	69	∗	∗	NOUN
ejpam-1535	740	70	=	=	SYM
ejpam-1535	740	71	�	�	PROPN
ejpam-1535	740	72	(	(	PUNCT
ejpam-1535	740	73	s∗e)θ	s∗e)θ	PROPN
ejpam-1535	740	74	�	�	PROPN
ejpam-1535	740	75	∗	∗	NOUN
ejpam-1535	740	76	=	=	SYM
ejpam-1535	740	77	(	(	PUNCT
ejpam-1535	740	78	eθ)∗	eθ)∗	PROPN
ejpam-1535	740	79	=	=	SYM
ejpam-1535	740	80	eθ	eθ	PROPN
ejpam-1535	740	81	.	.	PUNCT
ejpam-1535	741	1	thus	thus	ADV
ejpam-1535	741	2	r	r	X
ejpam-1535	741	3	(	(	PUNCT
ejpam-1535	741	4	(	(	PUNCT
ejpam-1535	741	5	se)θ	se)θ	NOUN
ejpam-1535	741	6	)	)	PUNCT
ejpam-1535	741	7	=	=	SYM
ejpam-1535	741	8	r	r	NOUN
ejpam-1535	741	9	(	(	PUNCT
ejpam-1535	741	10	(	(	PUNCT
ejpam-1535	741	11	sθ)(eθ	sθ)(eθ	PROPN
ejpam-1535	741	12	)	)	PUNCT
ejpam-1535	741	13	)	)	PUNCT
ejpam-1535	741	14	,	,	PUNCT
ejpam-1535	741	15	and	and	CCONJ
ejpam-1535	741	16	so	so	ADV
ejpam-1535	741	17	(	(	PUNCT
ejpam-1535	741	18	se)θ	se)θ	NOUN
ejpam-1535	741	19	=	=	SYM
ejpam-1535	741	20	(	(	PUNCT
ejpam-1535	741	21	sθ)(eθ	sθ)(eθ	PROPN
ejpam-1535	741	22	)	)	PUNCT
ejpam-1535	741	23	,	,	PUNCT
ejpam-1535	741	24	by	by	ADP
ejpam-1535	741	25	lemma	lemma	PROPN
ejpam-1535	741	26	5(c	5(c	NUM
ejpam-1535	741	27	)	)	PUNCT
ejpam-1535	741	28	.	.	PUNCT
ejpam-1535	742	1	it	it	PRON
ejpam-1535	742	2	follows	follow	VERB
ejpam-1535	742	3	in	in	ADP
ejpam-1535	742	4	a	a	DET
ejpam-1535	742	5	similar	similar	ADJ
ejpam-1535	742	6	manner	manner	NOUN
ejpam-1535	742	7	that	that	SCONJ
ejpam-1535	742	8	(	(	PUNCT
ejpam-1535	742	9	et)θ	et)θ	PROPN
ejpam-1535	742	10	=	=	SYM
ejpam-1535	742	11	(	(	PUNCT
ejpam-1535	742	12	eθ)(tθ	eθ)(tθ	PROPN
ejpam-1535	742	13	)	)	PUNCT
ejpam-1535	742	14	.	.	PUNCT
ejpam-1535	743	1	finally	finally	ADV
ejpam-1535	743	2	,	,	PUNCT
ejpam-1535	743	3	putting	put	VERB
ejpam-1535	743	4	all	all	DET
ejpam-1535	743	5	the	the	DET
ejpam-1535	743	6	pieces	piece	NOUN
ejpam-1535	743	7	together	together	ADV
ejpam-1535	743	8	,	,	PUNCT
ejpam-1535	743	9	we	we	PRON
ejpam-1535	743	10	have	have	VERB
ejpam-1535	743	11	:	:	PUNCT
ejpam-1535	743	12	(	(	PUNCT
ejpam-1535	743	13	st)θ	st)θ	PROPN
ejpam-1535	743	14	=	=	SYM
ejpam-1535	743	15	(	(	PUNCT
ejpam-1535	743	16	se)θ(et)θ	se)θ(et)θ	NOUN
ejpam-1535	743	17	=	=	SYM
ejpam-1535	743	18	(	(	PUNCT
ejpam-1535	743	19	sθ)(eθ)(eθ)(tθ	sθ)(eθ)(eθ)(tθ	NOUN
ejpam-1535	743	20	)	)	PUNCT
ejpam-1535	743	21	=	=	PUNCT
ejpam-1535	743	22	(	(	PUNCT
ejpam-1535	743	23	sθ)(eθ)(tθ	sθ)(eθ)(tθ	NOUN
ejpam-1535	743	24	)	)	PUNCT
ejpam-1535	743	25	=	=	SYM
ejpam-1535	743	26	(	(	PUNCT
ejpam-1535	743	27	sθ	sθ	PROPN
ejpam-1535	743	28	)	)	PUNCT
ejpam-1535	743	29	�	�	PROPN
ejpam-1535	743	30	(	(	PUNCT
ejpam-1535	743	31	s∗	s∗	PROPN
ejpam-1535	743	32	t+)θ	t+)θ	PROPN
ejpam-1535	743	33	�	�	PROPN
ejpam-1535	743	34	(	(	PUNCT
ejpam-1535	743	35	tθ	tθ	NOUN
ejpam-1535	743	36	)	)	PUNCT
ejpam-1535	743	37	=	=	SYM
ejpam-1535	743	38	(	(	PUNCT
ejpam-1535	743	39	sθ)(s∗θ)(t+θ)(tθ	sθ)(s∗θ)(t+θ)(tθ	NOUN
ejpam-1535	743	40	)	)	PUNCT
ejpam-1535	743	41	=	=	SYM
ejpam-1535	743	42	(	(	PUNCT
ejpam-1535	743	43	sθ)(sθ)∗(tθ)+(tθ	sθ)(sθ)∗(tθ)+(tθ	NOUN
ejpam-1535	743	44	)	)	PUNCT
ejpam-1535	743	45	=	=	PUNCT
ejpam-1535	743	46	(	(	PUNCT
ejpam-1535	743	47	sθ)(tθ	sθ)(tθ	PROPN
ejpam-1535	743	48	)	)	PUNCT
ejpam-1535	743	49	.	.	PUNCT
ejpam-1535	744	1	hence	hence	ADV
ejpam-1535	744	2	θ	θ	PROPN
ejpam-1535	744	3	is	be	AUX
ejpam-1535	744	4	a	a	DET
ejpam-1535	744	5	(	(	PUNCT
ejpam-1535	744	6	2,1,1)-morphism	2,1,1)-morphism	NUM
ejpam-1535	744	7	.	.	PUNCT
ejpam-1535	745	1	we	we	PRON
ejpam-1535	745	2	aim	aim	VERB
ejpam-1535	745	3	to	to	PART
ejpam-1535	745	4	obtain	obtain	VERB
ejpam-1535	745	5	an	an	DET
ejpam-1535	745	6	isomorphism	isomorphism	NOUN
ejpam-1535	745	7	of	of	ADP
ejpam-1535	745	8	categories	category	NOUN
ejpam-1535	745	9	involving	involve	VERB
ejpam-1535	745	10	the	the	DET
ejpam-1535	745	11	category	category	NOUN
ejpam-1535	745	12	of	of	ADP
ejpam-1535	745	13	restriction	restriction	NOUN
ejpam-1535	745	14	semigroups	semigroup	NOUN
ejpam-1535	745	15	and	and	CCONJ
ejpam-1535	745	16	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	745	17	.	.	PUNCT
ejpam-1535	746	1	we	we	PRON
ejpam-1535	746	2	therefore	therefore	ADV
ejpam-1535	746	3	need	need	VERB
ejpam-1535	746	4	to	to	PART
ejpam-1535	746	5	decide	decide	VERB
ejpam-1535	746	6	what	what	PRON
ejpam-1535	746	7	the	the	DET
ejpam-1535	746	8	arrows	arrow	NOUN
ejpam-1535	746	9	will	will	AUX
ejpam-1535	746	10	be	be	AUX
ejpam-1535	746	11	in	in	ADP
ejpam-1535	746	12	the	the	DET
ejpam-1535	746	13	corresponding	correspond	VERB
ejpam-1535	746	14	category	category	NOUN
ejpam-1535	746	15	of	of	ADP
ejpam-1535	746	16	inductive	inductive	ADJ
ejpam-1535	746	17	categories	category	NOUN
ejpam-1535	746	18	.	.	PUNCT
ejpam-1535	747	1	these	these	PRON
ejpam-1535	747	2	will	will	AUX
ejpam-1535	747	3	be	be	AUX
ejpam-1535	747	4	so	so	ADV
ejpam-1535	747	5	-	-	PUNCT
ejpam-1535	747	6	called	call	VERB
ejpam-1535	747	7	ordered	order	VERB
ejpam-1535	747	8	functors	functor	NOUN
ejpam-1535	747	9	.	.	PUNCT
ejpam-1535	748	1	we	we	PRON
ejpam-1535	748	2	note	note	VERB
ejpam-1535	748	3	that	that	SCONJ
ejpam-1535	748	4	,	,	PUNCT
ejpam-1535	748	5	just	just	ADV
ejpam-1535	748	6	like	like	ADP
ejpam-1535	748	7	categories	category	NOUN
ejpam-1535	748	8	,	,	PUNCT
ejpam-1535	748	9	we	we	PRON
ejpam-1535	748	10	will	will	AUX
ejpam-1535	748	11	be	be	AUX
ejpam-1535	748	12	using	use	VERB
ejpam-1535	748	13	the	the	DET
ejpam-1535	748	14	term	term	NOUN
ejpam-1535	748	15	“	"	PUNCT
ejpam-1535	748	16	functor	functor	NOUN
ejpam-1535	748	17	”	"	PUNCT
ejpam-1535	748	18	in	in	ADP
ejpam-1535	748	19	two	two	NUM
ejpam-1535	748	20	slightly	slightly	ADV
ejpam-1535	748	21	different	different	ADJ
ejpam-1535	748	22	,	,	PUNCT
ejpam-1535	748	23	though	though	SCONJ
ejpam-1535	748	24	equivalent	equivalent	ADJ
ejpam-1535	748	25	,	,	PUNCT
ejpam-1535	748	26	senses	sense	NOUN
ejpam-1535	748	27	,	,	PUNCT
ejpam-1535	748	28	depending	depend	VERB
ejpam-1535	748	29	on	on	ADP
ejpam-1535	748	30	how	how	SCONJ
ejpam-1535	748	31	we	we	PRON
ejpam-1535	748	32	are	be	AUX
ejpam-1535	748	33	regarding	regard	VERB
ejpam-1535	748	34	the	the	DET
ejpam-1535	748	35	underlying	underlie	VERB
ejpam-1535	748	36	categories	category	NOUN
ejpam-1535	748	37	:	:	PUNCT
ejpam-1535	748	38	we	we	PRON
ejpam-1535	748	39	will	will	AUX
ejpam-1535	748	40	have	have	VERB
ejpam-1535	748	41	functors	functor	NOUN
ejpam-1535	748	42	between	between	ADP
ejpam-1535	748	43	categories	category	NOUN
ejpam-1535	748	44	of	of	ADP
ejpam-1535	748	45	semigroups	semigroup	NOUN
ejpam-1535	748	46	,	,	PUNCT
ejpam-1535	748	47	say	say	INTJ
ejpam-1535	748	48	,	,	PUNCT
ejpam-1535	748	49	where	where	SCONJ
ejpam-1535	748	50	the	the	DET
ejpam-1535	748	51	categories	category	NOUN
ejpam-1535	748	52	are	be	AUX
ejpam-1535	748	53	viewed	view	VERB
ejpam-1535	748	54	in	in	ADP
ejpam-1535	748	55	sense	sense	NOUN
ejpam-1535	748	56	(	(	PUNCT
ejpam-1535	748	57	♠	♠	NOUN
ejpam-1535	748	58	)	)	PUNCT
ejpam-1535	748	59	,	,	PUNCT
ejpam-1535	748	60	and	and	CCONJ
ejpam-1535	748	61	functors	functor	NOUN
ejpam-1535	748	62	between	between	ADP
ejpam-1535	748	63	categories	category	NOUN
ejpam-1535	748	64	viewed	view	VERB
ejpam-1535	748	65	in	in	ADP
ejpam-1535	748	66	sense	sense	NOUN
ejpam-1535	748	67	(	(	PUNCT
ejpam-1535	748	68	♣	♣	NOUN
ejpam-1535	748	69	)	)	PUNCT
ejpam-1535	748	70	.	.	PUNCT
ejpam-1535	749	1	it	it	PRON
ejpam-1535	749	2	is	be	AUX
ejpam-1535	749	3	this	this	DET
ejpam-1535	749	4	latter	latter	ADJ
ejpam-1535	749	5	sense	sense	NOUN
ejpam-1535	749	6	of	of	ADP
ejpam-1535	749	7	“	"	PUNCT
ejpam-1535	749	8	functor	functor	PROPN
ejpam-1535	749	9	”	"	PUNCT
ejpam-1535	749	10	which	which	PRON
ejpam-1535	749	11	we	we	PRON
ejpam-1535	749	12	now	now	ADV
ejpam-1535	749	13	define	define	VERB
ejpam-1535	749	14	:	:	PUNCT
ejpam-1535	749	15	definition	definition	NOUN
ejpam-1535	749	16	14	14	NUM
ejpam-1535	749	17	.	.	PUNCT
ejpam-1535	750	1	let	let	VERB
ejpam-1535	750	2	c	c	NOUN
ejpam-1535	750	3	and	and	CCONJ
ejpam-1535	750	4	d	d	PROPN
ejpam-1535	750	5	be	be	AUX
ejpam-1535	750	6	categories	category	NOUN
ejpam-1535	750	7	.	.	PUNCT
ejpam-1535	751	1	a	a	DET
ejpam-1535	751	2	function	function	NOUN
ejpam-1535	751	3	φ	φ	NOUN
ejpam-1535	751	4	:	:	PUNCT
ejpam-1535	751	5	c	c	X
ejpam-1535	751	6	→	→	PUNCT
ejpam-1535	751	7	d	d	X
ejpam-1535	751	8	is	be	AUX
ejpam-1535	751	9	called	call	VERB
ejpam-1535	751	10	a	a	DET
ejpam-1535	751	11	functor	functor	NOUN
ejpam-1535	751	12	if	if	SCONJ
ejpam-1535	751	13	it	it	PRON
ejpam-1535	751	14	satisfies	satisfy	VERB
ejpam-1535	751	15	the	the	DET
ejpam-1535	751	16	following	follow	VERB
ejpam-1535	751	17	condition	condition	NOUN
ejpam-1535	751	18	:	:	PUNCT
ejpam-1535	751	19	(	(	PUNCT
ejpam-1535	751	20	f	f	X
ejpam-1535	751	21	)	)	PUNCT
ejpam-1535	751	22	if	if	SCONJ
ejpam-1535	751	23	∃x	∃x	PROPN
ejpam-1535	751	24	·	·	PUNCT
ejpam-1535	751	25	y	y	NOUN
ejpam-1535	751	26	in	in	ADP
ejpam-1535	751	27	c	c	PROPN
ejpam-1535	751	28	,	,	PUNCT
ejpam-1535	751	29	then	then	ADV
ejpam-1535	751	30	∃(xφ	∃(xφ	NOUN
ejpam-1535	751	31	)	)	PUNCT
ejpam-1535	751	32	·	·	PUNCT
ejpam-1535	751	33	(	(	PUNCT
ejpam-1535	751	34	yφ	yφ	NOUN
ejpam-1535	751	35	)	)	PUNCT
ejpam-1535	751	36	in	in	ADP
ejpam-1535	751	37	d	d	PROPN
ejpam-1535	751	38	and	and	CCONJ
ejpam-1535	751	39	(	(	PUNCT
ejpam-1535	751	40	xφ	xφ	PROPN
ejpam-1535	751	41	)	)	PUNCT
ejpam-1535	751	42	·	·	PUNCT
ejpam-1535	752	1	(	(	PUNCT
ejpam-1535	752	2	yφ	yφ	X
ejpam-1535	752	3	)	)	PUNCT
ejpam-1535	752	4	=	=	SYM
ejpam-1535	752	5	(	(	PUNCT
ejpam-1535	752	6	x	x	X
ejpam-1535	752	7	·	·	PUNCT
ejpam-1535	752	8	y)φ	y)φ	X
ejpam-1535	752	9	.	.	PUNCT
ejpam-1535	753	1	lemma	lemma	PROPN
ejpam-1535	753	2	13	13	NUM
ejpam-1535	753	3	(	(	PUNCT
ejpam-1535	753	4	[	[	X
ejpam-1535	753	5	f	f	X
ejpam-1535	753	6	]	]	X
ejpam-1535	753	7	)	)	PUNCT
ejpam-1535	753	8	.	.	PUNCT
ejpam-1535	754	1	let	let	VERB
ejpam-1535	754	2	φ	φ	NOUN
ejpam-1535	754	3	:	:	PUNCT
ejpam-1535	754	4	c	c	X
ejpam-1535	754	5	→	→	PUNCT
ejpam-1535	754	6	d	d	X
ejpam-1535	754	7	be	be	AUX
ejpam-1535	754	8	a	a	DET
ejpam-1535	754	9	functor	functor	NOUN
ejpam-1535	754	10	between	between	ADP
ejpam-1535	754	11	categories	category	NOUN
ejpam-1535	754	12	c	c	PROPN
ejpam-1535	754	13	and	and	CCONJ
ejpam-1535	754	14	d.	d.	PROPN
ejpam-1535	754	15	for	for	ADP
ejpam-1535	754	16	any	any	DET
ejpam-1535	754	17	x	x	SYM
ejpam-1535	754	18	∈	∈	PROPN
ejpam-1535	754	19	c	c	X
ejpam-1535	754	20	,	,	PUNCT
ejpam-1535	754	21	d(x)φ	d(x)φ	PROPN
ejpam-1535	754	22	=	=	SYM
ejpam-1535	754	23	d(xφ	d(xφ	NOUN
ejpam-1535	754	24	)	)	PUNCT
ejpam-1535	754	25	and	and	CCONJ
ejpam-1535	754	26	r(x)φ	r(x)φ	PROPN
ejpam-1535	754	27	=	=	SYM
ejpam-1535	754	28	r(xφ	r(xφ	PROPN
ejpam-1535	754	29	)	)	PUNCT
ejpam-1535	754	30	.	.	PUNCT
ejpam-1535	755	1	definition	definition	NOUN
ejpam-1535	755	2	15	15	NUM
ejpam-1535	755	3	.	.	PUNCT
ejpam-1535	756	1	let	let	VERB
ejpam-1535	757	1	c	c	NOUN
ejpam-1535	758	1	and	and	CCONJ
ejpam-1535	758	2	d	d	PROPN
ejpam-1535	758	3	be	be	AUX
ejpam-1535	758	4	ordered	order	VERB
ejpam-1535	758	5	categories	category	NOUN
ejpam-1535	758	6	.	.	PUNCT
ejpam-1535	759	1	a	a	DET
ejpam-1535	759	2	functor	functor	PROPN
ejpam-1535	759	3	φ	φ	PROPN
ejpam-1535	759	4	:	:	PUNCT
ejpam-1535	759	5	c	c	X
ejpam-1535	759	6	→	→	PUNCT
ejpam-1535	759	7	d	d	X
ejpam-1535	759	8	is	be	AUX
ejpam-1535	759	9	called	call	VERB
ejpam-1535	759	10	an	an	DET
ejpam-1535	759	11	ordered	order	VERB
ejpam-1535	759	12	functor	functor	NOUN
ejpam-1535	759	13	if	if	SCONJ
ejpam-1535	759	14	it	it	PRON
ejpam-1535	759	15	satisfies	satisfy	VERB
ejpam-1535	759	16	the	the	DET
ejpam-1535	759	17	following	follow	VERB
ejpam-1535	759	18	additional	additional	ADJ
ejpam-1535	759	19	condition	condition	NOUN
ejpam-1535	759	20	:	:	PUNCT
ejpam-1535	759	21	c.	c.	PROPN
ejpam-1535	759	22	hollings	holling	NOUN
ejpam-1535	759	23	/	/	SYM
ejpam-1535	759	24	eur	eur	PROPN
ejpam-1535	759	25	.	.	PUNCT
ejpam-1535	760	1	j.	j.	PROPN
ejpam-1535	760	2	pure	pure	PROPN
ejpam-1535	760	3	appl	appl	PROPN
ejpam-1535	760	4	.	.	PROPN
ejpam-1535	760	5	math	math	PROPN
ejpam-1535	760	6	,	,	PUNCT
ejpam-1535	760	7	5	5	NUM
ejpam-1535	760	8	(	(	PUNCT
ejpam-1535	760	9	2012	2012	NUM
ejpam-1535	760	10	)	)	PUNCT
ejpam-1535	760	11	,	,	PUNCT
ejpam-1535	760	12	414	414	NUM
ejpam-1535	760	13	-	-	SYM
ejpam-1535	760	14	450	450	NUM
ejpam-1535	760	15	440	440	NUM
ejpam-1535	760	16	(	(	PUNCT
ejpam-1535	760	17	of	of	ADP
ejpam-1535	760	18	)	)	PUNCT
ejpam-1535	760	19	if	if	SCONJ
ejpam-1535	760	20	x	x	PROPN
ejpam-1535	760	21	≤	≤	NUM
ejpam-1535	760	22	y	y	NOUN
ejpam-1535	760	23	in	in	ADP
ejpam-1535	760	24	c	c	PROPN
ejpam-1535	760	25	,	,	PUNCT
ejpam-1535	760	26	then	then	ADV
ejpam-1535	760	27	xφ	xφ	PROPN
ejpam-1535	760	28	≤	≤	PUNCT
ejpam-1535	760	29	yφ	yφ	PROPN
ejpam-1535	760	30	in	in	ADP
ejpam-1535	760	31	d.	d.	PROPN
ejpam-1535	760	32	lemma	lemma	PROPN
ejpam-1535	760	33	14	14	NUM
ejpam-1535	761	1	(	(	PUNCT
ejpam-1535	761	2	[	[	X
ejpam-1535	761	3	29	29	NUM
ejpam-1535	761	4	,	,	PUNCT
ejpam-1535	761	5	proposition	proposition	NOUN
ejpam-1535	761	6	4.1.2	4.1.2	NUM
ejpam-1535	761	7	]	]	PUNCT
ejpam-1535	761	8	)	)	PUNCT
ejpam-1535	761	9	.	.	PUNCT
ejpam-1535	762	1	let	let	VERB
ejpam-1535	762	2	φ	φ	NOUN
ejpam-1535	762	3	:	:	PUNCT
ejpam-1535	762	4	c	c	X
ejpam-1535	762	5	→	→	PUNCT
ejpam-1535	762	6	d	d	X
ejpam-1535	762	7	be	be	AUX
ejpam-1535	762	8	an	an	DET
ejpam-1535	762	9	ordered	order	VERB
ejpam-1535	762	10	functor	functor	NOUN
ejpam-1535	762	11	between	between	ADP
ejpam-1535	762	12	ordered	order	VERB
ejpam-1535	762	13	categories	category	NOUN
ejpam-1535	762	14	c	c	PROPN
ejpam-1535	762	15	and	and	CCONJ
ejpam-1535	762	16	d.	d.	PROPN
ejpam-1535	762	17	if	if	SCONJ
ejpam-1535	762	18	f	f	PROPN
ejpam-1535	762	19	∈	∈	PROPN
ejpam-1535	762	20	co	co	NOUN
ejpam-1535	762	21	is	be	AUX
ejpam-1535	762	22	such	such	ADJ
ejpam-1535	762	23	that	that	SCONJ
ejpam-1535	762	24	f	f	PROPN
ejpam-1535	762	25	≤	≤	X
ejpam-1535	762	26	r(a	r(a	PROPN
ejpam-1535	762	27	)	)	PUNCT
ejpam-1535	762	28	,	,	PUNCT
ejpam-1535	762	29	for	for	ADP
ejpam-1535	762	30	some	some	PRON
ejpam-1535	762	31	a	a	DET
ejpam-1535	762	32	∈	∈	PROPN
ejpam-1535	762	33	c	c	NOUN
ejpam-1535	762	34	,	,	PUNCT
ejpam-1535	762	35	then	then	ADV
ejpam-1535	762	36	(	(	PUNCT
ejpam-1535	762	37	a|	a|	PROPN
ejpam-1535	762	38	f	f	PROPN
ejpam-1535	762	39	)	)	PUNCT
ejpam-1535	762	40	φ	φ	PROPN
ejpam-1535	762	41	=	=	PUNCT
ejpam-1535	762	42	aφ|	aφ|	PROPN
ejpam-1535	762	43	f	f	PROPN
ejpam-1535	762	44	φ	φ	PROPN
ejpam-1535	762	45	.	.	PUNCT
ejpam-1535	763	1	similarly	similarly	ADV
ejpam-1535	763	2	,	,	PUNCT
ejpam-1535	763	3	if	if	SCONJ
ejpam-1535	763	4	f	f	PROPN
ejpam-1535	763	5	≤	≤	PUNCT
ejpam-1535	763	6	d(a	d(a	PROPN
ejpam-1535	763	7	)	)	PUNCT
ejpam-1535	763	8	,	,	PUNCT
ejpam-1535	763	9	then	then	ADV
ejpam-1535	763	10	(	(	PUNCT
ejpam-1535	763	11	f	f	PROPN
ejpam-1535	763	12	|a)φ	|a)φ	PROPN
ejpam-1535	763	13	=	=	PROPN
ejpam-1535	763	14	f	f	PROPN
ejpam-1535	763	15	φ|aφ	φ|aφ	NOUN
ejpam-1535	763	16	.	.	PUNCT
ejpam-1535	764	1	the	the	DET
ejpam-1535	764	2	following	follow	VERB
ejpam-1535	764	3	is	be	AUX
ejpam-1535	764	4	easy	easy	ADJ
ejpam-1535	764	5	to	to	PART
ejpam-1535	764	6	verify	verify	VERB
ejpam-1535	764	7	:	:	PUNCT
ejpam-1535	764	8	proposition	proposition	NOUN
ejpam-1535	764	9	4	4	NUM
ejpam-1535	764	10	(	(	PUNCT
ejpam-1535	764	11	f	f	NOUN
ejpam-1535	764	12	)	)	PUNCT
ejpam-1535	764	13	.	.	PUNCT
ejpam-1535	765	1	the	the	DET
ejpam-1535	765	2	composition	composition	NOUN
ejpam-1535	765	3	of	of	ADP
ejpam-1535	765	4	two	two	NUM
ejpam-1535	765	5	ordered	order	VERB
ejpam-1535	765	6	functors	functor	NOUN
ejpam-1535	765	7	is	be	AUX
ejpam-1535	765	8	also	also	ADV
ejpam-1535	765	9	an	an	DET
ejpam-1535	765	10	ordered	order	VERB
ejpam-1535	765	11	functor	functor	NOUN
ejpam-1535	765	12	.	.	PUNCT
ejpam-1535	766	1	consequently	consequently	ADV
ejpam-1535	766	2	,	,	PUNCT
ejpam-1535	766	3	inductive	inductive	ADJ
ejpam-1535	766	4	categories	category	NOUN
ejpam-1535	766	5	(	(	PUNCT
ejpam-1535	766	6	in	in	ADP
ejpam-1535	766	7	sense	sense	NOUN
ejpam-1535	766	8	(	(	PUNCT
ejpam-1535	766	9	♣	♣	NOUN
ejpam-1535	766	10	)	)	PUNCT
ejpam-1535	766	11	)	)	PUNCT
ejpam-1535	766	12	and	and	CCONJ
ejpam-1535	766	13	ordered	order	VERB
ejpam-1535	766	14	functors	functor	NOUN
ejpam-1535	766	15	form	form	VERB
ejpam-1535	766	16	a	a	DET
ejpam-1535	766	17	category	category	NOUN
ejpam-1535	766	18	(	(	PUNCT
ejpam-1535	766	19	in	in	ADP
ejpam-1535	766	20	sense	sense	NOUN
ejpam-1535	766	21	(	(	PUNCT
ejpam-1535	766	22	♠	♠	NOUN
ejpam-1535	766	23	)	)	PUNCT
ejpam-1535	766	24	)	)	PUNCT
ejpam-1535	766	25	.	.	PUNCT
ejpam-1535	767	1	before	before	SCONJ
ejpam-1535	767	2	we	we	PRON
ejpam-1535	767	3	prove	prove	VERB
ejpam-1535	767	4	the	the	DET
ejpam-1535	767	5	correspondence	correspondence	NOUN
ejpam-1535	767	6	between	between	ADP
ejpam-1535	767	7	ordered	order	VERB
ejpam-1535	767	8	functors	functor	NOUN
ejpam-1535	767	9	and	and	CCONJ
ejpam-1535	767	10	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	767	11	,	,	PUNCT
ejpam-1535	767	12	we	we	PRON
ejpam-1535	767	13	first	first	ADV
ejpam-1535	767	14	record	record	VERB
ejpam-1535	767	15	the	the	DET
ejpam-1535	767	16	following	follow	VERB
ejpam-1535	767	17	useful	useful	ADJ
ejpam-1535	767	18	result	result	NOUN
ejpam-1535	767	19	:	:	PUNCT
ejpam-1535	767	20	lemma	lemma	PROPN
ejpam-1535	767	21	15	15	NUM
ejpam-1535	767	22	(	(	PUNCT
ejpam-1535	767	23	[	[	X
ejpam-1535	767	24	22	22	NUM
ejpam-1535	767	25	,	,	PUNCT
ejpam-1535	767	26	lemma	lemma	PROPN
ejpam-1535	767	27	4.6	4.6	NUM
ejpam-1535	767	28	]	]	PUNCT
ejpam-1535	767	29	)	)	PUNCT
ejpam-1535	767	30	.	.	PUNCT
ejpam-1535	768	1	let	let	VERB
ejpam-1535	768	2	α	α	PRON
ejpam-1535	768	3	:	:	PUNCT
ejpam-1535	768	4	s	s	X
ejpam-1535	768	5	→	→	SYM
ejpam-1535	768	6	t	t	PROPN
ejpam-1535	768	7	be	be	AUX
ejpam-1535	768	8	an	an	DET
ejpam-1535	768	9	order	order	NOUN
ejpam-1535	768	10	-	-	PUNCT
ejpam-1535	768	11	preserving	preserve	VERB
ejpam-1535	768	12	function	function	NOUN
ejpam-1535	768	13	of	of	ADP
ejpam-1535	768	14	restriction	restriction	NOUN
ejpam-1535	768	15	semigroups	semigroup	NOUN
ejpam-1535	768	16	.	.	PUNCT
ejpam-1535	769	1	we	we	PRON
ejpam-1535	769	2	define	define	VERB
ejpam-1535	769	3	c(α	c(α	NOUN
ejpam-1535	769	4	)	)	PUNCT
ejpam-1535	769	5	:	:	PUNCT
ejpam-1535	769	6	c(s)→	c(s)→	ADJ
ejpam-1535	769	7	c(t	c(t	PROPN
ejpam-1535	769	8	)	)	PUNCT
ejpam-1535	769	9	to	to	PART
ejpam-1535	769	10	be	be	AUX
ejpam-1535	769	11	the	the	DET
ejpam-1535	769	12	same	same	ADJ
ejpam-1535	769	13	function	function	NOUN
ejpam-1535	769	14	on	on	ADP
ejpam-1535	769	15	the	the	DET
ejpam-1535	769	16	underlying	underlie	VERB
ejpam-1535	769	17	sets	set	NOUN
ejpam-1535	769	18	.	.	PUNCT
ejpam-1535	770	1	then	then	ADV
ejpam-1535	770	2	c(α	c(α	NOUN
ejpam-1535	770	3	)	)	PUNCT
ejpam-1535	770	4	is	be	AUX
ejpam-1535	770	5	order	order	NOUN
ejpam-1535	770	6	-	-	PUNCT
ejpam-1535	770	7	preserving	preserve	VERB
ejpam-1535	770	8	.	.	PUNCT
ejpam-1535	771	1	let	let	VERB
ejpam-1535	771	2	β	β	PRON
ejpam-1535	771	3	:	:	PUNCT
ejpam-1535	771	4	c	c	X
ejpam-1535	771	5	→	→	PUNCT
ejpam-1535	771	6	d	d	X
ejpam-1535	771	7	be	be	AUX
ejpam-1535	771	8	an	an	DET
ejpam-1535	771	9	order	order	NOUN
ejpam-1535	771	10	-	-	PUNCT
ejpam-1535	771	11	preserving	preserve	VERB
ejpam-1535	771	12	function	function	NOUN
ejpam-1535	771	13	of	of	ADP
ejpam-1535	771	14	inductive	inductive	ADJ
ejpam-1535	771	15	categories	category	NOUN
ejpam-1535	771	16	.	.	PUNCT
ejpam-1535	772	1	we	we	PRON
ejpam-1535	772	2	define	define	VERB
ejpam-1535	772	3	s(β	s(β	PROPN
ejpam-1535	772	4	)	)	PUNCT
ejpam-1535	772	5	:	:	PUNCT
ejpam-1535	773	1	s(c	s(c	X
ejpam-1535	773	2	)	)	PUNCT
ejpam-1535	773	3	→	→	SYM
ejpam-1535	773	4	s(d	s(d	NOUN
ejpam-1535	773	5	)	)	PUNCT
ejpam-1535	773	6	to	to	PART
ejpam-1535	773	7	be	be	AUX
ejpam-1535	773	8	the	the	DET
ejpam-1535	773	9	same	same	ADJ
ejpam-1535	773	10	function	function	NOUN
ejpam-1535	773	11	on	on	ADP
ejpam-1535	773	12	the	the	DET
ejpam-1535	773	13	underlying	underlie	VERB
ejpam-1535	773	14	sets	set	NOUN
ejpam-1535	773	15	.	.	PUNCT
ejpam-1535	774	1	then	then	ADV
ejpam-1535	774	2	s(β	s(β	PROPN
ejpam-1535	774	3	)	)	PUNCT
ejpam-1535	774	4	is	be	AUX
ejpam-1535	774	5	orderpreserving	orderpreserve	VERB
ejpam-1535	774	6	.	.	PUNCT
ejpam-1535	775	1	proposition	proposition	NOUN
ejpam-1535	775	2	5	5	NUM
ejpam-1535	775	3	(	(	PUNCT
ejpam-1535	775	4	[	[	X
ejpam-1535	775	5	22	22	NUM
ejpam-1535	775	6	,	,	PUNCT
ejpam-1535	775	7	proposition	proposition	NOUN
ejpam-1535	775	8	4.8	4.8	NUM
ejpam-1535	775	9	]	]	PUNCT
ejpam-1535	775	10	)	)	PUNCT
ejpam-1535	775	11	.	.	PUNCT
ejpam-1535	776	1	let	let	VERB
ejpam-1535	776	2	s	s	PRON
ejpam-1535	776	3	and	and	CCONJ
ejpam-1535	776	4	t	t	PROPN
ejpam-1535	776	5	be	be	VERB
ejpam-1535	776	6	restriction	restriction	NOUN
ejpam-1535	776	7	semigroups	semigroup	NOUN
ejpam-1535	776	8	with	with	ADP
ejpam-1535	776	9	respect	respect	NOUN
ejpam-1535	776	10	to	to	ADP
ejpam-1535	776	11	semilattices	semilattice	NOUN
ejpam-1535	776	12	e	e	NOUN
ejpam-1535	776	13	and	and	CCONJ
ejpam-1535	776	14	f	f	PROPN
ejpam-1535	776	15	,	,	PUNCT
ejpam-1535	776	16	respectively	respectively	ADV
ejpam-1535	776	17	.	.	PUNCT
ejpam-1535	777	1	let	let	VERB
ejpam-1535	777	2	θ	θ	NOUN
ejpam-1535	777	3	:	:	PUNCT
ejpam-1535	777	4	s→	s→	PROPN
ejpam-1535	777	5	t	t	NOUN
ejpam-1535	777	6	be	be	AUX
ejpam-1535	777	7	a	a	DET
ejpam-1535	777	8	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	777	9	.	.	PUNCT
ejpam-1535	778	1	we	we	PRON
ejpam-1535	778	2	define	define	VERB
ejpam-1535	778	3	θ	θ	NOUN
ejpam-1535	778	4	:	:	PUNCT
ejpam-1535	778	5	=	=	SYM
ejpam-1535	778	6	c(θ	c(θ	PROPN
ejpam-1535	778	7	)	)	PUNCT
ejpam-1535	778	8	:	:	PUNCT
ejpam-1535	778	9	c(s)→	c(s)→	ADJ
ejpam-1535	778	10	c(t	c(t	PROPN
ejpam-1535	778	11	)	)	PUNCT
ejpam-1535	778	12	to	to	PART
ejpam-1535	778	13	be	be	AUX
ejpam-1535	778	14	the	the	DET
ejpam-1535	778	15	same	same	ADJ
ejpam-1535	778	16	function	function	NOUN
ejpam-1535	778	17	on	on	ADP
ejpam-1535	778	18	the	the	DET
ejpam-1535	778	19	underlying	underlie	VERB
ejpam-1535	778	20	sets	set	NOUN
ejpam-1535	778	21	.	.	PUNCT
ejpam-1535	779	1	then	then	ADV
ejpam-1535	779	2	θ	θ	PROPN
ejpam-1535	779	3	is	be	AUX
ejpam-1535	779	4	an	an	DET
ejpam-1535	779	5	ordered	order	VERB
ejpam-1535	779	6	functor	functor	NOUN
ejpam-1535	779	7	with	with	ADP
ejpam-1535	779	8	respect	respect	NOUN
ejpam-1535	779	9	to	to	ADP
ejpam-1535	779	10	the	the	DET
ejpam-1535	779	11	restricted	restricted	ADJ
ejpam-1535	779	12	products	product	NOUN
ejpam-1535	779	13	in	in	ADP
ejpam-1535	779	14	c(s	c(	NOUN
ejpam-1535	779	15	)	)	PUNCT
ejpam-1535	779	16	and	and	CCONJ
ejpam-1535	779	17	c(t	c(t	PROPN
ejpam-1535	779	18	)	)	PUNCT
ejpam-1535	779	19	.	.	PUNCT
ejpam-1535	780	1	proposition	proposition	NOUN
ejpam-1535	780	2	6	6	NUM
ejpam-1535	780	3	(	(	PUNCT
ejpam-1535	780	4	[	[	X
ejpam-1535	780	5	22	22	NUM
ejpam-1535	780	6	,	,	PUNCT
ejpam-1535	780	7	proposition	proposition	NOUN
ejpam-1535	780	8	4.9	4.9	NUM
ejpam-1535	780	9	]	]	PUNCT
ejpam-1535	780	10	)	)	PUNCT
ejpam-1535	780	11	.	.	PUNCT
ejpam-1535	781	1	let	let	VERB
ejpam-1535	781	2	φ	φ	NOUN
ejpam-1535	781	3	:	:	PUNCT
ejpam-1535	781	4	c	c	X
ejpam-1535	781	5	→	→	PUNCT
ejpam-1535	781	6	d	d	X
ejpam-1535	781	7	be	be	AUX
ejpam-1535	781	8	an	an	DET
ejpam-1535	781	9	ordered	order	VERB
ejpam-1535	781	10	functor	functor	NOUN
ejpam-1535	781	11	of	of	ADP
ejpam-1535	781	12	inductive	inductive	ADJ
ejpam-1535	781	13	categories	category	NOUN
ejpam-1535	781	14	.	.	PUNCT
ejpam-1535	782	1	we	we	PRON
ejpam-1535	782	2	define	define	VERB
ejpam-1535	782	3	φ	φ	NOUN
ejpam-1535	782	4	:	:	PUNCT
ejpam-1535	782	5	=	=	SYM
ejpam-1535	782	6	s(φ	s(φ	PROPN
ejpam-1535	782	7	)	)	PUNCT
ejpam-1535	782	8	:	:	PUNCT
ejpam-1535	782	9	s(c)→	s(c)→	PROPN
ejpam-1535	782	10	s(d	s(d	NOUN
ejpam-1535	782	11	)	)	PUNCT
ejpam-1535	782	12	to	to	PART
ejpam-1535	782	13	be	be	AUX
ejpam-1535	782	14	the	the	DET
ejpam-1535	782	15	same	same	ADJ
ejpam-1535	782	16	function	function	NOUN
ejpam-1535	782	17	on	on	ADP
ejpam-1535	782	18	the	the	DET
ejpam-1535	782	19	underlying	underlie	VERB
ejpam-1535	782	20	sets	set	NOUN
ejpam-1535	782	21	.	.	PUNCT
ejpam-1535	783	1	then	then	ADV
ejpam-1535	783	2	φ	φ	PROPN
ejpam-1535	783	3	is	be	AUX
ejpam-1535	783	4	a	a	DET
ejpam-1535	783	5	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	783	6	with	with	ADP
ejpam-1535	783	7	respect	respect	NOUN
ejpam-1535	783	8	to	to	ADP
ejpam-1535	783	9	the	the	DET
ejpam-1535	783	10	pseudoproducts	pseudoproduct	NOUN
ejpam-1535	783	11	in	in	ADP
ejpam-1535	783	12	s(c	s(c	PROPN
ejpam-1535	783	13	)	)	PUNCT
ejpam-1535	783	14	and	and	CCONJ
ejpam-1535	783	15	s(d	s(d	NOUN
ejpam-1535	783	16	)	)	PUNCT
ejpam-1535	783	17	.	.	PUNCT
ejpam-1535	784	1	it	it	PRON
ejpam-1535	784	2	is	be	AUX
ejpam-1535	784	3	clear	clear	ADJ
ejpam-1535	784	4	that	that	SCONJ
ejpam-1535	784	5	if	if	SCONJ
ejpam-1535	784	6	θ	θ	PROPN
ejpam-1535	784	7	:	:	PUNCT
ejpam-1535	784	8	s	s	X
ejpam-1535	784	9	→	→	SYM
ejpam-1535	784	10	t	t	PROPN
ejpam-1535	784	11	is	be	AUX
ejpam-1535	784	12	a	a	DET
ejpam-1535	784	13	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	784	14	and	and	CCONJ
ejpam-1535	784	15	φ	φ	NOUN
ejpam-1535	784	16	:	:	PUNCT
ejpam-1535	785	1	c	c	X
ejpam-1535	785	2	→	→	PUNCT
ejpam-1535	785	3	d	d	NOUN
ejpam-1535	785	4	is	be	AUX
ejpam-1535	785	5	an	an	DET
ejpam-1535	785	6	ordered	ordered	ADJ
ejpam-1535	785	7	functor	functor	NOUN
ejpam-1535	785	8	,	,	PUNCT
ejpam-1535	785	9	then	then	ADV
ejpam-1535	785	10	s(c(θ	s(c(θ	NUM
ejpam-1535	785	11	)	)	PUNCT
ejpam-1535	785	12	)	)	PUNCT
ejpam-1535	786	1	=	=	SYM
ejpam-1535	786	2	θ	θ	PROPN
ejpam-1535	786	3	and	and	CCONJ
ejpam-1535	786	4	c(s(φ	c(s(φ	PROPN
ejpam-1535	786	5	)	)	PUNCT
ejpam-1535	786	6	)	)	PUNCT
ejpam-1535	787	1	=	=	PUNCT
ejpam-1535	787	2	φ	φ	X
ejpam-1535	787	3	.	.	PUNCT
ejpam-1535	788	1	furthermore	furthermore	ADV
ejpam-1535	788	2	,	,	PUNCT
ejpam-1535	788	3	if	if	SCONJ
ejpam-1535	788	4	θ	θ	PROPN
ejpam-1535	788	5	′	′	NUM
ejpam-1535	788	6	:	:	PUNCT
ejpam-1535	788	7	t	t	PROPN
ejpam-1535	788	8	→	→	SYM
ejpam-1535	788	9	t	t	PROPN
ejpam-1535	788	10	′	′	NOUN
ejpam-1535	788	11	is	be	AUX
ejpam-1535	788	12	another	another	DET
ejpam-1535	788	13	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	788	14	of	of	ADP
ejpam-1535	788	15	restriction	restriction	NOUN
ejpam-1535	788	16	semigroups	semigroup	NOUN
ejpam-1535	788	17	,	,	PUNCT
ejpam-1535	788	18	and	and	CCONJ
ejpam-1535	788	19	φ′	φ′	NUM
ejpam-1535	788	20	:	:	PUNCT
ejpam-1535	789	1	d→	d→	VERB
ejpam-1535	789	2	d′	d′	ADJ
ejpam-1535	789	3	is	be	AUX
ejpam-1535	789	4	another	another	DET
ejpam-1535	789	5	ordered	order	VERB
ejpam-1535	789	6	functor	functor	PROPN
ejpam-1535	789	7	of	of	ADP
ejpam-1535	789	8	inductive	inductive	ADJ
ejpam-1535	789	9	categories	category	NOUN
ejpam-1535	789	10	,	,	PUNCT
ejpam-1535	789	11	then	then	ADV
ejpam-1535	789	12	c(θθ	c(θθ	NOUN
ejpam-1535	789	13	′	′	NOUN
ejpam-1535	789	14	)	)	PUNCT
ejpam-1535	789	15	=	=	NOUN
ejpam-1535	789	16	c(θ)c(θ	c(θ)c(θ	NOUN
ejpam-1535	789	17	′	′	NOUN
ejpam-1535	789	18	)	)	PUNCT
ejpam-1535	789	19	and	and	CCONJ
ejpam-1535	789	20	s(φφ′	s(φφ′	NUM
ejpam-1535	789	21	)	)	PUNCT
ejpam-1535	789	22	=	=	PUNCT
ejpam-1535	789	23	s(φ)s(φ′	s(φ)s(φ′	ADJ
ejpam-1535	789	24	)	)	PUNCT
ejpam-1535	789	25	.	.	PUNCT
ejpam-1535	790	1	we	we	PRON
ejpam-1535	790	2	therefore	therefore	ADV
ejpam-1535	790	3	have	have	VERB
ejpam-1535	790	4	the	the	DET
ejpam-1535	790	5	following	follow	VERB
ejpam-1535	790	6	theorem	theorem	NOUN
ejpam-1535	790	7	and	and	CCONJ
ejpam-1535	790	8	its	its	PRON
ejpam-1535	790	9	corollaries	corollary	NOUN
ejpam-1535	790	10	:	:	PUNCT
ejpam-1535	790	11	theorem	theorem	NOUN
ejpam-1535	790	12	5	5	NUM
ejpam-1535	790	13	(	(	PUNCT
ejpam-1535	790	14	[	[	X
ejpam-1535	790	15	22	22	NUM
ejpam-1535	790	16	,	,	PUNCT
ejpam-1535	790	17	theorem	theorem	VERB
ejpam-1535	790	18	4.1	4.1	NUM
ejpam-1535	790	19	]	]	PUNCT
ejpam-1535	790	20	)	)	PUNCT
ejpam-1535	790	21	.	.	PUNCT
ejpam-1535	791	1	the	the	DET
ejpam-1535	791	2	category	category	NOUN
ejpam-1535	791	3	of	of	ADP
ejpam-1535	791	4	restriction	restriction	NOUN
ejpam-1535	791	5	semigroups	semigroup	NOUN
ejpam-1535	791	6	and	and	CCONJ
ejpam-1535	791	7	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	791	8	is	be	AUX
ejpam-1535	791	9	isomorphic	isomorphic	ADJ
ejpam-1535	791	10	to	to	ADP
ejpam-1535	791	11	the	the	DET
ejpam-1535	791	12	category	category	NOUN
ejpam-1535	791	13	of	of	ADP
ejpam-1535	791	14	inductive	inductive	ADJ
ejpam-1535	791	15	categories	category	NOUN
ejpam-1535	791	16	and	and	CCONJ
ejpam-1535	791	17	ordered	order	VERB
ejpam-1535	791	18	functors	functor	NOUN
ejpam-1535	791	19	.	.	PUNCT
ejpam-1535	792	1	corollary	corollary	ADJ
ejpam-1535	792	2	7	7	NUM
ejpam-1535	792	3	.	.	PUNCT
ejpam-1535	793	1	the	the	DET
ejpam-1535	793	2	category	category	NOUN
ejpam-1535	793	3	of	of	ADP
ejpam-1535	793	4	full	full	ADJ
ejpam-1535	793	5	restriction	restriction	NOUN
ejpam-1535	793	6	semigroups	semigroup	NOUN
ejpam-1535	793	7	and	and	CCONJ
ejpam-1535	793	8	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	793	9	is	be	AUX
ejpam-1535	793	10	isomorphic	isomorphic	ADJ
ejpam-1535	793	11	to	to	ADP
ejpam-1535	793	12	the	the	DET
ejpam-1535	793	13	category	category	NOUN
ejpam-1535	793	14	of	of	ADP
ejpam-1535	793	15	inductive	inductive	ADJ
ejpam-1535	793	16	unipotent	unipotent	ADJ
ejpam-1535	793	17	categories	category	NOUN
ejpam-1535	793	18	and	and	CCONJ
ejpam-1535	793	19	ordered	order	VERB
ejpam-1535	793	20	functors	functor	NOUN
ejpam-1535	793	21	.	.	PUNCT
ejpam-1535	794	1	corollary	corollary	ADJ
ejpam-1535	794	2	8	8	NUM
ejpam-1535	794	3	.	.	PUNCT
ejpam-1535	795	1	the	the	DET
ejpam-1535	795	2	category	category	NOUN
ejpam-1535	795	3	of	of	ADP
ejpam-1535	795	4	ample	ample	ADJ
ejpam-1535	795	5	semigroups	semigroup	NOUN
ejpam-1535	795	6	and	and	CCONJ
ejpam-1535	795	7	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	795	8	is	be	AUX
ejpam-1535	795	9	isomorphic	isomorphic	ADJ
ejpam-1535	795	10	to	to	ADP
ejpam-1535	795	11	the	the	DET
ejpam-1535	795	12	category	category	NOUN
ejpam-1535	795	13	of	of	ADP
ejpam-1535	795	14	inductive	inductive	ADJ
ejpam-1535	795	15	cancellative	cancellative	ADJ
ejpam-1535	795	16	categories	category	NOUN
ejpam-1535	795	17	and	and	CCONJ
ejpam-1535	795	18	ordered	order	VERB
ejpam-1535	795	19	functors	functor	NOUN
ejpam-1535	795	20	.	.	PUNCT
ejpam-1535	796	1	c.	c.	PROPN
ejpam-1535	796	2	hollings	holling	NOUN
ejpam-1535	796	3	/	/	SYM
ejpam-1535	796	4	eur	eur	PROPN
ejpam-1535	796	5	.	.	PUNCT
ejpam-1535	797	1	j.	j.	PROPN
ejpam-1535	797	2	pure	pure	PROPN
ejpam-1535	797	3	appl	appl	PROPN
ejpam-1535	797	4	.	.	PROPN
ejpam-1535	797	5	math	math	PROPN
ejpam-1535	797	6	,	,	PUNCT
ejpam-1535	797	7	5	5	NUM
ejpam-1535	797	8	(	(	PUNCT
ejpam-1535	797	9	2012	2012	NUM
ejpam-1535	797	10	)	)	PUNCT
ejpam-1535	797	11	,	,	PUNCT
ejpam-1535	797	12	414	414	NUM
ejpam-1535	797	13	-	-	SYM
ejpam-1535	797	14	450	450	NUM
ejpam-1535	797	15	441	441	NUM
ejpam-1535	797	16	7	7	NUM
ejpam-1535	797	17	.	.	PUNCT
ejpam-1535	798	1	morphisms	morphism	NOUN
ejpam-1535	798	2	and	and	CCONJ
ejpam-1535	798	3	inductive	inductive	ADJ
ejpam-1535	798	4	functors	functor	NOUN
ejpam-1535	798	5	we	we	PRON
ejpam-1535	798	6	turn	turn	VERB
ejpam-1535	798	7	now	now	ADV
ejpam-1535	798	8	to	to	ADP
ejpam-1535	798	9	the	the	DET
ejpam-1535	798	10	second	second	ADJ
ejpam-1535	798	11	type	type	NOUN
ejpam-1535	798	12	of	of	ADP
ejpam-1535	798	13	arrow	arrow	NOUN
ejpam-1535	798	14	to	to	PART
ejpam-1535	798	15	be	be	AUX
ejpam-1535	798	16	considered	consider	VERB
ejpam-1535	798	17	between	between	ADP
ejpam-1535	798	18	restriction	restriction	NOUN
ejpam-1535	798	19	semigroup	semigroup	NOUN
ejpam-1535	798	20	:	:	PUNCT
ejpam-1535	798	21	(	(	PUNCT
ejpam-1535	798	22	2,1,1)-morphisms	2,1,1)-morphism	NOUN
ejpam-1535	798	23	,	,	PUNCT
ejpam-1535	798	24	morphisms	morphism	NOUN
ejpam-1535	798	25	which	which	DET
ejpam-1535	798	26	respect	respect	VERB
ejpam-1535	798	27	+	+	CCONJ
ejpam-1535	798	28	and	and	CCONJ
ejpam-1535	798	29	∗.	∗.	PROPN
ejpam-1535	798	30	again	again	ADV
ejpam-1535	798	31	thinking	think	VERB
ejpam-1535	798	32	of	of	ADP
ejpam-1535	798	33	restriction	restriction	NOUN
ejpam-1535	798	34	semigroups	semigroup	NOUN
ejpam-1535	798	35	as	as	ADP
ejpam-1535	798	36	algebras	algebra	NOUN
ejpam-1535	798	37	of	of	ADP
ejpam-1535	798	38	type	type	NOUN
ejpam-1535	798	39	(	(	PUNCT
ejpam-1535	798	40	2,1,1	2,1,1	NUM
ejpam-1535	798	41	)	)	PUNCT
ejpam-1535	798	42	,	,	PUNCT
ejpam-1535	798	43	we	we	PRON
ejpam-1535	798	44	begin	begin	VERB
ejpam-1535	798	45	by	by	ADP
ejpam-1535	798	46	noting	note	VERB
ejpam-1535	798	47	the	the	DET
ejpam-1535	798	48	following	follow	VERB
ejpam-1535	798	49	fact	fact	NOUN
ejpam-1535	798	50	from	from	ADP
ejpam-1535	798	51	universal	universal	ADJ
ejpam-1535	798	52	algebra	algebra	NOUN
ejpam-1535	798	53	:	:	PUNCT
ejpam-1535	798	54	fact	fact	NOUN
ejpam-1535	798	55	1	1	NUM
ejpam-1535	798	56	(	(	PUNCT
ejpam-1535	798	57	[	[	X
ejpam-1535	798	58	f	f	X
ejpam-1535	798	59	]	]	X
ejpam-1535	798	60	)	)	PUNCT
ejpam-1535	798	61	.	.	PUNCT
ejpam-1535	799	1	the	the	DET
ejpam-1535	799	2	composition	composition	NOUN
ejpam-1535	799	3	of	of	ADP
ejpam-1535	799	4	two	two	NUM
ejpam-1535	799	5	(	(	PUNCT
ejpam-1535	799	6	2,1,1)-morphisms	2,1,1)-morphism	NOUN
ejpam-1535	799	7	is	be	AUX
ejpam-1535	799	8	also	also	ADV
ejpam-1535	799	9	a	a	DET
ejpam-1535	799	10	(	(	PUNCT
ejpam-1535	799	11	2,1,1)-morphism	2,1,1)-morphism	NUM
ejpam-1535	799	12	.	.	PUNCT
ejpam-1535	800	1	consequently	consequently	ADV
ejpam-1535	800	2	,	,	PUNCT
ejpam-1535	800	3	restriction	restriction	NOUN
ejpam-1535	800	4	semigroups	semigroup	NOUN
ejpam-1535	800	5	and	and	CCONJ
ejpam-1535	800	6	(	(	PUNCT
ejpam-1535	800	7	2,1,1)-morphisms	2,1,1)-morphism	NOUN
ejpam-1535	800	8	form	form	VERB
ejpam-1535	800	9	a	a	DET
ejpam-1535	800	10	category	category	NOUN
ejpam-1535	800	11	.	.	PUNCT
ejpam-1535	801	1	the	the	DET
ejpam-1535	801	2	functions	function	NOUN
ejpam-1535	801	3	between	between	ADP
ejpam-1535	801	4	inductive	inductive	ADJ
ejpam-1535	801	5	categories	category	NOUN
ejpam-1535	801	6	to	to	PART
ejpam-1535	801	7	which	which	PRON
ejpam-1535	801	8	(	(	PUNCT
ejpam-1535	801	9	2,1,1)-morphisms	2,1,1)-morphism	NOUN
ejpam-1535	801	10	will	will	AUX
ejpam-1535	801	11	correspond	correspond	VERB
ejpam-1535	801	12	are	be	AUX
ejpam-1535	801	13	so	so	ADV
ejpam-1535	801	14	-	-	PUNCT
ejpam-1535	801	15	called	call	VERB
ejpam-1535	801	16	inductive	inductive	ADJ
ejpam-1535	801	17	functors	functor	NOUN
ejpam-1535	801	18	,	,	PUNCT
ejpam-1535	801	19	which	which	PRON
ejpam-1535	801	20	we	we	PRON
ejpam-1535	801	21	define	define	VERB
ejpam-1535	801	22	by	by	ADP
ejpam-1535	801	23	building	build	VERB
ejpam-1535	801	24	upon	upon	SCONJ
ejpam-1535	801	25	definitions	definition	NOUN
ejpam-1535	801	26	14	14	NUM
ejpam-1535	801	27	and	and	CCONJ
ejpam-1535	801	28	15	15	NUM
ejpam-1535	801	29	:	:	PUNCT
ejpam-1535	801	30	definition	definition	NOUN
ejpam-1535	801	31	16	16	NUM
ejpam-1535	801	32	.	.	PUNCT
ejpam-1535	802	1	let	let	VERB
ejpam-1535	803	1	c	c	NOUN
ejpam-1535	804	1	and	and	CCONJ
ejpam-1535	804	2	d	d	AUX
ejpam-1535	804	3	be	be	AUX
ejpam-1535	804	4	inductive	inductive	ADJ
ejpam-1535	804	5	categories	category	NOUN
ejpam-1535	804	6	.	.	PUNCT
ejpam-1535	805	1	an	an	DET
ejpam-1535	805	2	ordered	order	VERB
ejpam-1535	805	3	functor	functor	PROPN
ejpam-1535	805	4	φ	φ	PROPN
ejpam-1535	805	5	:	:	PUNCT
ejpam-1535	805	6	c	c	X
ejpam-1535	805	7	→	→	PUNCT
ejpam-1535	805	8	d	d	X
ejpam-1535	805	9	is	be	AUX
ejpam-1535	805	10	called	call	VERB
ejpam-1535	805	11	an	an	DET
ejpam-1535	805	12	inductive	inductive	ADJ
ejpam-1535	805	13	functor	functor	NOUN
ejpam-1535	805	14	if	if	SCONJ
ejpam-1535	805	15	it	it	PRON
ejpam-1535	805	16	satisfies	satisfy	VERB
ejpam-1535	805	17	the	the	DET
ejpam-1535	805	18	following	follow	VERB
ejpam-1535	805	19	additional	additional	ADJ
ejpam-1535	805	20	condition	condition	NOUN
ejpam-1535	805	21	:	:	PUNCT
ejpam-1535	805	22	(	(	PUNCT
ejpam-1535	805	23	if	if	SCONJ
ejpam-1535	805	24	)	)	PUNCT
ejpam-1535	805	25	for	for	ADP
ejpam-1535	805	26	e	e	NOUN
ejpam-1535	805	27	,	,	PUNCT
ejpam-1535	805	28	f	f	PROPN
ejpam-1535	805	29	∈	∈	PROPN
ejpam-1535	805	30	co	co	NOUN
ejpam-1535	805	31	,	,	PUNCT
ejpam-1535	805	32	(	(	PUNCT
ejpam-1535	805	33	e	e	X
ejpam-1535	805	34	∧	∧	PROPN
ejpam-1535	805	35	f	f	PROPN
ejpam-1535	805	36	)	)	PUNCT
ejpam-1535	805	37	φ	φ	PROPN
ejpam-1535	805	38	=	=	SYM
ejpam-1535	805	39	eφ	eφ	PROPN
ejpam-1535	805	40	∧	∧	PROPN
ejpam-1535	805	41	f	f	PROPN
ejpam-1535	805	42	φ	φ	PROPN
ejpam-1535	805	43	.	.	PUNCT
ejpam-1535	806	1	lemma	lemma	PROPN
ejpam-1535	806	2	16	16	NUM
ejpam-1535	806	3	.	.	PUNCT
ejpam-1535	807	1	let	let	VERB
ejpam-1535	807	2	φ	φ	NOUN
ejpam-1535	807	3	:	:	PUNCT
ejpam-1535	807	4	c	c	X
ejpam-1535	807	5	→	→	PUNCT
ejpam-1535	807	6	d	d	X
ejpam-1535	807	7	be	be	AUX
ejpam-1535	807	8	an	an	DET
ejpam-1535	807	9	inductive	inductive	ADJ
ejpam-1535	807	10	functor	functor	NOUN
ejpam-1535	807	11	between	between	ADP
ejpam-1535	807	12	inductive	inductive	ADJ
ejpam-1535	807	13	categories	category	NOUN
ejpam-1535	807	14	c	c	PROPN
ejpam-1535	807	15	and	and	CCONJ
ejpam-1535	807	16	d.	d.	PROPN
ejpam-1535	807	17	then	then	ADV
ejpam-1535	807	18	xφ⊗	xφ⊗	PROPN
ejpam-1535	807	19	yφ	yφ	PROPN
ejpam-1535	808	1	=	=	PUNCT
ejpam-1535	808	2	(	(	PUNCT
ejpam-1535	808	3	x	x	PROPN
ejpam-1535	808	4	⊗	⊗	PROPN
ejpam-1535	808	5	y)φ	y)φ	PROPN
ejpam-1535	808	6	.	.	PUNCT
ejpam-1535	809	1	proof	proof	NOUN
ejpam-1535	809	2	.	.	PUNCT
ejpam-1535	810	1	we	we	PRON
ejpam-1535	810	2	have	have	VERB
ejpam-1535	810	3	xφ⊗	xφ⊗	PROPN
ejpam-1535	810	4	yφ	yφ	PROPN
ejpam-1535	810	5	=	=	SYM
ejpam-1535	810	6	�	�	PROPN
ejpam-1535	810	7	xφ|r(xφ)∧	xφ|r(xφ)∧	PROPN
ejpam-1535	810	8	d(yφ	d(yφ	PROPN
ejpam-1535	810	9	)	)	PUNCT
ejpam-1535	810	10	�	�	PROPN
ejpam-1535	810	11	·	·	PUNCT
ejpam-1535	810	12	�	�	PROPN
ejpam-1535	810	13	r(xφ)∧	r(xφ)∧	NOUN
ejpam-1535	810	14	d(yφ)|yφ	d(yφ)|yφ	PROPN
ejpam-1535	810	15	�	�	PROPN
ejpam-1535	810	16	=	=	SYM
ejpam-1535	810	17	�	�	PROPN
ejpam-1535	810	18	xφ|r(x)φ	xφ|r(x)φ	PROPN
ejpam-1535	810	19	∧	∧	PROPN
ejpam-1535	810	20	d(y)φ	d(y)φ	PROPN
ejpam-1535	810	21	�	�	PROPN
ejpam-1535	810	22	·	·	PUNCT
ejpam-1535	810	23	�	�	PROPN
ejpam-1535	811	1	r(x)φ	r(x)φ	PROPN
ejpam-1535	811	2	∧	∧	PROPN
ejpam-1535	811	3	d(y)φ|yφ	d(y)φ|yφ	PROPN
ejpam-1535	811	4	�	�	PROPN
ejpam-1535	811	5	,	,	PUNCT
ejpam-1535	811	6	by	by	ADP
ejpam-1535	811	7	lemma	lemma	PROPN
ejpam-1535	811	8	13	13	NUM
ejpam-1535	811	9	=	=	SYM
ejpam-1535	811	10	�	�	PROPN
ejpam-1535	811	11	xφ|(r(x)∧	xφ|(r(x)∧	VERB
ejpam-1535	811	12	d(y))φ	d(y))φ	PROPN
ejpam-1535	811	13	�	�	PROPN
ejpam-1535	811	14	·	·	PUNCT
ejpam-1535	811	15	�	�	PROPN
ejpam-1535	811	16	(	(	PUNCT
ejpam-1535	811	17	r(x)∧	r(x)∧	PROPN
ejpam-1535	811	18	d(y))φ|yφ	d(y))φ|yφ	PROPN
ejpam-1535	811	19	�	�	PROPN
ejpam-1535	811	20	,	,	PUNCT
ejpam-1535	811	21	by	by	ADP
ejpam-1535	811	22	(	(	PUNCT
ejpam-1535	811	23	if	if	SCONJ
ejpam-1535	811	24	)	)	PUNCT
ejpam-1535	811	25	=	=	SYM
ejpam-1535	811	26	(	(	PUNCT
ejpam-1535	811	27	x	x	NOUN
ejpam-1535	811	28	|r(x)∧	|r(x)∧	VERB
ejpam-1535	811	29	d(y))φ	d(y))φ	PROPN
ejpam-1535	811	30	·	·	PUNCT
ejpam-1535	811	31	(	(	PUNCT
ejpam-1535	811	32	r(x)∧	r(x)∧	PROPN
ejpam-1535	811	33	d(y)|y)φ	d(y)|y)φ	PROPN
ejpam-1535	811	34	,	,	PUNCT
ejpam-1535	811	35	by	by	ADP
ejpam-1535	811	36	lemma	lemma	PROPN
ejpam-1535	811	37	14	14	NUM
ejpam-1535	811	38	=	=	SYM
ejpam-1535	811	39	�	�	PROPN
ejpam-1535	811	40	(	(	PUNCT
ejpam-1535	811	41	x	x	PROPN
ejpam-1535	811	42	|r(x)∧	|r(x)∧	PROPN
ejpam-1535	811	43	d(y	d(y	NOUN
ejpam-1535	811	44	)	)	PUNCT
ejpam-1535	811	45	)	)	PUNCT
ejpam-1535	811	46	·	·	PUNCT
ejpam-1535	812	1	(	(	PUNCT
ejpam-1535	812	2	r(x)∧	r(x)∧	PROPN
ejpam-1535	812	3	d(y)|y	d(y)|y	PROPN
ejpam-1535	812	4	)	)	PUNCT
ejpam-1535	812	5	�	�	PROPN
ejpam-1535	812	6	φ	φ	PROPN
ejpam-1535	812	7	,	,	PUNCT
ejpam-1535	812	8	by	by	ADP
ejpam-1535	812	9	(	(	PUNCT
ejpam-1535	812	10	f	f	X
ejpam-1535	812	11	)	)	PUNCT
ejpam-1535	812	12	=	=	SYM
ejpam-1535	813	1	(	(	PUNCT
ejpam-1535	813	2	x	x	PROPN
ejpam-1535	813	3	⊗	⊗	PROPN
ejpam-1535	813	4	y)φ	y)φ	PROPN
ejpam-1535	813	5	,	,	PUNCT
ejpam-1535	813	6	as	as	SCONJ
ejpam-1535	813	7	required	require	VERB
ejpam-1535	813	8	.	.	PUNCT
ejpam-1535	814	1	the	the	DET
ejpam-1535	814	2	following	follow	VERB
ejpam-1535	814	3	is	be	AUX
ejpam-1535	814	4	an	an	DET
ejpam-1535	814	5	easy	easy	ADJ
ejpam-1535	814	6	consequence	consequence	NOUN
ejpam-1535	814	7	of	of	ADP
ejpam-1535	814	8	proposition	proposition	NOUN
ejpam-1535	814	9	4	4	NUM
ejpam-1535	814	10	:	:	PUNCT
ejpam-1535	814	11	proposition	proposition	NOUN
ejpam-1535	814	12	7	7	NUM
ejpam-1535	814	13	(	(	PUNCT
ejpam-1535	814	14	[	[	X
ejpam-1535	814	15	f	f	X
ejpam-1535	814	16	]	]	X
ejpam-1535	814	17	)	)	PUNCT
ejpam-1535	814	18	.	.	PUNCT
ejpam-1535	815	1	the	the	DET
ejpam-1535	815	2	composition	composition	NOUN
ejpam-1535	815	3	of	of	ADP
ejpam-1535	815	4	two	two	NUM
ejpam-1535	815	5	inductive	inductive	ADJ
ejpam-1535	815	6	functors	functor	NOUN
ejpam-1535	815	7	is	be	AUX
ejpam-1535	815	8	also	also	ADV
ejpam-1535	815	9	an	an	DET
ejpam-1535	815	10	inductive	inductive	ADJ
ejpam-1535	815	11	functor	functor	NOUN
ejpam-1535	815	12	.	.	PUNCT
ejpam-1535	816	1	consequently	consequently	ADV
ejpam-1535	816	2	,	,	PUNCT
ejpam-1535	816	3	inductive	inductive	ADJ
ejpam-1535	816	4	categories	category	NOUN
ejpam-1535	816	5	and	and	CCONJ
ejpam-1535	816	6	inductive	inductive	ADJ
ejpam-1535	816	7	functors	functors	PROPN
ejpam-1535	816	8	form	form	VERB
ejpam-1535	816	9	a	a	DET
ejpam-1535	816	10	category	category	NOUN
ejpam-1535	816	11	.	.	PUNCT
ejpam-1535	817	1	we	we	PRON
ejpam-1535	817	2	are	be	AUX
ejpam-1535	817	3	now	now	ADV
ejpam-1535	817	4	ready	ready	ADJ
ejpam-1535	817	5	to	to	PART
ejpam-1535	817	6	establish	establish	VERB
ejpam-1535	817	7	a	a	DET
ejpam-1535	817	8	correspondence	correspondence	NOUN
ejpam-1535	817	9	between	between	ADP
ejpam-1535	817	10	(	(	PUNCT
ejpam-1535	817	11	2,1,1)-morphisms	2,1,1)-morphisms	NUM
ejpam-1535	817	12	and	and	CCONJ
ejpam-1535	817	13	inductive	inductive	ADJ
ejpam-1535	817	14	functors	functor	NOUN
ejpam-1535	817	15	,	,	PUNCT
ejpam-1535	817	16	which	which	PRON
ejpam-1535	817	17	we	we	PRON
ejpam-1535	817	18	achieve	achieve	VERB
ejpam-1535	817	19	through	through	ADP
ejpam-1535	817	20	the	the	DET
ejpam-1535	817	21	combination	combination	NOUN
ejpam-1535	817	22	of	of	ADP
ejpam-1535	817	23	lemma	lemma	PROPN
ejpam-1535	817	24	12	12	NUM
ejpam-1535	817	25	with	with	ADP
ejpam-1535	817	26	propositions	proposition	NOUN
ejpam-1535	817	27	5	5	NUM
ejpam-1535	817	28	and	and	CCONJ
ejpam-1535	817	29	6	6	NUM
ejpam-1535	817	30	.	.	X
ejpam-1535	817	31	proposition	proposition	NOUN
ejpam-1535	817	32	8	8	NUM
ejpam-1535	817	33	.	.	PUNCT
ejpam-1535	818	1	let	let	VERB
ejpam-1535	818	2	ϕ	ϕ	NOUN
ejpam-1535	818	3	:	:	PUNCT
ejpam-1535	818	4	s	s	X
ejpam-1535	818	5	→	→	SYM
ejpam-1535	818	6	t	t	PROPN
ejpam-1535	818	7	be	be	AUX
ejpam-1535	818	8	a	a	DET
ejpam-1535	818	9	(	(	PUNCT
ejpam-1535	818	10	2,1,1)-morphism	2,1,1)-morphism	NUM
ejpam-1535	818	11	between	between	ADP
ejpam-1535	818	12	restriction	restriction	NOUN
ejpam-1535	818	13	semigroups	semigroup	NOUN
ejpam-1535	818	14	s	s	PART
ejpam-1535	818	15	and	and	CCONJ
ejpam-1535	818	16	t.	t.	NOUN
ejpam-1535	818	17	we	we	PRON
ejpam-1535	818	18	define	define	VERB
ejpam-1535	818	19	φ	φ	NOUN
ejpam-1535	818	20	:	:	PUNCT
ejpam-1535	818	21	=	=	SYM
ejpam-1535	818	22	c(ϕ	c(ϕ	PROPN
ejpam-1535	818	23	)	)	PUNCT
ejpam-1535	818	24	:	:	PUNCT
ejpam-1535	818	25	c(s)→	c(s)→	ADJ
ejpam-1535	818	26	c(t	c(t	PROPN
ejpam-1535	818	27	)	)	PUNCT
ejpam-1535	818	28	to	to	PART
ejpam-1535	818	29	be	be	AUX
ejpam-1535	818	30	the	the	DET
ejpam-1535	818	31	same	same	ADJ
ejpam-1535	818	32	function	function	NOUN
ejpam-1535	818	33	on	on	ADP
ejpam-1535	818	34	the	the	DET
ejpam-1535	818	35	underlying	underlie	VERB
ejpam-1535	818	36	sets	set	NOUN
ejpam-1535	818	37	.	.	PUNCT
ejpam-1535	819	1	then	then	ADV
ejpam-1535	819	2	φ	φ	PROPN
ejpam-1535	819	3	is	be	AUX
ejpam-1535	819	4	an	an	DET
ejpam-1535	819	5	inductive	inductive	ADJ
ejpam-1535	819	6	functor	functor	NOUN
ejpam-1535	819	7	with	with	ADP
ejpam-1535	819	8	respect	respect	NOUN
ejpam-1535	819	9	to	to	ADP
ejpam-1535	819	10	the	the	DET
ejpam-1535	819	11	restricted	restricted	ADJ
ejpam-1535	819	12	products	product	NOUN
ejpam-1535	819	13	in	in	ADP
ejpam-1535	819	14	c(s	c(	NOUN
ejpam-1535	819	15	)	)	PUNCT
ejpam-1535	819	16	and	and	CCONJ
ejpam-1535	819	17	c(t	c(t	PROPN
ejpam-1535	819	18	)	)	PUNCT
ejpam-1535	819	19	.	.	PUNCT
ejpam-1535	820	1	proof	proof	NOUN
ejpam-1535	820	2	.	.	PUNCT
ejpam-1535	821	1	as	as	ADP
ejpam-1535	821	2	a	a	DET
ejpam-1535	821	3	(	(	PUNCT
ejpam-1535	821	4	2,1,1)-morphism	2,1,1)-morphism	NUM
ejpam-1535	821	5	,	,	PUNCT
ejpam-1535	821	6	ϕ	ϕ	NOUN
ejpam-1535	821	7	is	be	AUX
ejpam-1535	821	8	a	a	DET
ejpam-1535	821	9	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	821	10	,	,	PUNCT
ejpam-1535	821	11	and	and	CCONJ
ejpam-1535	821	12	so	so	ADV
ejpam-1535	821	13	,	,	PUNCT
ejpam-1535	821	14	by	by	ADP
ejpam-1535	821	15	proposition	proposition	NOUN
ejpam-1535	821	16	5	5	NUM
ejpam-1535	821	17	,	,	PUNCT
ejpam-1535	821	18	φ	φ	PROPN
ejpam-1535	821	19	is	be	AUX
ejpam-1535	821	20	an	an	DET
ejpam-1535	821	21	ordered	order	VERB
ejpam-1535	821	22	functor	functor	NOUN
ejpam-1535	821	23	.	.	PUNCT
ejpam-1535	822	1	to	to	PART
ejpam-1535	822	2	see	see	VERB
ejpam-1535	822	3	that	that	SCONJ
ejpam-1535	822	4	φ	φ	PROPN
ejpam-1535	822	5	is	be	AUX
ejpam-1535	822	6	inductive	inductive	ADJ
ejpam-1535	822	7	,	,	PUNCT
ejpam-1535	822	8	we	we	PRON
ejpam-1535	822	9	simply	simply	ADV
ejpam-1535	822	10	observe	observe	VERB
ejpam-1535	822	11	that	that	SCONJ
ejpam-1535	822	12	eφ	eφ	PROPN
ejpam-1535	822	13	∧	∧	PROPN
ejpam-1535	822	14	f	f	PROPN
ejpam-1535	822	15	φ	φ	PROPN
ejpam-1535	822	16	=	=	SYM
ejpam-1535	823	1	eϕ	eϕ	PROPN
ejpam-1535	823	2	∧	∧	PROPN
ejpam-1535	823	3	f	f	PROPN
ejpam-1535	823	4	ϕ	ϕ	PROPN
ejpam-1535	823	5	=	=	SYM
ejpam-1535	823	6	(	(	PUNCT
ejpam-1535	823	7	eϕ	eϕ	NOUN
ejpam-1535	823	8	)	)	PUNCT
ejpam-1535	823	9	(	(	PUNCT
ejpam-1535	823	10	f	f	PROPN
ejpam-1535	823	11	ϕ	ϕ	NOUN
ejpam-1535	823	12	)	)	PUNCT
ejpam-1535	823	13	=	=	PUNCT
ejpam-1535	823	14	(	(	PUNCT
ejpam-1535	823	15	e	e	NOUN
ejpam-1535	823	16	f	f	PROPN
ejpam-1535	823	17	)	)	PUNCT
ejpam-1535	823	18	ϕ	ϕ	PROPN
ejpam-1535	823	19	=	=	PUNCT
ejpam-1535	823	20	(	(	PUNCT
ejpam-1535	823	21	e	e	PROPN
ejpam-1535	823	22	∧	∧	PROPN
ejpam-1535	823	23	f	f	PROPN
ejpam-1535	823	24	)	)	PUNCT
ejpam-1535	823	25	ϕ	ϕ	NOUN
ejpam-1535	823	26	=	=	PUNCT
ejpam-1535	823	27	(	(	PUNCT
ejpam-1535	823	28	e	e	PROPN
ejpam-1535	823	29	∧	∧	PROPN
ejpam-1535	823	30	f	f	PROPN
ejpam-1535	823	31	)	)	PUNCT
ejpam-1535	823	32	φ	φ	PROPN
ejpam-1535	823	33	,	,	PUNCT
ejpam-1535	823	34	for	for	ADP
ejpam-1535	823	35	e	e	NOUN
ejpam-1535	823	36	,	,	PUNCT
ejpam-1535	823	37	f	f	PROPN
ejpam-1535	823	38	∈	∈	PROPN
ejpam-1535	823	39	e.	e.	PROPN
ejpam-1535	823	40	c.	c.	PROPN
ejpam-1535	823	41	hollings	hollings	PROPN
ejpam-1535	823	42	/	/	SYM
ejpam-1535	823	43	eur	eur	PROPN
ejpam-1535	823	44	.	.	PUNCT
ejpam-1535	824	1	j.	j.	PROPN
ejpam-1535	824	2	pure	pure	PROPN
ejpam-1535	824	3	appl	appl	PROPN
ejpam-1535	824	4	.	.	PROPN
ejpam-1535	824	5	math	math	PROPN
ejpam-1535	824	6	,	,	PUNCT
ejpam-1535	824	7	5	5	NUM
ejpam-1535	824	8	(	(	PUNCT
ejpam-1535	824	9	2012	2012	NUM
ejpam-1535	824	10	)	)	PUNCT
ejpam-1535	824	11	,	,	PUNCT
ejpam-1535	824	12	414	414	NUM
ejpam-1535	824	13	-	-	SYM
ejpam-1535	824	14	450	450	NUM
ejpam-1535	824	15	442	442	NUM
ejpam-1535	824	16	proposition	proposition	NOUN
ejpam-1535	824	17	9	9	NUM
ejpam-1535	824	18	.	.	PUNCT
ejpam-1535	825	1	let	let	VERB
ejpam-1535	825	2	φ	φ	NOUN
ejpam-1535	825	3	:	:	PUNCT
ejpam-1535	825	4	c	c	X
ejpam-1535	825	5	→	→	PUNCT
ejpam-1535	825	6	d	d	X
ejpam-1535	825	7	be	be	AUX
ejpam-1535	825	8	an	an	DET
ejpam-1535	825	9	inductive	inductive	ADJ
ejpam-1535	825	10	functor	functor	NOUN
ejpam-1535	825	11	of	of	ADP
ejpam-1535	825	12	inductive	inductive	ADJ
ejpam-1535	825	13	categories	category	NOUN
ejpam-1535	825	14	c	c	PROPN
ejpam-1535	825	15	and	and	CCONJ
ejpam-1535	825	16	d.	d.	PROPN
ejpam-1535	825	17	we	we	PRON
ejpam-1535	825	18	define	define	VERB
ejpam-1535	825	19	φ	φ	NOUN
ejpam-1535	825	20	:	:	PUNCT
ejpam-1535	825	21	=	=	SYM
ejpam-1535	825	22	s(φ	s(φ	PROPN
ejpam-1535	825	23	)	)	PUNCT
ejpam-1535	825	24	:	:	PUNCT
ejpam-1535	826	1	s(c	s(c	X
ejpam-1535	826	2	)	)	PUNCT
ejpam-1535	826	3	→	→	SYM
ejpam-1535	826	4	s(d	s(d	NOUN
ejpam-1535	826	5	)	)	PUNCT
ejpam-1535	826	6	to	to	PART
ejpam-1535	826	7	be	be	AUX
ejpam-1535	826	8	the	the	DET
ejpam-1535	826	9	same	same	ADJ
ejpam-1535	826	10	function	function	NOUN
ejpam-1535	826	11	on	on	ADP
ejpam-1535	826	12	the	the	DET
ejpam-1535	826	13	underlying	underlie	VERB
ejpam-1535	826	14	sets	set	NOUN
ejpam-1535	826	15	.	.	PUNCT
ejpam-1535	827	1	then	then	ADV
ejpam-1535	827	2	φ	φ	PROPN
ejpam-1535	827	3	is	be	AUX
ejpam-1535	827	4	a	a	DET
ejpam-1535	827	5	(	(	PUNCT
ejpam-1535	827	6	2,1,1)-morphism	2,1,1)-morphism	NUM
ejpam-1535	827	7	with	with	ADP
ejpam-1535	827	8	respect	respect	NOUN
ejpam-1535	827	9	to	to	ADP
ejpam-1535	827	10	the	the	DET
ejpam-1535	827	11	pseudoproducts	pseudoproduct	NOUN
ejpam-1535	827	12	in	in	ADP
ejpam-1535	827	13	s(c	s(c	PROPN
ejpam-1535	827	14	)	)	PUNCT
ejpam-1535	827	15	and	and	CCONJ
ejpam-1535	827	16	s(d	s(d	PROPN
ejpam-1535	827	17	)	)	PUNCT
ejpam-1535	827	18	.	.	PUNCT
ejpam-1535	828	1	proof	proof	NOUN
ejpam-1535	828	2	.	.	PUNCT
ejpam-1535	829	1	that	that	SCONJ
ejpam-1535	829	2	φ	φ	PROPN
ejpam-1535	829	3	respects	respect	VERB
ejpam-1535	829	4	pseudoproducts	pseudoproduct	NOUN
ejpam-1535	829	5	follows	follow	VERB
ejpam-1535	829	6	from	from	ADP
ejpam-1535	829	7	lemma	lemma	PROPN
ejpam-1535	829	8	16	16	NUM
ejpam-1535	829	9	.	.	PUNCT
ejpam-1535	830	1	moreover	moreover	ADV
ejpam-1535	830	2	,	,	PUNCT
ejpam-1535	830	3	since	since	SCONJ
ejpam-1535	830	4	x+	x+	NUM
ejpam-1535	830	5	and	and	CCONJ
ejpam-1535	830	6	x∗	x∗	PROPN
ejpam-1535	830	7	in	in	ADP
ejpam-1535	830	8	s(c	s(c	NOUN
ejpam-1535	830	9	)	)	PUNCT
ejpam-1535	830	10	correspond	correspond	VERB
ejpam-1535	830	11	to	to	ADP
ejpam-1535	830	12	d(x	d(x	PROPN
ejpam-1535	830	13	)	)	PUNCT
ejpam-1535	830	14	and	and	CCONJ
ejpam-1535	830	15	r(x	r(x	NOUN
ejpam-1535	830	16	)	)	PUNCT
ejpam-1535	830	17	in	in	ADP
ejpam-1535	830	18	c	c	PROPN
ejpam-1535	830	19	,	,	PUNCT
ejpam-1535	830	20	we	we	PRON
ejpam-1535	830	21	see	see	VERB
ejpam-1535	830	22	that	that	PRON
ejpam-1535	830	23	φmust	φmust	AUX
ejpam-1535	830	24	preserve	preserve	VERB
ejpam-1535	830	25	both	both	DET
ejpam-1535	830	26	+	+	CCONJ
ejpam-1535	830	27	and	and	CCONJ
ejpam-1535	830	28	∗	∗	NOUN
ejpam-1535	830	29	,	,	PUNCT
ejpam-1535	830	30	thanks	thank	NOUN
ejpam-1535	830	31	to	to	ADP
ejpam-1535	830	32	lemma	lemma	PROPN
ejpam-1535	830	33	13	13	NUM
ejpam-1535	830	34	.	.	PUNCT
ejpam-1535	831	1	(	(	PUNCT
ejpam-1535	831	2	alternatively	alternatively	ADV
ejpam-1535	831	3	,	,	PUNCT
ejpam-1535	831	4	in	in	ADP
ejpam-1535	831	5	place	place	NOUN
ejpam-1535	831	6	of	of	ADP
ejpam-1535	831	7	lemma	lemma	PROPN
ejpam-1535	831	8	16	16	NUM
ejpam-1535	831	9	,	,	PUNCT
ejpam-1535	831	10	we	we	PRON
ejpam-1535	831	11	could	could	AUX
ejpam-1535	831	12	have	have	AUX
ejpam-1535	831	13	included	include	VERB
ejpam-1535	831	14	the	the	DET
ejpam-1535	831	15	weaker	weak	ADJ
ejpam-1535	831	16	result	result	NOUN
ejpam-1535	831	17	that	that	SCONJ
ejpam-1535	831	18	an	an	DET
ejpam-1535	831	19	inductive	inductive	ADJ
ejpam-1535	831	20	functor	functor	PROPN
ejpam-1535	831	21	respects	respect	NOUN
ejpam-1535	831	22	pseudoproducts	pseudoproduct	NOUN
ejpam-1535	831	23	of	of	ADP
ejpam-1535	831	24	idempotents	idempotent	NOUN
ejpam-1535	831	25	.	.	PUNCT
ejpam-1535	832	1	this	this	PRON
ejpam-1535	832	2	,	,	PUNCT
ejpam-1535	832	3	together	together	ADV
ejpam-1535	832	4	with	with	ADP
ejpam-1535	832	5	lemma	lemma	PROPN
ejpam-1535	832	6	12	12	NUM
ejpam-1535	832	7	,	,	PUNCT
ejpam-1535	832	8	would	would	AUX
ejpam-1535	832	9	then	then	ADV
ejpam-1535	832	10	give	give	VERB
ejpam-1535	832	11	the	the	DET
ejpam-1535	832	12	desired	desire	VERB
ejpam-1535	832	13	result	result	NOUN
ejpam-1535	832	14	.	.	PUNCT
ejpam-1535	832	15	)	)	PUNCT
ejpam-1535	833	1	proposition	proposition	NOUN
ejpam-1535	833	2	10	10	NUM
ejpam-1535	833	3	.	.	PUNCT
ejpam-1535	834	1	if	if	SCONJ
ejpam-1535	834	2	ϕ	ϕ	NOUN
ejpam-1535	834	3	:	:	PUNCT
ejpam-1535	834	4	s→	s→	PROPN
ejpam-1535	834	5	t	t	PROPN
ejpam-1535	834	6	is	be	AUX
ejpam-1535	834	7	a	a	DET
ejpam-1535	834	8	(	(	PUNCT
ejpam-1535	834	9	2,1,1)-morphism	2,1,1)-morphism	NUM
ejpam-1535	834	10	between	between	ADP
ejpam-1535	834	11	restriction	restriction	NOUN
ejpam-1535	834	12	semigroups	semigroup	NOUN
ejpam-1535	834	13	and	and	CCONJ
ejpam-1535	834	14	φ	φ	NOUN
ejpam-1535	834	15	:	:	PUNCT
ejpam-1535	835	1	c	c	X
ejpam-1535	835	2	→	→	PUNCT
ejpam-1535	835	3	d	d	NOUN
ejpam-1535	835	4	is	be	AUX
ejpam-1535	835	5	an	an	DET
ejpam-1535	835	6	inductive	inductive	ADJ
ejpam-1535	835	7	functor	functor	NOUN
ejpam-1535	835	8	between	between	ADP
ejpam-1535	835	9	inductive	inductive	ADJ
ejpam-1535	835	10	categories	category	NOUN
ejpam-1535	835	11	,	,	PUNCT
ejpam-1535	835	12	then	then	ADV
ejpam-1535	835	13	s(c(ϕ	s(c(ϕ	PROPN
ejpam-1535	835	14	)	)	PUNCT
ejpam-1535	835	15	)	)	PUNCT
ejpam-1535	836	1	=	=	SYM
ejpam-1535	836	2	ϕ	ϕ	PROPN
ejpam-1535	836	3	and	and	CCONJ
ejpam-1535	836	4	c(s(φ	c(s(φ	PROPN
ejpam-1535	836	5	)	)	PUNCT
ejpam-1535	836	6	)	)	PUNCT
ejpam-1535	837	1	=	=	SYM
ejpam-1535	837	2	φ	φ	X
ejpam-1535	837	3	.	.	PUNCT
ejpam-1535	838	1	proof	proof	NOUN
ejpam-1535	838	2	.	.	PUNCT
ejpam-1535	839	1	this	this	PRON
ejpam-1535	839	2	is	be	AUX
ejpam-1535	839	3	an	an	DET
ejpam-1535	839	4	easy	easy	ADJ
ejpam-1535	839	5	consequence	consequence	NOUN
ejpam-1535	839	6	of	of	ADP
ejpam-1535	839	7	propositions	proposition	NOUN
ejpam-1535	839	8	8	8	NUM
ejpam-1535	839	9	and	and	CCONJ
ejpam-1535	839	10	9	9	NUM
ejpam-1535	839	11	,	,	PUNCT
ejpam-1535	839	12	together	together	ADV
ejpam-1535	839	13	with	with	ADP
ejpam-1535	839	14	theorem	theorem	ADJ
ejpam-1535	839	15	4	4	NUM
ejpam-1535	839	16	.	.	PUNCT
ejpam-1535	839	17	observe	observe	VERB
ejpam-1535	839	18	that	that	SCONJ
ejpam-1535	839	19	if	if	SCONJ
ejpam-1535	839	20	ϕ′	ϕ′	X
ejpam-1535	839	21	:	:	PUNCT
ejpam-1535	839	22	t	t	PROPN
ejpam-1535	839	23	→	→	SYM
ejpam-1535	839	24	t	t	PROPN
ejpam-1535	839	25	′	′	NOUN
ejpam-1535	839	26	is	be	AUX
ejpam-1535	839	27	another	another	PRON
ejpam-1535	839	28	(	(	PUNCT
ejpam-1535	839	29	2,1,1)-morphism	2,1,1)-morphism	NUM
ejpam-1535	839	30	of	of	ADP
ejpam-1535	839	31	restriction	restriction	NOUN
ejpam-1535	839	32	semigroups	semigroup	NOUN
ejpam-1535	839	33	,	,	PUNCT
ejpam-1535	839	34	and	and	CCONJ
ejpam-1535	839	35	φ′	φ′	NUM
ejpam-1535	839	36	:	:	PUNCT
ejpam-1535	840	1	d	d	X
ejpam-1535	840	2	→	→	PUNCT
ejpam-1535	840	3	d′	d′	NOUN
ejpam-1535	840	4	is	be	AUX
ejpam-1535	840	5	another	another	DET
ejpam-1535	840	6	inductive	inductive	ADJ
ejpam-1535	840	7	functor	functor	PROPN
ejpam-1535	840	8	of	of	ADP
ejpam-1535	840	9	inductive	inductive	ADJ
ejpam-1535	840	10	categories	category	NOUN
ejpam-1535	840	11	,	,	PUNCT
ejpam-1535	840	12	then	then	ADV
ejpam-1535	840	13	c(ϕϕ′	c(ϕϕ′	PROPN
ejpam-1535	840	14	)	)	PUNCT
ejpam-1535	840	15	=	=	PUNCT
ejpam-1535	840	16	c(ϕ)c(ϕ′	c(ϕ)c(ϕ′	NOUN
ejpam-1535	840	17	)	)	PUNCT
ejpam-1535	840	18	and	and	CCONJ
ejpam-1535	840	19	s(φφ′	s(φφ′	NUM
ejpam-1535	840	20	)	)	PUNCT
ejpam-1535	840	21	=	=	PUNCT
ejpam-1535	840	22	s(φ)s(φ′	s(φ)s(φ′	ADJ
ejpam-1535	840	23	)	)	PUNCT
ejpam-1535	840	24	.	.	PUNCT
ejpam-1535	841	1	thus	thus	ADV
ejpam-1535	841	2	s	s	X
ejpam-1535	841	3	(	(	PUNCT
ejpam-1535	841	4	·	·	PUNCT
ejpam-1535	841	5	)	)	PUNCT
ejpam-1535	841	6	and	and	CCONJ
ejpam-1535	841	7	c	c	X
ejpam-1535	841	8	(	(	PUNCT
ejpam-1535	841	9	·	·	PUNCT
ejpam-1535	841	10	)	)	PUNCT
ejpam-1535	841	11	form	form	VERB
ejpam-1535	841	12	a	a	DET
ejpam-1535	841	13	pair	pair	NOUN
ejpam-1535	841	14	of	of	ADP
ejpam-1535	841	15	mutually	mutually	ADV
ejpam-1535	841	16	inverse	inverse	ADJ
ejpam-1535	841	17	functors∗∗	functors∗∗	NOUN
ejpam-1535	841	18	between	between	ADP
ejpam-1535	841	19	the	the	DET
ejpam-1535	841	20	category	category	NOUN
ejpam-1535	841	21	of	of	ADP
ejpam-1535	841	22	restriction	restriction	NOUN
ejpam-1535	841	23	semigroups	semigroup	NOUN
ejpam-1535	841	24	and	and	CCONJ
ejpam-1535	841	25	(	(	PUNCT
ejpam-1535	841	26	2,1,1)-morphisms	2,1,1)-morphism	NOUN
ejpam-1535	841	27	,	,	PUNCT
ejpam-1535	841	28	and	and	CCONJ
ejpam-1535	841	29	that	that	PRON
ejpam-1535	841	30	of	of	ADP
ejpam-1535	841	31	inductive	inductive	ADJ
ejpam-1535	841	32	categories	category	NOUN
ejpam-1535	841	33	and	and	CCONJ
ejpam-1535	841	34	inductive	inductive	ADJ
ejpam-1535	841	35	functors	functor	NOUN
ejpam-1535	841	36	.	.	PUNCT
ejpam-1535	842	1	theorems	theorems	PROPN
ejpam-1535	842	2	2	2	NUM
ejpam-1535	842	3	,	,	PUNCT
ejpam-1535	842	4	3	3	NUM
ejpam-1535	842	5	,	,	PUNCT
ejpam-1535	842	6	and	and	CCONJ
ejpam-1535	842	7	4	4	NUM
ejpam-1535	842	8	and	and	CCONJ
ejpam-1535	842	9	propositions	proposition	NOUN
ejpam-1535	842	10	8	8	NUM
ejpam-1535	842	11	,	,	PUNCT
ejpam-1535	842	12	9	9	NUM
ejpam-1535	842	13	and	and	CCONJ
ejpam-1535	842	14	10	10	NUM
ejpam-1535	842	15	can	can	AUX
ejpam-1535	842	16	therefore	therefore	ADV
ejpam-1535	842	17	be	be	AUX
ejpam-1535	842	18	brought	bring	VERB
ejpam-1535	842	19	together	together	ADV
ejpam-1535	842	20	into	into	ADP
ejpam-1535	842	21	the	the	DET
ejpam-1535	842	22	following	following	NOUN
ejpam-1535	842	23	:	:	PUNCT
ejpam-1535	842	24	theorem	theorem	NOUN
ejpam-1535	842	25	6	6	NUM
ejpam-1535	842	26	(	(	PUNCT
ejpam-1535	842	27	[	[	X
ejpam-1535	842	28	28	28	NUM
ejpam-1535	842	29	,	,	PUNCT
ejpam-1535	842	30	theorem	theorem	VERB
ejpam-1535	842	31	5.7	5.7	NUM
ejpam-1535	842	32	]	]	PUNCT
ejpam-1535	842	33	)	)	PUNCT
ejpam-1535	842	34	.	.	PUNCT
ejpam-1535	843	1	the	the	DET
ejpam-1535	843	2	category	category	NOUN
ejpam-1535	843	3	of	of	ADP
ejpam-1535	843	4	restriction	restriction	NOUN
ejpam-1535	843	5	semigroups	semigroup	NOUN
ejpam-1535	843	6	and	and	CCONJ
ejpam-1535	843	7	(	(	PUNCT
ejpam-1535	843	8	2,1,1)-morphisms	2,1,1)-morphism	NOUN
ejpam-1535	843	9	is	be	AUX
ejpam-1535	843	10	isomorphic	isomorphic	ADJ
ejpam-1535	843	11	to	to	ADP
ejpam-1535	843	12	the	the	DET
ejpam-1535	843	13	category	category	NOUN
ejpam-1535	843	14	of	of	ADP
ejpam-1535	843	15	inductive	inductive	ADJ
ejpam-1535	843	16	categories	category	NOUN
ejpam-1535	843	17	and	and	CCONJ
ejpam-1535	843	18	inductive	inductive	ADJ
ejpam-1535	843	19	functors	functor	NOUN
ejpam-1535	843	20	.	.	PUNCT
ejpam-1535	844	1	corollaries	corollary	NOUN
ejpam-1535	844	2	3	3	NUM
ejpam-1535	844	3	and	and	CCONJ
ejpam-1535	844	4	5	5	NUM
ejpam-1535	844	5	enable	enable	VERB
ejpam-1535	844	6	us	we	PRON
ejpam-1535	844	7	to	to	PART
ejpam-1535	844	8	write	write	VERB
ejpam-1535	844	9	down	down	ADP
ejpam-1535	844	10	the	the	DET
ejpam-1535	844	11	following	follow	VERB
ejpam-1535	844	12	specialisation	specialisation	NOUN
ejpam-1535	844	13	of	of	ADP
ejpam-1535	844	14	theorem	theorem	ADJ
ejpam-1535	844	15	6	6	NUM
ejpam-1535	844	16	:	:	PUNCT
ejpam-1535	844	17	corollary	corollary	ADJ
ejpam-1535	844	18	9	9	NUM
ejpam-1535	844	19	(	(	PUNCT
ejpam-1535	844	20	[	[	X
ejpam-1535	844	21	26	26	NUM
ejpam-1535	844	22	,	,	PUNCT
ejpam-1535	844	23	theorem	theorem	VERB
ejpam-1535	844	24	3.16	3.16	NUM
ejpam-1535	844	25	]	]	PUNCT
ejpam-1535	844	26	)	)	PUNCT
ejpam-1535	844	27	.	.	PUNCT
ejpam-1535	845	1	the	the	DET
ejpam-1535	845	2	category	category	NOUN
ejpam-1535	845	3	of	of	ADP
ejpam-1535	845	4	full	full	ADJ
ejpam-1535	845	5	restriction	restriction	NOUN
ejpam-1535	845	6	semigroups	semigroup	NOUN
ejpam-1535	845	7	and	and	CCONJ
ejpam-1535	845	8	(	(	PUNCT
ejpam-1535	845	9	2,1,1)morphisms	2,1,1)morphisms	NUM
ejpam-1535	845	10	is	be	AUX
ejpam-1535	845	11	isomorphic	isomorphic	ADJ
ejpam-1535	845	12	to	to	ADP
ejpam-1535	845	13	the	the	DET
ejpam-1535	845	14	category	category	NOUN
ejpam-1535	845	15	of	of	ADP
ejpam-1535	845	16	inductive	inductive	ADJ
ejpam-1535	845	17	unipotent	unipotent	ADJ
ejpam-1535	845	18	categories	category	NOUN
ejpam-1535	845	19	and	and	CCONJ
ejpam-1535	845	20	inductive	inductive	ADJ
ejpam-1535	845	21	functors	functor	NOUN
ejpam-1535	845	22	.	.	PUNCT
ejpam-1535	846	1	finally	finally	ADV
ejpam-1535	846	2	,	,	PUNCT
ejpam-1535	846	3	from	from	ADP
ejpam-1535	846	4	corollaries	corollary	NOUN
ejpam-1535	846	5	4	4	NUM
ejpam-1535	846	6	and	and	CCONJ
ejpam-1535	846	7	6	6	NUM
ejpam-1535	846	8	,	,	PUNCT
ejpam-1535	846	9	we	we	PRON
ejpam-1535	846	10	have	have	VERB
ejpam-1535	846	11	the	the	DET
ejpam-1535	846	12	following	follow	VERB
ejpam-1535	846	13	:	:	PUNCT
ejpam-1535	846	14	corollary	corollary	ADJ
ejpam-1535	846	15	10	10	NUM
ejpam-1535	846	16	.	.	PUNCT
ejpam-1535	847	1	the	the	DET
ejpam-1535	847	2	category	category	NOUN
ejpam-1535	847	3	of	of	ADP
ejpam-1535	847	4	ample	ample	ADJ
ejpam-1535	847	5	semigroups	semigroup	NOUN
ejpam-1535	847	6	and	and	CCONJ
ejpam-1535	847	7	(	(	PUNCT
ejpam-1535	847	8	2,1,1)-morphisms	2,1,1)-morphism	NOUN
ejpam-1535	847	9	is	be	AUX
ejpam-1535	847	10	isomorphic	isomorphic	ADJ
ejpam-1535	847	11	to	to	ADP
ejpam-1535	847	12	the	the	DET
ejpam-1535	847	13	category	category	NOUN
ejpam-1535	847	14	of	of	ADP
ejpam-1535	847	15	inductive	inductive	ADJ
ejpam-1535	847	16	cancellative	cancellative	ADJ
ejpam-1535	847	17	categories	category	NOUN
ejpam-1535	847	18	and	and	CCONJ
ejpam-1535	847	19	inductive	inductive	ADJ
ejpam-1535	847	20	functors	functor	NOUN
ejpam-1535	847	21	.	.	PUNCT
ejpam-1535	848	1	8	8	NUM
ejpam-1535	848	2	.	.	PUNCT
ejpam-1535	848	3	inverse	inverse	NOUN
ejpam-1535	848	4	semigroups	semigroup	NOUN
ejpam-1535	848	5	and	and	CCONJ
ejpam-1535	848	6	inductive	inductive	ADJ
ejpam-1535	848	7	groupoids	groupoid	NOUN
ejpam-1535	848	8	now	now	ADV
ejpam-1535	848	9	that	that	SCONJ
ejpam-1535	848	10	we	we	PRON
ejpam-1535	848	11	have	have	AUX
ejpam-1535	848	12	established	establish	VERB
ejpam-1535	848	13	a	a	DET
ejpam-1535	848	14	series	series	NOUN
ejpam-1535	848	15	of	of	ADP
ejpam-1535	848	16	category	category	NOUN
ejpam-1535	848	17	isomorphisms	isomorphism	NOUN
ejpam-1535	848	18	for	for	ADP
ejpam-1535	848	19	restriction	restriction	NOUN
ejpam-1535	848	20	semigroups	semigroup	NOUN
ejpam-1535	848	21	and	and	CCONJ
ejpam-1535	848	22	inductive	inductive	ADJ
ejpam-1535	848	23	categories	category	NOUN
ejpam-1535	848	24	,	,	PUNCT
ejpam-1535	848	25	we	we	PRON
ejpam-1535	848	26	are	be	AUX
ejpam-1535	848	27	ready	ready	ADJ
ejpam-1535	848	28	to	to	PART
ejpam-1535	848	29	turn	turn	VERB
ejpam-1535	848	30	our	our	PRON
ejpam-1535	848	31	attention	attention	NOUN
ejpam-1535	848	32	to	to	ADP
ejpam-1535	848	33	the	the	DET
ejpam-1535	848	34	special	special	ADJ
ejpam-1535	848	35	case	case	NOUN
ejpam-1535	848	36	of	of	ADP
ejpam-1535	848	37	inverse	inverse	NOUN
ejpam-1535	848	38	semigroups	semigroup	NOUN
ejpam-1535	848	39	.	.	PUNCT
ejpam-1535	849	1	as	as	SCONJ
ejpam-1535	849	2	noted	note	VERB
ejpam-1535	849	3	in	in	ADP
ejpam-1535	849	4	section	section	NOUN
ejpam-1535	849	5	3	3	NUM
ejpam-1535	849	6	,	,	PUNCT
ejpam-1535	849	7	these	these	PRON
ejpam-1535	849	8	may	may	AUX
ejpam-1535	849	9	be	be	AUX
ejpam-1535	849	10	regarded	regard	VERB
ejpam-1535	849	11	as	as	ADP
ejpam-1535	849	12	full	full	ADJ
ejpam-1535	849	13	restriction	restriction	NOUN
ejpam-1535	849	14	semigroups	semigroup	NOUN
ejpam-1535	849	15	with	with	ADP
ejpam-1535	849	16	a+	a+	PRON
ejpam-1535	849	17	=	=	SYM
ejpam-1535	849	18	aa−1	aa−1	PROPN
ejpam-1535	849	19	and	and	CCONJ
ejpam-1535	849	20	a∗	a∗	PROPN
ejpam-1535	849	21	=	=	SYM
ejpam-1535	849	22	a−1a	a−1a	PROPN
ejpam-1535	849	23	.	.	PUNCT
ejpam-1535	850	1	the	the	DET
ejpam-1535	850	2	particular	particular	ADJ
ejpam-1535	850	3	type	type	NOUN
ejpam-1535	850	4	of	of	ADP
ejpam-1535	850	5	inductive	inductive	ADJ
ejpam-1535	850	6	category	category	NOUN
ejpam-1535	850	7	to	to	PART
ejpam-1535	850	8	which	which	PRON
ejpam-1535	850	9	an	an	DET
ejpam-1535	850	10	inverse	inverse	NOUN
ejpam-1535	850	11	semigroup	semigroup	NOUN
ejpam-1535	850	12	will	will	AUX
ejpam-1535	850	13	correspond	correspond	VERB
ejpam-1535	850	14	,	,	PUNCT
ejpam-1535	850	15	under	under	ADP
ejpam-1535	850	16	the	the	DET
ejpam-1535	850	17	constructions	construction	NOUN
ejpam-1535	850	18	of	of	ADP
ejpam-1535	850	19	section	section	NOUN
ejpam-1535	850	20	5	5	NUM
ejpam-1535	850	21	,	,	PUNCT
ejpam-1535	850	22	is	be	AUX
ejpam-1535	850	23	a	a	DET
ejpam-1535	850	24	so	so	ADV
ejpam-1535	850	25	-	-	PUNCT
ejpam-1535	850	26	called	call	VERB
ejpam-1535	850	27	inductive	inductive	ADJ
ejpam-1535	850	28	groupoid	groupoid	NOUN
ejpam-1535	850	29	.	.	PUNCT
ejpam-1535	851	1	∗∗note	∗∗note	VERB
ejpam-1535	851	2	that	that	SCONJ
ejpam-1535	851	3	these	these	DET
ejpam-1535	851	4	functors	functor	NOUN
ejpam-1535	851	5	are	be	AUX
ejpam-1535	851	6	regarded	regard	VERB
ejpam-1535	851	7	as	as	ADP
ejpam-1535	851	8	functions	function	NOUN
ejpam-1535	851	9	between	between	ADP
ejpam-1535	851	10	categories	category	NOUN
ejpam-1535	851	11	in	in	ADP
ejpam-1535	851	12	sense	sense	NOUN
ejpam-1535	851	13	(	(	PUNCT
ejpam-1535	851	14	♠	♠	NOUN
ejpam-1535	851	15	)	)	PUNCT
ejpam-1535	851	16	.	.	PUNCT
ejpam-1535	852	1	c.	c.	PROPN
ejpam-1535	852	2	hollings	holling	NOUN
ejpam-1535	852	3	/	/	SYM
ejpam-1535	852	4	eur	eur	PROPN
ejpam-1535	852	5	.	.	PUNCT
ejpam-1535	853	1	j.	j.	PROPN
ejpam-1535	853	2	pure	pure	PROPN
ejpam-1535	853	3	appl	appl	PROPN
ejpam-1535	853	4	.	.	PROPN
ejpam-1535	853	5	math	math	PROPN
ejpam-1535	853	6	,	,	PUNCT
ejpam-1535	853	7	5	5	NUM
ejpam-1535	853	8	(	(	PUNCT
ejpam-1535	853	9	2012	2012	NUM
ejpam-1535	853	10	)	)	PUNCT
ejpam-1535	853	11	,	,	PUNCT
ejpam-1535	853	12	414	414	NUM
ejpam-1535	853	13	-	-	SYM
ejpam-1535	853	14	450	450	NUM
ejpam-1535	853	15	443	443	NUM
ejpam-1535	853	16	8.1	8.1	NUM
ejpam-1535	853	17	.	.	PUNCT
ejpam-1535	854	1	inductive	inductive	PROPN
ejpam-1535	854	2	groupoids	groupoids	PROPN
ejpam-1535	854	3	definition	definition	NOUN
ejpam-1535	854	4	17	17	NUM
ejpam-1535	854	5	.	.	PUNCT
ejpam-1535	855	1	let	let	AUX
ejpam-1535	855	2	(	(	PUNCT
ejpam-1535	855	3	g	g	NOUN
ejpam-1535	855	4	,	,	PUNCT
ejpam-1535	855	5	·	·	PUNCT
ejpam-1535	855	6	)	)	PUNCT
ejpam-1535	855	7	be	be	AUX
ejpam-1535	855	8	a	a	DET
ejpam-1535	855	9	small	small	ADJ
ejpam-1535	855	10	category	category	NOUN
ejpam-1535	855	11	.	.	PUNCT
ejpam-1535	856	1	we	we	PRON
ejpam-1535	856	2	call	call	VERB
ejpam-1535	856	3	(	(	PUNCT
ejpam-1535	856	4	g	g	NOUN
ejpam-1535	856	5	,	,	PUNCT
ejpam-1535	856	6	·	·	PUNCT
ejpam-1535	856	7	)	)	PUNCT
ejpam-1535	856	8	a	a	DET
ejpam-1535	856	9	groupoid	groupoid	NOUN
ejpam-1535	856	10	if	if	SCONJ
ejpam-1535	856	11	it	it	PRON
ejpam-1535	856	12	satisfies	satisfy	VERB
ejpam-1535	856	13	the	the	DET
ejpam-1535	856	14	following	follow	VERB
ejpam-1535	856	15	additional	additional	ADJ
ejpam-1535	856	16	condition	condition	NOUN
ejpam-1535	856	17	:	:	PUNCT
ejpam-1535	856	18	(	(	PUNCT
ejpam-1535	856	19	g	g	NOUN
ejpam-1535	856	20	)	)	PUNCT
ejpam-1535	856	21	for	for	ADP
ejpam-1535	856	22	every	every	DET
ejpam-1535	856	23	x	x	SYM
ejpam-1535	856	24	∈	∈	PROPN
ejpam-1535	856	25	g	g	NOUN
ejpam-1535	856	26	,	,	PUNCT
ejpam-1535	856	27	there	there	PRON
ejpam-1535	856	28	exists	exist	VERB
ejpam-1535	856	29	x−1	x−1	PROPN
ejpam-1535	856	30	∈	∈	PROPN
ejpam-1535	856	31	g	g	PROPN
ejpam-1535	856	32	such	such	ADJ
ejpam-1535	856	33	that	that	SCONJ
ejpam-1535	856	34	∃x	∃x	PROPN
ejpam-1535	856	35	·	·	PUNCT
ejpam-1535	856	36	x−1	x−1	NOUN
ejpam-1535	856	37	and	and	CCONJ
ejpam-1535	856	38	∃x−1	∃x−1	NOUN
ejpam-1535	856	39	·	·	PUNCT
ejpam-1535	856	40	x	x	PUNCT
ejpam-1535	856	41	with	with	ADP
ejpam-1535	856	42	x	x	X
ejpam-1535	856	43	·	·	PUNCT
ejpam-1535	856	44	x−1	x−1	PUNCT
ejpam-1535	856	45	=	=	SYM
ejpam-1535	856	46	d(x	d(x	PROPN
ejpam-1535	856	47	)	)	PUNCT
ejpam-1535	856	48	and	and	CCONJ
ejpam-1535	856	49	x−1	x−1	PROPN
ejpam-1535	856	50	·	·	PUNCT
ejpam-1535	856	51	x	x	X
ejpam-1535	856	52	=	=	PUNCT
ejpam-1535	856	53	r(x	r(x	PROPN
ejpam-1535	856	54	)	)	PUNCT
ejpam-1535	856	55	.	.	PUNCT
ejpam-1535	857	1	to	to	PART
ejpam-1535	857	2	put	put	VERB
ejpam-1535	857	3	this	this	PRON
ejpam-1535	857	4	another	another	DET
ejpam-1535	857	5	way	way	NOUN
ejpam-1535	857	6	:	:	PUNCT
ejpam-1535	857	7	a	a	DET
ejpam-1535	857	8	groupoid	groupoid	NOUN
ejpam-1535	857	9	is	be	AUX
ejpam-1535	857	10	a	a	DET
ejpam-1535	857	11	small	small	ADJ
ejpam-1535	857	12	category	category	NOUN
ejpam-1535	857	13	in	in	ADP
ejpam-1535	857	14	which	which	PRON
ejpam-1535	857	15	every	every	DET
ejpam-1535	857	16	arrow	arrow	NOUN
ejpam-1535	857	17	is	be	AUX
ejpam-1535	857	18	invertible	invertible	ADJ
ejpam-1535	857	19	.	.	PUNCT
ejpam-1535	858	1	lemma	lemma	PROPN
ejpam-1535	858	2	17	17	NUM
ejpam-1535	858	3	.	.	PUNCT
ejpam-1535	859	1	a	a	DET
ejpam-1535	859	2	groupoid	groupoid	NOUN
ejpam-1535	859	3	is	be	AUX
ejpam-1535	859	4	cancellative	cancellative	ADJ
ejpam-1535	859	5	in	in	ADP
ejpam-1535	859	6	the	the	DET
ejpam-1535	859	7	sense	sense	NOUN
ejpam-1535	859	8	of	of	ADP
ejpam-1535	859	9	definition	definition	NOUN
ejpam-1535	859	10	10	10	NUM
ejpam-1535	859	11	.	.	PUNCT
ejpam-1535	860	1	proof	proof	NOUN
ejpam-1535	860	2	.	.	PUNCT
ejpam-1535	861	1	let	let	VERB
ejpam-1535	861	2	(	(	PUNCT
ejpam-1535	861	3	g	g	NOUN
ejpam-1535	861	4	,	,	PUNCT
ejpam-1535	861	5	·	·	PUNCT
ejpam-1535	861	6	)	)	PUNCT
ejpam-1535	861	7	be	be	AUX
ejpam-1535	861	8	a	a	DET
ejpam-1535	861	9	groupoid	groupoid	NOUN
ejpam-1535	861	10	and	and	CCONJ
ejpam-1535	861	11	suppose	suppose	VERB
ejpam-1535	861	12	that	that	SCONJ
ejpam-1535	861	13	∃x	∃x	ADJ
ejpam-1535	861	14	·	·	PUNCT
ejpam-1535	861	15	z	z	NOUN
ejpam-1535	861	16	and	and	CCONJ
ejpam-1535	861	17	∃y	∃y	PROPN
ejpam-1535	861	18	·	·	PUNCT
ejpam-1535	861	19	z	z	NOUN
ejpam-1535	861	20	with	with	ADP
ejpam-1535	861	21	x	x	X
ejpam-1535	861	22	·	·	PUNCT
ejpam-1535	861	23	z	z	X
ejpam-1535	861	24	=	=	SYM
ejpam-1535	861	25	y	y	PROPN
ejpam-1535	861	26	·	·	PUNCT
ejpam-1535	861	27	z.	z.	PROPN
ejpam-1535	861	28	thus	thus	ADV
ejpam-1535	861	29	r(x	r(x	VERB
ejpam-1535	861	30	)	)	PUNCT
ejpam-1535	861	31	=	=	PUNCT
ejpam-1535	861	32	r(y	r(y	VERB
ejpam-1535	861	33	)	)	PUNCT
ejpam-1535	861	34	=	=	SYM
ejpam-1535	861	35	d(z	d(z	PROPN
ejpam-1535	861	36	)	)	PUNCT
ejpam-1535	861	37	.	.	PUNCT
ejpam-1535	862	1	note	note	VERB
ejpam-1535	862	2	that	that	SCONJ
ejpam-1535	862	3	since	since	SCONJ
ejpam-1535	862	4	∃z	∃z	PROPN
ejpam-1535	862	5	·	·	PUNCT
ejpam-1535	863	1	z−1	z−1	NUM
ejpam-1535	863	2	,	,	PUNCT
ejpam-1535	863	3	we	we	PRON
ejpam-1535	863	4	may	may	AUX
ejpam-1535	863	5	conclude	conclude	VERB
ejpam-1535	863	6	that	that	SCONJ
ejpam-1535	863	7	both	both	CCONJ
ejpam-1535	863	8	x	x	X
ejpam-1535	863	9	·	·	PUNCT
ejpam-1535	863	10	(	(	PUNCT
ejpam-1535	863	11	z	z	NOUN
ejpam-1535	863	12	·	·	PUNCT
ejpam-1535	863	13	z−1	z−1	NUM
ejpam-1535	863	14	)	)	PUNCT
ejpam-1535	863	15	and	and	CCONJ
ejpam-1535	863	16	(	(	PUNCT
ejpam-1535	863	17	x	x	SYM
ejpam-1535	863	18	·	·	PUNCT
ejpam-1535	863	19	z	z	X
ejpam-1535	863	20	)	)	PUNCT
ejpam-1535	863	21	·	·	PUNCT
ejpam-1535	864	1	z−1	z−1	NUM
ejpam-1535	864	2	are	be	AUX
ejpam-1535	864	3	defined	define	VERB
ejpam-1535	864	4	.	.	PUNCT
ejpam-1535	865	1	similarly	similarly	ADV
ejpam-1535	865	2	for	for	ADP
ejpam-1535	865	3	y	y	PROPN
ejpam-1535	865	4	·	·	PUNCT
ejpam-1535	865	5	(	(	PUNCT
ejpam-1535	865	6	z	z	X
ejpam-1535	865	7	·	·	PUNCT
ejpam-1535	865	8	z−1	z−1	NUM
ejpam-1535	865	9	)	)	PUNCT
ejpam-1535	865	10	and	and	CCONJ
ejpam-1535	865	11	(	(	PUNCT
ejpam-1535	865	12	y	y	PROPN
ejpam-1535	865	13	·	·	PUNCT
ejpam-1535	865	14	z	z	X
ejpam-1535	865	15	)	)	PUNCT
ejpam-1535	865	16	·	·	PUNCT
ejpam-1535	866	1	z−1	z−1	X
ejpam-1535	866	2	.	.	PUNCT
ejpam-1535	867	1	then	then	ADV
ejpam-1535	867	2	x	x	X
ejpam-1535	867	3	·	·	PUNCT
ejpam-1535	867	4	z	z	X
ejpam-1535	867	5	=	=	PUNCT
ejpam-1535	867	6	y	y	PROPN
ejpam-1535	867	7	·	·	PUNCT
ejpam-1535	867	8	z	z	X
ejpam-1535	868	1	=	=	NOUN
ejpam-1535	868	2	⇒	⇒	NOUN
ejpam-1535	868	3	(	(	PUNCT
ejpam-1535	868	4	x	x	X
ejpam-1535	868	5	·	·	PUNCT
ejpam-1535	868	6	z	z	X
ejpam-1535	868	7	)	)	PUNCT
ejpam-1535	868	8	·	·	PUNCT
ejpam-1535	869	1	z−1	z−1	NUM
ejpam-1535	869	2	=	=	SYM
ejpam-1535	869	3	(	(	PUNCT
ejpam-1535	869	4	y	y	PROPN
ejpam-1535	869	5	·	·	PUNCT
ejpam-1535	869	6	z	z	X
ejpam-1535	869	7	)	)	PUNCT
ejpam-1535	869	8	·	·	PUNCT
ejpam-1535	870	1	z−1	z−1	NUM
ejpam-1535	870	2	=	=	NOUN
ejpam-1535	870	3	⇒	⇒	NOUN
ejpam-1535	870	4	x	x	X
ejpam-1535	870	5	·	·	PUNCT
ejpam-1535	870	6	(	(	PUNCT
ejpam-1535	870	7	z	z	NOUN
ejpam-1535	870	8	·	·	PUNCT
ejpam-1535	870	9	z−1	z−1	X
ejpam-1535	870	10	)	)	PUNCT
ejpam-1535	870	11	=	=	SYM
ejpam-1535	871	1	y	y	PROPN
ejpam-1535	871	2	·	·	PUNCT
ejpam-1535	871	3	(	(	PUNCT
ejpam-1535	871	4	z	z	X
ejpam-1535	871	5	·	·	PUNCT
ejpam-1535	871	6	z−1	z−1	X
ejpam-1535	871	7	)	)	PUNCT
ejpam-1535	871	8	=	=	NOUN
ejpam-1535	871	9	⇒	⇒	NOUN
ejpam-1535	871	10	x	x	X
ejpam-1535	871	11	·	·	PUNCT
ejpam-1535	871	12	d(z	d(z	X
ejpam-1535	871	13	)	)	PUNCT
ejpam-1535	871	14	=	=	SYM
ejpam-1535	871	15	y	y	PROPN
ejpam-1535	871	16	·	·	PUNCT
ejpam-1535	871	17	d(z	d(z	PROPN
ejpam-1535	871	18	)	)	PUNCT
ejpam-1535	872	1	=	=	NOUN
ejpam-1535	872	2	⇒	⇒	NOUN
ejpam-1535	872	3	x	x	PUNCT
ejpam-1535	872	4	=	=	SYM
ejpam-1535	872	5	y	y	PROPN
ejpam-1535	872	6	,	,	PUNCT
ejpam-1535	872	7	since	since	SCONJ
ejpam-1535	872	8	d(z	d(z	NOUN
ejpam-1535	872	9	)	)	PUNCT
ejpam-1535	872	10	=	=	SYM
ejpam-1535	872	11	r(x	r(x	PROPN
ejpam-1535	872	12	)	)	PUNCT
ejpam-1535	872	13	=	=	PUNCT
ejpam-1535	872	14	r(y	r(y	VERB
ejpam-1535	872	15	)	)	PUNCT
ejpam-1535	872	16	.	.	PUNCT
ejpam-1535	873	1	the	the	DET
ejpam-1535	873	2	second	second	ADJ
ejpam-1535	873	3	part	part	NOUN
ejpam-1535	873	4	is	be	AUX
ejpam-1535	873	5	similar	similar	ADJ
ejpam-1535	873	6	.	.	PUNCT
ejpam-1535	874	1	in	in	ADP
ejpam-1535	874	2	particular	particular	ADJ
ejpam-1535	874	3	,	,	PUNCT
ejpam-1535	874	4	a	a	DET
ejpam-1535	874	5	groupoid	groupoid	NOUN
ejpam-1535	874	6	is	be	AUX
ejpam-1535	874	7	necessarily	necessarily	ADV
ejpam-1535	874	8	unipotent	unipotent	ADJ
ejpam-1535	874	9	.	.	PUNCT
ejpam-1535	875	1	we	we	PRON
ejpam-1535	875	2	observe	observe	VERB
ejpam-1535	875	3	also	also	ADV
ejpam-1535	875	4	that	that	SCONJ
ejpam-1535	875	5	the	the	DET
ejpam-1535	875	6	inverses	inverse	NOUN
ejpam-1535	875	7	in	in	ADP
ejpam-1535	875	8	a	a	DET
ejpam-1535	875	9	groupoid	groupoid	NOUN
ejpam-1535	875	10	behave	behave	VERB
ejpam-1535	875	11	in	in	ADP
ejpam-1535	875	12	the	the	DET
ejpam-1535	875	13	manner	manner	NOUN
ejpam-1535	875	14	in	in	ADP
ejpam-1535	875	15	which	which	PRON
ejpam-1535	875	16	we	we	PRON
ejpam-1535	875	17	would	would	AUX
ejpam-1535	875	18	expect	expect	VERB
ejpam-1535	875	19	them	they	PRON
ejpam-1535	875	20	to	to	PART
ejpam-1535	875	21	:	:	PUNCT
ejpam-1535	875	22	lemma	lemma	PROPN
ejpam-1535	875	23	18	18	NUM
ejpam-1535	875	24	(	(	PUNCT
ejpam-1535	875	25	[	[	X
ejpam-1535	875	26	f	f	X
ejpam-1535	875	27	]	]	X
ejpam-1535	875	28	)	)	PUNCT
ejpam-1535	875	29	.	.	PUNCT
ejpam-1535	876	1	let	let	AUX
ejpam-1535	876	2	(	(	PUNCT
ejpam-1535	876	3	g	g	NOUN
ejpam-1535	876	4	,	,	PUNCT
ejpam-1535	876	5	·	·	PUNCT
ejpam-1535	876	6	)	)	PUNCT
ejpam-1535	876	7	be	be	AUX
ejpam-1535	876	8	a	a	DET
ejpam-1535	876	9	groupoid	groupoid	NOUN
ejpam-1535	876	10	.	.	PUNCT
ejpam-1535	877	1	then	then	ADV
ejpam-1535	877	2	(	(	PUNCT
ejpam-1535	877	3	a	a	X
ejpam-1535	877	4	)	)	PUNCT
ejpam-1535	877	5	r(x	r(x	NOUN
ejpam-1535	877	6	)	)	PUNCT
ejpam-1535	877	7	=	=	SYM
ejpam-1535	877	8	d(x−1	d(x−1	NOUN
ejpam-1535	877	9	)	)	PUNCT
ejpam-1535	877	10	and	and	CCONJ
ejpam-1535	877	11	d(x	d(x	NOUN
ejpam-1535	877	12	)	)	PUNCT
ejpam-1535	877	13	=	=	SYM
ejpam-1535	877	14	r(x−1	r(x−1	NOUN
ejpam-1535	877	15	)	)	PUNCT
ejpam-1535	877	16	;	;	PUNCT
ejpam-1535	877	17	(	(	PUNCT
ejpam-1535	877	18	b	b	X
ejpam-1535	877	19	)	)	PUNCT
ejpam-1535	877	20	for	for	ADP
ejpam-1535	877	21	each	each	DET
ejpam-1535	877	22	x	x	SYM
ejpam-1535	877	23	∈	∈	PROPN
ejpam-1535	877	24	g	g	PROPN
ejpam-1535	877	25	,	,	PUNCT
ejpam-1535	877	26	x−1	x−1	PROPN
ejpam-1535	877	27	is	be	AUX
ejpam-1535	877	28	unique	unique	ADJ
ejpam-1535	877	29	;	;	PUNCT
ejpam-1535	877	30	(	(	PUNCT
ejpam-1535	877	31	c	c	X
ejpam-1535	877	32	)	)	PUNCT
ejpam-1535	877	33	(	(	PUNCT
ejpam-1535	877	34	x−1)−1	x−1)−1	X
ejpam-1535	877	35	=	=	SYM
ejpam-1535	877	36	x.	x.	NOUN
ejpam-1535	877	37	note	note	VERB
ejpam-1535	877	38	that	that	SCONJ
ejpam-1535	877	39	in	in	ADP
ejpam-1535	877	40	the	the	DET
ejpam-1535	877	41	case	case	NOUN
ejpam-1535	877	42	of	of	ADP
ejpam-1535	877	43	a	a	DET
ejpam-1535	877	44	groupoid	groupoid	NOUN
ejpam-1535	877	45	,	,	PUNCT
ejpam-1535	877	46	the	the	DET
ejpam-1535	877	47	local	local	ADJ
ejpam-1535	877	48	submonoids	submonoid	NOUN
ejpam-1535	877	49	mor(e	mor(e	PROPN
ejpam-1535	877	50	,	,	PUNCT
ejpam-1535	877	51	e	e	NOUN
ejpam-1535	877	52	)	)	PUNCT
ejpam-1535	877	53	are	be	AUX
ejpam-1535	877	54	in	in	ADP
ejpam-1535	877	55	fact	fact	NOUN
ejpam-1535	877	56	local	local	ADJ
ejpam-1535	877	57	subgroups	subgroup	NOUN
ejpam-1535	877	58	.	.	PUNCT
ejpam-1535	878	1	thus	thus	ADV
ejpam-1535	878	2	,	,	PUNCT
ejpam-1535	878	3	a	a	DET
ejpam-1535	878	4	groupoid	groupoid	NOUN
ejpam-1535	878	5	with	with	ADP
ejpam-1535	878	6	one	one	NUM
ejpam-1535	878	7	identity	identity	NOUN
ejpam-1535	878	8	is	be	AUX
ejpam-1535	878	9	necessarily	necessarily	ADV
ejpam-1535	878	10	a	a	DET
ejpam-1535	878	11	group	group	NOUN
ejpam-1535	878	12	:	:	PUNCT
ejpam-1535	878	13	a	a	DET
ejpam-1535	878	14	groupoid	groupoid	NOUN
ejpam-1535	878	15	may	may	AUX
ejpam-1535	878	16	be	be	AUX
ejpam-1535	878	17	regarded	regard	VERB
ejpam-1535	878	18	as	as	ADP
ejpam-1535	878	19	a	a	DET
ejpam-1535	878	20	generalisation	generalisation	NOUN
ejpam-1535	878	21	of	of	ADP
ejpam-1535	878	22	a	a	DET
ejpam-1535	878	23	group	group	NOUN
ejpam-1535	878	24	,	,	PUNCT
ejpam-1535	878	25	which	which	PRON
ejpam-1535	878	26	perhaps	perhaps	ADV
ejpam-1535	878	27	goes	go	VERB
ejpam-1535	878	28	some	some	DET
ejpam-1535	878	29	way	way	NOUN
ejpam-1535	878	30	towards	towards	ADP
ejpam-1535	878	31	explaining	explain	VERB
ejpam-1535	878	32	why	why	SCONJ
ejpam-1535	878	33	the	the	DET
ejpam-1535	878	34	notion	notion	NOUN
ejpam-1535	878	35	of	of	ADP
ejpam-1535	878	36	a	a	DET
ejpam-1535	878	37	groupoid	groupoid	NOUN
ejpam-1535	878	38	arose	arise	VERB
ejpam-1535	878	39	before	before	ADP
ejpam-1535	878	40	that	that	PRON
ejpam-1535	878	41	of	of	ADP
ejpam-1535	878	42	a	a	DET
ejpam-1535	878	43	category	category	NOUN
ejpam-1535	878	44	,	,	PUNCT
ejpam-1535	878	45	as	as	SCONJ
ejpam-1535	878	46	we	we	PRON
ejpam-1535	878	47	saw	see	VERB
ejpam-1535	878	48	section	section	NOUN
ejpam-1535	878	49	2.††	2.††	PROPN
ejpam-1535	878	50	we	we	PRON
ejpam-1535	878	51	must	must	AUX
ejpam-1535	878	52	now	now	ADV
ejpam-1535	878	53	introduce	introduce	VERB
ejpam-1535	878	54	an	an	DET
ejpam-1535	878	55	ordering	ordering	NOUN
ejpam-1535	878	56	onto	onto	ADP
ejpam-1535	878	57	a	a	DET
ejpam-1535	878	58	groupoid	groupoid	NOUN
ejpam-1535	878	59	(	(	PUNCT
ejpam-1535	878	60	g	g	NOUN
ejpam-1535	878	61	,	,	PUNCT
ejpam-1535	878	62	·	·	PUNCT
ejpam-1535	878	63	):	):	PUNCT
ejpam-1535	878	64	definition	definition	NOUN
ejpam-1535	878	65	18	18	NUM
ejpam-1535	878	66	.	.	PUNCT
ejpam-1535	879	1	let	let	AUX
ejpam-1535	879	2	(	(	PUNCT
ejpam-1535	879	3	g	g	NOUN
ejpam-1535	879	4	,	,	PUNCT
ejpam-1535	879	5	·	·	PUNCT
ejpam-1535	879	6	)	)	PUNCT
ejpam-1535	879	7	be	be	AUX
ejpam-1535	879	8	a	a	DET
ejpam-1535	879	9	groupoid	groupoid	NOUN
ejpam-1535	879	10	and	and	CCONJ
ejpam-1535	879	11	suppose	suppose	VERB
ejpam-1535	879	12	that	that	SCONJ
ejpam-1535	879	13	g	g	PROPN
ejpam-1535	879	14	is	be	AUX
ejpam-1535	879	15	partially	partially	ADV
ejpam-1535	879	16	ordered	order	VERB
ejpam-1535	879	17	by	by	ADP
ejpam-1535	879	18	≤.	≤.	NOUN
ejpam-1535	879	19	then	then	ADV
ejpam-1535	879	20	we	we	PRON
ejpam-1535	879	21	call	call	VERB
ejpam-1535	879	22	(	(	PUNCT
ejpam-1535	879	23	g	g	NOUN
ejpam-1535	879	24	,	,	PUNCT
ejpam-1535	879	25	·	·	PUNCT
ejpam-1535	879	26	,	,	PUNCT
ejpam-1535	879	27	≤	≤	NUM
ejpam-1535	879	28	)	)	PUNCT
ejpam-1535	879	29	an	an	DET
ejpam-1535	879	30	ordered	order	VERB
ejpam-1535	879	31	groupoid	groupoid	NOUN
ejpam-1535	879	32	if	if	SCONJ
ejpam-1535	879	33	it	it	PRON
ejpam-1535	879	34	satisfies	satisfy	VERB
ejpam-1535	879	35	conditions	condition	NOUN
ejpam-1535	879	36	(	(	PUNCT
ejpam-1535	879	37	or1	or1	NOUN
ejpam-1535	879	38	)	)	PUNCT
ejpam-1535	879	39	and	and	CCONJ
ejpam-1535	879	40	(	(	PUNCT
ejpam-1535	879	41	or3	or3	PROPN
ejpam-1535	879	42	)	)	PUNCT
ejpam-1535	879	43	,	,	PUNCT
ejpam-1535	879	44	together	together	ADV
ejpam-1535	879	45	with	with	ADP
ejpam-1535	879	46	the	the	DET
ejpam-1535	879	47	following	following	NOUN
ejpam-1535	879	48	in	in	ADP
ejpam-1535	879	49	place	place	NOUN
ejpam-1535	879	50	of	of	ADP
ejpam-1535	879	51	(	(	PUNCT
ejpam-1535	879	52	or2	or2	PROPN
ejpam-1535	879	53	):	):	PUNCT
ejpam-1535	879	54	(	(	PUNCT
ejpam-1535	879	55	or2′	or2′	X
ejpam-1535	879	56	)	)	PUNCT
ejpam-1535	879	57	if	if	SCONJ
ejpam-1535	879	58	a	a	DET
ejpam-1535	879	59	≤	≤	NUM
ejpam-1535	879	60	b	b	NOUN
ejpam-1535	879	61	,	,	PUNCT
ejpam-1535	880	1	then	then	ADV
ejpam-1535	880	2	a−1	a−1	PROPN
ejpam-1535	880	3	≤	≤	PROPN
ejpam-1535	880	4	b−1	b−1	PROPN
ejpam-1535	880	5	.	.	PUNCT
ejpam-1535	881	1	††see	††see	PROPN
ejpam-1535	881	2	footnote	footnote	VERB
ejpam-1535	881	3	§	§	PROPN
ejpam-1535	881	4	on	on	ADP
ejpam-1535	881	5	page	page	NOUN
ejpam-1535	881	6	420	420	NUM
ejpam-1535	881	7	.	.	PUNCT
ejpam-1535	882	1	c.	c.	NOUN
ejpam-1535	882	2	hollings	holling	NOUN
ejpam-1535	882	3	/	/	SYM
ejpam-1535	882	4	eur	eur	PROPN
ejpam-1535	882	5	.	.	PUNCT
ejpam-1535	883	1	j.	j.	PROPN
ejpam-1535	883	2	pure	pure	PROPN
ejpam-1535	883	3	appl	appl	PROPN
ejpam-1535	883	4	.	.	PROPN
ejpam-1535	883	5	math	math	PROPN
ejpam-1535	883	6	,	,	PUNCT
ejpam-1535	883	7	5	5	NUM
ejpam-1535	883	8	(	(	PUNCT
ejpam-1535	883	9	2012	2012	NUM
ejpam-1535	883	10	)	)	PUNCT
ejpam-1535	883	11	,	,	PUNCT
ejpam-1535	883	12	414	414	NUM
ejpam-1535	883	13	-	-	SYM
ejpam-1535	883	14	450	450	NUM
ejpam-1535	883	15	444	444	NUM
ejpam-1535	883	16	notice	notice	NOUN
ejpam-1535	883	17	that	that	SCONJ
ejpam-1535	883	18	an	an	DET
ejpam-1535	883	19	inductive	inductive	ADJ
ejpam-1535	883	20	category	category	NOUN
ejpam-1535	883	21	which	which	PRON
ejpam-1535	883	22	is	be	AUX
ejpam-1535	883	23	also	also	ADV
ejpam-1535	883	24	a	a	DET
ejpam-1535	883	25	groupoid	groupoid	NOUN
ejpam-1535	883	26	necessarily	necessarily	ADV
ejpam-1535	883	27	satisfies	satisfy	VERB
ejpam-1535	883	28	(	(	PUNCT
ejpam-1535	883	29	or2′	or2′	ADJ
ejpam-1535	883	30	):	):	PUNCT
ejpam-1535	884	1	if	if	SCONJ
ejpam-1535	884	2	a	a	DET
ejpam-1535	884	3	≤	≤	NUM
ejpam-1535	884	4	b	b	NOUN
ejpam-1535	884	5	in	in	ADP
ejpam-1535	884	6	the	the	DET
ejpam-1535	884	7	category	category	NOUN
ejpam-1535	884	8	,	,	PUNCT
ejpam-1535	884	9	then	then	ADV
ejpam-1535	884	10	a	a	DET
ejpam-1535	884	11	≤	≤	PROPN
ejpam-1535	884	12	b	b	NOUN
ejpam-1535	884	13	in	in	ADP
ejpam-1535	884	14	the	the	DET
ejpam-1535	884	15	corresponding	corresponding	ADJ
ejpam-1535	884	16	semigroup	semigroup	NOUN
ejpam-1535	884	17	,	,	PUNCT
ejpam-1535	884	18	which	which	PRON
ejpam-1535	884	19	means	mean	VERB
ejpam-1535	884	20	that	that	SCONJ
ejpam-1535	884	21	a	a	DET
ejpam-1535	884	22	=	=	SYM
ejpam-1535	884	23	e⊗	e⊗	PROPN
ejpam-1535	884	24	b	b	PROPN
ejpam-1535	884	25	,	,	PUNCT
ejpam-1535	884	26	for	for	ADP
ejpam-1535	884	27	some	some	DET
ejpam-1535	884	28	idempotent	idempotent	ADJ
ejpam-1535	884	29	e.	e.	PROPN
ejpam-1535	884	30	but	but	CCONJ
ejpam-1535	884	31	then	then	ADV
ejpam-1535	884	32	a−1	a−1	PROPN
ejpam-1535	884	33	=	=	SYM
ejpam-1535	884	34	b−1	b−1	PROPN
ejpam-1535	884	35	⊗	⊗	PROPN
ejpam-1535	884	36	e	e	NOUN
ejpam-1535	884	37	,	,	PUNCT
ejpam-1535	884	38	whence	whence	PROPN
ejpam-1535	884	39	a−1	a−1	PROPN
ejpam-1535	884	40	≤	≤	PUNCT
ejpam-1535	884	41	b−1	b−1	PROPN
ejpam-1535	884	42	.	.	PUNCT
ejpam-1535	885	1	in	in	ADP
ejpam-1535	885	2	fact	fact	NOUN
ejpam-1535	885	3	,	,	PUNCT
ejpam-1535	885	4	(	(	PUNCT
ejpam-1535	885	5	or2	or2	NOUN
ejpam-1535	885	6	)	)	PUNCT
ejpam-1535	885	7	still	still	ADV
ejpam-1535	885	8	holds	hold	VERB
ejpam-1535	885	9	in	in	ADP
ejpam-1535	885	10	an	an	DET
ejpam-1535	885	11	ordered	ordered	ADJ
ejpam-1535	885	12	groupoid	groupoid	NOUN
ejpam-1535	885	13	:	:	PUNCT
ejpam-1535	885	14	lemma	lemma	PROPN
ejpam-1535	885	15	19	19	NUM
ejpam-1535	885	16	(	(	PUNCT
ejpam-1535	885	17	[	[	X
ejpam-1535	885	18	29	29	NUM
ejpam-1535	885	19	,	,	PUNCT
ejpam-1535	885	20	proposition	proposition	NOUN
ejpam-1535	885	21	4.1.3(1	4.1.3(1	NUM
ejpam-1535	885	22	)	)	PUNCT
ejpam-1535	885	23	]	]	PUNCT
ejpam-1535	885	24	)	)	PUNCT
ejpam-1535	885	25	.	.	PUNCT
ejpam-1535	886	1	an	an	DET
ejpam-1535	886	2	ordered	order	VERB
ejpam-1535	886	3	groupoid	groupoid	NOUN
ejpam-1535	886	4	(	(	PUNCT
ejpam-1535	886	5	g	g	PROPN
ejpam-1535	886	6	,	,	PUNCT
ejpam-1535	886	7	·	·	PUNCT
ejpam-1535	886	8	,	,	PUNCT
ejpam-1535	886	9	≤	≤	NUM
ejpam-1535	886	10	)	)	PUNCT
ejpam-1535	886	11	satisfies	satisfie	NOUN
ejpam-1535	886	12	(	(	PUNCT
ejpam-1535	886	13	or2	or2	NOUN
ejpam-1535	886	14	)	)	PUNCT
ejpam-1535	886	15	.	.	PUNCT
ejpam-1535	887	1	proof	proof	NOUN
ejpam-1535	887	2	.	.	PUNCT
ejpam-1535	888	1	suppose	suppose	VERB
ejpam-1535	888	2	that	that	SCONJ
ejpam-1535	888	3	a	a	DET
ejpam-1535	888	4	≤	≤	PROPN
ejpam-1535	888	5	b.	b.	NOUN
ejpam-1535	888	6	we	we	PRON
ejpam-1535	888	7	have	have	VERB
ejpam-1535	888	8	that	that	DET
ejpam-1535	888	9	a−1	a−1	PROPN
ejpam-1535	888	10	≤	≤	PROPN
ejpam-1535	888	11	b−1	b−1	PROPN
ejpam-1535	888	12	,	,	PUNCT
ejpam-1535	888	13	by	by	ADP
ejpam-1535	888	14	(	(	PUNCT
ejpam-1535	888	15	or2′	or2′	ADJ
ejpam-1535	888	16	)	)	PUNCT
ejpam-1535	888	17	,	,	PUNCT
ejpam-1535	888	18	and	and	CCONJ
ejpam-1535	888	19	we	we	PRON
ejpam-1535	888	20	know	know	VERB
ejpam-1535	888	21	that	that	SCONJ
ejpam-1535	888	22	∃a	∃a	NOUN
ejpam-1535	888	23	·	·	PUNCT
ejpam-1535	888	24	a−1	a−1	NOUN
ejpam-1535	888	25	and	and	CCONJ
ejpam-1535	888	26	∃b	∃b	PROPN
ejpam-1535	888	27	·	·	PUNCT
ejpam-1535	888	28	b−1	b−1	PROPN
ejpam-1535	888	29	.	.	PUNCT
ejpam-1535	889	1	therefore	therefore	ADV
ejpam-1535	889	2	,	,	PUNCT
ejpam-1535	889	3	a	a	DET
ejpam-1535	889	4	·	·	PUNCT
ejpam-1535	889	5	a−1	a−1	PROPN
ejpam-1535	889	6	≤	≤	PROPN
ejpam-1535	889	7	b	b	X
ejpam-1535	889	8	·	·	PUNCT
ejpam-1535	889	9	b−1	b−1	NOUN
ejpam-1535	889	10	,	,	PUNCT
ejpam-1535	889	11	by	by	ADP
ejpam-1535	889	12	(	(	PUNCT
ejpam-1535	889	13	or1	or1	NOUN
ejpam-1535	889	14	)	)	PUNCT
ejpam-1535	889	15	,	,	PUNCT
ejpam-1535	889	16	hence	hence	ADV
ejpam-1535	889	17	d(a)≤	d(a)≤	NOUN
ejpam-1535	889	18	d(b	d(b	PROPN
ejpam-1535	889	19	)	)	PUNCT
ejpam-1535	889	20	.	.	PUNCT
ejpam-1535	890	1	similarly	similarly	ADV
ejpam-1535	890	2	,	,	PUNCT
ejpam-1535	890	3	r(a)≤	r(a)≤	PROPN
ejpam-1535	890	4	r(b	r(b	PROPN
ejpam-1535	890	5	)	)	PUNCT
ejpam-1535	890	6	.	.	PUNCT
ejpam-1535	891	1	thus	thus	ADV
ejpam-1535	891	2	,	,	PUNCT
ejpam-1535	891	3	an	an	DET
ejpam-1535	891	4	ordered	order	VERB
ejpam-1535	891	5	groupoid	groupoid	NOUN
ejpam-1535	891	6	,	,	PUNCT
ejpam-1535	891	7	in	in	ADP
ejpam-1535	891	8	the	the	DET
ejpam-1535	891	9	sense	sense	NOUN
ejpam-1535	891	10	of	of	ADP
ejpam-1535	891	11	definition	definition	NOUN
ejpam-1535	891	12	18	18	NUM
ejpam-1535	891	13	,	,	PUNCT
ejpam-1535	891	14	is	be	AUX
ejpam-1535	891	15	an	an	DET
ejpam-1535	891	16	ordered	order	VERB
ejpam-1535	891	17	category	category	NOUN
ejpam-1535	891	18	,	,	PUNCT
ejpam-1535	891	19	in	in	ADP
ejpam-1535	891	20	the	the	DET
ejpam-1535	891	21	sense	sense	NOUN
ejpam-1535	891	22	of	of	ADP
ejpam-1535	891	23	definition	definition	NOUN
ejpam-1535	891	24	11	11	NUM
ejpam-1535	891	25	.	.	PUNCT
ejpam-1535	892	1	similarly	similarly	ADV
ejpam-1535	892	2	,	,	PUNCT
ejpam-1535	892	3	if	if	SCONJ
ejpam-1535	892	4	we	we	PRON
ejpam-1535	892	5	give	give	VERB
ejpam-1535	892	6	the	the	DET
ejpam-1535	892	7	following	follow	VERB
ejpam-1535	892	8	very	very	ADV
ejpam-1535	892	9	natural	natural	ADJ
ejpam-1535	892	10	definition	definition	NOUN
ejpam-1535	892	11	for	for	ADP
ejpam-1535	892	12	an	an	DET
ejpam-1535	892	13	inductive	inductive	ADJ
ejpam-1535	892	14	groupoid	groupoid	NOUN
ejpam-1535	892	15	,	,	PUNCT
ejpam-1535	892	16	then	then	ADV
ejpam-1535	892	17	an	an	DET
ejpam-1535	892	18	inductive	inductive	ADJ
ejpam-1535	892	19	groupoid	groupoid	NOUN
ejpam-1535	892	20	is	be	AUX
ejpam-1535	892	21	an	an	DET
ejpam-1535	892	22	inductive	inductive	ADJ
ejpam-1535	892	23	category	category	NOUN
ejpam-1535	892	24	,	,	PUNCT
ejpam-1535	892	25	in	in	ADP
ejpam-1535	892	26	the	the	DET
ejpam-1535	892	27	sense	sense	NOUN
ejpam-1535	892	28	of	of	ADP
ejpam-1535	892	29	definition	definition	NOUN
ejpam-1535	892	30	12	12	NUM
ejpam-1535	892	31	:	:	PUNCT
ejpam-1535	892	32	definition	definition	NOUN
ejpam-1535	892	33	19	19	NUM
ejpam-1535	892	34	.	.	PUNCT
ejpam-1535	893	1	let	let	AUX
ejpam-1535	893	2	(	(	PUNCT
ejpam-1535	893	3	g	g	NOUN
ejpam-1535	893	4	,	,	PUNCT
ejpam-1535	893	5	·	·	PUNCT
ejpam-1535	893	6	,	,	PUNCT
ejpam-1535	893	7	≤	≤	NUM
ejpam-1535	893	8	)	)	PUNCT
ejpam-1535	893	9	be	be	VERB
ejpam-1535	893	10	an	an	DET
ejpam-1535	893	11	ordered	ordered	ADJ
ejpam-1535	893	12	groupoid	groupoid	NOUN
ejpam-1535	893	13	.	.	PUNCT
ejpam-1535	894	1	we	we	PRON
ejpam-1535	894	2	call	call	VERB
ejpam-1535	894	3	(	(	PUNCT
ejpam-1535	894	4	g	g	NOUN
ejpam-1535	894	5	,	,	PUNCT
ejpam-1535	894	6	·	·	PUNCT
ejpam-1535	894	7	,	,	PUNCT
ejpam-1535	894	8	≤	≤	NUM
ejpam-1535	894	9	)	)	PUNCT
ejpam-1535	894	10	an	an	DET
ejpam-1535	894	11	inductive	inductive	ADJ
ejpam-1535	894	12	groupoid	groupoid	NOUN
ejpam-1535	894	13	if	if	SCONJ
ejpam-1535	894	14	it	it	PRON
ejpam-1535	894	15	also	also	ADV
ejpam-1535	894	16	satisfies	satisfy	VERB
ejpam-1535	894	17	(	(	PUNCT
ejpam-1535	894	18	in	in	ADP
ejpam-1535	894	19	)	)	PUNCT
ejpam-1535	894	20	.	.	PUNCT
ejpam-1535	895	1	an	an	DET
ejpam-1535	895	2	inductive	inductive	ADJ
ejpam-1535	895	3	groupoid	groupoid	NOUN
ejpam-1535	895	4	has	have	VERB
ejpam-1535	895	5	many	many	ADJ
ejpam-1535	895	6	nice	nice	ADJ
ejpam-1535	895	7	properties	property	NOUN
ejpam-1535	895	8	,	,	PUNCT
ejpam-1535	895	9	amongst	amongst	ADP
ejpam-1535	895	10	which	which	PRON
ejpam-1535	895	11	is	be	AUX
ejpam-1535	895	12	the	the	DET
ejpam-1535	895	13	possibility	possibility	NOUN
ejpam-1535	895	14	of	of	ADP
ejpam-1535	895	15	expressing	express	VERB
ejpam-1535	895	16	the	the	DET
ejpam-1535	895	17	corestriction	corestriction	NOUN
ejpam-1535	895	18	in	in	ADP
ejpam-1535	895	19	terms	term	NOUN
ejpam-1535	895	20	of	of	ADP
ejpam-1535	895	21	the	the	DET
ejpam-1535	895	22	restriction	restriction	NOUN
ejpam-1535	895	23	,	,	PUNCT
ejpam-1535	895	24	and	and	CCONJ
ejpam-1535	895	25	vice	vice	ADV
ejpam-1535	895	26	versa	versa	ADV
ejpam-1535	895	27	:	:	PUNCT
ejpam-1535	895	28	lemma	lemma	PROPN
ejpam-1535	895	29	20	20	NUM
ejpam-1535	895	30	(	(	PUNCT
ejpam-1535	895	31	[	[	X
ejpam-1535	895	32	36	36	NUM
ejpam-1535	895	33	,	,	PUNCT
ejpam-1535	895	34	proposition	proposition	NOUN
ejpam-1535	895	35	3.1	3.1	NUM
ejpam-1535	895	36	]	]	PUNCT
ejpam-1535	895	37	)	)	PUNCT
ejpam-1535	895	38	.	.	PUNCT
ejpam-1535	896	1	let	let	AUX
ejpam-1535	896	2	(	(	PUNCT
ejpam-1535	896	3	g	g	NOUN
ejpam-1535	896	4	,	,	PUNCT
ejpam-1535	896	5	·	·	PUNCT
ejpam-1535	896	6	,	,	PUNCT
ejpam-1535	896	7	≤	≤	NUM
ejpam-1535	896	8	)	)	PUNCT
ejpam-1535	896	9	be	be	VERB
ejpam-1535	896	10	an	an	DET
ejpam-1535	896	11	ordered	order	VERB
ejpam-1535	896	12	groupoid	groupoid	NOUN
ejpam-1535	896	13	and	and	CCONJ
ejpam-1535	896	14	suppose	suppose	VERB
ejpam-1535	896	15	that	that	SCONJ
ejpam-1535	896	16	f	f	PROPN
ejpam-1535	896	17	≤	≤	PUNCT
ejpam-1535	896	18	d(a	d(a	PROPN
ejpam-1535	896	19	)	)	PUNCT
ejpam-1535	896	20	,	,	PUNCT
ejpam-1535	896	21	for	for	SCONJ
ejpam-1535	896	22	some	some	DET
ejpam-1535	896	23	f	f	PROPN
ejpam-1535	896	24	∈	∈	PROPN
ejpam-1535	896	25	go	go	VERB
ejpam-1535	896	26	and	and	CCONJ
ejpam-1535	896	27	some	some	DET
ejpam-1535	896	28	a	a	DET
ejpam-1535	896	29	∈	∈	PROPN
ejpam-1535	896	30	g.	g.	NOUN
ejpam-1535	897	1	then	then	ADV
ejpam-1535	897	2	the	the	DET
ejpam-1535	897	3	restriction	restriction	NOUN
ejpam-1535	897	4	f	f	PROPN
ejpam-1535	897	5	|a	|a	PRON
ejpam-1535	897	6	may	may	AUX
ejpam-1535	897	7	be	be	AUX
ejpam-1535	897	8	expressed	express	VERB
ejpam-1535	897	9	in	in	ADP
ejpam-1535	897	10	terms	term	NOUN
ejpam-1535	897	11	of	of	ADP
ejpam-1535	897	12	the	the	DET
ejpam-1535	897	13	corestriction	corestriction	NOUN
ejpam-1535	897	14	:	:	PUNCT
ejpam-1535	897	15	f	f	PROPN
ejpam-1535	897	16	|a	|a	X
ejpam-1535	897	17	=	=	SYM
ejpam-1535	897	18	(	(	PUNCT
ejpam-1535	897	19	a−1|	a−1|	PROPN
ejpam-1535	897	20	f	f	PROPN
ejpam-1535	897	21	)	)	PUNCT
ejpam-1535	897	22	−1	−1	NOUN
ejpam-1535	897	23	.	.	PUNCT
ejpam-1535	898	1	dually	dually	PROPN
ejpam-1535	898	2	,	,	PUNCT
ejpam-1535	898	3	if	if	SCONJ
ejpam-1535	898	4	f	f	PROPN
ejpam-1535	898	5	≤	≤	X
ejpam-1535	898	6	r(a	r(a	PROPN
ejpam-1535	898	7	)	)	PUNCT
ejpam-1535	899	1	,	,	PUNCT
ejpam-1535	899	2	then	then	ADV
ejpam-1535	899	3	a|	a|	PROPN
ejpam-1535	899	4	f	f	PROPN
ejpam-1535	899	5	=	=	PRON
ejpam-1535	900	1	(	(	PUNCT
ejpam-1535	900	2	f	f	PROPN
ejpam-1535	900	3	|a−1)−1	|a−1)−1	PROPN
ejpam-1535	900	4	.	.	PUNCT
ejpam-1535	901	1	we	we	PRON
ejpam-1535	901	2	now	now	ADV
ejpam-1535	901	3	turn	turn	VERB
ejpam-1535	901	4	our	our	PRON
ejpam-1535	901	5	attention	attention	NOUN
ejpam-1535	901	6	to	to	ADP
ejpam-1535	901	7	the	the	DET
ejpam-1535	901	8	specialisation	specialisation	NOUN
ejpam-1535	901	9	of	of	ADP
ejpam-1535	901	10	the	the	DET
ejpam-1535	901	11	results	result	NOUN
ejpam-1535	901	12	of	of	ADP
ejpam-1535	901	13	the	the	DET
ejpam-1535	901	14	preceding	precede	VERB
ejpam-1535	901	15	sections	section	NOUN
ejpam-1535	901	16	to	to	ADP
ejpam-1535	901	17	the	the	DET
ejpam-1535	901	18	case	case	NOUN
ejpam-1535	901	19	of	of	ADP
ejpam-1535	901	20	inverse	inverse	NOUN
ejpam-1535	901	21	semigroups	semigroup	NOUN
ejpam-1535	901	22	and	and	CCONJ
ejpam-1535	901	23	inductive	inductive	ADJ
ejpam-1535	901	24	groupoids	groupoid	NOUN
ejpam-1535	901	25	.	.	PUNCT
ejpam-1535	902	1	we	we	PRON
ejpam-1535	902	2	begin	begin	VERB
ejpam-1535	902	3	by	by	ADP
ejpam-1535	902	4	making	make	VERB
ejpam-1535	902	5	the	the	DET
ejpam-1535	902	6	easy	easy	ADJ
ejpam-1535	902	7	observation	observation	NOUN
ejpam-1535	902	8	that	that	SCONJ
ejpam-1535	902	9	the	the	DET
ejpam-1535	902	10	restricted	restricted	ADJ
ejpam-1535	902	11	product	product	NOUN
ejpam-1535	902	12	of	of	ADP
ejpam-1535	902	13	(	(	PUNCT
ejpam-1535	902	14	7	7	NUM
ejpam-1535	902	15	)	)	PUNCT
ejpam-1535	902	16	may	may	AUX
ejpam-1535	902	17	be	be	AUX
ejpam-1535	902	18	rewritten	rewrite	VERB
ejpam-1535	902	19	as	as	SCONJ
ejpam-1535	902	20	follows	follow	VERB
ejpam-1535	902	21	in	in	ADP
ejpam-1535	902	22	an	an	DET
ejpam-1535	902	23	inverse	inverse	NOUN
ejpam-1535	902	24	semigroup	semigroup	NOUN
ejpam-1535	902	25	:	:	PUNCT
ejpam-1535	902	26	a	a	DET
ejpam-1535	902	27	·	·	PUNCT
ejpam-1535	902	28	b	b	X
ejpam-1535	902	29	=	=	SYM
ejpam-1535	902	30	(	(	PUNCT
ejpam-1535	902	31	ab	ab	X
ejpam-1535	902	32	if	if	SCONJ
ejpam-1535	902	33	a−1a	a−1a	PROPN
ejpam-1535	902	34	=	=	SYM
ejpam-1535	902	35	bb−1	bb−1	NOUN
ejpam-1535	902	36	;	;	PUNCT
ejpam-1535	902	37	undefined	undefined	ADJ
ejpam-1535	902	38	otherwise	otherwise	ADV
ejpam-1535	902	39	.	.	PUNCT
ejpam-1535	903	1	(	(	PUNCT
ejpam-1535	903	2	9	9	X
ejpam-1535	903	3	)	)	PUNCT
ejpam-1535	903	4	we	we	PRON
ejpam-1535	903	5	have	have	VERB
ejpam-1535	903	6	the	the	DET
ejpam-1535	903	7	following	follow	VERB
ejpam-1535	903	8	corollary	corollary	NOUN
ejpam-1535	903	9	to	to	ADP
ejpam-1535	903	10	theorem	theorem	ADJ
ejpam-1535	903	11	2	2	NUM
ejpam-1535	903	12	:	:	PUNCT
ejpam-1535	903	13	theorem	theorem	NOUN
ejpam-1535	903	14	7	7	NUM
ejpam-1535	903	15	(	(	PUNCT
ejpam-1535	903	16	[	[	X
ejpam-1535	903	17	45	45	NUM
ejpam-1535	903	18	,	,	PUNCT
ejpam-1535	903	19	p.	p.	NOUN
ejpam-1535	903	20	109	109	NUM
ejpam-1535	903	21	]	]	PUNCT
ejpam-1535	903	22	)	)	PUNCT
ejpam-1535	903	23	.	.	PUNCT
ejpam-1535	904	1	let	let	VERB
ejpam-1535	904	2	s	s	PRON
ejpam-1535	904	3	be	be	AUX
ejpam-1535	904	4	an	an	DET
ejpam-1535	904	5	inverse	inverse	NOUN
ejpam-1535	904	6	semigroup	semigroup	NOUN
ejpam-1535	904	7	with	with	ADP
ejpam-1535	904	8	natural	natural	ADJ
ejpam-1535	904	9	partial	partial	ADJ
ejpam-1535	904	10	order	order	NOUN
ejpam-1535	904	11	≤.	≤.	NOUN
ejpam-1535	904	12	then	then	ADV
ejpam-1535	904	13	(	(	PUNCT
ejpam-1535	904	14	s	s	X
ejpam-1535	904	15	,	,	PUNCT
ejpam-1535	904	16	·	·	PUNCT
ejpam-1535	904	17	,	,	PUNCT
ejpam-1535	904	18	≤	≤	NUM
ejpam-1535	904	19	)	)	PUNCT
ejpam-1535	904	20	is	be	AUX
ejpam-1535	904	21	an	an	DET
ejpam-1535	904	22	inductive	inductive	ADJ
ejpam-1535	904	23	groupoid	groupoid	NOUN
ejpam-1535	904	24	with	with	ADP
ejpam-1535	904	25	so	so	ADV
ejpam-1535	904	26	=	=	SYM
ejpam-1535	904	27	e(s	e(s	PROPN
ejpam-1535	904	28	)	)	PUNCT
ejpam-1535	904	29	,	,	PUNCT
ejpam-1535	904	30	d(x	d(x	PROPN
ejpam-1535	904	31	)	)	PUNCT
ejpam-1535	905	1	=	=	PUNCT
ejpam-1535	905	2	x	x	PUNCT
ejpam-1535	905	3	x−1	x−1	PROPN
ejpam-1535	905	4	and	and	CCONJ
ejpam-1535	905	5	r(x	r(x	PROPN
ejpam-1535	905	6	)	)	PUNCT
ejpam-1535	906	1	=	=	PUNCT
ejpam-1535	907	1	x−1	x−1	PROPN
ejpam-1535	907	2	x	x	PUNCT
ejpam-1535	907	3	,	,	PUNCT
ejpam-1535	907	4	where	where	SCONJ
ejpam-1535	907	5	·	·	PUNCT
ejpam-1535	907	6	is	be	AUX
ejpam-1535	907	7	the	the	DET
ejpam-1535	907	8	restricted	restricted	ADJ
ejpam-1535	907	9	product	product	NOUN
ejpam-1535	907	10	of	of	ADP
ejpam-1535	907	11	(	(	PUNCT
ejpam-1535	907	12	9	9	NUM
ejpam-1535	907	13	)	)	PUNCT
ejpam-1535	907	14	.	.	PUNCT
ejpam-1535	908	1	proof	proof	NOUN
ejpam-1535	908	2	.	.	PUNCT
ejpam-1535	909	1	by	by	ADP
ejpam-1535	909	2	corollary	corollary	ADJ
ejpam-1535	909	3	3	3	NUM
ejpam-1535	909	4	,	,	PUNCT
ejpam-1535	909	5	(	(	PUNCT
ejpam-1535	909	6	s	s	X
ejpam-1535	909	7	,	,	PUNCT
ejpam-1535	909	8	·	·	PUNCT
ejpam-1535	909	9	,	,	PUNCT
ejpam-1535	909	10	≤	≤	NUM
ejpam-1535	909	11	)	)	PUNCT
ejpam-1535	909	12	is	be	AUX
ejpam-1535	909	13	an	an	DET
ejpam-1535	909	14	inductive	inductive	ADJ
ejpam-1535	909	15	unipotent	unipotent	ADJ
ejpam-1535	909	16	category	category	NOUN
ejpam-1535	909	17	.	.	PUNCT
ejpam-1535	910	1	we	we	PRON
ejpam-1535	910	2	must	must	AUX
ejpam-1535	910	3	verify	verify	VERB
ejpam-1535	910	4	that	that	DET
ejpam-1535	910	5	condition	condition	NOUN
ejpam-1535	910	6	(	(	PUNCT
ejpam-1535	910	7	g	g	NOUN
ejpam-1535	910	8	)	)	PUNCT
ejpam-1535	910	9	holds	hold	VERB
ejpam-1535	910	10	.	.	PUNCT
ejpam-1535	911	1	for	for	ADP
ejpam-1535	911	2	clarity	clarity	NOUN
ejpam-1535	911	3	,	,	PUNCT
ejpam-1535	911	4	let	let	VERB
ejpam-1535	911	5	y	y	PRON
ejpam-1535	911	6	be	be	AUX
ejpam-1535	911	7	the	the	DET
ejpam-1535	911	8	inverse	inverse	NOUN
ejpam-1535	911	9	of	of	ADP
ejpam-1535	911	10	x	x	PUNCT
ejpam-1535	911	11	in	in	ADP
ejpam-1535	911	12	the	the	DET
ejpam-1535	911	13	original	original	ADJ
ejpam-1535	911	14	semigroup	semigroup	NOUN
ejpam-1535	911	15	.	.	PUNCT
ejpam-1535	912	1	we	we	PRON
ejpam-1535	912	2	observe	observe	VERB
ejpam-1535	912	3	that	that	SCONJ
ejpam-1535	912	4	x	x	PROPN
ejpam-1535	912	5	x−1	x−1	PROPN
ejpam-1535	912	6	=	=	PUNCT
ejpam-1535	912	7	y−1	y−1	PROPN
ejpam-1535	912	8	y	y	PROPN
ejpam-1535	912	9	,	,	PUNCT
ejpam-1535	912	10	so	so	SCONJ
ejpam-1535	912	11	∃x	∃x	ADJ
ejpam-1535	912	12	·	·	PUNCT
ejpam-1535	912	13	y	y	NOUN
ejpam-1535	912	14	in	in	ADP
ejpam-1535	912	15	(	(	PUNCT
ejpam-1535	912	16	s	s	X
ejpam-1535	912	17	,	,	PUNCT
ejpam-1535	912	18	·	·	PUNCT
ejpam-1535	912	19	)	)	PUNCT
ejpam-1535	912	20	.	.	PUNCT
ejpam-1535	913	1	moreover	moreover	ADV
ejpam-1535	913	2	,	,	PUNCT
ejpam-1535	913	3	x	x	X
ejpam-1535	913	4	·	·	PUNCT
ejpam-1535	913	5	y	y	X
ejpam-1535	913	6	=	=	PUNCT
ejpam-1535	913	7	x	x	PROPN
ejpam-1535	913	8	x−1	x−1	PROPN
ejpam-1535	913	9	=	=	SYM
ejpam-1535	913	10	d(x	d(x	PROPN
ejpam-1535	913	11	)	)	PUNCT
ejpam-1535	913	12	,	,	PUNCT
ejpam-1535	913	13	as	as	SCONJ
ejpam-1535	913	14	required	require	VERB
ejpam-1535	913	15	.	.	PUNCT
ejpam-1535	914	1	similarly	similarly	ADV
ejpam-1535	914	2	,	,	PUNCT
ejpam-1535	914	3	∃y	∃y	PROPN
ejpam-1535	914	4	·	·	PUNCT
ejpam-1535	915	1	x	x	PUNCT
ejpam-1535	915	2	and	and	CCONJ
ejpam-1535	915	3	y	y	PROPN
ejpam-1535	915	4	·	·	PUNCT
ejpam-1535	915	5	x	x	X
ejpam-1535	915	6	=	=	PUNCT
ejpam-1535	915	7	r(x	r(x	PROPN
ejpam-1535	915	8	)	)	PUNCT
ejpam-1535	915	9	.	.	PUNCT
ejpam-1535	916	1	corollary	corollary	ADJ
ejpam-1535	916	2	3	3	NUM
ejpam-1535	916	3	tells	tell	VERB
ejpam-1535	916	4	us	we	PRON
ejpam-1535	916	5	that	that	SCONJ
ejpam-1535	916	6	(	(	PUNCT
ejpam-1535	916	7	s	s	X
ejpam-1535	916	8	,	,	PUNCT
ejpam-1535	916	9	·	·	PUNCT
ejpam-1535	916	10	,	,	PUNCT
ejpam-1535	916	11	≤	≤	NUM
ejpam-1535	916	12	)	)	PUNCT
ejpam-1535	916	13	satisfies	satisfy	VERB
ejpam-1535	916	14	condition	condition	NOUN
ejpam-1535	916	15	(	(	PUNCT
ejpam-1535	916	16	or2	or2	PROPN
ejpam-1535	916	17	)	)	PUNCT
ejpam-1535	916	18	but	but	CCONJ
ejpam-1535	916	19	we	we	PRON
ejpam-1535	916	20	must	must	AUX
ejpam-1535	916	21	verify	verify	VERB
ejpam-1535	916	22	that	that	SCONJ
ejpam-1535	916	23	it	it	PRON
ejpam-1535	916	24	also	also	ADV
ejpam-1535	916	25	satisfies	satisfy	VERB
ejpam-1535	916	26	the	the	DET
ejpam-1535	916	27	stronger	strong	ADJ
ejpam-1535	916	28	(	(	PUNCT
ejpam-1535	916	29	or2′	or2′	ADJ
ejpam-1535	916	30	)	)	PUNCT
ejpam-1535	916	31	.	.	PUNCT
ejpam-1535	917	1	suppose	suppose	VERB
ejpam-1535	917	2	that	that	SCONJ
ejpam-1535	917	3	a	a	DET
ejpam-1535	917	4	≤	≤	PROPN
ejpam-1535	917	5	b	b	NOUN
ejpam-1535	917	6	in	in	ADP
ejpam-1535	917	7	(	(	PUNCT
ejpam-1535	917	8	s	s	NOUN
ejpam-1535	917	9	,	,	PUNCT
ejpam-1535	917	10	·	·	PUNCT
ejpam-1535	917	11	,	,	PUNCT
ejpam-1535	917	12	≤	≤	NUM
ejpam-1535	917	13	)	)	PUNCT
ejpam-1535	917	14	.	.	PUNCT
ejpam-1535	918	1	then	then	ADV
ejpam-1535	918	2	a	a	DET
ejpam-1535	918	3	≤	≤	PROPN
ejpam-1535	918	4	b	b	NOUN
ejpam-1535	918	5	in	in	ADP
ejpam-1535	918	6	(	(	PUNCT
ejpam-1535	918	7	s,⊗	s,⊗	NOUN
ejpam-1535	918	8	)	)	PUNCT
ejpam-1535	918	9	,	,	PUNCT
ejpam-1535	918	10	so	so	ADV
ejpam-1535	918	11	a	a	DET
ejpam-1535	918	12	=	=	SYM
ejpam-1535	918	13	eb	eb	PROPN
ejpam-1535	918	14	,	,	PUNCT
ejpam-1535	918	15	for	for	ADP
ejpam-1535	918	16	some	some	DET
ejpam-1535	918	17	e	e	PROPN
ejpam-1535	918	18	∈	∈	PROPN
ejpam-1535	918	19	e(s	e(s	PROPN
ejpam-1535	918	20	)	)	PUNCT
ejpam-1535	918	21	.	.	PUNCT
ejpam-1535	919	1	since	since	SCONJ
ejpam-1535	919	2	ordering	ordering	NOUN
ejpam-1535	919	3	and	and	CCONJ
ejpam-1535	919	4	multiplication	multiplication	NOUN
ejpam-1535	919	5	are	be	AUX
ejpam-1535	919	6	compatible	compatible	ADJ
ejpam-1535	919	7	in	in	ADP
ejpam-1535	919	8	the	the	DET
ejpam-1535	919	9	semigroup	semigroup	NOUN
ejpam-1535	919	10	,	,	PUNCT
ejpam-1535	919	11	we	we	PRON
ejpam-1535	919	12	have	have	VERB
ejpam-1535	919	13	a−1	a−1	PROPN
ejpam-1535	919	14	≤	≤	NOUN
ejpam-1535	919	15	(	(	PUNCT
ejpam-1535	919	16	eb)−1	eb)−1	NOUN
ejpam-1535	919	17	=	=	SYM
ejpam-1535	919	18	b−1e	b−1e	ADJ
ejpam-1535	919	19	≤	≤	NUM
ejpam-1535	919	20	b−1	b−1	PROPN
ejpam-1535	919	21	.	.	PUNCT
ejpam-1535	920	1	therefore	therefore	ADV
ejpam-1535	920	2	a−1	a−1	PROPN
ejpam-1535	920	3	≤	≤	VERB
ejpam-1535	920	4	b−1	b−1	PROPN
ejpam-1535	920	5	in	in	ADP
ejpam-1535	920	6	(	(	PUNCT
ejpam-1535	920	7	s	s	X
ejpam-1535	920	8	,	,	PUNCT
ejpam-1535	920	9	·	·	PUNCT
ejpam-1535	920	10	,	,	PUNCT
ejpam-1535	920	11	≤	≤	NUM
ejpam-1535	920	12	)	)	PUNCT
ejpam-1535	920	13	.	.	PUNCT
ejpam-1535	921	1	conversely	conversely	ADV
ejpam-1535	921	2	,	,	PUNCT
ejpam-1535	921	3	we	we	PRON
ejpam-1535	921	4	have	have	VERB
ejpam-1535	921	5	the	the	DET
ejpam-1535	921	6	following	follow	VERB
ejpam-1535	921	7	:	:	PUNCT
ejpam-1535	921	8	c.	c.	PROPN
ejpam-1535	921	9	hollings	hollings	PROPN
ejpam-1535	921	10	/	/	SYM
ejpam-1535	921	11	eur	eur	PROPN
ejpam-1535	921	12	.	.	PUNCT
ejpam-1535	922	1	j.	j.	PROPN
ejpam-1535	922	2	pure	pure	PROPN
ejpam-1535	922	3	appl	appl	PROPN
ejpam-1535	922	4	.	.	PROPN
ejpam-1535	922	5	math	math	PROPN
ejpam-1535	922	6	,	,	PUNCT
ejpam-1535	922	7	5	5	NUM
ejpam-1535	922	8	(	(	PUNCT
ejpam-1535	922	9	2012	2012	NUM
ejpam-1535	922	10	)	)	PUNCT
ejpam-1535	922	11	,	,	PUNCT
ejpam-1535	922	12	414	414	NUM
ejpam-1535	922	13	-	-	SYM
ejpam-1535	922	14	450	450	NUM
ejpam-1535	922	15	445	445	NUM
ejpam-1535	922	16	theorem	theorem	VERB
ejpam-1535	922	17	8	8	NUM
ejpam-1535	922	18	(	(	PUNCT
ejpam-1535	922	19	[	[	X
ejpam-1535	922	20	45	45	NUM
ejpam-1535	922	21	,	,	PUNCT
ejpam-1535	922	22	theorem	theorem	VERB
ejpam-1535	922	23	3.4	3.4	NUM
ejpam-1535	922	24	]	]	PUNCT
ejpam-1535	922	25	)	)	PUNCT
ejpam-1535	922	26	.	.	PUNCT
ejpam-1535	923	1	if	if	SCONJ
ejpam-1535	923	2	(	(	PUNCT
ejpam-1535	923	3	g	g	NOUN
ejpam-1535	923	4	,	,	PUNCT
ejpam-1535	923	5	·	·	PUNCT
ejpam-1535	923	6	,	,	PUNCT
ejpam-1535	923	7	≤	≤	NUM
ejpam-1535	923	8	)	)	PUNCT
ejpam-1535	923	9	is	be	AUX
ejpam-1535	923	10	an	an	DET
ejpam-1535	923	11	inductive	inductive	ADJ
ejpam-1535	923	12	groupoid	groupoid	NOUN
ejpam-1535	923	13	,	,	PUNCT
ejpam-1535	923	14	then	then	ADV
ejpam-1535	923	15	(	(	PUNCT
ejpam-1535	923	16	g,⊗	g,⊗	NOUN
ejpam-1535	923	17	)	)	PUNCT
ejpam-1535	923	18	is	be	AUX
ejpam-1535	923	19	an	an	DET
ejpam-1535	923	20	inverse	inverse	NOUN
ejpam-1535	923	21	semigroup	semigroup	NOUN
ejpam-1535	923	22	,	,	PUNCT
ejpam-1535	923	23	where	where	SCONJ
ejpam-1535	923	24	⊗	⊗	PROPN
ejpam-1535	923	25	is	be	AUX
ejpam-1535	923	26	the	the	DET
ejpam-1535	923	27	pseudoproduct	pseudoproduct	NOUN
ejpam-1535	923	28	of	of	ADP
ejpam-1535	923	29	(	(	PUNCT
ejpam-1535	923	30	6	6	NUM
ejpam-1535	923	31	)	)	PUNCT
ejpam-1535	923	32	.	.	PUNCT
ejpam-1535	924	1	proof	proof	NOUN
ejpam-1535	924	2	.	.	PUNCT
ejpam-1535	925	1	by	by	ADP
ejpam-1535	925	2	corollary	corollary	ADJ
ejpam-1535	925	3	5	5	NUM
ejpam-1535	925	4	,	,	PUNCT
ejpam-1535	925	5	(	(	PUNCT
ejpam-1535	925	6	g,⊗	g,⊗	NOUN
ejpam-1535	925	7	)	)	PUNCT
ejpam-1535	925	8	is	be	AUX
ejpam-1535	925	9	a	a	DET
ejpam-1535	925	10	full	full	ADJ
ejpam-1535	925	11	restriction	restriction	NOUN
ejpam-1535	925	12	semigroup	semigroup	NOUN
ejpam-1535	925	13	.	.	PUNCT
ejpam-1535	926	1	we	we	PRON
ejpam-1535	926	2	therefore	therefore	ADV
ejpam-1535	926	3	know	know	VERB
ejpam-1535	926	4	that	that	SCONJ
ejpam-1535	926	5	e(g	e(g	NOUN
ejpam-1535	926	6	)	)	PUNCT
ejpam-1535	927	1	=	=	PUNCT
ejpam-1535	927	2	go	go	VERB
ejpam-1535	927	3	and	and	CCONJ
ejpam-1535	927	4	,	,	PUNCT
ejpam-1535	927	5	from	from	ADP
ejpam-1535	927	6	the	the	DET
ejpam-1535	927	7	proof	proof	NOUN
ejpam-1535	927	8	of	of	ADP
ejpam-1535	927	9	theorem	theorem	NOUN
ejpam-1535	927	10	3	3	NUM
ejpam-1535	927	11	,	,	PUNCT
ejpam-1535	927	12	that	that	SCONJ
ejpam-1535	927	13	these	these	DET
ejpam-1535	927	14	idempotents	idempotent	NOUN
ejpam-1535	927	15	commute	commute	VERB
ejpam-1535	927	16	with	with	ADP
ejpam-1535	927	17	respect	respect	NOUN
ejpam-1535	927	18	to	to	ADP
ejpam-1535	927	19	⊗.	⊗.	NOUN
ejpam-1535	927	20	it	it	PRON
ejpam-1535	927	21	remains	remain	VERB
ejpam-1535	927	22	to	to	PART
ejpam-1535	927	23	show	show	VERB
ejpam-1535	927	24	that	that	SCONJ
ejpam-1535	927	25	the	the	DET
ejpam-1535	927	26	groupoid	groupoid	PROPN
ejpam-1535	927	27	inverses	inverse	VERB
ejpam-1535	927	28	in	in	ADP
ejpam-1535	927	29	(	(	PUNCT
ejpam-1535	927	30	g	g	PROPN
ejpam-1535	927	31	,	,	PUNCT
ejpam-1535	927	32	·	·	PUNCT
ejpam-1535	927	33	,	,	PUNCT
ejpam-1535	927	34	≤	≤	NUM
ejpam-1535	927	35	)	)	PUNCT
ejpam-1535	927	36	serve	serve	VERB
ejpam-1535	927	37	as	as	ADP
ejpam-1535	927	38	semigroup	semigroup	PROPN
ejpam-1535	927	39	inverses	inverse	NOUN
ejpam-1535	927	40	in	in	ADP
ejpam-1535	927	41	(	(	PUNCT
ejpam-1535	927	42	g,⊗	g,⊗	NOUN
ejpam-1535	927	43	)	)	PUNCT
ejpam-1535	927	44	.	.	PUNCT
ejpam-1535	928	1	let	let	VERB
ejpam-1535	928	2	x−1	x−1	PROPN
ejpam-1535	928	3	be	be	AUX
ejpam-1535	928	4	the	the	DET
ejpam-1535	928	5	inverse	inverse	NOUN
ejpam-1535	928	6	of	of	ADP
ejpam-1535	928	7	x	x	PROPN
ejpam-1535	928	8	∈	∈	PROPN
ejpam-1535	928	9	g	g	NOUN
ejpam-1535	928	10	in	in	ADP
ejpam-1535	928	11	the	the	DET
ejpam-1535	928	12	sense	sense	NOUN
ejpam-1535	928	13	of	of	ADP
ejpam-1535	928	14	condition	condition	NOUN
ejpam-1535	928	15	(	(	PUNCT
ejpam-1535	928	16	g	g	NOUN
ejpam-1535	928	17	)	)	PUNCT
ejpam-1535	928	18	.	.	PUNCT
ejpam-1535	929	1	then	then	ADV
ejpam-1535	929	2	,	,	PUNCT
ejpam-1535	929	3	since	since	SCONJ
ejpam-1535	929	4	·	·	PUNCT
ejpam-1535	929	5	and	and	CCONJ
ejpam-1535	929	6	⊗	⊗	PROPN
ejpam-1535	929	7	coincide	coincide	NOUN
ejpam-1535	929	8	whenever	whenever	SCONJ
ejpam-1535	929	9	the	the	DET
ejpam-1535	929	10	former	former	ADJ
ejpam-1535	929	11	is	be	AUX
ejpam-1535	929	12	defined	define	VERB
ejpam-1535	929	13	,	,	PUNCT
ejpam-1535	929	14	we	we	PRON
ejpam-1535	929	15	have	have	VERB
ejpam-1535	929	16	(	(	PUNCT
ejpam-1535	929	17	x	x	PROPN
ejpam-1535	929	18	⊗	⊗	PROPN
ejpam-1535	929	19	x−1)⊗	x−1)⊗	PROPN
ejpam-1535	929	20	x	x	X
ejpam-1535	930	1	=	=	PUNCT
ejpam-1535	930	2	(	(	PUNCT
ejpam-1535	930	3	x	x	X
ejpam-1535	930	4	·	·	PUNCT
ejpam-1535	930	5	x−1)⊗	x−1)⊗	NOUN
ejpam-1535	930	6	x	x	X
ejpam-1535	931	1	=	=	SYM
ejpam-1535	931	2	d(x)⊗	d(x)⊗	NOUN
ejpam-1535	931	3	x	x	X
ejpam-1535	931	4	=	=	SYM
ejpam-1535	931	5	d(x	d(x	PROPN
ejpam-1535	931	6	)	)	PUNCT
ejpam-1535	931	7	·	·	PUNCT
ejpam-1535	931	8	x	x	PUNCT
ejpam-1535	932	1	=	=	PUNCT
ejpam-1535	932	2	x	x	X
ejpam-1535	932	3	.	.	PUNCT
ejpam-1535	933	1	similarly	similarly	ADV
ejpam-1535	933	2	,	,	PUNCT
ejpam-1535	933	3	x−1⊗	x−1⊗	PROPN
ejpam-1535	933	4	x	x	PUNCT
ejpam-1535	934	1	⊗	⊗	PROPN
ejpam-1535	934	2	x−1	x−1	PROPN
ejpam-1535	934	3	=	=	SYM
ejpam-1535	934	4	x−1	x−1	PROPN
ejpam-1535	934	5	.	.	PUNCT
ejpam-1535	935	1	let	let	VERB
ejpam-1535	935	2	s	s	PRON
ejpam-1535	935	3	be	be	AUX
ejpam-1535	935	4	an	an	DET
ejpam-1535	935	5	inverse	inverse	NOUN
ejpam-1535	935	6	semigroup	semigroup	NOUN
ejpam-1535	935	7	.	.	PUNCT
ejpam-1535	936	1	we	we	PRON
ejpam-1535	936	2	will	will	AUX
ejpam-1535	936	3	denote	denote	VERB
ejpam-1535	936	4	the	the	DET
ejpam-1535	936	5	inductive	inductive	ADJ
ejpam-1535	936	6	groupoid	groupoid	NOUN
ejpam-1535	936	7	associated	associate	VERB
ejpam-1535	936	8	with	with	ADP
ejpam-1535	936	9	s	s	PRON
ejpam-1535	936	10	by	by	ADP
ejpam-1535	936	11	g(s	g(	NOUN
ejpam-1535	936	12	)	)	PUNCT
ejpam-1535	936	13	.	.	PUNCT
ejpam-1535	937	1	similarly	similarly	ADV
ejpam-1535	937	2	,	,	PUNCT
ejpam-1535	937	3	if	if	SCONJ
ejpam-1535	937	4	g	g	PROPN
ejpam-1535	937	5	is	be	AUX
ejpam-1535	937	6	an	an	DET
ejpam-1535	937	7	inductive	inductive	ADJ
ejpam-1535	937	8	groupoid	groupoid	NOUN
ejpam-1535	937	9	,	,	PUNCT
ejpam-1535	937	10	then	then	ADV
ejpam-1535	937	11	we	we	PRON
ejpam-1535	937	12	will	will	AUX
ejpam-1535	937	13	denote	denote	VERB
ejpam-1535	937	14	its	its	PRON
ejpam-1535	937	15	associated	associated	ADJ
ejpam-1535	937	16	inverse	inverse	NOUN
ejpam-1535	937	17	semigroup	semigroup	NOUN
ejpam-1535	937	18	by	by	ADP
ejpam-1535	937	19	i(g	i(g	NOUN
ejpam-1535	937	20	)	)	PUNCT
ejpam-1535	937	21	.	.	PUNCT
ejpam-1535	938	1	the	the	DET
ejpam-1535	938	2	following	follow	VERB
ejpam-1535	938	3	is	be	AUX
ejpam-1535	938	4	an	an	DET
ejpam-1535	938	5	easy	easy	ADJ
ejpam-1535	938	6	consequence	consequence	NOUN
ejpam-1535	938	7	of	of	ADP
ejpam-1535	938	8	theorem	theorem	ADJ
ejpam-1535	938	9	4	4	NUM
ejpam-1535	938	10	:	:	PUNCT
ejpam-1535	938	11	theorem	theorem	NOUN
ejpam-1535	938	12	9	9	NUM
ejpam-1535	938	13	(	(	PUNCT
ejpam-1535	938	14	[	[	X
ejpam-1535	938	15	29	29	NUM
ejpam-1535	938	16	,	,	PUNCT
ejpam-1535	938	17	proposition	proposition	NOUN
ejpam-1535	938	18	4.1.7(2),(3	4.1.7(2),(3	NOUN
ejpam-1535	938	19	)	)	PUNCT
ejpam-1535	938	20	]	]	PUNCT
ejpam-1535	938	21	)	)	PUNCT
ejpam-1535	938	22	.	.	PUNCT
ejpam-1535	939	1	let	let	VERB
ejpam-1535	939	2	s	s	PRON
ejpam-1535	939	3	be	be	AUX
ejpam-1535	939	4	an	an	DET
ejpam-1535	939	5	inverse	inverse	NOUN
ejpam-1535	939	6	semigroup	semigroup	NOUN
ejpam-1535	939	7	and	and	CCONJ
ejpam-1535	939	8	g	g	PROPN
ejpam-1535	939	9	be	be	AUX
ejpam-1535	939	10	an	an	DET
ejpam-1535	939	11	inductive	inductive	ADJ
ejpam-1535	939	12	groupoid	groupoid	NOUN
ejpam-1535	939	13	.	.	PUNCT
ejpam-1535	940	1	then	then	ADV
ejpam-1535	940	2	i(g(s	i(g(s	NOUN
ejpam-1535	940	3	)	)	PUNCT
ejpam-1535	940	4	)	)	PUNCT
ejpam-1535	941	1	=	=	SYM
ejpam-1535	941	2	s	s	PROPN
ejpam-1535	941	3	and	and	CCONJ
ejpam-1535	941	4	g(i(g	g(i(g	PROPN
ejpam-1535	941	5	)	)	PUNCT
ejpam-1535	941	6	)	)	PUNCT
ejpam-1535	942	1	=	=	PUNCT
ejpam-1535	942	2	g.	g.	NOUN
ejpam-1535	942	3	as	as	ADP
ejpam-1535	942	4	in	in	ADP
ejpam-1535	942	5	the	the	DET
ejpam-1535	942	6	more	more	ADV
ejpam-1535	942	7	general	general	ADJ
ejpam-1535	942	8	case	case	NOUN
ejpam-1535	942	9	of	of	ADP
ejpam-1535	942	10	restriction	restriction	NOUN
ejpam-1535	942	11	semigroups	semigroup	NOUN
ejpam-1535	942	12	and	and	CCONJ
ejpam-1535	942	13	inductive	inductive	ADJ
ejpam-1535	942	14	categories	category	NOUN
ejpam-1535	942	15	,	,	PUNCT
ejpam-1535	942	16	we	we	PRON
ejpam-1535	942	17	are	be	AUX
ejpam-1535	942	18	aiming	aim	VERB
ejpam-1535	942	19	to	to	PART
ejpam-1535	942	20	prove	prove	VERB
ejpam-1535	942	21	an	an	DET
ejpam-1535	942	22	isomorphism	isomorphism	NOUN
ejpam-1535	942	23	of	of	ADP
ejpam-1535	942	24	categories	category	NOUN
ejpam-1535	942	25	for	for	ADP
ejpam-1535	942	26	inverse	inverse	NOUN
ejpam-1535	942	27	semigroups	semigroup	NOUN
ejpam-1535	942	28	and	and	CCONJ
ejpam-1535	942	29	inductive	inductive	ADJ
ejpam-1535	942	30	groupoids	groupoid	NOUN
ejpam-1535	942	31	.	.	PUNCT
ejpam-1535	943	1	we	we	PRON
ejpam-1535	943	2	have	have	AUX
ejpam-1535	943	3	dealt	deal	VERB
ejpam-1535	943	4	with	with	ADP
ejpam-1535	943	5	the	the	DET
ejpam-1535	943	6	“	"	PUNCT
ejpam-1535	943	7	objects	object	NOUN
ejpam-1535	943	8	”	"	PUNCT
ejpam-1535	943	9	parts	part	NOUN
ejpam-1535	943	10	,	,	PUNCT
ejpam-1535	943	11	so	so	SCONJ
ejpam-1535	943	12	we	we	PRON
ejpam-1535	943	13	must	must	AUX
ejpam-1535	943	14	now	now	ADV
ejpam-1535	943	15	turn	turn	VERB
ejpam-1535	943	16	our	our	PRON
ejpam-1535	943	17	attention	attention	NOUN
ejpam-1535	943	18	to	to	ADP
ejpam-1535	943	19	the	the	DET
ejpam-1535	943	20	arrows	arrow	NOUN
ejpam-1535	943	21	;	;	PUNCT
ejpam-1535	943	22	we	we	PRON
ejpam-1535	943	23	take	take	VERB
ejpam-1535	943	24	each	each	PRON
ejpam-1535	943	25	of	of	ADP
ejpam-1535	943	26	the	the	DET
ejpam-1535	943	27	previously	previously	ADV
ejpam-1535	943	28	considered	consider	VERB
ejpam-1535	943	29	cases	case	NOUN
ejpam-1535	943	30	in	in	ADP
ejpam-1535	943	31	turn	turn	NOUN
ejpam-1535	943	32	.	.	PUNCT
ejpam-1535	944	1	8.2	8.2	NUM
ejpam-1535	944	2	.	.	PUNCT
ejpam-1535	944	3	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	944	4	and	and	CCONJ
ejpam-1535	944	5	ordered	order	VERB
ejpam-1535	944	6	functors	functor	VERB
ejpam-1535	944	7	the	the	DET
ejpam-1535	944	8	notion	notion	NOUN
ejpam-1535	944	9	of	of	ADP
ejpam-1535	944	10	a	a	DET
ejpam-1535	944	11	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	944	12	was	be	AUX
ejpam-1535	944	13	originally	originally	ADV
ejpam-1535	944	14	introduced	introduce	VERB
ejpam-1535	944	15	in	in	ADP
ejpam-1535	944	16	[	[	X
ejpam-1535	944	17	32	32	NUM
ejpam-1535	944	18	]	]	PUNCT
ejpam-1535	944	19	for	for	ADP
ejpam-1535	944	20	inverse	inverse	NOUN
ejpam-1535	944	21	semigroups	semigroup	NOUN
ejpam-1535	944	22	with	with	ADP
ejpam-1535	944	23	the	the	DET
ejpam-1535	944	24	following	follow	VERB
ejpam-1535	944	25	definition	definition	NOUN
ejpam-1535	944	26	:	:	PUNCT
ejpam-1535	944	27	definition	definition	NOUN
ejpam-1535	944	28	20	20	NUM
ejpam-1535	944	29	.	.	PUNCT
ejpam-1535	945	1	let	let	VERB
ejpam-1535	945	2	s	s	PRON
ejpam-1535	945	3	and	and	CCONJ
ejpam-1535	945	4	t	t	PROPN
ejpam-1535	945	5	be	be	AUX
ejpam-1535	945	6	inverse	inverse	NOUN
ejpam-1535	945	7	semigroups	semigroup	NOUN
ejpam-1535	945	8	.	.	PUNCT
ejpam-1535	946	1	a	a	DET
ejpam-1535	946	2	function	function	NOUN
ejpam-1535	946	3	θ	θ	NOUN
ejpam-1535	946	4	:	:	PUNCT
ejpam-1535	946	5	s	s	X
ejpam-1535	946	6	→	→	SYM
ejpam-1535	946	7	t	t	PROPN
ejpam-1535	946	8	is	be	AUX
ejpam-1535	946	9	called	call	VERB
ejpam-1535	946	10	a	a	DET
ejpam-1535	946	11	∨premorphism	∨premorphism	NOUN
ejpam-1535	946	12	if	if	SCONJ
ejpam-1535	946	13	(	(	PUNCT
ejpam-1535	946	14	st)θ	st)θ	PROPN
ejpam-1535	946	15	≤	≤	NOUN
ejpam-1535	946	16	(	(	PUNCT
ejpam-1535	946	17	sθ)(tθ	sθ)(tθ	PROPN
ejpam-1535	946	18	)	)	PUNCT
ejpam-1535	946	19	.	.	PUNCT
ejpam-1535	947	1	given	give	VERB
ejpam-1535	947	2	that	that	SCONJ
ejpam-1535	947	3	we	we	PRON
ejpam-1535	947	4	included	include	VERB
ejpam-1535	947	5	a	a	DET
ejpam-1535	947	6	condition	condition	NOUN
ejpam-1535	947	7	relating	relate	VERB
ejpam-1535	947	8	to	to	ADP
ejpam-1535	947	9	+	+	PUNCT
ejpam-1535	947	10	and	and	CCONJ
ejpam-1535	947	11	∗	∗	NOUN
ejpam-1535	947	12	in	in	ADP
ejpam-1535	947	13	the	the	DET
ejpam-1535	947	14	definition	definition	NOUN
ejpam-1535	947	15	of	of	ADP
ejpam-1535	947	16	a	a	DET
ejpam-1535	947	17	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	947	18	for	for	ADP
ejpam-1535	947	19	restriction	restriction	NOUN
ejpam-1535	947	20	semigroups	semigroup	NOUN
ejpam-1535	947	21	,	,	PUNCT
ejpam-1535	947	22	it	it	PRON
ejpam-1535	947	23	is	be	AUX
ejpam-1535	947	24	perhaps	perhaps	ADV
ejpam-1535	947	25	a	a	DET
ejpam-1535	947	26	little	little	ADJ
ejpam-1535	947	27	surprising	surprising	ADJ
ejpam-1535	947	28	that	that	SCONJ
ejpam-1535	947	29	we	we	PRON
ejpam-1535	947	30	make	make	VERB
ejpam-1535	947	31	no	no	DET
ejpam-1535	947	32	mention	mention	NOUN
ejpam-1535	947	33	of	of	ADP
ejpam-1535	947	34	inverses	inverse	NOUN
ejpam-1535	947	35	in	in	ADP
ejpam-1535	947	36	the	the	DET
ejpam-1535	947	37	definition	definition	NOUN
ejpam-1535	947	38	for	for	ADP
ejpam-1535	947	39	inverse	inverse	NOUN
ejpam-1535	947	40	semigroups	semigroup	NOUN
ejpam-1535	947	41	.	.	PUNCT
ejpam-1535	948	1	in	in	ADP
ejpam-1535	948	2	fact	fact	NOUN
ejpam-1535	948	3	,	,	PUNCT
ejpam-1535	948	4	there	there	PRON
ejpam-1535	948	5	is	be	VERB
ejpam-1535	948	6	no	no	DET
ejpam-1535	948	7	real	real	ADJ
ejpam-1535	948	8	omission	omission	NOUN
ejpam-1535	948	9	here	here	ADV
ejpam-1535	948	10	:	:	PUNCT
ejpam-1535	948	11	lemma	lemma	PROPN
ejpam-1535	948	12	21	21	NUM
ejpam-1535	948	13	(	(	PUNCT
ejpam-1535	948	14	[	[	X
ejpam-1535	948	15	29	29	NUM
ejpam-1535	948	16	,	,	PUNCT
ejpam-1535	948	17	theorem	theorem	VERB
ejpam-1535	948	18	3.1.5	3.1.5	NOUN
ejpam-1535	948	19	]	]	PUNCT
ejpam-1535	948	20	)	)	PUNCT
ejpam-1535	948	21	.	.	PUNCT
ejpam-1535	949	1	let	let	VERB
ejpam-1535	949	2	θ	θ	NOUN
ejpam-1535	949	3	:	:	PUNCT
ejpam-1535	949	4	s	s	X
ejpam-1535	949	5	→	→	SYM
ejpam-1535	949	6	t	t	PROPN
ejpam-1535	949	7	be	be	AUX
ejpam-1535	949	8	a	a	DET
ejpam-1535	949	9	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	949	10	of	of	ADP
ejpam-1535	949	11	inverse	inverse	NOUN
ejpam-1535	949	12	semigroups	semigroup	NOUN
ejpam-1535	949	13	,	,	PUNCT
ejpam-1535	949	14	as	as	ADP
ejpam-1535	949	15	in	in	ADP
ejpam-1535	949	16	definition	definition	NOUN
ejpam-1535	949	17	20	20	NUM
ejpam-1535	949	18	.	.	PUNCT
ejpam-1535	950	1	then	then	ADV
ejpam-1535	950	2	θ	θ	PROPN
ejpam-1535	950	3	respects	respect	VERB
ejpam-1535	950	4	inverses	inverse	NOUN
ejpam-1535	950	5	and	and	CCONJ
ejpam-1535	950	6	the	the	DET
ejpam-1535	950	7	natural	natural	ADJ
ejpam-1535	950	8	partial	partial	ADJ
ejpam-1535	950	9	order	order	NOUN
ejpam-1535	950	10	.	.	PUNCT
ejpam-1535	951	1	we	we	PRON
ejpam-1535	951	2	have	have	AUX
ejpam-1535	951	3	so	so	ADV
ejpam-1535	951	4	far	far	ADV
ejpam-1535	951	5	been	be	AUX
ejpam-1535	951	6	a	a	DET
ejpam-1535	951	7	little	little	ADJ
ejpam-1535	951	8	sloppy	sloppy	ADJ
ejpam-1535	951	9	in	in	ADP
ejpam-1535	951	10	referring	refer	VERB
ejpam-1535	951	11	to	to	ADP
ejpam-1535	951	12	both	both	DET
ejpam-1535	951	13	the	the	DET
ejpam-1535	951	14	function	function	NOUN
ejpam-1535	951	15	of	of	ADP
ejpam-1535	951	16	definition	definition	NOUN
ejpam-1535	951	17	13	13	NUM
ejpam-1535	951	18	and	and	CCONJ
ejpam-1535	951	19	that	that	PRON
ejpam-1535	951	20	of	of	ADP
ejpam-1535	951	21	definition	definition	NOUN
ejpam-1535	951	22	20	20	NUM
ejpam-1535	951	23	as	as	ADP
ejpam-1535	951	24	“	"	PUNCT
ejpam-1535	951	25	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	951	26	”	"	PUNCT
ejpam-1535	951	27	.	.	PUNCT
ejpam-1535	952	1	in	in	ADP
ejpam-1535	952	2	fact	fact	NOUN
ejpam-1535	952	3	,	,	PUNCT
ejpam-1535	952	4	there	there	PRON
ejpam-1535	952	5	is	be	VERB
ejpam-1535	952	6	no	no	DET
ejpam-1535	952	7	ambiguity	ambiguity	NOUN
ejpam-1535	952	8	:	:	PUNCT
ejpam-1535	952	9	lemma	lemma	PROPN
ejpam-1535	952	10	22	22	NUM
ejpam-1535	952	11	.	.	PUNCT
ejpam-1535	953	1	let	let	VERB
ejpam-1535	953	2	θ	θ	NOUN
ejpam-1535	953	3	:	:	PUNCT
ejpam-1535	953	4	s→	s→	PROPN
ejpam-1535	953	5	t	t	NOUN
ejpam-1535	953	6	be	be	AUX
ejpam-1535	953	7	a	a	DET
ejpam-1535	953	8	function	function	NOUN
ejpam-1535	953	9	between	between	ADP
ejpam-1535	953	10	inverse	inverse	NOUN
ejpam-1535	953	11	semigroups	semigroup	NOUN
ejpam-1535	953	12	.	.	PUNCT
ejpam-1535	954	1	then	then	ADV
ejpam-1535	954	2	θ	θ	PROPN
ejpam-1535	954	3	is	be	AUX
ejpam-1535	954	4	a	a	DET
ejpam-1535	954	5	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	954	6	in	in	ADP
ejpam-1535	954	7	the	the	DET
ejpam-1535	954	8	sense	sense	NOUN
ejpam-1535	954	9	of	of	ADP
ejpam-1535	954	10	definition	definition	NOUN
ejpam-1535	954	11	20	20	NUM
ejpam-1535	954	12	if	if	SCONJ
ejpam-1535	954	13	and	and	CCONJ
ejpam-1535	954	14	only	only	ADV
ejpam-1535	954	15	if	if	SCONJ
ejpam-1535	954	16	it	it	PRON
ejpam-1535	954	17	is	be	AUX
ejpam-1535	954	18	a	a	DET
ejpam-1535	954	19	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	954	20	in	in	ADP
ejpam-1535	954	21	the	the	DET
ejpam-1535	954	22	sense	sense	NOUN
ejpam-1535	954	23	of	of	ADP
ejpam-1535	954	24	definition	definition	NOUN
ejpam-1535	954	25	13	13	NUM
ejpam-1535	954	26	.	.	PUNCT
ejpam-1535	955	1	c.	c.	PROPN
ejpam-1535	955	2	hollings	holling	NOUN
ejpam-1535	955	3	/	/	SYM
ejpam-1535	955	4	eur	eur	PROPN
ejpam-1535	955	5	.	.	PUNCT
ejpam-1535	956	1	j.	j.	PROPN
ejpam-1535	956	2	pure	pure	PROPN
ejpam-1535	956	3	appl	appl	PROPN
ejpam-1535	956	4	.	.	PROPN
ejpam-1535	956	5	math	math	PROPN
ejpam-1535	956	6	,	,	PUNCT
ejpam-1535	956	7	5	5	NUM
ejpam-1535	956	8	(	(	PUNCT
ejpam-1535	956	9	2012	2012	NUM
ejpam-1535	956	10	)	)	PUNCT
ejpam-1535	956	11	,	,	PUNCT
ejpam-1535	956	12	414	414	NUM
ejpam-1535	956	13	-	-	SYM
ejpam-1535	956	14	450	450	NUM
ejpam-1535	956	15	446	446	NUM
ejpam-1535	956	16	proof	proof	NOUN
ejpam-1535	956	17	.	.	PUNCT
ejpam-1535	957	1	(	(	PUNCT
ejpam-1535	957	2	⇐	⇐	ADJ
ejpam-1535	957	3	)	)	PUNCT
ejpam-1535	957	4	immediate	immediate	ADJ
ejpam-1535	957	5	.	.	PUNCT
ejpam-1535	958	1	(	(	PUNCT
ejpam-1535	958	2	⇒	⇒	PROPN
ejpam-1535	958	3	)	)	PUNCT
ejpam-1535	958	4	suppose	suppose	VERB
ejpam-1535	958	5	that	that	SCONJ
ejpam-1535	958	6	θ	θ	NOUN
ejpam-1535	958	7	:	:	PUNCT
ejpam-1535	958	8	s→	s→	PROPN
ejpam-1535	958	9	t	t	PROPN
ejpam-1535	958	10	is	be	AUX
ejpam-1535	958	11	a	a	DET
ejpam-1535	958	12	∨-premorphism	∨-premorphism	NOUN
ejpam-1535	958	13	in	in	ADP
ejpam-1535	958	14	the	the	DET
ejpam-1535	958	15	sense	sense	NOUN
ejpam-1535	958	16	of	of	ADP
ejpam-1535	958	17	definition	definition	NOUN
ejpam-1535	958	18	20	20	NUM
ejpam-1535	958	19	.	.	PUNCT
ejpam-1535	959	1	then	then	ADV
ejpam-1535	959	2	s+θ	s+θ	NUM
ejpam-1535	959	3	=	=	SYM
ejpam-1535	959	4	(	(	PUNCT
ejpam-1535	959	5	ss−1)θ	ss−1)θ	X
ejpam-1535	959	6	≤	≤	X
ejpam-1535	959	7	(	(	PUNCT
ejpam-1535	959	8	sθ)(s−1θ	sθ)(s−1θ	ADJ
ejpam-1535	959	9	)	)	PUNCT
ejpam-1535	959	10	=	=	PUNCT
ejpam-1535	959	11	(	(	PUNCT
ejpam-1535	959	12	sθ)(sθ)−1	sθ)(sθ)−1	NOUN
ejpam-1535	959	13	=	=	SYM
ejpam-1535	959	14	(	(	PUNCT
ejpam-1535	959	15	sθ)+	sθ)+	PROPN
ejpam-1535	959	16	,	,	PUNCT
ejpam-1535	959	17	using	use	VERB
ejpam-1535	959	18	lemma	lemma	PROPN
ejpam-1535	959	19	21	21	NUM
ejpam-1535	959	20	.	.	PUNCT
ejpam-1535	960	1	similarly	similarly	ADV
ejpam-1535	960	2	,	,	PUNCT
ejpam-1535	960	3	s∗θ	s∗θ	ADJ
ejpam-1535	960	4	≤	≤	NUM
ejpam-1535	960	5	(	(	PUNCT
ejpam-1535	960	6	sθ)∗.	sθ)∗.	NOUN
ejpam-1535	960	7	we	we	PRON
ejpam-1535	960	8	note	note	VERB
ejpam-1535	960	9	the	the	DET
ejpam-1535	960	10	following	following	NOUN
ejpam-1535	960	11	:	:	PUNCT
ejpam-1535	960	12	lemma	lemma	PROPN
ejpam-1535	960	13	23	23	NUM
ejpam-1535	960	14	(	(	PUNCT
ejpam-1535	960	15	[	[	X
ejpam-1535	960	16	32	32	NUM
ejpam-1535	960	17	,	,	PUNCT
ejpam-1535	960	18	corollary	corollary	NOUN
ejpam-1535	960	19	2.2	2.2	NUM
ejpam-1535	960	20	]	]	PUNCT
ejpam-1535	960	21	)	)	PUNCT
ejpam-1535	960	22	.	.	PUNCT
ejpam-1535	961	1	inverse	inverse	NOUN
ejpam-1535	961	2	semigroups	semigroup	NOUN
ejpam-1535	961	3	and	and	CCONJ
ejpam-1535	961	4	∨-premorphisms	∨-premorphism	VERB
ejpam-1535	961	5	form	form	VERB
ejpam-1535	961	6	a	a	DET
ejpam-1535	961	7	category	category	NOUN
ejpam-1535	961	8	.	.	PUNCT
ejpam-1535	962	1	we	we	PRON
ejpam-1535	962	2	then	then	ADV
ejpam-1535	962	3	have	have	VERB
ejpam-1535	962	4	an	an	DET
ejpam-1535	962	5	immediate	immediate	ADJ
ejpam-1535	962	6	corollary	corollary	NOUN
ejpam-1535	962	7	to	to	AUX
ejpam-1535	962	8	theorem	theorem	VERB
ejpam-1535	962	9	5	5	NUM
ejpam-1535	962	10	:	:	PUNCT
ejpam-1535	962	11	theorem	theorem	NOUN
ejpam-1535	962	12	10	10	NUM
ejpam-1535	962	13	(	(	PUNCT
ejpam-1535	962	14	[	[	X
ejpam-1535	962	15	27	27	NUM
ejpam-1535	962	16	,	,	PUNCT
ejpam-1535	962	17	theorem	theorem	VERB
ejpam-1535	962	18	3.5(i	3.5(i	NUM
ejpam-1535	962	19	)	)	PUNCT
ejpam-1535	962	20	]	]	PUNCT
ejpam-1535	962	21	)	)	PUNCT
ejpam-1535	962	22	.	.	PUNCT
ejpam-1535	963	1	the	the	DET
ejpam-1535	963	2	category	category	NOUN
ejpam-1535	963	3	of	of	ADP
ejpam-1535	963	4	inverse	inverse	NOUN
ejpam-1535	963	5	semigroups	semigroup	NOUN
ejpam-1535	963	6	and	and	CCONJ
ejpam-1535	963	7	∨-premorphisms	∨-premorphism	NOUN
ejpam-1535	963	8	is	be	AUX
ejpam-1535	963	9	isomorphic	isomorphic	ADJ
ejpam-1535	963	10	to	to	ADP
ejpam-1535	963	11	the	the	DET
ejpam-1535	963	12	category	category	NOUN
ejpam-1535	963	13	of	of	ADP
ejpam-1535	963	14	inductive	inductive	ADJ
ejpam-1535	963	15	groupoids	groupoid	NOUN
ejpam-1535	963	16	and	and	CCONJ
ejpam-1535	963	17	ordered	order	VERB
ejpam-1535	963	18	functors	functor	NOUN
ejpam-1535	963	19	.	.	PUNCT
ejpam-1535	964	1	this	this	PRON
ejpam-1535	964	2	is	be	AUX
ejpam-1535	964	3	of	of	ADP
ejpam-1535	964	4	course	course	NOUN
ejpam-1535	964	5	the	the	DET
ejpam-1535	964	6	first	first	ADJ
ejpam-1535	964	7	part	part	NOUN
ejpam-1535	964	8	of	of	ADP
ejpam-1535	964	9	the	the	DET
ejpam-1535	964	10	original	original	ADJ
ejpam-1535	964	11	esn	esn	PROPN
ejpam-1535	964	12	theorem	theorem	PROPN
ejpam-1535	964	13	(	(	PUNCT
ejpam-1535	964	14	theorem	theorem	NOUN
ejpam-1535	964	15	1	1	NUM
ejpam-1535	964	16	)	)	PUNCT
ejpam-1535	964	17	.	.	PUNCT
ejpam-1535	965	1	8.3	8.3	NUM
ejpam-1535	965	2	.	.	PUNCT
ejpam-1535	966	1	morphisms	morphism	NOUN
ejpam-1535	966	2	and	and	CCONJ
ejpam-1535	966	3	inductive	inductive	ADJ
ejpam-1535	966	4	functors	functor	NOUN
ejpam-1535	966	5	we	we	PRON
ejpam-1535	966	6	now	now	ADV
ejpam-1535	966	7	take	take	VERB
ejpam-1535	966	8	the	the	DET
ejpam-1535	966	9	functions	function	NOUN
ejpam-1535	966	10	between	between	ADP
ejpam-1535	966	11	inverse	inverse	NOUN
ejpam-1535	966	12	semigroups	semigroup	NOUN
ejpam-1535	966	13	to	to	PART
ejpam-1535	966	14	be	be	AUX
ejpam-1535	966	15	(	(	PUNCT
ejpam-1535	966	16	inverse	inverse	NOUN
ejpam-1535	966	17	semigroup	semigroup	NOUN
ejpam-1535	966	18	)	)	PUNCT
ejpam-1535	966	19	morphisms	morphism	VERB
ejpam-1535	966	20	.	.	PUNCT
ejpam-1535	967	1	we	we	PRON
ejpam-1535	967	2	make	make	VERB
ejpam-1535	967	3	the	the	DET
ejpam-1535	967	4	following	follow	VERB
ejpam-1535	967	5	very	very	ADV
ejpam-1535	967	6	easy	easy	ADJ
ejpam-1535	967	7	observation	observation	NOUN
ejpam-1535	967	8	:	:	PUNCT
ejpam-1535	967	9	proposition	proposition	NOUN
ejpam-1535	967	10	11	11	NUM
ejpam-1535	967	11	(	(	PUNCT
ejpam-1535	967	12	[	[	X
ejpam-1535	967	13	f	f	X
ejpam-1535	967	14	]	]	X
ejpam-1535	967	15	)	)	PUNCT
ejpam-1535	967	16	.	.	PUNCT
ejpam-1535	968	1	inverse	inverse	NOUN
ejpam-1535	968	2	semigroups	semigroup	NOUN
ejpam-1535	968	3	and	and	CCONJ
ejpam-1535	968	4	morphisms	morphism	NOUN
ejpam-1535	968	5	form	form	VERB
ejpam-1535	968	6	a	a	DET
ejpam-1535	968	7	category	category	NOUN
ejpam-1535	968	8	.	.	PUNCT
ejpam-1535	969	1	the	the	DET
ejpam-1535	969	2	functions	function	NOUN
ejpam-1535	969	3	between	between	ADP
ejpam-1535	969	4	the	the	DET
ejpam-1535	969	5	corresponding	corresponding	ADJ
ejpam-1535	969	6	inductive	inductive	ADJ
ejpam-1535	969	7	groupoids	groupoid	NOUN
ejpam-1535	969	8	will	will	AUX
ejpam-1535	969	9	be	be	AUX
ejpam-1535	969	10	inductive	inductive	ADJ
ejpam-1535	969	11	functors	functor	NOUN
ejpam-1535	969	12	,	,	PUNCT
ejpam-1535	969	13	just	just	ADV
ejpam-1535	969	14	as	as	ADP
ejpam-1535	969	15	in	in	ADP
ejpam-1535	969	16	the	the	DET
ejpam-1535	969	17	case	case	NOUN
ejpam-1535	969	18	of	of	ADP
ejpam-1535	969	19	restriction	restriction	NOUN
ejpam-1535	969	20	semigroups	semigroup	NOUN
ejpam-1535	969	21	and	and	CCONJ
ejpam-1535	969	22	inductive	inductive	ADJ
ejpam-1535	969	23	categories	category	NOUN
ejpam-1535	969	24	.	.	PUNCT
ejpam-1535	970	1	we	we	PRON
ejpam-1535	970	2	first	first	ADV
ejpam-1535	970	3	note	note	VERB
ejpam-1535	970	4	the	the	DET
ejpam-1535	970	5	following	following	NOUN
ejpam-1535	970	6	:	:	PUNCT
ejpam-1535	970	7	lemma	lemma	PROPN
ejpam-1535	970	8	24	24	NUM
ejpam-1535	970	9	.	.	PUNCT
ejpam-1535	971	1	let	let	VERB
ejpam-1535	971	2	g	g	NOUN
ejpam-1535	971	3	and	and	CCONJ
ejpam-1535	971	4	h	h	PROPN
ejpam-1535	971	5	be	be	AUX
ejpam-1535	971	6	groupoids	groupoid	NOUN
ejpam-1535	971	7	and	and	CCONJ
ejpam-1535	971	8	let	let	VERB
ejpam-1535	971	9	φ	φ	NOUN
ejpam-1535	971	10	:	:	PUNCT
ejpam-1535	971	11	g	g	PROPN
ejpam-1535	971	12	→	→	SYM
ejpam-1535	971	13	h	h	NOUN
ejpam-1535	971	14	be	be	AUX
ejpam-1535	971	15	a	a	DET
ejpam-1535	971	16	functor	functor	NOUN
ejpam-1535	971	17	,	,	PUNCT
ejpam-1535	971	18	in	in	ADP
ejpam-1535	971	19	the	the	DET
ejpam-1535	971	20	sense	sense	NOUN
ejpam-1535	971	21	of	of	ADP
ejpam-1535	971	22	definition	definition	NOUN
ejpam-1535	971	23	14	14	NUM
ejpam-1535	971	24	.	.	PUNCT
ejpam-1535	972	1	then	then	ADV
ejpam-1535	972	2	(	(	PUNCT
ejpam-1535	972	3	gφ)−1	gφ)−1	NOUN
ejpam-1535	972	4	=	=	SYM
ejpam-1535	972	5	g−1φ	g−1φ	NOUN
ejpam-1535	972	6	.	.	PUNCT
ejpam-1535	973	1	proof	proof	NOUN
ejpam-1535	973	2	.	.	PUNCT
ejpam-1535	974	1	we	we	PRON
ejpam-1535	974	2	know	know	VERB
ejpam-1535	974	3	that	that	SCONJ
ejpam-1535	974	4	∃g	∃g	PRON
ejpam-1535	974	5	·	·	PUNCT
ejpam-1535	974	6	g−1	g−1	ADJ
ejpam-1535	974	7	,	,	PUNCT
ejpam-1535	974	8	so	so	ADV
ejpam-1535	974	9	∃(gφ	∃(gφ	ADJ
ejpam-1535	974	10	)	)	PUNCT
ejpam-1535	974	11	·	·	PUNCT
ejpam-1535	974	12	(	(	PUNCT
ejpam-1535	974	13	g−1φ	g−1φ	NOUN
ejpam-1535	974	14	)	)	PUNCT
ejpam-1535	974	15	,	,	PUNCT
ejpam-1535	974	16	by	by	ADP
ejpam-1535	974	17	(	(	PUNCT
ejpam-1535	974	18	f	f	NOUN
ejpam-1535	974	19	)	)	PUNCT
ejpam-1535	974	20	.	.	PUNCT
ejpam-1535	975	1	moreover	moreover	ADV
ejpam-1535	975	2	,	,	PUNCT
ejpam-1535	975	3	we	we	PRON
ejpam-1535	975	4	have	have	VERB
ejpam-1535	975	5	(	(	PUNCT
ejpam-1535	975	6	gφ	gφ	NOUN
ejpam-1535	975	7	)	)	PUNCT
ejpam-1535	975	8	·	·	PUNCT
ejpam-1535	976	1	(	(	PUNCT
ejpam-1535	976	2	g−1φ	g−1φ	X
ejpam-1535	976	3	)	)	PUNCT
ejpam-1535	976	4	=	=	SYM
ejpam-1535	976	5	(	(	PUNCT
ejpam-1535	976	6	g	g	NOUN
ejpam-1535	976	7	·	·	PUNCT
ejpam-1535	976	8	g−1)φ	g−1)φ	NOUN
ejpam-1535	977	1	=	=	SYM
ejpam-1535	977	2	d(g)φ	d(g)φ	PROPN
ejpam-1535	977	3	=	=	SYM
ejpam-1535	977	4	d(gφ	d(gφ	PROPN
ejpam-1535	977	5	)	)	PUNCT
ejpam-1535	977	6	,	,	PUNCT
ejpam-1535	977	7	by	by	ADP
ejpam-1535	977	8	lemma	lemma	PROPN
ejpam-1535	977	9	13	13	NUM
ejpam-1535	977	10	.	.	PUNCT
ejpam-1535	978	1	similarly	similarly	ADV
ejpam-1535	978	2	,	,	PUNCT
ejpam-1535	978	3	we	we	PRON
ejpam-1535	978	4	have	have	VERB
ejpam-1535	978	5	that	that	DET
ejpam-1535	978	6	∃(g−1φ	∃(g−1φ	NOUN
ejpam-1535	978	7	)	)	PUNCT
ejpam-1535	978	8	·	·	PUNCT
ejpam-1535	979	1	(	(	PUNCT
ejpam-1535	979	2	gφ	gφ	NOUN
ejpam-1535	979	3	)	)	PUNCT
ejpam-1535	979	4	and	and	CCONJ
ejpam-1535	979	5	(	(	PUNCT
ejpam-1535	979	6	g−1φ	g−1φ	NOUN
ejpam-1535	979	7	)	)	PUNCT
ejpam-1535	979	8	·	·	PUNCT
ejpam-1535	979	9	(	(	PUNCT
ejpam-1535	979	10	gφ	gφ	NOUN
ejpam-1535	979	11	)	)	PUNCT
ejpam-1535	979	12	=	=	PUNCT
ejpam-1535	980	1	r(gφ	r(gφ	NOUN
ejpam-1535	980	2	)	)	PUNCT
ejpam-1535	980	3	.	.	PUNCT
ejpam-1535	981	1	the	the	DET
ejpam-1535	981	2	result	result	NOUN
ejpam-1535	981	3	then	then	ADV
ejpam-1535	981	4	follows	follow	VERB
ejpam-1535	981	5	from	from	ADP
ejpam-1535	981	6	lemma	lemma	PROPN
ejpam-1535	981	7	18(b	18(b	NUM
ejpam-1535	981	8	)	)	PUNCT
ejpam-1535	981	9	.	.	PUNCT
ejpam-1535	982	1	we	we	PRON
ejpam-1535	982	2	see	see	VERB
ejpam-1535	982	3	then	then	ADV
ejpam-1535	982	4	that	that	SCONJ
ejpam-1535	982	5	functors	functor	NOUN
ejpam-1535	982	6	are	be	AUX
ejpam-1535	982	7	suitable	suitable	ADJ
ejpam-1535	982	8	functions	function	NOUN
ejpam-1535	982	9	to	to	PART
ejpam-1535	982	10	consider	consider	VERB
ejpam-1535	982	11	between	between	ADP
ejpam-1535	982	12	groupoids	groupoid	NOUN
ejpam-1535	982	13	;	;	PUNCT
ejpam-1535	982	14	inductive	inductive	ADJ
ejpam-1535	982	15	functors	functor	NOUN
ejpam-1535	982	16	are	be	AUX
ejpam-1535	982	17	therefore	therefore	ADV
ejpam-1535	982	18	appropriate	appropriate	ADJ
ejpam-1535	982	19	arrows	arrow	NOUN
ejpam-1535	982	20	to	to	PART
ejpam-1535	982	21	consider	consider	VERB
ejpam-1535	982	22	between	between	ADP
ejpam-1535	982	23	inductive	inductive	ADJ
ejpam-1535	982	24	groupoids	groupoid	NOUN
ejpam-1535	982	25	.	.	PUNCT
ejpam-1535	983	1	the	the	DET
ejpam-1535	983	2	following	follow	VERB
ejpam-1535	983	3	is	be	AUX
ejpam-1535	983	4	an	an	DET
ejpam-1535	983	5	easy	easy	ADJ
ejpam-1535	983	6	consequence	consequence	NOUN
ejpam-1535	983	7	of	of	ADP
ejpam-1535	983	8	proposition	proposition	NOUN
ejpam-1535	983	9	7	7	NUM
ejpam-1535	983	10	:	:	PUNCT
ejpam-1535	983	11	proposition	proposition	NOUN
ejpam-1535	983	12	12	12	NUM
ejpam-1535	983	13	(	(	PUNCT
ejpam-1535	983	14	[	[	X
ejpam-1535	983	15	f	f	X
ejpam-1535	983	16	]	]	X
ejpam-1535	983	17	)	)	PUNCT
ejpam-1535	983	18	.	.	PUNCT
ejpam-1535	984	1	inductive	inductive	ADJ
ejpam-1535	984	2	groupoids	groupoid	NOUN
ejpam-1535	984	3	and	and	CCONJ
ejpam-1535	984	4	inductive	inductive	ADJ
ejpam-1535	984	5	functors	functors	PROPN
ejpam-1535	984	6	form	form	VERB
ejpam-1535	984	7	a	a	DET
ejpam-1535	984	8	category	category	NOUN
ejpam-1535	984	9	.	.	PUNCT
ejpam-1535	985	1	the	the	DET
ejpam-1535	985	2	appropriate	appropriate	ADJ
ejpam-1535	985	3	specialisations	specialisation	NOUN
ejpam-1535	985	4	of	of	ADP
ejpam-1535	985	5	propositions	proposition	NOUN
ejpam-1535	985	6	8	8	NUM
ejpam-1535	985	7	,	,	PUNCT
ejpam-1535	985	8	9	9	NUM
ejpam-1535	985	9	and	and	CCONJ
ejpam-1535	985	10	10	10	NUM
ejpam-1535	985	11	are	be	AUX
ejpam-1535	985	12	clear	clear	ADJ
ejpam-1535	985	13	:	:	PUNCT
ejpam-1535	985	14	proposition	proposition	NOUN
ejpam-1535	985	15	13	13	NUM
ejpam-1535	985	16	.	.	PUNCT
ejpam-1535	986	1	let	let	VERB
ejpam-1535	986	2	ϕ	ϕ	NOUN
ejpam-1535	986	3	:	:	PUNCT
ejpam-1535	986	4	s→	s→	PROPN
ejpam-1535	986	5	t	t	NOUN
ejpam-1535	986	6	be	be	AUX
ejpam-1535	986	7	a	a	DET
ejpam-1535	986	8	morphism	morphism	NOUN
ejpam-1535	986	9	between	between	ADP
ejpam-1535	986	10	inverse	inverse	NOUN
ejpam-1535	986	11	semigroups	semigroup	NOUN
ejpam-1535	986	12	s	s	PART
ejpam-1535	986	13	and	and	CCONJ
ejpam-1535	986	14	t.	t.	NOUN
ejpam-1535	986	15	we	we	PRON
ejpam-1535	986	16	define	define	VERB
ejpam-1535	986	17	φ	φ	NOUN
ejpam-1535	986	18	:	:	PUNCT
ejpam-1535	987	1	=	=	SYM
ejpam-1535	987	2	g(ϕ	g(ϕ	PROPN
ejpam-1535	987	3	)	)	PUNCT
ejpam-1535	987	4	:	:	PUNCT
ejpam-1535	987	5	g(s)→	g(s)→	NOUN
ejpam-1535	987	6	g(t	g(t	PROPN
ejpam-1535	987	7	)	)	PUNCT
ejpam-1535	987	8	to	to	PART
ejpam-1535	987	9	be	be	AUX
ejpam-1535	987	10	the	the	DET
ejpam-1535	987	11	same	same	ADJ
ejpam-1535	987	12	function	function	NOUN
ejpam-1535	987	13	on	on	ADP
ejpam-1535	987	14	the	the	DET
ejpam-1535	987	15	underlying	underlie	VERB
ejpam-1535	987	16	sets	set	NOUN
ejpam-1535	987	17	.	.	PUNCT
ejpam-1535	988	1	then	then	ADV
ejpam-1535	988	2	φ	φ	PROPN
ejpam-1535	988	3	is	be	AUX
ejpam-1535	988	4	an	an	DET
ejpam-1535	988	5	inductive	inductive	ADJ
ejpam-1535	988	6	functor	functor	NOUN
ejpam-1535	988	7	with	with	ADP
ejpam-1535	988	8	respect	respect	NOUN
ejpam-1535	988	9	to	to	ADP
ejpam-1535	988	10	the	the	DET
ejpam-1535	988	11	restricted	restricted	ADJ
ejpam-1535	988	12	products	product	NOUN
ejpam-1535	988	13	in	in	ADP
ejpam-1535	988	14	g(s	g(s	NOUN
ejpam-1535	988	15	)	)	PUNCT
ejpam-1535	988	16	and	and	CCONJ
ejpam-1535	988	17	g(t	g(t	PROPN
ejpam-1535	988	18	)	)	PUNCT
ejpam-1535	988	19	.	.	PUNCT
ejpam-1535	989	1	references	reference	NOUN
ejpam-1535	989	2	447	447	NUM
ejpam-1535	989	3	proposition	proposition	NOUN
ejpam-1535	989	4	14	14	NUM
ejpam-1535	989	5	.	.	PUNCT
ejpam-1535	990	1	let	let	VERB
ejpam-1535	990	2	φ	φ	NOUN
ejpam-1535	990	3	:	:	PUNCT
ejpam-1535	990	4	g	g	PROPN
ejpam-1535	990	5	→	→	SYM
ejpam-1535	990	6	h	h	NOUN
ejpam-1535	990	7	be	be	AUX
ejpam-1535	990	8	an	an	DET
ejpam-1535	990	9	inductive	inductive	ADJ
ejpam-1535	990	10	functor	functor	NOUN
ejpam-1535	990	11	of	of	ADP
ejpam-1535	990	12	inductive	inductive	ADJ
ejpam-1535	990	13	groupoids	groupoids	PROPN
ejpam-1535	990	14	g	g	PROPN
ejpam-1535	990	15	and	and	CCONJ
ejpam-1535	990	16	h.	h.	PROPN
ejpam-1535	990	17	we	we	PRON
ejpam-1535	990	18	define	define	VERB
ejpam-1535	990	19	φ	φ	NOUN
ejpam-1535	990	20	:	:	PUNCT
ejpam-1535	990	21	=	=	SYM
ejpam-1535	990	22	s(φ	s(φ	PROPN
ejpam-1535	990	23	)	)	PUNCT
ejpam-1535	990	24	:	:	PUNCT
ejpam-1535	991	1	i(g	i(g	NOUN
ejpam-1535	991	2	)	)	PUNCT
ejpam-1535	991	3	→	→	SYM
ejpam-1535	991	4	i(h	i(h	NOUN
ejpam-1535	991	5	)	)	PUNCT
ejpam-1535	991	6	to	to	PART
ejpam-1535	991	7	be	be	AUX
ejpam-1535	991	8	the	the	DET
ejpam-1535	991	9	same	same	ADJ
ejpam-1535	991	10	function	function	NOUN
ejpam-1535	991	11	on	on	ADP
ejpam-1535	991	12	the	the	DET
ejpam-1535	991	13	underlying	underlie	VERB
ejpam-1535	991	14	sets	set	NOUN
ejpam-1535	991	15	.	.	PUNCT
ejpam-1535	992	1	then	then	ADV
ejpam-1535	992	2	φ	φ	PROPN
ejpam-1535	992	3	is	be	AUX
ejpam-1535	992	4	a	a	DET
ejpam-1535	992	5	morphism	morphism	NOUN
ejpam-1535	992	6	with	with	ADP
ejpam-1535	992	7	respect	respect	NOUN
ejpam-1535	992	8	to	to	ADP
ejpam-1535	992	9	the	the	DET
ejpam-1535	992	10	pseudoproducts	pseudoproduct	NOUN
ejpam-1535	992	11	in	in	ADP
ejpam-1535	992	12	i(g	i(g	NOUN
ejpam-1535	992	13	)	)	PUNCT
ejpam-1535	992	14	and	and	CCONJ
ejpam-1535	992	15	i(h	i(h	NOUN
ejpam-1535	992	16	)	)	PUNCT
ejpam-1535	992	17	.	.	PUNCT
ejpam-1535	993	1	proposition	proposition	NOUN
ejpam-1535	993	2	15	15	NUM
ejpam-1535	993	3	.	.	PUNCT
ejpam-1535	994	1	if	if	SCONJ
ejpam-1535	994	2	ϕ	ϕ	NOUN
ejpam-1535	994	3	:	:	PUNCT
ejpam-1535	994	4	s	s	X
ejpam-1535	994	5	→	→	SYM
ejpam-1535	994	6	t	t	PROPN
ejpam-1535	994	7	is	be	AUX
ejpam-1535	994	8	a	a	DET
ejpam-1535	994	9	morphism	morphism	NOUN
ejpam-1535	994	10	between	between	ADP
ejpam-1535	994	11	inverse	inverse	NOUN
ejpam-1535	994	12	semigroups	semigroup	NOUN
ejpam-1535	994	13	and	and	CCONJ
ejpam-1535	994	14	φ	φ	NOUN
ejpam-1535	994	15	:	:	PUNCT
ejpam-1535	994	16	g	g	NOUN
ejpam-1535	994	17	→	→	SYM
ejpam-1535	994	18	h	h	NOUN
ejpam-1535	994	19	is	be	AUX
ejpam-1535	994	20	an	an	DET
ejpam-1535	994	21	inductive	inductive	ADJ
ejpam-1535	994	22	functor	functor	NOUN
ejpam-1535	994	23	between	between	ADP
ejpam-1535	994	24	inductive	inductive	ADJ
ejpam-1535	994	25	groupoids	groupoid	NOUN
ejpam-1535	994	26	,	,	PUNCT
ejpam-1535	994	27	then	then	ADV
ejpam-1535	994	28	i(g(ϕ	i(g(ϕ	PROPN
ejpam-1535	994	29	)	)	PUNCT
ejpam-1535	994	30	)	)	PUNCT
ejpam-1535	995	1	=	=	SYM
ejpam-1535	995	2	ϕ	ϕ	NOUN
ejpam-1535	995	3	and	and	CCONJ
ejpam-1535	995	4	g(i(φ	g(i(φ	NOUN
ejpam-1535	995	5	)	)	PUNCT
ejpam-1535	995	6	)	)	PUNCT
ejpam-1535	996	1	=	=	PUNCT
ejpam-1535	996	2	φ	φ	X
ejpam-1535	996	3	.	.	PUNCT
ejpam-1535	997	1	moreover	moreover	ADV
ejpam-1535	997	2	,	,	PUNCT
ejpam-1535	997	3	if	if	SCONJ
ejpam-1535	997	4	ϕ′	ϕ′	PRON
ejpam-1535	997	5	:	:	PUNCT
ejpam-1535	997	6	t	t	PROPN
ejpam-1535	997	7	→	→	SYM
ejpam-1535	997	8	t	t	PROPN
ejpam-1535	997	9	′	′	NOUN
ejpam-1535	997	10	is	be	AUX
ejpam-1535	997	11	another	another	DET
ejpam-1535	997	12	morphism	morphism	NOUN
ejpam-1535	997	13	of	of	ADP
ejpam-1535	997	14	inverse	inverse	NOUN
ejpam-1535	997	15	semigroups	semigroup	NOUN
ejpam-1535	997	16	,	,	PUNCT
ejpam-1535	997	17	and	and	CCONJ
ejpam-1535	997	18	φ′	φ′	NUM
ejpam-1535	997	19	:	:	PUNCT
ejpam-1535	997	20	h	h	NOUN
ejpam-1535	997	21	→	→	SYM
ejpam-1535	997	22	h	h	NOUN
ejpam-1535	997	23	′	′	NOUN
ejpam-1535	997	24	is	be	AUX
ejpam-1535	997	25	another	another	DET
ejpam-1535	997	26	inductive	inductive	ADJ
ejpam-1535	997	27	functor	functor	PROPN
ejpam-1535	997	28	of	of	ADP
ejpam-1535	997	29	inductive	inductive	ADJ
ejpam-1535	997	30	groupoids	groupoid	NOUN
ejpam-1535	997	31	,	,	PUNCT
ejpam-1535	997	32	then	then	ADV
ejpam-1535	997	33	g(ϕϕ′	g(ϕϕ′	ADJ
ejpam-1535	997	34	)	)	PUNCT
ejpam-1535	997	35	=	=	PUNCT
ejpam-1535	997	36	g(ϕ)g(ϕ′	g(ϕ)g(ϕ′	NOUN
ejpam-1535	997	37	)	)	PUNCT
ejpam-1535	997	38	and	and	CCONJ
ejpam-1535	997	39	i(φφ′	i(φφ′	PROPN
ejpam-1535	997	40	)	)	PUNCT
ejpam-1535	997	41	=	=	SYM
ejpam-1535	997	42	i(φ)i(φ′	i(φ)i(φ′	NOUN
ejpam-1535	997	43	)	)	PUNCT
ejpam-1535	997	44	.	.	PUNCT
ejpam-1535	998	1	thus	thus	ADV
ejpam-1535	998	2	i	i	PRON
ejpam-1535	998	3	(	(	PUNCT
ejpam-1535	998	4	·	·	PUNCT
ejpam-1535	998	5	)	)	PUNCT
ejpam-1535	998	6	and	and	CCONJ
ejpam-1535	998	7	g	g	PROPN
ejpam-1535	998	8	(	(	PUNCT
ejpam-1535	998	9	·	·	PUNCT
ejpam-1535	998	10	)	)	PUNCT
ejpam-1535	998	11	form	form	VERB
ejpam-1535	998	12	a	a	DET
ejpam-1535	998	13	pair	pair	NOUN
ejpam-1535	998	14	of	of	ADP
ejpam-1535	998	15	mutually	mutually	ADV
ejpam-1535	998	16	inverse	inverse	ADJ
ejpam-1535	998	17	functors‡‡	functors‡‡	NOUN
ejpam-1535	998	18	between	between	ADP
ejpam-1535	998	19	the	the	DET
ejpam-1535	998	20	category	category	NOUN
ejpam-1535	998	21	of	of	ADP
ejpam-1535	998	22	inverse	inverse	NOUN
ejpam-1535	998	23	semigroups	semigroup	NOUN
ejpam-1535	998	24	and	and	CCONJ
ejpam-1535	998	25	morphisms	morphism	NOUN
ejpam-1535	998	26	,	,	PUNCT
ejpam-1535	998	27	and	and	CCONJ
ejpam-1535	998	28	that	that	PRON
ejpam-1535	998	29	of	of	ADP
ejpam-1535	998	30	inductive	inductive	ADJ
ejpam-1535	998	31	groupoids	groupoid	NOUN
ejpam-1535	998	32	and	and	CCONJ
ejpam-1535	998	33	inductive	inductive	ADJ
ejpam-1535	998	34	functors	functor	NOUN
ejpam-1535	998	35	.	.	PUNCT
ejpam-1535	999	1	we	we	PRON
ejpam-1535	999	2	may	may	AUX
ejpam-1535	999	3	therefore	therefore	ADV
ejpam-1535	999	4	write	write	VERB
ejpam-1535	999	5	down	down	ADP
ejpam-1535	999	6	the	the	DET
ejpam-1535	999	7	following	follow	VERB
ejpam-1535	999	8	corollary	corollary	NOUN
ejpam-1535	999	9	to	to	ADP
ejpam-1535	999	10	theorem	theorem	NOUN
ejpam-1535	999	11	6	6	NUM
ejpam-1535	999	12	in	in	ADP
ejpam-1535	999	13	the	the	DET
ejpam-1535	999	14	inverse	inverse	NOUN
ejpam-1535	999	15	case	case	NOUN
ejpam-1535	999	16	:	:	PUNCT
ejpam-1535	999	17	theorem	theorem	VERB
ejpam-1535	999	18	11	11	NUM
ejpam-1535	999	19	(	(	PUNCT
ejpam-1535	999	20	[	[	X
ejpam-1535	999	21	27	27	NUM
ejpam-1535	999	22	,	,	PUNCT
ejpam-1535	999	23	theorem	theorem	ADJ
ejpam-1535	999	24	3.5(ii	3.5(ii	NUM
ejpam-1535	999	25	)	)	PUNCT
ejpam-1535	999	26	]	]	PUNCT
ejpam-1535	999	27	)	)	PUNCT
ejpam-1535	999	28	.	.	PUNCT
ejpam-1535	1000	1	the	the	DET
ejpam-1535	1000	2	category	category	NOUN
ejpam-1535	1000	3	of	of	ADP
ejpam-1535	1000	4	inverse	inverse	NOUN
ejpam-1535	1000	5	semigroups	semigroup	NOUN
ejpam-1535	1000	6	and	and	CCONJ
ejpam-1535	1000	7	morphisms	morphism	NOUN
ejpam-1535	1000	8	is	be	AUX
ejpam-1535	1000	9	isomorphic	isomorphic	ADJ
ejpam-1535	1000	10	to	to	ADP
ejpam-1535	1000	11	the	the	DET
ejpam-1535	1000	12	category	category	NOUN
ejpam-1535	1000	13	of	of	ADP
ejpam-1535	1000	14	inductive	inductive	ADJ
ejpam-1535	1000	15	groupoids	groupoid	NOUN
ejpam-1535	1000	16	and	and	CCONJ
ejpam-1535	1000	17	inductive	inductive	ADJ
ejpam-1535	1000	18	functors	functor	NOUN
ejpam-1535	1000	19	.	.	PUNCT
ejpam-1535	1001	1	this	this	PRON
ejpam-1535	1001	2	is	be	AUX
ejpam-1535	1001	3	,	,	PUNCT
ejpam-1535	1001	4	of	of	ADP
ejpam-1535	1001	5	course	course	NOUN
ejpam-1535	1001	6	,	,	PUNCT
ejpam-1535	1001	7	the	the	DET
ejpam-1535	1001	8	second	second	ADJ
ejpam-1535	1001	9	half	half	NOUN
ejpam-1535	1001	10	of	of	ADP
ejpam-1535	1001	11	the	the	DET
ejpam-1535	1001	12	original	original	ADJ
ejpam-1535	1001	13	esn	esn	PROPN
ejpam-1535	1001	14	theorem	theorem	PROPN
ejpam-1535	1001	15	(	(	PUNCT
ejpam-1535	1001	16	theorem	theorem	NOUN
ejpam-1535	1001	17	1	1	NUM
ejpam-1535	1001	18	)	)	PUNCT
ejpam-1535	1001	19	.	.	PUNCT
ejpam-1535	1002	1	acknowledgements	acknowledgement	NOUN
ejpam-1535	1002	2	this	this	DET
ejpam-1535	1002	3	article	article	NOUN
ejpam-1535	1002	4	was	be	AUX
ejpam-1535	1002	5	begun	begin	VERB
ejpam-1535	1002	6	when	when	SCONJ
ejpam-1535	1002	7	the	the	DET
ejpam-1535	1002	8	author	author	NOUN
ejpam-1535	1002	9	was	be	AUX
ejpam-1535	1002	10	a	a	DET
ejpam-1535	1002	11	post	post	ADJ
ejpam-1535	1002	12	-	-	ADJ
ejpam-1535	1002	13	doctoral	doctoral	ADJ
ejpam-1535	1002	14	researcher	researcher	NOUN
ejpam-1535	1002	15	at	at	ADP
ejpam-1535	1002	16	the	the	DET
ejpam-1535	1002	17	centro	centro	X
ejpam-1535	1002	18	de	de	X
ejpam-1535	1002	19	álgebra	álgebra	PROPN
ejpam-1535	1002	20	da	da	PROPN
ejpam-1535	1002	21	universidade	universidade	PROPN
ejpam-1535	1002	22	de	de	PROPN
ejpam-1535	1002	23	lisboa	lisboa	PROPN
ejpam-1535	1002	24	,	,	PUNCT
ejpam-1535	1002	25	funded	fund	VERB
ejpam-1535	1002	26	by	by	ADP
ejpam-1535	1002	27	fct	fct	ADJ
ejpam-1535	1002	28	post	post	ADJ
ejpam-1535	1002	29	-	-	ADJ
ejpam-1535	1002	30	doctoral	doctoral	ADJ
ejpam-1535	1002	31	research	research	NOUN
ejpam-1535	1002	32	grant	grant	NOUN
ejpam-1535	1002	33	sfrh	sfrh	NOUN
ejpam-1535	1002	34	/	/	SYM
ejpam-1535	1002	35	bpd/34698/2007	bpd/34698/2007	ADJ
ejpam-1535	1002	36	,	,	PUNCT
ejpam-1535	1002	37	and	and	CCONJ
ejpam-1535	1002	38	also	also	ADV
ejpam-1535	1002	39	project	project	VERB
ejpam-1535	1002	40	pocti/	pocti/	NUM
ejpam-1535	1002	41	0143/2007	0143/2007	NUM
ejpam-1535	1002	42	of	of	ADP
ejpam-1535	1002	43	caul	caul	NOUN
ejpam-1535	1002	44	,	,	PUNCT
ejpam-1535	1002	45	financed	finance	VERB
ejpam-1535	1002	46	by	by	ADP
ejpam-1535	1002	47	fct	fct	NOUN
ejpam-1535	1002	48	and	and	CCONJ
ejpam-1535	1002	49	feder	feder	PROPN
ejpam-1535	1002	50	.	.	PUNCT
ejpam-1535	1003	1	it	it	PRON
ejpam-1535	1003	2	was	be	AUX
ejpam-1535	1003	3	completed	complete	VERB
ejpam-1535	1003	4	after	after	SCONJ
ejpam-1535	1003	5	the	the	DET
ejpam-1535	1003	6	author	author	NOUN
ejpam-1535	1003	7	had	have	AUX
ejpam-1535	1003	8	moved	move	VERB
ejpam-1535	1003	9	to	to	ADP
ejpam-1535	1003	10	the	the	DET
ejpam-1535	1003	11	mathematical	mathematical	ADJ
ejpam-1535	1003	12	institute	institute	NOUN
ejpam-1535	1003	13	of	of	ADP
ejpam-1535	1003	14	the	the	DET
ejpam-1535	1003	15	university	university	NOUN
ejpam-1535	1003	16	of	of	ADP
ejpam-1535	1003	17	oxford	oxford	PROPN
ejpam-1535	1003	18	to	to	PART
ejpam-1535	1003	19	take	take	VERB
ejpam-1535	1003	20	up	up	ADP
ejpam-1535	1003	21	a	a	DET
ejpam-1535	1003	22	post	post	ADJ
ejpam-1535	1003	23	-	-	ADJ
ejpam-1535	1003	24	doctoral	doctoral	ADJ
ejpam-1535	1003	25	post	post	NOUN
ejpam-1535	1003	26	funded	fund	VERB
ejpam-1535	1003	27	by	by	ADP
ejpam-1535	1003	28	research	research	NOUN
ejpam-1535	1003	29	project	project	NOUN
ejpam-1535	1003	30	grant	grant	VERB
ejpam-1535	1003	31	f/08	f/08	ADJ
ejpam-1535	1003	32	772	772	NUM
ejpam-1535	1003	33	/	/	SYM
ejpam-1535	1003	34	f	f	NOUN
ejpam-1535	1003	35	from	from	ADP
ejpam-1535	1003	36	the	the	DET
ejpam-1535	1003	37	leverhulme	leverhulme	PROPN
ejpam-1535	1003	38	trust	trust	NOUN
ejpam-1535	1003	39	.	.	PUNCT
ejpam-1535	1004	1	references	reference	NOUN
ejpam-1535	1004	2	[	[	X
ejpam-1535	1004	3	1	1	X
ejpam-1535	1004	4	]	]	PUNCT
ejpam-1535	1004	5	s.	s.	PROPN
ejpam-1535	1004	6	armstrong	armstrong	PROPN
ejpam-1535	1004	7	,	,	PUNCT
ejpam-1535	1004	8	the	the	DET
ejpam-1535	1004	9	structure	structure	NOUN
ejpam-1535	1004	10	of	of	ADP
ejpam-1535	1004	11	type	type	NOUN
ejpam-1535	1004	12	a	a	DET
ejpam-1535	1004	13	semigroups	semigroup	NOUN
ejpam-1535	1004	14	,	,	PUNCT
ejpam-1535	1004	15	semigroup	semigroup	PROPN
ejpam-1535	1004	16	forum	forum	PROPN
ejpam-1535	1004	17	29	29	NUM
ejpam-1535	1004	18	(	(	PUNCT
ejpam-1535	1004	19	1984	1984	NUM
ejpam-1535	1004	20	)	)	PUNCT
ejpam-1535	1004	21	319	319	NUM
ejpam-1535	1004	22	–	–	PUNCT
ejpam-1535	1004	23	336	336	NUM
ejpam-1535	1004	24	.	.	PUNCT
ejpam-1535	1005	1	[	[	X
ejpam-1535	1005	2	2	2	X
ejpam-1535	1005	3	]	]	PUNCT
ejpam-1535	1005	4	g.	g.	NOUN
ejpam-1535	1005	5	birkhoff	birkhoff	NOUN
ejpam-1535	1005	6	and	and	CCONJ
ejpam-1535	1005	7	m.	m.	PROPN
ejpam-1535	1005	8	k.	k.	PROPN
ejpam-1535	1005	9	bennett	bennett	PROPN
ejpam-1535	1005	10	,	,	PUNCT
ejpam-1535	1005	11	felix	felix	PROPN
ejpam-1535	1005	12	klein	klein	PROPN
ejpam-1535	1005	13	and	and	CCONJ
ejpam-1535	1005	14	his	his	PRON
ejpam-1535	1005	15	“	"	PUNCT
ejpam-1535	1005	16	erlanger	erlanger	PROPN
ejpam-1535	1005	17	programm	programm	PROPN
ejpam-1535	1005	18	”	"	PUNCT
ejpam-1535	1005	19	,	,	PUNCT
ejpam-1535	1005	20	in	in	ADP
ejpam-1535	1005	21	:	:	PUNCT
ejpam-1535	1005	22	w.	w.	PROPN
ejpam-1535	1005	23	aspray	aspray	PROPN
ejpam-1535	1005	24	and	and	CCONJ
ejpam-1535	1005	25	p.	p.	PROPN
ejpam-1535	1005	26	kitcher	kitcher	PROPN
ejpam-1535	1005	27	(	(	PUNCT
ejpam-1535	1005	28	eds	ed	NOUN
ejpam-1535	1005	29	.	.	PUNCT
ejpam-1535	1005	30	)	)	PUNCT
ejpam-1535	1005	31	,	,	PUNCT
ejpam-1535	1005	32	history	history	NOUN
ejpam-1535	1005	33	and	and	CCONJ
ejpam-1535	1005	34	philosophy	philosophy	NOUN
ejpam-1535	1005	35	of	of	ADP
ejpam-1535	1005	36	modern	modern	ADJ
ejpam-1535	1005	37	mathematics	mathematic	NOUN
ejpam-1535	1005	38	,	,	PUNCT
ejpam-1535	1005	39	minnesota	minnesota	PROPN
ejpam-1535	1005	40	studies	study	NOUN
ejpam-1535	1005	41	in	in	ADP
ejpam-1535	1005	42	the	the	DET
ejpam-1535	1005	43	philosophy	philosophy	NOUN
ejpam-1535	1005	44	of	of	ADP
ejpam-1535	1005	45	science	science	NOUN
ejpam-1535	1005	46	,	,	PUNCT
ejpam-1535	1005	47	vol	vol	NOUN
ejpam-1535	1005	48	.	.	PUNCT
ejpam-1535	1006	1	xi	xi	PROPN
ejpam-1535	1006	2	,	,	PUNCT
ejpam-1535	1006	3	university	university	PROPN
ejpam-1535	1006	4	of	of	ADP
ejpam-1535	1006	5	minnesota	minnesota	PROPN
ejpam-1535	1006	6	press	press	PROPN
ejpam-1535	1006	7	,	,	PUNCT
ejpam-1535	1006	8	minneapolis	minneapolis	PROPN
ejpam-1535	1006	9	,	,	PUNCT
ejpam-1535	1006	10	1988	1988	NUM
ejpam-1535	1006	11	,	,	PUNCT
ejpam-1535	1006	12	pp	pp	ADP
ejpam-1535	1006	13	.	.	PUNCT
ejpam-1535	1007	1	145–176	145–176	NUM
ejpam-1535	1007	2	.	.	PUNCT
ejpam-1535	1008	1	[	[	X
ejpam-1535	1008	2	3	3	X
ejpam-1535	1008	3	]	]	X
ejpam-1535	1008	4	h.	h.	PROPN
ejpam-1535	1008	5	brandt	brandt	PROPN
ejpam-1535	1008	6	,	,	PUNCT
ejpam-1535	1008	7	über	über	PROPN
ejpam-1535	1008	8	eine	eine	PROPN
ejpam-1535	1008	9	verallgemeinerung	verallgemeinerung	PROPN
ejpam-1535	1008	10	des	des	PROPN
ejpam-1535	1008	11	gruppenbegriffes	gruppenbegriffes	PROPN
ejpam-1535	1008	12	,	,	PUNCT
ejpam-1535	1008	13	mathematische	mathematische	NOUN
ejpam-1535	1008	14	annalen	annalen	VERB
ejpam-1535	1008	15	96	96	NUM
ejpam-1535	1008	16	(	(	PUNCT
ejpam-1535	1008	17	1926	1926	NUM
ejpam-1535	1008	18	)	)	PUNCT
ejpam-1535	1009	1	360–366	360–366	NUM
ejpam-1535	1009	2	.	.	PUNCT
ejpam-1535	1010	1	[	[	X
ejpam-1535	1010	2	4	4	NUM
ejpam-1535	1010	3	]	]	X
ejpam-1535	1010	4	r.	r.	PROPN
ejpam-1535	1010	5	brown	brown	PROPN
ejpam-1535	1010	6	,	,	PUNCT
ejpam-1535	1010	7	from	from	ADP
ejpam-1535	1010	8	groups	group	NOUN
ejpam-1535	1010	9	to	to	ADP
ejpam-1535	1010	10	groupoids	groupoid	NOUN
ejpam-1535	1010	11	:	:	PUNCT
ejpam-1535	1010	12	a	a	DET
ejpam-1535	1010	13	brief	brief	ADJ
ejpam-1535	1010	14	survey	survey	NOUN
ejpam-1535	1010	15	,	,	PUNCT
ejpam-1535	1010	16	bulletin	bulletin	NOUN
ejpam-1535	1010	17	of	of	ADP
ejpam-1535	1010	18	the	the	DET
ejpam-1535	1010	19	london	london	PROPN
ejpam-1535	1010	20	mathematical	mathematical	ADJ
ejpam-1535	1010	21	society	society	NOUN
ejpam-1535	1010	22	19	19	NUM
ejpam-1535	1010	23	(	(	PUNCT
ejpam-1535	1010	24	1987	1987	NUM
ejpam-1535	1010	25	)	)	PUNCT
ejpam-1535	1011	1	113–134	113–134	NUM
ejpam-1535	1011	2	.	.	PUNCT
ejpam-1535	1012	1	[	[	X
ejpam-1535	1012	2	5	5	NUM
ejpam-1535	1012	3	]	]	X
ejpam-1535	1012	4	r.	r.	PROPN
ejpam-1535	1012	5	brown	brown	PROPN
ejpam-1535	1012	6	,	,	PUNCT
ejpam-1535	1012	7	groupoids	groupoid	NOUN
ejpam-1535	1012	8	and	and	CCONJ
ejpam-1535	1012	9	crossed	cross	VERB
ejpam-1535	1012	10	objects	object	NOUN
ejpam-1535	1012	11	in	in	ADP
ejpam-1535	1012	12	algebraic	algebraic	ADJ
ejpam-1535	1012	13	topology	topology	NOUN
ejpam-1535	1012	14	,	,	PUNCT
ejpam-1535	1012	15	homology	homology	NOUN
ejpam-1535	1012	16	,	,	PUNCT
ejpam-1535	1012	17	homotopy	homotopy	NOUN
ejpam-1535	1012	18	and	and	CCONJ
ejpam-1535	1012	19	applications	application	NOUN
ejpam-1535	1012	20	1(1	1(1	NUM
ejpam-1535	1012	21	)	)	PUNCT
ejpam-1535	1012	22	(	(	PUNCT
ejpam-1535	1012	23	1999	1999	NUM
ejpam-1535	1012	24	)	)	PUNCT
ejpam-1535	1012	25	1–78	1–78	PROPN
ejpam-1535	1012	26	.	.	PUNCT
ejpam-1535	1013	1	‡‡between	‡‡between	NUM
ejpam-1535	1013	2	categories	category	NOUN
ejpam-1535	1013	3	viewed	view	VERB
ejpam-1535	1013	4	in	in	ADP
ejpam-1535	1013	5	sense	sense	NOUN
ejpam-1535	1013	6	(	(	PUNCT
ejpam-1535	1013	7	♠	♠	NOUN
ejpam-1535	1013	8	)	)	PUNCT
ejpam-1535	1013	9	.	.	PUNCT
ejpam-1535	1014	1	references	reference	NOUN
ejpam-1535	1014	2	448	448	NUM
ejpam-1535	1015	1	[	[	X
ejpam-1535	1015	2	6	6	NUM
ejpam-1535	1015	3	]	]	PUNCT
ejpam-1535	1015	4	r.	r.	PROPN
ejpam-1535	1015	5	brown	brown	PROPN
ejpam-1535	1015	6	,	,	PUNCT
ejpam-1535	1015	7	three	three	NUM
ejpam-1535	1015	8	themes	theme	NOUN
ejpam-1535	1015	9	in	in	ADP
ejpam-1535	1015	10	the	the	DET
ejpam-1535	1015	11	work	work	NOUN
ejpam-1535	1015	12	of	of	ADP
ejpam-1535	1015	13	charles	charles	PROPN
ejpam-1535	1015	14	ehresmann	ehresmann	PROPN
ejpam-1535	1015	15	:	:	PUNCT
ejpam-1535	1015	16	local	local	ADJ
ejpam-1535	1015	17	-	-	PUNCT
ejpam-1535	1015	18	to	to	ADP
ejpam-1535	1015	19	-	-	PUNCT
ejpam-1535	1015	20	global	global	ADJ
ejpam-1535	1015	21	;	;	PUNCT
ejpam-1535	1015	22	groupoids	groupoid	NOUN
ejpam-1535	1015	23	;	;	PUNCT
ejpam-1535	1015	24	higher	high	ADJ
ejpam-1535	1015	25	dimensions	dimension	NOUN
ejpam-1535	1015	26	,	,	PUNCT
ejpam-1535	1015	27	in	in	ADP
ejpam-1535	1015	28	:	:	PUNCT
ejpam-1535	1015	29	jan	jan	PROPN
ejpam-1535	1015	30	kubarski	kubarski	PROPN
ejpam-1535	1015	31	,	,	PUNCT
ejpam-1535	1015	32	jean	jean	PROPN
ejpam-1535	1015	33	pradines	pradine	NOUN
ejpam-1535	1015	34	,	,	PUNCT
ejpam-1535	1015	35	tomasz	tomasz	PROPN
ejpam-1535	1015	36	rybicki	rybicki	PROPN
ejpam-1535	1015	37	and	and	CCONJ
ejpam-1535	1015	38	robert	robert	PROPN
ejpam-1535	1015	39	wolak	wolak	PROPN
ejpam-1535	1015	40	(	(	PUNCT
ejpam-1535	1015	41	eds	ed	NOUN
ejpam-1535	1015	42	.	.	PUNCT
ejpam-1535	1015	43	)	)	PUNCT
ejpam-1535	1015	44	,	,	PUNCT
ejpam-1535	1015	45	geometry	geometry	NOUN
ejpam-1535	1015	46	and	and	CCONJ
ejpam-1535	1015	47	topology	topology	NOUN
ejpam-1535	1015	48	of	of	ADP
ejpam-1535	1015	49	manifolds	manifold	NOUN
ejpam-1535	1015	50	,	,	PUNCT
ejpam-1535	1015	51	banach	banach	NOUN
ejpam-1535	1015	52	center	center	NOUN
ejpam-1535	1015	53	publications	publication	NOUN
ejpam-1535	1015	54	76	76	NUM
ejpam-1535	1015	55	,	,	PUNCT
ejpam-1535	1015	56	polish	polish	PROPN
ejpam-1535	1015	57	academy	academy	PROPN
ejpam-1535	1015	58	of	of	ADP
ejpam-1535	1015	59	sciences	sciences	PROPN
ejpam-1535	1015	60	,	,	PUNCT
ejpam-1535	1015	61	warsaw	warsaw	PROPN
ejpam-1535	1015	62	,	,	PUNCT
ejpam-1535	1015	63	2007	2007	NUM
ejpam-1535	1015	64	,	,	PUNCT
ejpam-1535	1015	65	pp	pp	ADJ
ejpam-1535	1015	66	.	.	PUNCT
ejpam-1535	1016	1	51–63	51–63	NUM
ejpam-1535	1016	2	.	.	PUNCT
ejpam-1535	1017	1	[	[	X
ejpam-1535	1017	2	7	7	X
ejpam-1535	1017	3	]	]	X
ejpam-1535	1017	4	leo	leo	PROPN
ejpam-1535	1017	5	corry	corry	PROPN
ejpam-1535	1017	6	,	,	PUNCT
ejpam-1535	1017	7	modern	modern	ADJ
ejpam-1535	1017	8	algebra	algebra	NOUN
ejpam-1535	1017	9	and	and	CCONJ
ejpam-1535	1017	10	the	the	DET
ejpam-1535	1017	11	rise	rise	NOUN
ejpam-1535	1017	12	of	of	ADP
ejpam-1535	1017	13	mathematical	mathematical	ADJ
ejpam-1535	1017	14	structures	structure	NOUN
ejpam-1535	1017	15	,	,	PUNCT
ejpam-1535	1017	16	2nd	2nd	ADJ
ejpam-1535	1017	17	revised	revise	VERB
ejpam-1535	1017	18	ed	ed	NOUN
ejpam-1535	1017	19	.	.	PROPN
ejpam-1535	1017	20	,	,	PUNCT
ejpam-1535	1017	21	birkhäuser	birkhäuser	NOUN
ejpam-1535	1017	22	,	,	PUNCT
ejpam-1535	1017	23	2004	2004	NUM
ejpam-1535	1017	24	.	.	PUNCT
ejpam-1535	1018	1	[	[	X
ejpam-1535	1018	2	8	8	NUM
ejpam-1535	1018	3	]	]	X
ejpam-1535	1018	4	r.	r.	PROPN
ejpam-1535	1018	5	croisot	croisot	PROPN
ejpam-1535	1018	6	,	,	PUNCT
ejpam-1535	1018	7	une	une	PROPN
ejpam-1535	1018	8	interprétation	interprétation	NOUN
ejpam-1535	1018	9	des	des	PROPN
ejpam-1535	1018	10	relations	relation	NOUN
ejpam-1535	1018	11	d’équivalence	d’équivalence	NOUN
ejpam-1535	1018	12	dans	dan	NOUN
ejpam-1535	1018	13	un	un	PROPN
ejpam-1535	1018	14	ensemble	ensemble	PROPN
ejpam-1535	1018	15	,	,	PUNCT
ejpam-1535	1018	16	comptes	compte	VERB
ejpam-1535	1018	17	rendus	rendus	PROPN
ejpam-1535	1018	18	de	de	PROPN
ejpam-1535	1018	19	l’académie	l’académie	PROPN
ejpam-1535	1018	20	des	des	PROPN
ejpam-1535	1018	21	sciences	sciences	PROPN
ejpam-1535	1018	22	de	de	PROPN
ejpam-1535	1018	23	paris	paris	PROPN
ejpam-1535	1018	24	226	226	NUM
ejpam-1535	1018	25	(	(	PUNCT
ejpam-1535	1018	26	1948	1948	NUM
ejpam-1535	1018	27	)	)	PUNCT
ejpam-1535	1018	28	616–617	616–617	NUM
ejpam-1535	1018	29	.	.	PUNCT
ejpam-1535	1019	1	[	[	X
ejpam-1535	1019	2	9	9	NUM
ejpam-1535	1019	3	]	]	X
ejpam-1535	1019	4	ch	ch	NOUN
ejpam-1535	1019	5	.	.	PROPN
ejpam-1535	1019	6	ehresmann	ehresmann	PROPN
ejpam-1535	1019	7	,	,	PUNCT
ejpam-1535	1019	8	gattungen	gattungen	PROPN
ejpam-1535	1019	9	von	von	PROPN
ejpam-1535	1019	10	lokalen	lokalen	PROPN
ejpam-1535	1019	11	strukturen	strukturen	PROPN
ejpam-1535	1019	12	,	,	PUNCT
ejpam-1535	1019	13	jahresbericht	jahresbericht	PROPN
ejpam-1535	1019	14	der	der	PROPN
ejpam-1535	1019	15	deutschen	deutschen	PROPN
ejpam-1535	1019	16	mathematiker	mathematiker	PROPN
ejpam-1535	1019	17	-	-	PUNCT
ejpam-1535	1019	18	vereinigung	vereinigung	PROPN
ejpam-1535	1019	19	60	60	NUM
ejpam-1535	1019	20	(	(	PUNCT
ejpam-1535	1019	21	1957	1957	NUM
ejpam-1535	1019	22	)	)	PUNCT
ejpam-1535	1019	23	49–77	49–77	NUM
ejpam-1535	1019	24	.	.	PUNCT
ejpam-1535	1020	1	[	[	X
ejpam-1535	1020	2	10	10	NUM
ejpam-1535	1020	3	]	]	X
ejpam-1535	1020	4	ch	ch	NOUN
ejpam-1535	1020	5	.	.	PROPN
ejpam-1535	1020	6	ehresmann	ehresmann	PROPN
ejpam-1535	1020	7	,	,	PUNCT
ejpam-1535	1020	8	catégories	catégorie	NOUN
ejpam-1535	1020	9	inductives	inductive	NOUN
ejpam-1535	1020	10	et	et	PROPN
ejpam-1535	1020	11	pseudogroupes	pseudogroupe	NOUN
ejpam-1535	1020	12	,	,	PUNCT
ejpam-1535	1020	13	annales	annales	PROPN
ejpam-1535	1020	14	de	de	PROPN
ejpam-1535	1020	15	l’institut	l’institut	X
ejpam-1535	1020	16	fourier	fourier	NOUN
ejpam-1535	1020	17	,	,	PUNCT
ejpam-1535	1020	18	grenoble	grenoble	ADJ
ejpam-1535	1020	19	10	10	NUM
ejpam-1535	1020	20	(	(	PUNCT
ejpam-1535	1020	21	1960	1960	NUM
ejpam-1535	1020	22	)	)	PUNCT
ejpam-1535	1020	23	307–336	307–336	NUM
ejpam-1535	1020	24	.	.	PUNCT
ejpam-1535	1021	1	[	[	X
ejpam-1535	1021	2	11	11	NUM
ejpam-1535	1021	3	]	]	X
ejpam-1535	1021	4	ch	ch	NOUN
ejpam-1535	1021	5	.	.	PROPN
ejpam-1535	1021	6	ehresmann	ehresmann	PROPN
ejpam-1535	1021	7	,	,	PUNCT
ejpam-1535	1021	8	oeuvres	oeuvre	VERB
ejpam-1535	1021	9	complètes	complète	NOUN
ejpam-1535	1021	10	et	et	NOUN
ejpam-1535	1021	11	commentèes	commentèe	NOUN
ejpam-1535	1021	12	(	(	PUNCT
ejpam-1535	1021	13	a.	a.	NOUN
ejpam-1535	1021	14	c.	c.	PROPN
ejpam-1535	1021	15	ehresmann	ehresmann	PROPN
ejpam-1535	1021	16	,	,	PUNCT
ejpam-1535	1021	17	ed	ed	NOUN
ejpam-1535	1021	18	.	.	PUNCT
ejpam-1535	1021	19	)	)	PUNCT
ejpam-1535	1021	20	,	,	PUNCT
ejpam-1535	1021	21	supplements	supplement	NOUN
ejpam-1535	1021	22	to	to	ADP
ejpam-1535	1021	23	cahiers	cahier	NOUN
ejpam-1535	1021	24	de	de	X
ejpam-1535	1021	25	topologie	topologie	PROPN
ejpam-1535	1021	26	et	et	PROPN
ejpam-1535	1021	27	géométrie	géométrie	VERB
ejpam-1535	1021	28	différentielle	différentielle	NOUN
ejpam-1535	1021	29	,	,	PUNCT
ejpam-1535	1021	30	amiens	amien	NOUN
ejpam-1535	1021	31	,	,	PUNCT
ejpam-1535	1021	32	1980–83	1980–83	NUM
ejpam-1535	1021	33	.	.	PUNCT
ejpam-1535	1022	1	[	[	X
ejpam-1535	1022	2	12	12	NUM
ejpam-1535	1022	3	]	]	PUNCT
ejpam-1535	1022	4	s.	s.	PROPN
ejpam-1535	1022	5	eilenberg	eilenberg	PROPN
ejpam-1535	1022	6	and	and	CCONJ
ejpam-1535	1022	7	s.	s.	PROPN
ejpam-1535	1022	8	mac	mac	PROPN
ejpam-1535	1022	9	lane	lane	PROPN
ejpam-1535	1022	10	,	,	PUNCT
ejpam-1535	1022	11	the	the	DET
ejpam-1535	1022	12	general	general	ADJ
ejpam-1535	1022	13	theory	theory	NOUN
ejpam-1535	1022	14	of	of	ADP
ejpam-1535	1022	15	natural	natural	ADJ
ejpam-1535	1022	16	equivalences	equivalence	NOUN
ejpam-1535	1022	17	,	,	PUNCT
ejpam-1535	1022	18	transactions	transaction	NOUN
ejpam-1535	1022	19	of	of	ADP
ejpam-1535	1022	20	the	the	DET
ejpam-1535	1022	21	american	american	PROPN
ejpam-1535	1022	22	mathematical	mathematical	PROPN
ejpam-1535	1022	23	society	society	NOUN
ejpam-1535	1022	24	58	58	NUM
ejpam-1535	1022	25	(	(	PUNCT
ejpam-1535	1022	26	1945	1945	NUM
ejpam-1535	1022	27	)	)	PUNCT
ejpam-1535	1022	28	231–294	231–294	NUM
ejpam-1535	1022	29	.	.	PUNCT
ejpam-1535	1023	1	[	[	X
ejpam-1535	1023	2	13	13	NUM
ejpam-1535	1023	3	]	]	PUNCT
ejpam-1535	1023	4	j.	j.	PROPN
ejpam-1535	1023	5	fountain	fountain	PROPN
ejpam-1535	1023	6	,	,	PUNCT
ejpam-1535	1023	7	a	a	DET
ejpam-1535	1023	8	class	class	NOUN
ejpam-1535	1023	9	of	of	ADP
ejpam-1535	1023	10	right	right	ADJ
ejpam-1535	1023	11	pp	pp	ADP
ejpam-1535	1023	12	monoids	monoid	NOUN
ejpam-1535	1023	13	,	,	PUNCT
ejpam-1535	1023	14	quarterly	quarterly	ADJ
ejpam-1535	1023	15	journal	journal	NOUN
ejpam-1535	1023	16	of	of	ADP
ejpam-1535	1023	17	mathematics	mathematic	NOUN
ejpam-1535	1023	18	,	,	PUNCT
ejpam-1535	1023	19	oxford	oxford	PROPN
ejpam-1535	1023	20	(	(	PUNCT
ejpam-1535	1023	21	2	2	NUM
ejpam-1535	1023	22	)	)	SYM
ejpam-1535	1023	23	28	28	NUM
ejpam-1535	1023	24	(	(	PUNCT
ejpam-1535	1023	25	1977	1977	NUM
ejpam-1535	1023	26	)	)	PUNCT
ejpam-1535	1023	27	285–300	285–300	NUM
ejpam-1535	1023	28	.	.	PUNCT
ejpam-1535	1024	1	[	[	X
ejpam-1535	1024	2	14	14	NUM
ejpam-1535	1024	3	]	]	X
ejpam-1535	1024	4	j.	j.	PROPN
ejpam-1535	1024	5	fountain	fountain	PROPN
ejpam-1535	1024	6	,	,	PUNCT
ejpam-1535	1024	7	adequate	adequate	ADJ
ejpam-1535	1024	8	semigroups	semigroup	NOUN
ejpam-1535	1024	9	,	,	PUNCT
ejpam-1535	1024	10	proceedings	proceeding	NOUN
ejpam-1535	1024	11	of	of	ADP
ejpam-1535	1024	12	the	the	DET
ejpam-1535	1024	13	edinburgh	edinburgh	PROPN
ejpam-1535	1024	14	mathematical	mathematical	PROPN
ejpam-1535	1024	15	society	society	NOUN
ejpam-1535	1024	16	(	(	PUNCT
ejpam-1535	1024	17	2	2	NUM
ejpam-1535	1024	18	)	)	PUNCT
ejpam-1535	1024	19	22	22	NUM
ejpam-1535	1024	20	(	(	PUNCT
ejpam-1535	1024	21	1979	1979	NUM
ejpam-1535	1024	22	)	)	PUNCT
ejpam-1535	1024	23	113–125	113–125	NUM
ejpam-1535	1024	24	.	.	PUNCT
ejpam-1535	1025	1	[	[	X
ejpam-1535	1025	2	15	15	NUM
ejpam-1535	1025	3	]	]	X
ejpam-1535	1025	4	v.	v.	PROPN
ejpam-1535	1025	5	gould	gould	PROPN
ejpam-1535	1025	6	,	,	PUNCT
ejpam-1535	1025	7	(	(	PUNCT
ejpam-1535	1025	8	weakly	weakly	ADV
ejpam-1535	1025	9	)	)	PUNCT
ejpam-1535	1025	10	left	leave	VERB
ejpam-1535	1025	11	e	e	NOUN
ejpam-1535	1025	12	-	-	ADJ
ejpam-1535	1025	13	ample	ample	ADJ
ejpam-1535	1025	14	semigroups	semigroup	NOUN
ejpam-1535	1025	15	(	(	PUNCT
ejpam-1535	1025	16	a.k.a	a.k.a	INTJ
ejpam-1535	1025	17	.	.	PROPN
ejpam-1535	1025	18	notes	note	NOUN
ejpam-1535	1025	19	on	on	ADP
ejpam-1535	1025	20	restriction	restriction	NOUN
ejpam-1535	1025	21	semigroups	semigroup	NOUN
ejpam-1535	1025	22	and	and	CCONJ
ejpam-1535	1025	23	related	related	ADJ
ejpam-1535	1025	24	structures	structure	NOUN
ejpam-1535	1025	25	)	)	PUNCT
ejpam-1535	1025	26	,	,	PUNCT
ejpam-1535	1025	27	http://www	http://www	PROPN
ejpam-1535	1025	28	-	-	PUNCT
ejpam-1535	1025	29	users.york.a	users.york.a	PROPN
ejpam-1535	1025	30	.uk/~varg1	.uk/~varg1	PROPN
ejpam-1535	1025	31	/	/	SYM
ejpam-1535	1025	32	restri	restri	ADJ
ejpam-1535	1025	33	tion.pdf	tion.pdf	X
ejpam-1535	1025	34	[	[	X
ejpam-1535	1025	35	16	16	NUM
ejpam-1535	1025	36	]	]	PUNCT
ejpam-1535	1025	37	v.	v.	PROPN
ejpam-1535	1025	38	gould	gould	PROPN
ejpam-1535	1025	39	and	and	CCONJ
ejpam-1535	1025	40	c.	c.	PROPN
ejpam-1535	1025	41	hollings	holling	NOUN
ejpam-1535	1025	42	,	,	PUNCT
ejpam-1535	1025	43	partial	partial	ADJ
ejpam-1535	1025	44	actions	action	NOUN
ejpam-1535	1025	45	of	of	ADP
ejpam-1535	1025	46	inverse	inverse	NOUN
ejpam-1535	1025	47	and	and	CCONJ
ejpam-1535	1025	48	weakly	weakly	ADJ
ejpam-1535	1025	49	left	left	ADJ
ejpam-1535	1025	50	e	e	NOUN
ejpam-1535	1025	51	-	-	ADJ
ejpam-1535	1025	52	ample	ample	ADJ
ejpam-1535	1025	53	semigroups	semigroup	NOUN
ejpam-1535	1025	54	,	,	PUNCT
ejpam-1535	1025	55	journal	journal	NOUN
ejpam-1535	1025	56	of	of	ADP
ejpam-1535	1025	57	the	the	DET
ejpam-1535	1025	58	australian	australian	ADJ
ejpam-1535	1025	59	mathematical	mathematical	ADJ
ejpam-1535	1025	60	society	society	PROPN
ejpam-1535	1025	61	86(3	86(3	PROPN
ejpam-1535	1025	62	)	)	PUNCT
ejpam-1535	1025	63	(	(	PUNCT
ejpam-1535	1025	64	2009	2009	NUM
ejpam-1535	1025	65	)	)	PUNCT
ejpam-1535	1026	1	355–377	355–377	NUM
ejpam-1535	1026	2	.	.	PUNCT
ejpam-1535	1027	1	[	[	X
ejpam-1535	1027	2	17	17	NUM
ejpam-1535	1027	3	]	]	X
ejpam-1535	1027	4	v.	v.	PROPN
ejpam-1535	1027	5	gould	gould	PROPN
ejpam-1535	1027	6	and	and	CCONJ
ejpam-1535	1027	7	c.	c.	PROPN
ejpam-1535	1027	8	hollings	holling	NOUN
ejpam-1535	1027	9	,	,	PUNCT
ejpam-1535	1027	10	restriction	restriction	NOUN
ejpam-1535	1027	11	semigroups	semigroup	NOUN
ejpam-1535	1027	12	and	and	CCONJ
ejpam-1535	1027	13	inductive	inductive	ADJ
ejpam-1535	1027	14	constellations	constellation	NOUN
ejpam-1535	1027	15	,	,	PUNCT
ejpam-1535	1027	16	communications	communication	NOUN
ejpam-1535	1027	17	in	in	ADP
ejpam-1535	1027	18	algebra	algebra	PROPN
ejpam-1535	1027	19	38(1	38(1	NUM
ejpam-1535	1027	20	)	)	PUNCT
ejpam-1535	1027	21	(	(	PUNCT
ejpam-1535	1027	22	2010	2010	NUM
ejpam-1535	1027	23	)	)	PUNCT
ejpam-1535	1027	24	261–287	261–287	NUM
ejpam-1535	1027	25	.	.	PUNCT
ejpam-1535	1028	1	[	[	X
ejpam-1535	1028	2	18	18	NUM
ejpam-1535	1028	3	]	]	PUNCT
ejpam-1535	1028	4	m.	m.	NOUN
ejpam-1535	1028	5	haskell	haskell	PROPN
ejpam-1535	1028	6	,	,	PUNCT
ejpam-1535	1028	7	a	a	DET
ejpam-1535	1028	8	comparative	comparative	ADJ
ejpam-1535	1028	9	review	review	NOUN
ejpam-1535	1028	10	of	of	ADP
ejpam-1535	1028	11	recent	recent	ADJ
ejpam-1535	1028	12	researches	research	NOUN
ejpam-1535	1028	13	in	in	ADP
ejpam-1535	1028	14	geometry	geometry	NOUN
ejpam-1535	1028	15	,	,	PUNCT
ejpam-1535	1028	16	bulletin	bulletin	NOUN
ejpam-1535	1028	17	of	of	ADP
ejpam-1535	1028	18	the	the	DET
ejpam-1535	1028	19	new	new	PROPN
ejpam-1535	1028	20	york	york	PROPN
ejpam-1535	1028	21	mathematical	mathematical	PROPN
ejpam-1535	1028	22	society	society	NOUN
ejpam-1535	1028	23	2	2	NUM
ejpam-1535	1028	24	(	(	PUNCT
ejpam-1535	1028	25	1892–1893	1892–1893	NUM
ejpam-1535	1028	26	)	)	PUNCT
ejpam-1535	1028	27	215–249	215–249	NUM
ejpam-1535	1028	28	.	.	PUNCT
ejpam-1535	1029	1	[	[	X
ejpam-1535	1029	2	19	19	NUM
ejpam-1535	1029	3	]	]	X
ejpam-1535	1029	4	t.	t.	PROPN
ejpam-1535	1029	5	hawkins	hawkins	PROPN
ejpam-1535	1029	6	,	,	PUNCT
ejpam-1535	1029	7	the	the	DET
ejpam-1535	1029	8	erlanger	erlanger	PROPN
ejpam-1535	1029	9	programm	programm	PROPN
ejpam-1535	1029	10	of	of	ADP
ejpam-1535	1029	11	felix	felix	PROPN
ejpam-1535	1029	12	klein	klein	PROPN
ejpam-1535	1029	13	:	:	PUNCT
ejpam-1535	1029	14	reflections	reflection	NOUN
ejpam-1535	1029	15	on	on	ADP
ejpam-1535	1029	16	its	its	PRON
ejpam-1535	1029	17	place	place	NOUN
ejpam-1535	1029	18	in	in	ADP
ejpam-1535	1029	19	the	the	DET
ejpam-1535	1029	20	history	history	NOUN
ejpam-1535	1029	21	of	of	ADP
ejpam-1535	1029	22	mathematics	mathematic	NOUN
ejpam-1535	1029	23	,	,	PUNCT
ejpam-1535	1029	24	historia	historia	PROPN
ejpam-1535	1029	25	mathematica	mathematica	PROPN
ejpam-1535	1029	26	11	11	NUM
ejpam-1535	1029	27	(	(	PUNCT
ejpam-1535	1029	28	1984	1984	NUM
ejpam-1535	1029	29	)	)	PUNCT
ejpam-1535	1030	1	442–470	442–470	NUM
ejpam-1535	1030	2	.	.	PUNCT
ejpam-1535	1031	1	[	[	X
ejpam-1535	1031	2	20	20	NUM
ejpam-1535	1031	3	]	]	X
ejpam-1535	1031	4	c.	c.	PROPN
ejpam-1535	1031	5	hollings	holling	NOUN
ejpam-1535	1031	6	,	,	PUNCT
ejpam-1535	1031	7	from	from	ADP
ejpam-1535	1031	8	right	right	ADJ
ejpam-1535	1031	9	pp	pp	ADV
ejpam-1535	1031	10	monoids	monoid	NOUN
ejpam-1535	1031	11	to	to	ADP
ejpam-1535	1031	12	restriction	restriction	NOUN
ejpam-1535	1031	13	semigroups	semigroup	NOUN
ejpam-1535	1031	14	:	:	PUNCT
ejpam-1535	1031	15	a	a	DET
ejpam-1535	1031	16	survey	survey	NOUN
ejpam-1535	1031	17	,	,	PUNCT
ejpam-1535	1031	18	european	european	PROPN
ejpam-1535	1031	19	journal	journal	PROPN
ejpam-1535	1031	20	of	of	ADP
ejpam-1535	1031	21	pure	pure	ADJ
ejpam-1535	1031	22	and	and	CCONJ
ejpam-1535	1031	23	applied	applied	ADJ
ejpam-1535	1031	24	mathematics	mathematic	NOUN
ejpam-1535	1031	25	2(1	2(1	NUM
ejpam-1535	1031	26	)	)	PUNCT
ejpam-1535	1031	27	(	(	PUNCT
ejpam-1535	1031	28	2009	2009	NUM
ejpam-1535	1031	29	)	)	PUNCT
ejpam-1535	1031	30	21–37	21–37	NUM
ejpam-1535	1031	31	.	.	PUNCT
ejpam-1535	1032	1	[	[	X
ejpam-1535	1032	2	21	21	NUM
ejpam-1535	1032	3	]	]	X
ejpam-1535	1032	4	c.	c.	PROPN
ejpam-1535	1032	5	hollings	hollings	PROPN
ejpam-1535	1032	6	,	,	PUNCT
ejpam-1535	1032	7	the	the	DET
ejpam-1535	1032	8	early	early	ADJ
ejpam-1535	1032	9	development	development	NOUN
ejpam-1535	1032	10	of	of	ADP
ejpam-1535	1032	11	the	the	DET
ejpam-1535	1032	12	algebraic	algebraic	ADJ
ejpam-1535	1032	13	theory	theory	NOUN
ejpam-1535	1032	14	of	of	ADP
ejpam-1535	1032	15	semigroups	semigroup	NOUN
ejpam-1535	1032	16	,	,	PUNCT
ejpam-1535	1032	17	archive	archive	NOUN
ejpam-1535	1032	18	for	for	ADP
ejpam-1535	1032	19	the	the	DET
ejpam-1535	1032	20	history	history	NOUN
ejpam-1535	1032	21	of	of	ADP
ejpam-1535	1032	22	exact	exact	ADJ
ejpam-1535	1032	23	sciences	science	NOUN
ejpam-1535	1032	24	63(5	63(5	NOUN
ejpam-1535	1032	25	)	)	PUNCT
ejpam-1535	1032	26	(	(	PUNCT
ejpam-1535	1032	27	2009	2009	NUM
ejpam-1535	1032	28	)	)	PUNCT
ejpam-1535	1032	29	497–536	497–536	NUM
ejpam-1535	1032	30	.	.	PUNCT
ejpam-1535	1033	1	references	reference	NOUN
ejpam-1535	1033	2	449	449	NUM
ejpam-1535	1034	1	[	[	X
ejpam-1535	1034	2	22	22	NUM
ejpam-1535	1034	3	]	]	PUNCT
ejpam-1535	1034	4	c.	c.	PROPN
ejpam-1535	1034	5	hollings	holling	NOUN
ejpam-1535	1034	6	,	,	PUNCT
ejpam-1535	1034	7	extending	extend	VERB
ejpam-1535	1034	8	the	the	DET
ejpam-1535	1034	9	ehresmann	ehresmann	PROPN
ejpam-1535	1034	10	–	–	PUNCT
ejpam-1535	1034	11	schein	schein	PROPN
ejpam-1535	1034	12	–	–	PUNCT
ejpam-1535	1034	13	nambooripad	nambooripad	NOUN
ejpam-1535	1034	14	theorem	theorem	NOUN
ejpam-1535	1034	15	,	,	PUNCT
ejpam-1535	1034	16	semigroup	semigroup	PROPN
ejpam-1535	1034	17	forum	forum	PROPN
ejpam-1535	1034	18	80(3	80(3	NUM
ejpam-1535	1034	19	)	)	PUNCT
ejpam-1535	1034	20	(	(	PUNCT
ejpam-1535	1034	21	2010	2010	NUM
ejpam-1535	1034	22	)	)	PUNCT
ejpam-1535	1034	23	453–476	453–476	NUM
ejpam-1535	1034	24	.	.	PUNCT
ejpam-1535	1035	1	[	[	X
ejpam-1535	1035	2	23	23	NUM
ejpam-1535	1035	3	]	]	PUNCT
ejpam-1535	1035	4	j.	j.	PROPN
ejpam-1535	1035	5	m.	m.	PROPN
ejpam-1535	1035	6	howie	howie	PROPN
ejpam-1535	1035	7	,	,	PUNCT
ejpam-1535	1035	8	fundamentals	fundamental	NOUN
ejpam-1535	1035	9	of	of	ADP
ejpam-1535	1035	10	semigroup	semigroup	PROPN
ejpam-1535	1035	11	theory	theory	NOUN
ejpam-1535	1035	12	,	,	PUNCT
ejpam-1535	1035	13	lms	lms	NOUN
ejpam-1535	1035	14	monographs	monograph	NOUN
ejpam-1535	1035	15	,	,	PUNCT
ejpam-1535	1035	16	no	no	INTJ
ejpam-1535	1035	17	.	.	NOUN
ejpam-1535	1035	18	12	12	NUM
ejpam-1535	1035	19	,	,	PUNCT
ejpam-1535	1035	20	clarendon	clarendon	PROPN
ejpam-1535	1035	21	press	press	NOUN
ejpam-1535	1035	22	,	,	PUNCT
ejpam-1535	1035	23	oxford	oxford	NOUN
ejpam-1535	1035	24	,	,	PUNCT
ejpam-1535	1035	25	1995	1995	NUM
ejpam-1535	1035	26	.	.	PUNCT
ejpam-1535	1036	1	[	[	X
ejpam-1535	1036	2	24	24	NUM
ejpam-1535	1036	3	]	]	X
ejpam-1535	1036	4	n.	n.	PROPN
ejpam-1535	1036	5	jacobson	jacobson	PROPN
ejpam-1535	1036	6	,	,	PUNCT
ejpam-1535	1036	7	basic	basic	ADJ
ejpam-1535	1036	8	algebra	algebra	NOUN
ejpam-1535	1036	9	,	,	PUNCT
ejpam-1535	1036	10	volume	volume	NOUN
ejpam-1535	1036	11	ii	ii	PROPN
ejpam-1535	1036	12	,	,	PUNCT
ejpam-1535	1036	13	w.	w.	PROPN
ejpam-1535	1036	14	h.	h.	PROPN
ejpam-1535	1036	15	freeman	freeman	PROPN
ejpam-1535	1036	16	and	and	CCONJ
ejpam-1535	1036	17	co.	co.	PROPN
ejpam-1535	1036	18	,	,	PUNCT
ejpam-1535	1036	19	san	san	PROPN
ejpam-1535	1036	20	francisco	francisco	PROPN
ejpam-1535	1036	21	,	,	PUNCT
ejpam-1535	1036	22	1980	1980	NUM
ejpam-1535	1036	23	.	.	PUNCT
ejpam-1535	1037	1	[	[	X
ejpam-1535	1037	2	25	25	NUM
ejpam-1535	1037	3	]	]	X
ejpam-1535	1037	4	f.	f.	PROPN
ejpam-1535	1037	5	klein	klein	PROPN
ejpam-1535	1037	6	,	,	PUNCT
ejpam-1535	1037	7	vergleichende	vergleichende	NOUN
ejpam-1535	1037	8	betrachtungen	betrachtungen	PROPN
ejpam-1535	1037	9	über	über	PROPN
ejpam-1535	1037	10	neuere	neuere	PROPN
ejpam-1535	1037	11	geometrische	geometrische	PROPN
ejpam-1535	1037	12	forschungen	forschungen	PROPN
ejpam-1535	1037	13	,	,	PUNCT
ejpam-1535	1037	14	mathematische	mathematische	NOUN
ejpam-1535	1037	15	annalen	annalen	VERB
ejpam-1535	1037	16	43	43	NUM
ejpam-1535	1037	17	(	(	PUNCT
ejpam-1535	1037	18	1893	1893	NUM
ejpam-1535	1037	19	)	)	PUNCT
ejpam-1535	1037	20	63–100	63–100	NOUN
ejpam-1535	1037	21	.	.	PUNCT
ejpam-1535	1038	1	[	[	X
ejpam-1535	1038	2	26	26	NUM
ejpam-1535	1038	3	]	]	PUNCT
ejpam-1535	1038	4	m.	m.	NOUN
ejpam-1535	1038	5	v.	v.	ADP
ejpam-1535	1038	6	lawson	lawson	PROPN
ejpam-1535	1038	7	,	,	PUNCT
ejpam-1535	1038	8	the	the	DET
ejpam-1535	1038	9	structure	structure	NOUN
ejpam-1535	1038	10	theory	theory	NOUN
ejpam-1535	1038	11	of	of	ADP
ejpam-1535	1038	12	abundant	abundant	ADJ
ejpam-1535	1038	13	semigroups	semigroup	NOUN
ejpam-1535	1038	14	,	,	PUNCT
ejpam-1535	1038	15	dphil	dphil	ADJ
ejpam-1535	1038	16	thesis	thesis	NOUN
ejpam-1535	1038	17	,	,	PUNCT
ejpam-1535	1038	18	university	university	PROPN
ejpam-1535	1038	19	of	of	ADP
ejpam-1535	1038	20	york	york	PROPN
ejpam-1535	1038	21	,	,	PUNCT
ejpam-1535	1038	22	1985	1985	NUM
ejpam-1535	1038	23	.	.	PUNCT
ejpam-1535	1039	1	[	[	X
ejpam-1535	1039	2	27	27	NUM
ejpam-1535	1039	3	]	]	PUNCT
ejpam-1535	1039	4	m.	m.	NOUN
ejpam-1535	1039	5	v.	v.	ADP
ejpam-1535	1039	6	lawson	lawson	PROPN
ejpam-1535	1039	7	,	,	PUNCT
ejpam-1535	1039	8	the	the	DET
ejpam-1535	1039	9	geometric	geometric	ADJ
ejpam-1535	1039	10	theory	theory	NOUN
ejpam-1535	1039	11	of	of	ADP
ejpam-1535	1039	12	inverse	inverse	NOUN
ejpam-1535	1039	13	semigroups	semigroup	NOUN
ejpam-1535	1040	1	i	i	PRON
ejpam-1535	1040	2	:	:	PUNCT
ejpam-1535	1040	3	e	e	X
ejpam-1535	1040	4	-	-	ADJ
ejpam-1535	1040	5	unitary	unitary	ADJ
ejpam-1535	1040	6	inverse	inverse	NOUN
ejpam-1535	1040	7	semigroups	semigroup	NOUN
ejpam-1535	1040	8	,	,	PUNCT
ejpam-1535	1040	9	journal	journal	NOUN
ejpam-1535	1040	10	of	of	ADP
ejpam-1535	1040	11	pure	pure	ADJ
ejpam-1535	1040	12	and	and	CCONJ
ejpam-1535	1040	13	applied	applied	ADJ
ejpam-1535	1040	14	algebra	algebra	NOUN
ejpam-1535	1040	15	67	67	NUM
ejpam-1535	1040	16	(	(	PUNCT
ejpam-1535	1040	17	1990	1990	NUM
ejpam-1535	1040	18	)	)	PUNCT
ejpam-1535	1040	19	151–177	151–177	NUM
ejpam-1535	1040	20	.	.	PUNCT
ejpam-1535	1041	1	[	[	X
ejpam-1535	1041	2	28	28	NUM
ejpam-1535	1041	3	]	]	X
ejpam-1535	1041	4	m.	m.	NOUN
ejpam-1535	1041	5	v.	v.	ADP
ejpam-1535	1041	6	lawson	lawson	PROPN
ejpam-1535	1041	7	,	,	PUNCT
ejpam-1535	1041	8	semigroups	semigroups	X
ejpam-1535	1041	9	and	and	CCONJ
ejpam-1535	1041	10	ordered	order	VERB
ejpam-1535	1041	11	categories	category	NOUN
ejpam-1535	1041	12	i	i	PRON
ejpam-1535	1041	13	:	:	PUNCT
ejpam-1535	1041	14	the	the	DET
ejpam-1535	1041	15	reduced	reduced	ADJ
ejpam-1535	1041	16	case	case	NOUN
ejpam-1535	1041	17	,	,	PUNCT
ejpam-1535	1041	18	journal	journal	NOUN
ejpam-1535	1041	19	of	of	ADP
ejpam-1535	1041	20	algebra	algebra	NOUN
ejpam-1535	1041	21	141	141	NUM
ejpam-1535	1041	22	(	(	PUNCT
ejpam-1535	1041	23	1991	1991	NUM
ejpam-1535	1041	24	)	)	PUNCT
ejpam-1535	1041	25	422–462	422–462	NUM
ejpam-1535	1041	26	.	.	PUNCT
ejpam-1535	1042	1	[	[	X
ejpam-1535	1042	2	29	29	NUM
ejpam-1535	1042	3	]	]	X
ejpam-1535	1042	4	m.	m.	NOUN
ejpam-1535	1042	5	v.	v.	PROPN
ejpam-1535	1042	6	lawson	lawson	PROPN
ejpam-1535	1042	7	,	,	PUNCT
ejpam-1535	1042	8	inverse	inverse	NOUN
ejpam-1535	1042	9	semigroups	semigroup	NOUN
ejpam-1535	1042	10	:	:	PUNCT
ejpam-1535	1042	11	the	the	DET
ejpam-1535	1042	12	theory	theory	NOUN
ejpam-1535	1042	13	of	of	ADP
ejpam-1535	1042	14	partial	partial	ADJ
ejpam-1535	1042	15	symmetries	symmetry	NOUN
ejpam-1535	1042	16	,	,	PUNCT
ejpam-1535	1042	17	world	world	NOUN
ejpam-1535	1042	18	scientific	scientific	ADJ
ejpam-1535	1042	19	,	,	PUNCT
ejpam-1535	1042	20	1998	1998	NUM
ejpam-1535	1042	21	.	.	PUNCT
ejpam-1535	1043	1	[	[	X
ejpam-1535	1043	2	30	30	NUM
ejpam-1535	1043	3	]	]	X
ejpam-1535	1043	4	m.	m.	NOUN
ejpam-1535	1043	5	v.	v.	ADP
ejpam-1535	1043	6	lawson	lawson	PROPN
ejpam-1535	1043	7	,	,	PUNCT
ejpam-1535	1043	8	s.	s.	PROPN
ejpam-1535	1043	9	w.	w.	PROPN
ejpam-1535	1043	10	margolis	margolis	PROPN
ejpam-1535	1043	11	and	and	CCONJ
ejpam-1535	1043	12	b.	b.	PROPN
ejpam-1535	1043	13	steinberg	steinberg	PROPN
ejpam-1535	1043	14	,	,	PUNCT
ejpam-1535	1043	15	expansions	expansion	NOUN
ejpam-1535	1043	16	of	of	ADP
ejpam-1535	1043	17	inverse	inverse	NOUN
ejpam-1535	1043	18	semigroups	semigroup	NOUN
ejpam-1535	1043	19	,	,	PUNCT
ejpam-1535	1043	20	journal	journal	NOUN
ejpam-1535	1043	21	of	of	ADP
ejpam-1535	1043	22	the	the	DET
ejpam-1535	1043	23	australian	australian	ADJ
ejpam-1535	1043	24	mathematics	mathematics	PROPN
ejpam-1535	1043	25	society	society	NOUN
ejpam-1535	1043	26	80	80	NUM
ejpam-1535	1043	27	(	(	PUNCT
ejpam-1535	1043	28	2006	2006	NUM
ejpam-1535	1043	29	)	)	PUNCT
ejpam-1535	1043	30	205–228	205–228	NUM
ejpam-1535	1043	31	.	.	PUNCT
ejpam-1535	1044	1	[	[	X
ejpam-1535	1044	2	31	31	NUM
ejpam-1535	1044	3	]	]	PUNCT
ejpam-1535	1044	4	s.	s.	PROPN
ejpam-1535	1044	5	lie	lie	PROPN
ejpam-1535	1044	6	,	,	PUNCT
ejpam-1535	1044	7	die	die	VERB
ejpam-1535	1044	8	grundlagen	grundlagen	PROPN
ejpam-1535	1044	9	für	für	PROPN
ejpam-1535	1044	10	die	die	VERB
ejpam-1535	1044	11	theorie	theorie	PROPN
ejpam-1535	1044	12	der	der	PROPN
ejpam-1535	1044	13	unendlichen	unendlichen	SCONJ
ejpam-1535	1044	14	kontinuierlichen	kontinuierlichen	PROPN
ejpam-1535	1044	15	transformationsgruppen	transformationsgruppen	PROPN
ejpam-1535	1044	16	i	i	PROPN
ejpam-1535	1044	17	,	,	PUNCT
ejpam-1535	1044	18	leipzig	leipzig	PROPN
ejpam-1535	1044	19	,	,	PUNCT
ejpam-1535	1044	20	berichte	berichte	VERB
ejpam-1535	1044	21	3	3	NUM
ejpam-1535	1044	22	(	(	PUNCT
ejpam-1535	1044	23	1891	1891	NUM
ejpam-1535	1044	24	)	)	PUNCT
ejpam-1535	1045	1	316–352	316–352	NUM
ejpam-1535	1045	2	;	;	PUNCT
ejpam-1535	1045	3	ii	ii	NOUN
ejpam-1535	1045	4	,	,	PUNCT
ejpam-1535	1045	5	ibid	ibid	NOUN
ejpam-1535	1045	6	.	.	PUNCT
ejpam-1535	1046	1	353–393	353–393	NUM
ejpam-1535	1046	2	.	.	PUNCT
ejpam-1535	1047	1	[	[	X
ejpam-1535	1047	2	32	32	NUM
ejpam-1535	1047	3	]	]	PUNCT
ejpam-1535	1047	4	d.	d.	PROPN
ejpam-1535	1047	5	b.	b.	PROPN
ejpam-1535	1047	6	mcalister	mcalister	PROPN
ejpam-1535	1047	7	,	,	PUNCT
ejpam-1535	1047	8	∨-prehomomorphisms	∨-prehomomorphism	NOUN
ejpam-1535	1047	9	on	on	ADP
ejpam-1535	1047	10	inverse	inverse	NOUN
ejpam-1535	1047	11	semigroups	semigroup	NOUN
ejpam-1535	1047	12	,	,	PUNCT
ejpam-1535	1047	13	pacific	pacific	PROPN
ejpam-1535	1047	14	journal	journal	NOUN
ejpam-1535	1047	15	of	of	ADP
ejpam-1535	1047	16	mathematics	mathematics	PROPN
ejpam-1535	1047	17	67	67	NUM
ejpam-1535	1047	18	(	(	PUNCT
ejpam-1535	1047	19	1976	1976	NUM
ejpam-1535	1047	20	)	)	PUNCT
ejpam-1535	1047	21	215–231	215–231	NUM
ejpam-1535	1047	22	.	.	PUNCT
ejpam-1535	1048	1	[	[	X
ejpam-1535	1048	2	33	33	NUM
ejpam-1535	1048	3	]	]	X
ejpam-1535	1048	4	j.	j.	PROPN
ejpam-1535	1048	5	meakin	meakin	PROPN
ejpam-1535	1048	6	,	,	PUNCT
ejpam-1535	1048	7	on	on	ADP
ejpam-1535	1048	8	the	the	DET
ejpam-1535	1048	9	structure	structure	NOUN
ejpam-1535	1048	10	of	of	ADP
ejpam-1535	1048	11	inverse	inverse	NOUN
ejpam-1535	1048	12	semigroups	semigroup	NOUN
ejpam-1535	1048	13	,	,	PUNCT
ejpam-1535	1048	14	semigroup	semigroup	PROPN
ejpam-1535	1048	15	forum	forum	PROPN
ejpam-1535	1048	16	12	12	NUM
ejpam-1535	1048	17	(	(	PUNCT
ejpam-1535	1048	18	1976	1976	NUM
ejpam-1535	1048	19	)	)	PUNCT
ejpam-1535	1048	20	6–14	6–14	PROPN
ejpam-1535	1048	21	.	.	PUNCT
ejpam-1535	1049	1	[	[	X
ejpam-1535	1049	2	34	34	NUM
ejpam-1535	1049	3	]	]	PUNCT
ejpam-1535	1049	4	k.	k.	PROPN
ejpam-1535	1049	5	s.	s.	PROPN
ejpam-1535	1049	6	s.	s.	PROPN
ejpam-1535	1049	7	nambooripad	nambooripad	PROPN
ejpam-1535	1049	8	,	,	PUNCT
ejpam-1535	1049	9	structure	structure	NOUN
ejpam-1535	1049	10	of	of	ADP
ejpam-1535	1049	11	regular	regular	ADJ
ejpam-1535	1049	12	semigroups	semigroup	NOUN
ejpam-1535	1049	13	,	,	PUNCT
ejpam-1535	1049	14	phd	phd	NOUN
ejpam-1535	1049	15	thesis	thesis	NOUN
ejpam-1535	1049	16	,	,	PUNCT
ejpam-1535	1049	17	university	university	NOUN
ejpam-1535	1049	18	of	of	ADP
ejpam-1535	1049	19	kerala	kerala	PROPN
ejpam-1535	1049	20	,	,	PUNCT
ejpam-1535	1049	21	1973	1973	NUM
ejpam-1535	1049	22	.	.	PUNCT
ejpam-1535	1050	1	[	[	X
ejpam-1535	1050	2	35	35	NUM
ejpam-1535	1050	3	]	]	PUNCT
ejpam-1535	1050	4	k.	k.	PROPN
ejpam-1535	1050	5	s.	s.	PROPN
ejpam-1535	1050	6	s.	s.	PROPN
ejpam-1535	1050	7	nambooripad	nambooripad	PROPN
ejpam-1535	1050	8	,	,	PUNCT
ejpam-1535	1050	9	structure	structure	NOUN
ejpam-1535	1050	10	of	of	ADP
ejpam-1535	1050	11	regular	regular	ADJ
ejpam-1535	1050	12	semigroups	semigroup	NOUN
ejpam-1535	1050	13	,	,	PUNCT
ejpam-1535	1050	14	i.	i.	PROPN
ejpam-1535	1050	15	fundamental	fundamental	ADJ
ejpam-1535	1050	16	regular	regular	ADJ
ejpam-1535	1050	17	semigroups	semigroup	NOUN
ejpam-1535	1050	18	,	,	PUNCT
ejpam-1535	1050	19	semigroup	semigroup	PROPN
ejpam-1535	1050	20	forum	forum	NOUN
ejpam-1535	1050	21	9	9	NUM
ejpam-1535	1050	22	(	(	PUNCT
ejpam-1535	1050	23	1975	1975	NUM
ejpam-1535	1050	24	)	)	PUNCT
ejpam-1535	1051	1	354–363	354–363	NUM
ejpam-1535	1051	2	;	;	PUNCT
ejpam-1535	1051	3	ii	ii	X
ejpam-1535	1051	4	.	.	PUNCT
ejpam-1535	1052	1	the	the	DET
ejpam-1535	1052	2	general	general	ADJ
ejpam-1535	1052	3	case	case	NOUN
ejpam-1535	1052	4	,	,	PUNCT
ejpam-1535	1052	5	ibid	ibid	NOUN
ejpam-1535	1052	6	.	.	PUNCT
ejpam-1535	1053	1	364–371	364–371	NUM
ejpam-1535	1053	2	.	.	PUNCT
ejpam-1535	1054	1	[	[	X
ejpam-1535	1054	2	36	36	NUM
ejpam-1535	1054	3	]	]	PUNCT
ejpam-1535	1054	4	k.	k.	PROPN
ejpam-1535	1054	5	s.	s.	PROPN
ejpam-1535	1054	6	s.	s.	PROPN
ejpam-1535	1054	7	nambooripad	nambooripad	PROPN
ejpam-1535	1054	8	,	,	PUNCT
ejpam-1535	1054	9	structure	structure	NOUN
ejpam-1535	1054	10	of	of	ADP
ejpam-1535	1054	11	regular	regular	ADJ
ejpam-1535	1054	12	semigroups	semigroup	NOUN
ejpam-1535	1054	13	i	i	PRON
ejpam-1535	1054	14	,	,	PUNCT
ejpam-1535	1054	15	memoirs	memoir	NOUN
ejpam-1535	1054	16	of	of	ADP
ejpam-1535	1054	17	the	the	DET
ejpam-1535	1054	18	american	american	PROPN
ejpam-1535	1054	19	mathematical	mathematical	PROPN
ejpam-1535	1054	20	society	society	NOUN
ejpam-1535	1054	21	22	22	NUM
ejpam-1535	1054	22	(	(	PUNCT
ejpam-1535	1054	23	1979	1979	NUM
ejpam-1535	1054	24	)	)	PUNCT
ejpam-1535	1055	1	no	no	INTJ
ejpam-1535	1055	2	.	.	NOUN
ejpam-1535	1056	1	224	224	NUM
ejpam-1535	1056	2	.	.	PUNCT
ejpam-1535	1057	1	[	[	X
ejpam-1535	1057	2	37	37	NUM
ejpam-1535	1057	3	]	]	PUNCT
ejpam-1535	1057	4	k.	k.	PROPN
ejpam-1535	1057	5	s.	s.	PROPN
ejpam-1535	1057	6	s.	s.	PROPN
ejpam-1535	1057	7	nambooripad	nambooripad	PROPN
ejpam-1535	1057	8	and	and	CCONJ
ejpam-1535	1057	9	r.	r.	PROPN
ejpam-1535	1057	10	veeramony	veeramony	PROPN
ejpam-1535	1057	11	,	,	PUNCT
ejpam-1535	1057	12	subdirect	subdirect	NOUN
ejpam-1535	1057	13	products	product	NOUN
ejpam-1535	1057	14	of	of	ADP
ejpam-1535	1057	15	regular	regular	ADJ
ejpam-1535	1057	16	semigroups	semigroup	NOUN
ejpam-1535	1057	17	,	,	PUNCT
ejpam-1535	1057	18	semigroup	semigroup	PROPN
ejpam-1535	1057	19	forum	forum	PROPN
ejpam-1535	1057	20	27	27	NUM
ejpam-1535	1057	21	(	(	PUNCT
ejpam-1535	1057	22	1983	1983	NUM
ejpam-1535	1057	23	)	)	PUNCT
ejpam-1535	1057	24	265–307	265–307	NUM
ejpam-1535	1057	25	.	.	PUNCT
ejpam-1535	1058	1	[	[	X
ejpam-1535	1058	2	38	38	NUM
ejpam-1535	1058	3	]	]	PUNCT
ejpam-1535	1058	4	g.	g.	PROPN
ejpam-1535	1058	5	b.	b.	PROPN
ejpam-1535	1058	6	preston	preston	PROPN
ejpam-1535	1058	7	,	,	PUNCT
ejpam-1535	1058	8	some	some	DET
ejpam-1535	1058	9	problems	problem	NOUN
ejpam-1535	1058	10	in	in	ADP
ejpam-1535	1058	11	the	the	DET
ejpam-1535	1058	12	theory	theory	NOUN
ejpam-1535	1058	13	of	of	ADP
ejpam-1535	1058	14	ideals	ideal	NOUN
ejpam-1535	1058	15	,	,	PUNCT
ejpam-1535	1058	16	dphil	dphil	ADJ
ejpam-1535	1058	17	thesis	thesis	NOUN
ejpam-1535	1058	18	,	,	PUNCT
ejpam-1535	1058	19	university	university	NOUN
ejpam-1535	1058	20	of	of	ADP
ejpam-1535	1058	21	oxford	oxford	PROPN
ejpam-1535	1058	22	,	,	PUNCT
ejpam-1535	1058	23	1953	1953	NUM
ejpam-1535	1058	24	.	.	PUNCT
ejpam-1535	1058	25	references	reference	NOUN
ejpam-1535	1058	26	450	450	NUM
ejpam-1535	1058	27	[	[	SYM
ejpam-1535	1058	28	39	39	NUM
ejpam-1535	1058	29	]	]	PUNCT
ejpam-1535	1058	30	g.	g.	PROPN
ejpam-1535	1058	31	b.	b.	PROPN
ejpam-1535	1058	32	preston	preston	PROPN
ejpam-1535	1058	33	,	,	PUNCT
ejpam-1535	1058	34	inverse	inverse	ADJ
ejpam-1535	1058	35	semi	semi	NOUN
ejpam-1535	1058	36	-	-	NOUN
ejpam-1535	1058	37	groups	group	NOUN
ejpam-1535	1058	38	,	,	PUNCT
ejpam-1535	1058	39	journal	journal	NOUN
ejpam-1535	1058	40	of	of	ADP
ejpam-1535	1058	41	the	the	DET
ejpam-1535	1058	42	london	london	PROPN
ejpam-1535	1058	43	mathematical	mathematical	ADJ
ejpam-1535	1058	44	society	society	NOUN
ejpam-1535	1058	45	29	29	NUM
ejpam-1535	1058	46	(	(	PUNCT
ejpam-1535	1058	47	1954	1954	NUM
ejpam-1535	1058	48	)	)	PUNCT
ejpam-1535	1058	49	396–403	396–403	NUM
ejpam-1535	1058	50	.	.	PUNCT
ejpam-1535	1059	1	[	[	X
ejpam-1535	1059	2	40	40	NUM
ejpam-1535	1059	3	]	]	PUNCT
ejpam-1535	1059	4	g.	g.	PROPN
ejpam-1535	1059	5	b.	b.	PROPN
ejpam-1535	1059	6	preston	preston	PROPN
ejpam-1535	1059	7	,	,	PUNCT
ejpam-1535	1059	8	inverse	inverse	ADJ
ejpam-1535	1059	9	semi	semi	NOUN
ejpam-1535	1059	10	-	-	NOUN
ejpam-1535	1059	11	groups	group	NOUN
ejpam-1535	1059	12	with	with	ADP
ejpam-1535	1059	13	minimal	minimal	ADJ
ejpam-1535	1059	14	right	right	ADJ
ejpam-1535	1059	15	ideals	ideal	NOUN
ejpam-1535	1059	16	,	,	PUNCT
ejpam-1535	1059	17	journal	journal	NOUN
ejpam-1535	1059	18	of	of	ADP
ejpam-1535	1059	19	the	the	DET
ejpam-1535	1059	20	london	london	PROPN
ejpam-1535	1059	21	mathematical	mathematical	ADJ
ejpam-1535	1059	22	society	society	NOUN
ejpam-1535	1059	23	29	29	NUM
ejpam-1535	1059	24	(	(	PUNCT
ejpam-1535	1059	25	1954	1954	NUM
ejpam-1535	1059	26	)	)	PUNCT
ejpam-1535	1059	27	404–411	404–411	NUM
ejpam-1535	1059	28	.	.	PUNCT
ejpam-1535	1060	1	[	[	X
ejpam-1535	1060	2	41	41	NUM
ejpam-1535	1060	3	]	]	X
ejpam-1535	1060	4	g.	g.	PROPN
ejpam-1535	1060	5	b.	b.	PROPN
ejpam-1535	1060	6	preston	preston	PROPN
ejpam-1535	1060	7	,	,	PUNCT
ejpam-1535	1060	8	representations	representation	NOUN
ejpam-1535	1060	9	of	of	ADP
ejpam-1535	1060	10	inverse	inverse	NOUN
ejpam-1535	1060	11	semi	semi	NOUN
ejpam-1535	1060	12	-	-	NOUN
ejpam-1535	1060	13	groups	group	NOUN
ejpam-1535	1060	14	,	,	PUNCT
ejpam-1535	1060	15	journal	journal	NOUN
ejpam-1535	1060	16	of	of	ADP
ejpam-1535	1060	17	the	the	DET
ejpam-1535	1060	18	london	london	PROPN
ejpam-1535	1060	19	mathematical	mathematical	ADJ
ejpam-1535	1060	20	society	society	NOUN
ejpam-1535	1060	21	29	29	NUM
ejpam-1535	1060	22	(	(	PUNCT
ejpam-1535	1060	23	1954	1954	NUM
ejpam-1535	1060	24	)	)	PUNCT
ejpam-1535	1060	25	411–419	411–419	NUM
ejpam-1535	1060	26	.	.	PUNCT
ejpam-1535	1061	1	[	[	X
ejpam-1535	1061	2	42	42	NUM
ejpam-1535	1061	3	]	]	X
ejpam-1535	1061	4	g.	g.	PROPN
ejpam-1535	1061	5	b.	b.	PROPN
ejpam-1535	1061	6	preston	preston	PROPN
ejpam-1535	1061	7	,	,	PUNCT
ejpam-1535	1061	8	personal	personal	ADJ
ejpam-1535	1061	9	reminiscences	reminiscence	NOUN
ejpam-1535	1061	10	of	of	ADP
ejpam-1535	1061	11	the	the	DET
ejpam-1535	1061	12	early	early	ADJ
ejpam-1535	1061	13	history	history	NOUN
ejpam-1535	1061	14	of	of	ADP
ejpam-1535	1061	15	semigroups	semigroup	NOUN
ejpam-1535	1061	16	,	,	PUNCT
ejpam-1535	1061	17	in	in	ADP
ejpam-1535	1061	18	:	:	PUNCT
ejpam-1535	1061	19	t.	t.	PROPN
ejpam-1535	1061	20	e.	e.	PROPN
ejpam-1535	1061	21	hall	hall	PROPN
ejpam-1535	1061	22	,	,	PUNCT
ejpam-1535	1061	23	p.	p.	PROPN
ejpam-1535	1061	24	r.	r.	PROPN
ejpam-1535	1061	25	jones	jones	PROPN
ejpam-1535	1061	26	and	and	CCONJ
ejpam-1535	1061	27	j.	j.	PROPN
ejpam-1535	1061	28	c.	c.	PROPN
ejpam-1535	1061	29	meakin	meakin	PROPN
ejpam-1535	1061	30	(	(	PUNCT
ejpam-1535	1061	31	eds	eds	PROPN
ejpam-1535	1061	32	.	.	PUNCT
ejpam-1535	1061	33	)	)	PUNCT
ejpam-1535	1061	34	,	,	PUNCT
ejpam-1535	1061	35	monash	monash	PROPN
ejpam-1535	1061	36	conference	conference	PROPN
ejpam-1535	1061	37	on	on	ADP
ejpam-1535	1061	38	semigroup	semigroup	PROPN
ejpam-1535	1061	39	theory	theory	NOUN
ejpam-1535	1061	40	,	,	PUNCT
ejpam-1535	1061	41	melbourne	melbourne	PROPN
ejpam-1535	1061	42	1990	1990	NUM
ejpam-1535	1061	43	,	,	PUNCT
ejpam-1535	1061	44	world	world	NOUN
ejpam-1535	1061	45	scientific	scientific	ADJ
ejpam-1535	1061	46	,	,	PUNCT
ejpam-1535	1061	47	river	river	NOUN
ejpam-1535	1061	48	edge	edge	NOUN
ejpam-1535	1061	49	,	,	PUNCT
ejpam-1535	1061	50	nj	nj	PROPN
ejpam-1535	1061	51	,	,	PUNCT
ejpam-1535	1061	52	1991	1991	NUM
ejpam-1535	1061	53	,	,	PUNCT
ejpam-1535	1061	54	pp	pp	ADJ
ejpam-1535	1061	55	.	.	PUNCT
ejpam-1535	1061	56	16–30	16–30	NUM
ejpam-1535	1061	57	.	.	PUNCT
ejpam-1535	1062	1	[	[	X
ejpam-1535	1062	2	43	43	NUM
ejpam-1535	1062	3	]	]	X
ejpam-1535	1062	4	d.	d.	PROPN
ejpam-1535	1062	5	rees	rees	PROPN
ejpam-1535	1062	6	,	,	PUNCT
ejpam-1535	1062	7	on	on	ADP
ejpam-1535	1062	8	the	the	DET
ejpam-1535	1062	9	group	group	NOUN
ejpam-1535	1062	10	of	of	ADP
ejpam-1535	1062	11	a	a	DET
ejpam-1535	1062	12	set	set	NOUN
ejpam-1535	1062	13	of	of	ADP
ejpam-1535	1062	14	partial	partial	ADJ
ejpam-1535	1062	15	transformations	transformation	NOUN
ejpam-1535	1062	16	,	,	PUNCT
ejpam-1535	1062	17	journal	journal	NOUN
ejpam-1535	1062	18	of	of	ADP
ejpam-1535	1062	19	the	the	DET
ejpam-1535	1062	20	london	london	PROPN
ejpam-1535	1062	21	mathematical	mathematical	ADJ
ejpam-1535	1062	22	society	society	NOUN
ejpam-1535	1062	23	22	22	NUM
ejpam-1535	1062	24	(	(	PUNCT
ejpam-1535	1062	25	1947	1947	NUM
ejpam-1535	1062	26	)	)	PUNCT
ejpam-1535	1062	27	281–284	281–284	NUM
ejpam-1535	1062	28	.	.	PUNCT
ejpam-1535	1063	1	[	[	X
ejpam-1535	1063	2	44	44	NUM
ejpam-1535	1063	3	]	]	PUNCT
ejpam-1535	1063	4	b.	b.	PROPN
ejpam-1535	1063	5	m.	m.	PROPN
ejpam-1535	1063	6	schein	schein	PROPN
ejpam-1535	1063	7	,	,	PUNCT
ejpam-1535	1063	8	on	on	ADP
ejpam-1535	1063	9	the	the	DET
ejpam-1535	1063	10	theory	theory	NOUN
ejpam-1535	1063	11	of	of	ADP
ejpam-1535	1063	12	generalised	generalised	ADJ
ejpam-1535	1063	13	heaps	heap	NOUN
ejpam-1535	1063	14	and	and	CCONJ
ejpam-1535	1063	15	generalised	generalised	ADJ
ejpam-1535	1063	16	groups	group	NOUN
ejpam-1535	1063	17	,	,	PUNCT
ejpam-1535	1063	18	in	in	ADP
ejpam-1535	1063	19	:	:	PUNCT
ejpam-1535	1063	20	v.	v.	PROPN
ejpam-1535	1063	21	v.	v.	ADP
ejpam-1535	1063	22	wagner	wagner	PROPN
ejpam-1535	1063	23	(	(	PUNCT
ejpam-1535	1063	24	ed	ed	NOUN
ejpam-1535	1063	25	.	.	PUNCT
ejpam-1535	1063	26	)	)	PUNCT
ejpam-1535	1063	27	,	,	PUNCT
ejpam-1535	1063	28	theory	theory	NOUN
ejpam-1535	1063	29	of	of	ADP
ejpam-1535	1063	30	semigroups	semigroup	NOUN
ejpam-1535	1063	31	and	and	CCONJ
ejpam-1535	1063	32	its	its	PRON
ejpam-1535	1063	33	applications	application	NOUN
ejpam-1535	1063	34	,	,	PUNCT
ejpam-1535	1063	35	vol	vol	NOUN
ejpam-1535	1063	36	.	.	PROPN
ejpam-1535	1063	37	1	1	NUM
ejpam-1535	1063	38	,	,	PUNCT
ejpam-1535	1063	39	university	university	NOUN
ejpam-1535	1063	40	of	of	ADP
ejpam-1535	1063	41	saratov	saratov	PROPN
ejpam-1535	1063	42	,	,	PUNCT
ejpam-1535	1063	43	saratov	saratov	PROPN
ejpam-1535	1063	44	,	,	PUNCT
ejpam-1535	1063	45	1965	1965	NUM
ejpam-1535	1063	46	,	,	PUNCT
ejpam-1535	1063	47	pp	pp	ADJ
ejpam-1535	1063	48	.	.	PUNCT
ejpam-1535	1064	1	286–324	286–324	NUM
ejpam-1535	1064	2	(	(	PUNCT
ejpam-1535	1064	3	in	in	ADP
ejpam-1535	1064	4	russian	russian	PROPN
ejpam-1535	1064	5	)	)	PUNCT
ejpam-1535	1064	6	;	;	PUNCT
ejpam-1535	1064	7	expanded	expand	VERB
ejpam-1535	1064	8	english	english	ADJ
ejpam-1535	1064	9	translation	translation	NOUN
ejpam-1535	1064	10	:	:	PUNCT
ejpam-1535	1065	1	[	[	X
ejpam-1535	1065	2	45	45	NUM
ejpam-1535	1065	3	]	]	PUNCT
ejpam-1535	1065	4	.	.	PUNCT
ejpam-1535	1066	1	[	[	X
ejpam-1535	1066	2	45	45	NUM
ejpam-1535	1066	3	]	]	X
ejpam-1535	1066	4	b.	b.	PROPN
ejpam-1535	1066	5	m.	m.	PROPN
ejpam-1535	1066	6	schein	schein	PROPN
ejpam-1535	1066	7	,	,	PUNCT
ejpam-1535	1066	8	on	on	ADP
ejpam-1535	1066	9	the	the	DET
ejpam-1535	1066	10	theory	theory	NOUN
ejpam-1535	1066	11	of	of	ADP
ejpam-1535	1066	12	inverse	inverse	NOUN
ejpam-1535	1066	13	semigroups	semigroup	NOUN
ejpam-1535	1066	14	and	and	CCONJ
ejpam-1535	1066	15	generalised	generalised	ADJ
ejpam-1535	1066	16	grouds	groud	NOUN
ejpam-1535	1066	17	,	,	PUNCT
ejpam-1535	1066	18	american	american	PROPN
ejpam-1535	1066	19	mathematical	mathematical	ADJ
ejpam-1535	1066	20	society	society	NOUN
ejpam-1535	1066	21	translations	translation	NOUN
ejpam-1535	1066	22	(	(	PUNCT
ejpam-1535	1066	23	2	2	NUM
ejpam-1535	1066	24	)	)	SYM
ejpam-1535	1066	25	113	113	NUM
ejpam-1535	1066	26	(	(	PUNCT
ejpam-1535	1066	27	1979	1979	NUM
ejpam-1535	1066	28	)	)	PUNCT
ejpam-1535	1066	29	89–122	89–122	PROPN
ejpam-1535	1066	30	;	;	PUNCT
ejpam-1535	1066	31	expanded	expand	VERB
ejpam-1535	1066	32	english	english	ADJ
ejpam-1535	1066	33	translation	translation	NOUN
ejpam-1535	1066	34	of	of	ADP
ejpam-1535	1066	35	[	[	X
ejpam-1535	1066	36	44	44	NUM
ejpam-1535	1066	37	]	]	PUNCT
ejpam-1535	1066	38	.	.	PUNCT
ejpam-1535	1067	1	[	[	X
ejpam-1535	1067	2	46	46	NUM
ejpam-1535	1067	3	]	]	X
ejpam-1535	1067	4	b.	b.	PROPN
ejpam-1535	1067	5	m.	m.	PROPN
ejpam-1535	1067	6	schein	schein	PROPN
ejpam-1535	1067	7	,	,	PUNCT
ejpam-1535	1067	8	prehistory	prehistory	NOUN
ejpam-1535	1067	9	of	of	ADP
ejpam-1535	1067	10	the	the	DET
ejpam-1535	1067	11	theory	theory	NOUN
ejpam-1535	1067	12	of	of	ADP
ejpam-1535	1067	13	inverse	inverse	NOUN
ejpam-1535	1067	14	semigroups	semigroup	NOUN
ejpam-1535	1067	15	,	,	PUNCT
ejpam-1535	1067	16	in	in	ADP
ejpam-1535	1067	17	:	:	PUNCT
ejpam-1535	1067	18	robert	robert	PROPN
ejpam-1535	1067	19	j.	j.	PROPN
ejpam-1535	1067	20	koch	koch	PROPN
ejpam-1535	1067	21	and	and	CCONJ
ejpam-1535	1067	22	john	john	PROPN
ejpam-1535	1067	23	a.	a.	PROPN
ejpam-1535	1067	24	hildebrandt	hildebrandt	PROPN
ejpam-1535	1067	25	(	(	PUNCT
ejpam-1535	1067	26	eds	ed	NOUN
ejpam-1535	1067	27	.	.	PUNCT
ejpam-1535	1067	28	)	)	PUNCT
ejpam-1535	1067	29	,	,	PUNCT
ejpam-1535	1067	30	proceedings	proceeding	NOUN
ejpam-1535	1067	31	of	of	ADP
ejpam-1535	1067	32	the	the	DET
ejpam-1535	1067	33	1986	1986	NUM
ejpam-1535	1067	34	lsu	lsu	NOUN
ejpam-1535	1067	35	semigroup	semigroup	PROPN
ejpam-1535	1067	36	conference	conference	NOUN
ejpam-1535	1067	37	(	(	PUNCT
ejpam-1535	1067	38	kochfest	kochfest	ADJ
ejpam-1535	1067	39	60	60	NUM
ejpam-1535	1067	40	)	)	PUNCT
ejpam-1535	1067	41	,	,	PUNCT
ejpam-1535	1067	42	louisiana	louisiana	PROPN
ejpam-1535	1067	43	state	state	PROPN
ejpam-1535	1067	44	university	university	PROPN
ejpam-1535	1067	45	,	,	PUNCT
ejpam-1535	1067	46	baton	baton	NOUN
ejpam-1535	1067	47	rouge	rouge	NOUN
ejpam-1535	1067	48	,	,	PUNCT
ejpam-1535	1067	49	la	la	NOUN
ejpam-1535	1067	50	,	,	PUNCT
ejpam-1535	1067	51	1986	1986	NUM
ejpam-1535	1067	52	,	,	PUNCT
ejpam-1535	1067	53	pp	pp	ADJ
ejpam-1535	1067	54	.	.	PUNCT
ejpam-1535	1068	1	72–76	72–76	X
ejpam-1535	1068	2	.	.	PUNCT
ejpam-1535	1069	1	[	[	X
ejpam-1535	1069	2	47	47	NUM
ejpam-1535	1069	3	]	]	X
ejpam-1535	1069	4	b.	b.	PROPN
ejpam-1535	1069	5	m.	m.	PROPN
ejpam-1535	1069	6	schein	schein	PROPN
ejpam-1535	1069	7	,	,	PUNCT
ejpam-1535	1069	8	book	book	NOUN
ejpam-1535	1069	9	review	review	NOUN
ejpam-1535	1069	10	:	:	PUNCT
ejpam-1535	1069	11	‘	'	PUNCT
ejpam-1535	1069	12	inverse	inverse	ADJ
ejpam-1535	1069	13	semigroups	semigroup	NOUN
ejpam-1535	1069	14	:	:	PUNCT
ejpam-1535	1069	15	the	the	DET
ejpam-1535	1069	16	theory	theory	NOUN
ejpam-1535	1069	17	of	of	ADP
ejpam-1535	1069	18	partial	partial	ADJ
ejpam-1535	1069	19	symmetries	symmetry	NOUN
ejpam-1535	1069	20	’	'	PUNCT
ejpam-1535	1069	21	by	by	ADP
ejpam-1535	1069	22	mark	mark	PROPN
ejpam-1535	1069	23	v.	v.	PROPN
ejpam-1535	1069	24	lawson	lawson	PROPN
ejpam-1535	1069	25	,	,	PUNCT
ejpam-1535	1069	26	semigroup	semigroup	PROPN
ejpam-1535	1069	27	forum	forum	PROPN
ejpam-1535	1069	28	65	65	NUM
ejpam-1535	1069	29	(	(	PUNCT
ejpam-1535	1069	30	2002	2002	NUM
ejpam-1535	1069	31	)	)	PUNCT
ejpam-1535	1069	32	149–158	149–158	NUM
ejpam-1535	1069	33	.	.	PUNCT
ejpam-1535	1070	1	[	[	X
ejpam-1535	1070	2	48	48	NUM
ejpam-1535	1070	3	]	]	PUNCT
ejpam-1535	1070	4	j.	j.	PROPN
ejpam-1535	1070	5	a.	a.	PROPN
ejpam-1535	1070	6	schouten	schouten	PROPN
ejpam-1535	1070	7	and	and	CCONJ
ejpam-1535	1070	8	j.	j.	PROPN
ejpam-1535	1070	9	haantjes	haantjes	PROPN
ejpam-1535	1070	10	,	,	PUNCT
ejpam-1535	1070	11	on	on	ADP
ejpam-1535	1070	12	the	the	DET
ejpam-1535	1070	13	theory	theory	NOUN
ejpam-1535	1070	14	of	of	ADP
ejpam-1535	1070	15	the	the	DET
ejpam-1535	1070	16	geometric	geometric	ADJ
ejpam-1535	1070	17	object	object	NOUN
ejpam-1535	1070	18	,	,	PUNCT
ejpam-1535	1070	19	proceedings	proceeding	NOUN
ejpam-1535	1070	20	of	of	ADP
ejpam-1535	1070	21	the	the	DET
ejpam-1535	1070	22	london	london	PROPN
ejpam-1535	1070	23	mathematical	mathematical	ADJ
ejpam-1535	1070	24	society	society	NOUN
ejpam-1535	1070	25	42	42	NUM
ejpam-1535	1070	26	(	(	PUNCT
ejpam-1535	1070	27	1937	1937	NUM
ejpam-1535	1070	28	)	)	PUNCT
ejpam-1535	1071	1	356–376	356–376	NUM
ejpam-1535	1071	2	.	.	PUNCT
ejpam-1535	1072	1	[	[	X
ejpam-1535	1072	2	49	49	NUM
ejpam-1535	1072	3	]	]	X
ejpam-1535	1072	4	o.	o.	PROPN
ejpam-1535	1072	5	veblen	veblen	PROPN
ejpam-1535	1072	6	and	and	CCONJ
ejpam-1535	1072	7	j.	j.	PROPN
ejpam-1535	1072	8	h.	h.	PROPN
ejpam-1535	1072	9	c.	c.	PROPN
ejpam-1535	1072	10	whitehead	whitehead	PROPN
ejpam-1535	1072	11	,	,	PUNCT
ejpam-1535	1072	12	the	the	DET
ejpam-1535	1072	13	foundations	foundation	NOUN
ejpam-1535	1072	14	of	of	ADP
ejpam-1535	1072	15	differential	differential	ADJ
ejpam-1535	1072	16	geometry	geometry	NOUN
ejpam-1535	1072	17	,	,	PUNCT
ejpam-1535	1072	18	cambridge	cambridge	PROPN
ejpam-1535	1072	19	tract	tract	NOUN
ejpam-1535	1072	20	no	no	INTJ
ejpam-1535	1072	21	.	.	PROPN
ejpam-1535	1072	22	24	24	NUM
ejpam-1535	1072	23	,	,	PUNCT
ejpam-1535	1072	24	cambridge	cambridge	PROPN
ejpam-1535	1072	25	university	university	PROPN
ejpam-1535	1072	26	press	press	PROPN
ejpam-1535	1072	27	,	,	PUNCT
ejpam-1535	1072	28	cambridge	cambridge	PROPN
ejpam-1535	1072	29	,	,	PUNCT
ejpam-1535	1072	30	1932	1932	NUM
ejpam-1535	1072	31	.	.	PUNCT
ejpam-1535	1073	1	[	[	X
ejpam-1535	1073	2	50	50	NUM
ejpam-1535	1073	3	]	]	PUNCT
ejpam-1535	1073	4	v.	v.	PROPN
ejpam-1535	1073	5	v.	v.	PROPN
ejpam-1535	1073	6	wagner	wagner	PROPN
ejpam-1535	1073	7	,	,	PUNCT
ejpam-1535	1073	8	on	on	ADP
ejpam-1535	1073	9	the	the	DET
ejpam-1535	1073	10	theory	theory	NOUN
ejpam-1535	1073	11	of	of	ADP
ejpam-1535	1073	12	partial	partial	ADJ
ejpam-1535	1073	13	transformations	transformation	NOUN
ejpam-1535	1073	14	,	,	PUNCT
ejpam-1535	1073	15	doklady	doklady	NOUN
ejpam-1535	1073	16	akademii	akademii	NOUN
ejpam-1535	1073	17	nauk	nauk	NOUN
ejpam-1535	1073	18	sssr	sssr	NOUN
ejpam-1535	1073	19	84	84	NUM
ejpam-1535	1073	20	(	(	PUNCT
ejpam-1535	1073	21	1952	1952	NUM
ejpam-1535	1073	22	)	)	PUNCT
ejpam-1535	1074	1	653–656	653–656	NUM
ejpam-1535	1074	2	(	(	PUNCT
ejpam-1535	1074	3	in	in	ADP
ejpam-1535	1074	4	russian	russian	NOUN
ejpam-1535	1074	5	)	)	PUNCT
ejpam-1535	1074	6	.	.	PUNCT
ejpam-1535	1075	1	[	[	X
ejpam-1535	1075	2	51	51	NUM
ejpam-1535	1075	3	]	]	X
ejpam-1535	1075	4	v.	v.	PROPN
ejpam-1535	1075	5	v.	v.	PROPN
ejpam-1535	1075	6	wagner	wagner	PROPN
ejpam-1535	1075	7	,	,	PUNCT
ejpam-1535	1075	8	generalised	generalised	ADJ
ejpam-1535	1075	9	groups	group	NOUN
ejpam-1535	1075	10	,	,	PUNCT
ejpam-1535	1075	11	doklady	doklady	NOUN
ejpam-1535	1075	12	akademii	akademii	NOUN
ejpam-1535	1075	13	nauk	nauk	NOUN
ejpam-1535	1075	14	sssr	sssr	NOUN
ejpam-1535	1075	15	84	84	NUM
ejpam-1535	1075	16	(	(	PUNCT
ejpam-1535	1075	17	1952	1952	NUM
ejpam-1535	1075	18	)	)	PUNCT
ejpam-1535	1075	19	1119–1122	1119–1122	NUM
ejpam-1535	1075	20	(	(	PUNCT
ejpam-1535	1075	21	in	in	ADP
ejpam-1535	1075	22	russian	russian	NOUN
ejpam-1535	1075	23	)	)	PUNCT
ejpam-1535	1075	24	.	.	PUNCT
ejpam-1535	1076	1	[	[	X
ejpam-1535	1076	2	52	52	NUM
ejpam-1535	1076	3	]	]	PUNCT
ejpam-1535	1076	4	v.	v.	PROPN
ejpam-1535	1076	5	v.	v.	PROPN
ejpam-1535	1076	6	wagner	wagner	PROPN
ejpam-1535	1076	7	,	,	PUNCT
ejpam-1535	1076	8	theory	theory	NOUN
ejpam-1535	1076	9	of	of	ADP
ejpam-1535	1076	10	generalised	generalised	ADJ
ejpam-1535	1076	11	heaps	heap	NOUN
ejpam-1535	1076	12	and	and	CCONJ
ejpam-1535	1076	13	generalised	generalised	ADJ
ejpam-1535	1076	14	groups	group	NOUN
ejpam-1535	1076	15	,	,	PUNCT
ejpam-1535	1076	16	matematicheskii	matematicheskii	NOUN
ejpam-1535	1076	17	sbornik	sbornik	ADJ
ejpam-1535	1076	18	(	(	PUNCT
ejpam-1535	1076	19	n.s	n.s	PROPN
ejpam-1535	1076	20	.	.	PROPN
ejpam-1535	1076	21	)	)	PUNCT
ejpam-1535	1077	1	32(74	32(74	NUM
ejpam-1535	1077	2	)	)	PUNCT
ejpam-1535	1077	3	(	(	PUNCT
ejpam-1535	1077	4	1953	1953	NUM
ejpam-1535	1077	5	)	)	PUNCT
ejpam-1535	1078	1	545–632	545–632	NUM
ejpam-1535	1078	2	(	(	PUNCT
ejpam-1535	1078	3	in	in	ADP
ejpam-1535	1078	4	russian	russian	NOUN
ejpam-1535	1078	5	)	)	PUNCT
ejpam-1535	1078	6	.	.	PUNCT
ejpam-1535	1079	1	[	[	X
ejpam-1535	1079	2	53	53	NUM
ejpam-1535	1079	3	]	]	X
ejpam-1535	1079	4	h.	h.	NOUN
ejpam-1535	1079	5	wussing	wussing	NOUN
ejpam-1535	1079	6	,	,	PUNCT
ejpam-1535	1079	7	die	die	VERB
ejpam-1535	1079	8	genesis	genesis	PROPN
ejpam-1535	1079	9	des	des	PROPN
ejpam-1535	1079	10	abstrakten	abstrakten	PROPN
ejpam-1535	1079	11	gruppenbegriffes	gruppenbegriffes	NOUN
ejpam-1535	1079	12	,	,	PUNCT
ejpam-1535	1079	13	deutscher	deutscher	PROPN
ejpam-1535	1079	14	verlag	verlag	PROPN
ejpam-1535	1079	15	der	der	PROPN
ejpam-1535	1079	16	wissenschaften	wissenschaften	NOUN
ejpam-1535	1079	17	,	,	PUNCT
ejpam-1535	1079	18	berlin	berlin	PROPN
ejpam-1535	1079	19	,	,	PUNCT
ejpam-1535	1079	20	1969	1969	NUM
ejpam-1535	1079	21	;	;	PUNCT
ejpam-1535	1079	22	english	english	ADJ
ejpam-1535	1079	23	translation	translation	NOUN
ejpam-1535	1079	24	:	:	PUNCT
ejpam-1535	1079	25	mit	mit	PROPN
ejpam-1535	1079	26	press	press	NOUN
ejpam-1535	1079	27	,	,	PUNCT
ejpam-1535	1079	28	1984	1984	NUM
ejpam-1535	1079	29	.	.	PUNCT