id	sid	tid	token	lemma	pos
ejpam-97	1	1	european	european	PROPN
ejpam-97	1	2	journal	journal	PROPN
ejpam-97	1	3	of	of	ADP
ejpam-97	1	4	pure	pure	ADJ
ejpam-97	1	5	and	and	CCONJ
ejpam-97	1	6	applied	apply	VERB
ejpam-97	1	7	mathematics	mathematic	NOUN
ejpam-97	1	8	vol	vol	NOUN
ejpam-97	1	9	.	.	PROPN
ejpam-97	2	1	1	1	NUM
ejpam-97	2	2	,	,	PUNCT
ejpam-97	2	3	no	no	INTJ
ejpam-97	2	4	.	.	NOUN
ejpam-97	2	5	4	4	NUM
ejpam-97	2	6	,	,	PUNCT
ejpam-97	2	7	2008	2008	NUM
ejpam-97	2	8	,	,	PUNCT
ejpam-97	2	9	(	(	PUNCT
ejpam-97	2	10	41	41	NUM
ejpam-97	2	11	-	-	SYM
ejpam-97	2	12	55	55	NUM
ejpam-97	2	13	)	)	PUNCT
ejpam-97	2	14	issn	issn	PROPN
ejpam-97	2	15	1307	1307	NUM
ejpam-97	2	16	-	-	SYM
ejpam-97	2	17	5543	5543	NUM
ejpam-97	2	18	–	–	PUNCT
ejpam-97	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-97	2	20	sequentially	sequentially	ADV
ejpam-97	2	21	pure	pure	ADJ
ejpam-97	2	22	monomorphisms	monomorphism	NOUN
ejpam-97	2	23	of	of	ADP
ejpam-97	2	24	acts	act	NOUN
ejpam-97	2	25	over	over	ADP
ejpam-97	2	26	semigroups	semigroups	PROPN
ejpam-97	2	27	h.	h.	PROPN
ejpam-97	2	28	barzegar	barzegar	PROPN
ejpam-97	2	29	,	,	PUNCT
ejpam-97	2	30	mohammad	mohammad	PROPN
ejpam-97	2	31	mehdi	mehdi	PROPN
ejpam-97	2	32	ebrahim∗,†	ebrahim∗,†	PROPN
ejpam-97	2	33	department	department	PROPN
ejpam-97	2	34	of	of	ADP
ejpam-97	2	35	mathematics	mathematic	NOUN
ejpam-97	2	36	,	,	PUNCT
ejpam-97	2	37	shahid	shahid	PROPN
ejpam-97	2	38	beheshti	beheshti	PROPN
ejpam-97	2	39	university	university	NOUN
ejpam-97	2	40	,	,	PUNCT
ejpam-97	2	41	tehran	tehran	PROPN
ejpam-97	2	42	19839	19839	NUM
ejpam-97	2	43	,	,	PUNCT
ejpam-97	2	44	iran	iran	PROPN
ejpam-97	2	45	abstract	abstract	NOUN
ejpam-97	2	46	.	.	PUNCT
ejpam-97	3	1	any	any	DET
ejpam-97	3	2	notion	notion	NOUN
ejpam-97	3	3	of	of	ADP
ejpam-97	3	4	purity	purity	NOUN
ejpam-97	3	5	is	be	AUX
ejpam-97	3	6	normally	normally	ADV
ejpam-97	3	7	defined	define	VERB
ejpam-97	3	8	in	in	ADP
ejpam-97	3	9	terms	term	NOUN
ejpam-97	3	10	of	of	ADP
ejpam-97	3	11	solvability	solvability	NOUN
ejpam-97	3	12	of	of	ADP
ejpam-97	3	13	some	some	DET
ejpam-97	3	14	set	set	NOUN
ejpam-97	3	15	of	of	ADP
ejpam-97	3	16	equations	equation	NOUN
ejpam-97	3	17	.	.	PUNCT
ejpam-97	4	1	in	in	ADP
ejpam-97	4	2	this	this	DET
ejpam-97	4	3	paper	paper	NOUN
ejpam-97	4	4	we	we	PRON
ejpam-97	4	5	first	first	ADV
ejpam-97	4	6	take	take	VERB
ejpam-97	4	7	this	this	DET
ejpam-97	4	8	point	point	NOUN
ejpam-97	4	9	of	of	ADP
ejpam-97	4	10	view	view	NOUN
ejpam-97	4	11	to	to	PART
ejpam-97	4	12	introduce	introduce	VERB
ejpam-97	4	13	a	a	DET
ejpam-97	4	14	kind	kind	NOUN
ejpam-97	4	15	of	of	ADP
ejpam-97	4	16	purity	purity	NOUN
ejpam-97	4	17	,	,	PUNCT
ejpam-97	4	18	called	call	VERB
ejpam-97	4	19	sequential	sequential	ADJ
ejpam-97	4	20	purity	purity	NOUN
ejpam-97	4	21	,	,	PUNCT
ejpam-97	4	22	for	for	ADP
ejpam-97	4	23	acts	act	NOUN
ejpam-97	4	24	over	over	ADP
ejpam-97	4	25	semigroups	semigroup	NOUN
ejpam-97	4	26	(	(	PUNCT
ejpam-97	4	27	which	which	PRON
ejpam-97	4	28	is	be	AUX
ejpam-97	4	29	of	of	ADP
ejpam-97	4	30	some	some	DET
ejpam-97	4	31	interest	interest	NOUN
ejpam-97	4	32	to	to	ADP
ejpam-97	4	33	computer	computer	NOUN
ejpam-97	4	34	scientists	scientist	NOUN
ejpam-97	4	35	,	,	PUNCT
ejpam-97	4	36	too	too	ADV
ejpam-97	4	37	)	)	PUNCT
ejpam-97	4	38	,	,	PUNCT
ejpam-97	4	39	and	and	CCONJ
ejpam-97	4	40	then	then	ADV
ejpam-97	4	41	show	show	VERB
ejpam-97	4	42	that	that	SCONJ
ejpam-97	4	43	it	it	PRON
ejpam-97	4	44	is	be	AUX
ejpam-97	4	45	actually	actually	ADV
ejpam-97	4	46	equivalent	equivalent	ADJ
ejpam-97	4	47	to	to	ADP
ejpam-97	4	48	c	c	PROPN
ejpam-97	4	49	p	p	NOUN
ejpam-97	4	50	-	-	PUNCT
ejpam-97	4	51	purity	purity	NOUN
ejpam-97	4	52	resulting	result	VERB
ejpam-97	4	53	from	from	ADP
ejpam-97	4	54	a	a	DET
ejpam-97	4	55	closure	closure	NOUN
ejpam-97	4	56	operator	operator	NOUN
ejpam-97	4	57	.	.	PUNCT
ejpam-97	5	1	the	the	DET
ejpam-97	5	2	main	main	ADJ
ejpam-97	5	3	objective	objective	NOUN
ejpam-97	5	4	of	of	ADP
ejpam-97	5	5	the	the	DET
ejpam-97	5	6	paper	paper	NOUN
ejpam-97	5	7	is	be	AUX
ejpam-97	5	8	to	to	PART
ejpam-97	5	9	study	study	VERB
ejpam-97	5	10	properties	property	NOUN
ejpam-97	5	11	of	of	ADP
ejpam-97	5	12	the	the	DET
ejpam-97	5	13	category	category	NOUN
ejpam-97	5	14	of	of	ADP
ejpam-97	5	15	all	all	DET
ejpam-97	5	16	acts	act	NOUN
ejpam-97	5	17	over	over	ADP
ejpam-97	5	18	a	a	DET
ejpam-97	5	19	semigroup	semigroup	NOUN
ejpam-97	5	20	with	with	ADP
ejpam-97	5	21	respect	respect	NOUN
ejpam-97	5	22	to	to	ADP
ejpam-97	5	23	sequentially	sequentially	ADV
ejpam-97	5	24	pure	pure	ADJ
ejpam-97	5	25	monomorphisms	monomorphism	NOUN
ejpam-97	5	26	.	.	PUNCT
ejpam-97	6	1	these	these	DET
ejpam-97	6	2	properties	property	NOUN
ejpam-97	6	3	are	be	AUX
ejpam-97	6	4	usually	usually	ADV
ejpam-97	6	5	needed	need	VERB
ejpam-97	6	6	to	to	PART
ejpam-97	6	7	study	study	VERB
ejpam-97	6	8	the	the	DET
ejpam-97	6	9	homological	homological	ADJ
ejpam-97	6	10	notions	notion	NOUN
ejpam-97	6	11	,	,	PUNCT
ejpam-97	6	12	such	such	ADJ
ejpam-97	6	13	as	as	ADP
ejpam-97	6	14	injectivity	injectivity	NOUN
ejpam-97	6	15	,	,	PUNCT
ejpam-97	6	16	of	of	ADP
ejpam-97	6	17	acts	act	NOUN
ejpam-97	6	18	.	.	PUNCT
ejpam-97	7	1	ams	am	NOUN
ejpam-97	7	2	subject	subject	ADJ
ejpam-97	7	3	classifications	classification	NOUN
ejpam-97	7	4	:	:	PUNCT
ejpam-97	7	5	18a20	18a20	NUM
ejpam-97	7	6	,	,	PUNCT
ejpam-97	7	7	18a30	18a30	NUM
ejpam-97	7	8	,	,	PUNCT
ejpam-97	7	9	20m30	20m30	NUM
ejpam-97	7	10	,	,	PUNCT
ejpam-97	7	11	20m50	20m50	NUM
ejpam-97	7	12	key	key	ADJ
ejpam-97	7	13	words	word	NOUN
ejpam-97	7	14	:	:	PUNCT
ejpam-97	7	15	action	action	NOUN
ejpam-97	7	16	of	of	ADP
ejpam-97	7	17	a	a	DET
ejpam-97	7	18	semigroup	semigroup	NOUN
ejpam-97	7	19	,	,	PUNCT
ejpam-97	7	20	purity	purity	NOUN
ejpam-97	7	21	1	1	NUM
ejpam-97	7	22	.	.	PUNCT
ejpam-97	7	23	introduction	introduction	NOUN
ejpam-97	7	24	and	and	CCONJ
ejpam-97	7	25	preliminaries	preliminary	NOUN
ejpam-97	7	26	to	to	PART
ejpam-97	7	27	study	study	VERB
ejpam-97	7	28	mathematical	mathematical	ADJ
ejpam-97	7	29	notions	notion	NOUN
ejpam-97	7	30	in	in	ADP
ejpam-97	7	31	a	a	DET
ejpam-97	7	32	categorya	categorya	NOUN
ejpam-97	7	33	with	with	ADP
ejpam-97	7	34	respect	respect	NOUN
ejpam-97	7	35	to	to	ADP
ejpam-97	7	36	a	a	DET
ejpam-97	7	37	classm	classm	NOUN
ejpam-97	7	38	of	of	ADP
ejpam-97	7	39	its	its	PRON
ejpam-97	7	40	morphisms	morphism	NOUN
ejpam-97	7	41	,	,	PUNCT
ejpam-97	7	42	one	one	PRON
ejpam-97	7	43	should	should	AUX
ejpam-97	7	44	know	know	VERB
ejpam-97	7	45	some	some	PRON
ejpam-97	7	46	of	of	ADP
ejpam-97	7	47	the	the	DET
ejpam-97	7	48	categorical	categorical	ADJ
ejpam-97	7	49	properties	property	NOUN
ejpam-97	7	50	of	of	ADP
ejpam-97	7	51	the	the	DET
ejpam-97	7	52	pair	pair	NOUN
ejpam-97	7	53	(	(	PUNCT
ejpam-97	7	54	a	a	PRON
ejpam-97	7	55	,	,	PUNCT
ejpam-97	7	56	m	m	NOUN
ejpam-97	7	57	)	)	PUNCT
ejpam-97	7	58	.	.	PUNCT
ejpam-97	8	1	one	one	NUM
ejpam-97	8	2	of	of	ADP
ejpam-97	8	3	the	the	DET
ejpam-97	8	4	very	very	ADV
ejpam-97	8	5	useful	useful	ADJ
ejpam-97	8	6	categories	category	NOUN
ejpam-97	8	7	in	in	ADP
ejpam-97	8	8	many	many	ADJ
ejpam-97	8	9	branches	branch	NOUN
ejpam-97	8	10	of	of	ADP
ejpam-97	8	11	mathematics	mathematic	NOUN
ejpam-97	8	12	,	,	PUNCT
ejpam-97	8	13	as	as	ADV
ejpam-97	8	14	well	well	ADV
ejpam-97	8	15	as	as	ADP
ejpam-97	8	16	in	in	ADP
ejpam-97	8	17	computer	computer	NOUN
ejpam-97	8	18	sciences	science	NOUN
ejpam-97	8	19	,	,	PUNCT
ejpam-97	8	20	is	be	AUX
ejpam-97	8	21	the	the	DET
ejpam-97	8	22	category	category	NOUN
ejpam-97	8	23	act	act	NOUN
ejpam-97	8	24	-	-	PUNCT
ejpam-97	8	25	s	s	NOUN
ejpam-97	8	26	of	of	ADP
ejpam-97	8	27	sets	set	NOUN
ejpam-97	8	28	with	with	ADP
ejpam-97	8	29	a	a	DET
ejpam-97	8	30	right	right	ADJ
ejpam-97	8	31	action	action	NOUN
ejpam-97	8	32	of	of	ADP
ejpam-97	8	33	a	a	DET
ejpam-97	8	34	semigroup	semigroup	NOUN
ejpam-97	8	35	s	s	X
ejpam-97	8	36	on	on	ADP
ejpam-97	8	37	them	they	PRON
ejpam-97	8	38	.	.	PUNCT
ejpam-97	9	1	in	in	ADP
ejpam-97	9	2	this	this	DET
ejpam-97	9	3	paper	paper	NOUN
ejpam-97	9	4	we	we	PRON
ejpam-97	9	5	take	take	VERB
ejpam-97	9	6	a	a	PRON
ejpam-97	9	7	to	to	PART
ejpam-97	9	8	be	be	AUX
ejpam-97	9	9	this	this	DET
ejpam-97	9	10	category	category	NOUN
ejpam-97	9	11	and	and	CCONJ
ejpam-97	9	12	mp	mp	NOUN
ejpam-97	9	13	to	to	PART
ejpam-97	9	14	be	be	AUX
ejpam-97	9	15	a	a	DET
ejpam-97	9	16	particularly	particularly	ADV
ejpam-97	9	17	interesting	interesting	ADJ
ejpam-97	9	18	class	class	NOUN
ejpam-97	9	19	of	of	ADP
ejpam-97	9	20	monomorphisms	monomorphism	NOUN
ejpam-97	9	21	,	,	PUNCT
ejpam-97	9	22	to	to	PART
ejpam-97	9	23	be	be	AUX
ejpam-97	9	24	called	call	VERB
ejpam-97	9	25	sequentially	sequentially	ADV
ejpam-97	9	26	pure	pure	ADJ
ejpam-97	9	27	,	,	PUNCT
ejpam-97	9	28	and	and	CCONJ
ejpam-97	9	29	investigate	investigate	VERB
ejpam-97	9	30	its	its	PRON
ejpam-97	9	31	categorical	categorical	ADJ
ejpam-97	9	32	properties	property	NOUN
ejpam-97	9	33	.	.	PUNCT
ejpam-97	10	1	first	first	ADV
ejpam-97	10	2	we	we	PRON
ejpam-97	10	3	give	give	VERB
ejpam-97	10	4	the	the	DET
ejpam-97	10	5	following	follow	VERB
ejpam-97	10	6	preliminaries	preliminary	NOUN
ejpam-97	10	7	needed	need	VERB
ejpam-97	10	8	in	in	ADP
ejpam-97	10	9	the	the	DET
ejpam-97	10	10	sequel	sequel	NOUN
ejpam-97	10	11	.	.	PUNCT
ejpam-97	11	1	1.1	1.1	NUM
ejpam-97	11	2	.	.	PUNCT
ejpam-97	12	1	the	the	DET
ejpam-97	12	2	category	category	NOUN
ejpam-97	12	3	of	of	ADP
ejpam-97	12	4	acts	act	NOUN
ejpam-97	12	5	over	over	ADP
ejpam-97	12	6	semigroups	semigroup	NOUN
ejpam-97	12	7	first	first	ADV
ejpam-97	12	8	recall	recall	VERB
ejpam-97	12	9	the	the	DET
ejpam-97	12	10	following	following	NOUN
ejpam-97	12	11	,	,	PUNCT
ejpam-97	12	12	for	for	ADP
ejpam-97	12	13	example	example	NOUN
ejpam-97	12	14	from	from	ADP
ejpam-97	12	15	[	[	X
ejpam-97	12	16	13	13	NUM
ejpam-97	12	17	]	]	PUNCT
ejpam-97	12	18	or	or	CCONJ
ejpam-97	12	19	[	[	X
ejpam-97	12	20	5	5	NUM
ejpam-97	12	21	]	]	PUNCT
ejpam-97	12	22	.	.	PUNCT
ejpam-97	13	1	let	let	VERB
ejpam-97	13	2	s	s	PRON
ejpam-97	13	3	be	be	AUX
ejpam-97	13	4	a	a	DET
ejpam-97	13	5	semigroup	semigroup	NOUN
ejpam-97	13	6	and	and	CCONJ
ejpam-97	13	7	a	a	DET
ejpam-97	13	8	be	be	AUX
ejpam-97	13	9	a	a	DET
ejpam-97	13	10	set	set	NOUN
ejpam-97	13	11	.	.	PUNCT
ejpam-97	14	1	if	if	SCONJ
ejpam-97	14	2	we	we	PRON
ejpam-97	14	3	have	have	VERB
ejpam-97	14	4	a	a	DET
ejpam-97	14	5	mapping	mapping	NOUN
ejpam-97	14	6	µ	µ	NOUN
ejpam-97	14	7	:	:	PUNCT
ejpam-97	14	8	a×	a×	VERB
ejpam-97	14	9	s→	s→	PUNCT
ejpam-97	14	10	a	a	DET
ejpam-97	14	11	(	(	PUNCT
ejpam-97	14	12	a	a	PRON
ejpam-97	14	13	,	,	PUNCT
ejpam-97	14	14	s	s	NOUN
ejpam-97	14	15	)	)	PUNCT
ejpam-97	14	16	7−→	7−→	NOUN
ejpam-97	14	17	as	as	ADP
ejpam-97	14	18	:	:	PUNCT
ejpam-97	14	19	=	=	SYM
ejpam-97	14	20	µ(a	µ(a	PROPN
ejpam-97	14	21	,	,	PUNCT
ejpam-97	14	22	s	s	NOUN
ejpam-97	14	23	)	)	PUNCT
ejpam-97	14	24	such	such	ADJ
ejpam-97	14	25	that	that	PRON
ejpam-97	14	26	a(st	a(st	PROPN
ejpam-97	14	27	)	)	PUNCT
ejpam-97	14	28	=	=	PUNCT
ejpam-97	15	1	(	(	PUNCT
ejpam-97	15	2	as)t	as)t	NOUN
ejpam-97	15	3	for	for	ADP
ejpam-97	15	4	a	a	DET
ejpam-97	15	5	∈	∈	PROPN
ejpam-97	15	6	a	a	PRON
ejpam-97	15	7	,	,	PUNCT
ejpam-97	15	8	s	s	PROPN
ejpam-97	15	9	,	,	PUNCT
ejpam-97	15	10	t	t	PROPN
ejpam-97	15	11	∈	∈	PROPN
ejpam-97	15	12	s	s	X
ejpam-97	15	13	,	,	PUNCT
ejpam-97	15	14	we	we	PRON
ejpam-97	15	15	call	call	VERB
ejpam-97	15	16	a	a	DET
ejpam-97	15	17	a	a	PRON
ejpam-97	15	18	(	(	PUNCT
ejpam-97	15	19	right	right	ADJ
ejpam-97	15	20	)	)	PUNCT
ejpam-97	15	21	s	s	NOUN
ejpam-97	15	22	-	-	PUNCT
ejpam-97	15	23	act	act	NOUN
ejpam-97	15	24	or	or	CCONJ
ejpam-97	15	25	a	a	DET
ejpam-97	15	26	(	(	PUNCT
ejpam-97	15	27	right	right	ADJ
ejpam-97	15	28	)	)	PUNCT
ejpam-97	15	29	act	act	NOUN
ejpam-97	15	30	over	over	ADP
ejpam-97	15	31	s.	s.	PROPN
ejpam-97	15	32	if	if	SCONJ
ejpam-97	15	33	s	s	PROPN
ejpam-97	15	34	is	be	AUX
ejpam-97	15	35	a	a	DET
ejpam-97	15	36	monoid	monoid	NOUN
ejpam-97	15	37	with	with	ADP
ejpam-97	15	38	an	an	DET
ejpam-97	15	39	identity	identity	NOUN
ejpam-97	15	40	1	1	NUM
ejpam-97	15	41	,	,	PUNCT
ejpam-97	15	42	we	we	PRON
ejpam-97	15	43	usually	usually	ADV
ejpam-97	15	44	also	also	ADV
ejpam-97	15	45	require	require	VERB
ejpam-97	15	46	that	that	SCONJ
ejpam-97	15	47	a1=	a1=	PROPN
ejpam-97	15	48	a	a	DET
ejpam-97	15	49	for	for	ADP
ejpam-97	15	50	a	a	DET
ejpam-97	15	51	∈	∈	PROPN
ejpam-97	15	52	a.	a.	NOUN
ejpam-97	15	53	∗corresponding	∗corresponde	VERB
ejpam-97	15	54	author	author	NOUN
ejpam-97	15	55	.	.	PUNCT
ejpam-97	16	1	email	email	NOUN
ejpam-97	16	2	addresses	address	NOUN
ejpam-97	16	3	:	:	PUNCT
ejpam-97	16	4	m-ebrahimi@sbu.ac.ir	m-ebrahimi@sbu.ac.ir	PROPN
ejpam-97	16	5	(	(	PUNCT
ejpam-97	16	6	m.m	m.m	PROPN
ejpam-97	16	7	.	.	PROPN
ejpam-97	16	8	ebrahimi	ebrahimi	PROPN
ejpam-97	16	9	)	)	PUNCT
ejpam-97	16	10	†m.m	†m.m	PROPN
ejpam-97	16	11	.	.	PUNCT
ejpam-97	17	1	ebrahimi	ebrahimi	PROPN
ejpam-97	17	2	would	would	AUX
ejpam-97	17	3	like	like	VERB
ejpam-97	17	4	to	to	PART
ejpam-97	17	5	acknowledge	acknowledge	VERB
ejpam-97	17	6	the	the	DET
ejpam-97	17	7	financial	financial	ADJ
ejpam-97	17	8	support	support	NOUN
ejpam-97	17	9	from	from	ADP
ejpam-97	17	10	iran	iran	PROPN
ejpam-97	17	11	national	national	PROPN
ejpam-97	17	12	science	science	PROPN
ejpam-97	17	13	foundation	foundation	PROPN
ejpam-97	17	14	(	(	PUNCT
ejpam-97	17	15	insf	insf	ADJ
ejpam-97	17	16	)	)	PUNCT
ejpam-97	17	17	with	with	ADP
ejpam-97	17	18	thanks	thank	NOUN
ejpam-97	17	19	.	.	PUNCT
ejpam-97	18	1	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-97	19	1	41	41	NUM
ejpam-97	20	1	c	c	X
ejpam-97	20	2	©	©	PROPN
ejpam-97	20	3	2008	2008	NUM
ejpam-97	20	4	ejpam	ejpam	VERB
ejpam-97	20	5	all	all	DET
ejpam-97	20	6	rights	right	NOUN
ejpam-97	20	7	reserved	reserve	VERB
ejpam-97	20	8	.	.	PUNCT
ejpam-97	21	1	h.	h.	PROPN
ejpam-97	21	2	barzegar	barzegar	PROPN
ejpam-97	21	3	and	and	CCONJ
ejpam-97	21	4	m.m	m.m	PROPN
ejpam-97	21	5	.	.	PROPN
ejpam-97	21	6	ebrahimi	ebrahimi	PROPN
ejpam-97	21	7	/	/	SYM
ejpam-97	21	8	eur	eur	PROPN
ejpam-97	21	9	.	.	PUNCT
ejpam-97	22	1	j.	j.	PROPN
ejpam-97	22	2	pure	pure	PROPN
ejpam-97	22	3	appl	appl	PROPN
ejpam-97	22	4	.	.	PROPN
ejpam-97	22	5	math	math	PROPN
ejpam-97	22	6	,	,	PUNCT
ejpam-97	22	7	1	1	NUM
ejpam-97	22	8	(	(	PUNCT
ejpam-97	22	9	2008	2008	NUM
ejpam-97	22	10	)	)	PUNCT
ejpam-97	22	11	,	,	PUNCT
ejpam-97	22	12	(	(	PUNCT
ejpam-97	22	13	41	41	NUM
ejpam-97	22	14	-	-	SYM
ejpam-97	22	15	55	55	NUM
ejpam-97	22	16	)	)	PUNCT
ejpam-97	22	17	42	42	NUM
ejpam-97	22	18	in	in	ADP
ejpam-97	22	19	fact	fact	NOUN
ejpam-97	22	20	,	,	PUNCT
ejpam-97	22	21	an	an	DET
ejpam-97	22	22	s	s	NOUN
ejpam-97	22	23	-	-	PUNCT
ejpam-97	22	24	act	act	NOUN
ejpam-97	22	25	is	be	AUX
ejpam-97	22	26	a	a	DET
ejpam-97	22	27	universal	universal	ADJ
ejpam-97	22	28	algebra	algebra	NOUN
ejpam-97	22	29	(	(	PUNCT
ejpam-97	22	30	a	a	PRON
ejpam-97	22	31	,	,	PUNCT
ejpam-97	22	32	(	(	PUNCT
ejpam-97	22	33	µs)s∈s	µs)s∈s	NOUN
ejpam-97	22	34	)	)	PUNCT
ejpam-97	22	35	where	where	SCONJ
ejpam-97	22	36	each	each	PRON
ejpam-97	22	37	µs	µs	X
ejpam-97	22	38	:	:	PUNCT
ejpam-97	22	39	a	a	PRON
ejpam-97	22	40	→	→	X
ejpam-97	22	41	a	a	PRON
ejpam-97	22	42	is	be	AUX
ejpam-97	22	43	a	a	DET
ejpam-97	22	44	unary	unary	ADJ
ejpam-97	22	45	operation	operation	NOUN
ejpam-97	22	46	on	on	ADP
ejpam-97	22	47	a	a	DET
ejpam-97	22	48	such	such	ADJ
ejpam-97	22	49	that	that	DET
ejpam-97	22	50	µs	µs	ADP
ejpam-97	22	51	◦	◦	NOUN
ejpam-97	22	52	µt	µt	NOUN
ejpam-97	22	53	=	=	ADJ
ejpam-97	22	54	µst	µst	NOUN
ejpam-97	22	55	for	for	ADP
ejpam-97	22	56	each	each	DET
ejpam-97	22	57	s	s	PROPN
ejpam-97	22	58	,	,	PUNCT
ejpam-97	22	59	t	t	PROPN
ejpam-97	22	60	∈	∈	PROPN
ejpam-97	22	61	s	s	X
ejpam-97	22	62	,	,	PUNCT
ejpam-97	22	63	and	and	CCONJ
ejpam-97	22	64	µ1	µ1	PROPN
ejpam-97	22	65	=	=	SYM
ejpam-97	22	66	ida	ida	PROPN
ejpam-97	22	67	if	if	SCONJ
ejpam-97	22	68	s	s	PROPN
ejpam-97	22	69	has	have	VERB
ejpam-97	22	70	an	an	DET
ejpam-97	22	71	identity	identity	NOUN
ejpam-97	22	72	1	1	NUM
ejpam-97	22	73	.	.	PUNCT
ejpam-97	23	1	an	an	DET
ejpam-97	23	2	element	element	NOUN
ejpam-97	23	3	a	a	PRON
ejpam-97	23	4	of	of	ADP
ejpam-97	23	5	an	an	DET
ejpam-97	23	6	s	s	PROPN
ejpam-97	23	7	-	-	NOUN
ejpam-97	23	8	act	act	NOUN
ejpam-97	23	9	a	a	PRON
ejpam-97	23	10	is	be	AUX
ejpam-97	23	11	called	call	VERB
ejpam-97	23	12	a	a	DET
ejpam-97	23	13	fixed	fix	VERB
ejpam-97	23	14	or	or	CCONJ
ejpam-97	23	15	a	a	DET
ejpam-97	23	16	zero	zero	NUM
ejpam-97	23	17	element	element	NOUN
ejpam-97	23	18	if	if	SCONJ
ejpam-97	23	19	as	as	SCONJ
ejpam-97	23	20	=	=	X
ejpam-97	23	21	a	a	PRON
ejpam-97	23	22	for	for	ADP
ejpam-97	23	23	all	all	PRON
ejpam-97	23	24	s	s	PROPN
ejpam-97	23	25	∈	∈	PROPN
ejpam-97	23	26	s.	s.	PROPN
ejpam-97	23	27	note	note	VERB
ejpam-97	23	28	that	that	SCONJ
ejpam-97	23	29	one	one	PRON
ejpam-97	23	30	can	can	AUX
ejpam-97	23	31	always	always	ADV
ejpam-97	23	32	adjoin	adjoin	VERB
ejpam-97	23	33	a	a	DET
ejpam-97	23	34	zero	zero	NUM
ejpam-97	23	35	element	element	NOUN
ejpam-97	23	36	to	to	ADP
ejpam-97	23	37	a	a	PRON
ejpam-97	23	38	and	and	CCONJ
ejpam-97	23	39	get	get	VERB
ejpam-97	23	40	an	an	DET
ejpam-97	23	41	act	act	NOUN
ejpam-97	23	42	a0	a0	NOUN
ejpam-97	23	43	=	=	SYM
ejpam-97	23	44	a∪{0	a∪{0	PROPN
ejpam-97	23	45	}	}	PUNCT
ejpam-97	23	46	with	with	ADP
ejpam-97	23	47	a	a	DET
ejpam-97	23	48	zero	zero	NUM
ejpam-97	23	49	element	element	NOUN
ejpam-97	23	50	.	.	PUNCT
ejpam-97	24	1	let	let	VERB
ejpam-97	24	2	a	a	DET
ejpam-97	24	3	be	be	AUX
ejpam-97	24	4	an	an	DET
ejpam-97	24	5	s	s	NOUN
ejpam-97	24	6	-	-	NOUN
ejpam-97	24	7	act	act	NOUN
ejpam-97	24	8	and	and	CCONJ
ejpam-97	24	9	a′	a′	PROPN
ejpam-97	24	10	⊆	⊆	NUM
ejpam-97	24	11	a.	a.	NOUN
ejpam-97	24	12	then	then	ADV
ejpam-97	24	13	a′	a′	PROPN
ejpam-97	24	14	is	be	AUX
ejpam-97	24	15	called	call	VERB
ejpam-97	24	16	a	a	DET
ejpam-97	24	17	subact	subact	NOUN
ejpam-97	24	18	of	of	ADP
ejpam-97	24	19	a	a	DET
ejpam-97	24	20	if	if	SCONJ
ejpam-97	25	1	a′s	a′s	ADJ
ejpam-97	25	2	∈	∈	PROPN
ejpam-97	25	3	a′	a′	NOUN
ejpam-97	25	4	for	for	ADP
ejpam-97	25	5	all	all	DET
ejpam-97	25	6	s	s	PART
ejpam-97	25	7	∈	∈	PROPN
ejpam-97	25	8	s	s	NOUN
ejpam-97	25	9	and	and	CCONJ
ejpam-97	25	10	a′	a′	NOUN
ejpam-97	25	11	∈	∈	PROPN
ejpam-97	25	12	a′.	a′.	NOUN
ejpam-97	25	13	note	note	VERB
ejpam-97	25	14	that	that	SCONJ
ejpam-97	25	15	the	the	DET
ejpam-97	25	16	semigroup	semigroup	NOUN
ejpam-97	25	17	s	s	VERB
ejpam-97	25	18	can	can	AUX
ejpam-97	25	19	itself	itself	PRON
ejpam-97	25	20	be	be	AUX
ejpam-97	25	21	regarded	regard	VERB
ejpam-97	25	22	as	as	ADP
ejpam-97	25	23	an	an	DET
ejpam-97	25	24	s	s	NOUN
ejpam-97	25	25	-	-	NOUN
ejpam-97	25	26	act	act	NOUN
ejpam-97	25	27	with	with	ADP
ejpam-97	25	28	its	its	PRON
ejpam-97	25	29	multiplication	multiplication	NOUN
ejpam-97	25	30	as	as	ADP
ejpam-97	25	31	its	its	PRON
ejpam-97	25	32	action	action	NOUN
ejpam-97	25	33	.	.	PUNCT
ejpam-97	26	1	a	a	DET
ejpam-97	26	2	subact	subact	NOUN
ejpam-97	26	3	of	of	ADP
ejpam-97	26	4	the	the	DET
ejpam-97	26	5	s	s	NOUN
ejpam-97	26	6	-	-	NOUN
ejpam-97	26	7	act	act	NOUN
ejpam-97	26	8	s	s	PART
ejpam-97	26	9	is	be	AUX
ejpam-97	26	10	called	call	VERB
ejpam-97	26	11	a	a	DET
ejpam-97	26	12	right	right	ADJ
ejpam-97	26	13	ideal	ideal	NOUN
ejpam-97	26	14	of	of	ADP
ejpam-97	26	15	the	the	DET
ejpam-97	26	16	semigroup	semigroup	PROPN
ejpam-97	26	17	s.	s.	PROPN
ejpam-97	26	18	a	a	DET
ejpam-97	26	19	homomorphism	homomorphism	PROPN
ejpam-97	26	20	(	(	PUNCT
ejpam-97	26	21	also	also	ADV
ejpam-97	26	22	called	call	VERB
ejpam-97	26	23	an	an	DET
ejpam-97	26	24	equivariant	equivariant	ADJ
ejpam-97	26	25	map	map	NOUN
ejpam-97	26	26	,	,	PUNCT
ejpam-97	26	27	or	or	CCONJ
ejpam-97	26	28	an	an	DET
ejpam-97	26	29	s	s	NOUN
ejpam-97	26	30	-	-	NOUN
ejpam-97	26	31	map	map	NOUN
ejpam-97	26	32	)	)	PUNCT
ejpam-97	26	33	from	from	ADP
ejpam-97	26	34	an	an	DET
ejpam-97	26	35	s	s	PROPN
ejpam-97	26	36	-	-	PUNCT
ejpam-97	26	37	act	act	NOUN
ejpam-97	26	38	a	a	PRON
ejpam-97	26	39	to	to	ADP
ejpam-97	26	40	an	an	DET
ejpam-97	26	41	s	s	NOUN
ejpam-97	26	42	-	-	PUNCT
ejpam-97	26	43	act	act	NOUN
ejpam-97	26	44	b	b	NOUN
ejpam-97	26	45	is	be	AUX
ejpam-97	26	46	a	a	DET
ejpam-97	26	47	function	function	NOUN
ejpam-97	26	48	from	from	ADP
ejpam-97	26	49	a	a	PRON
ejpam-97	26	50	to	to	ADP
ejpam-97	26	51	b	b	NOUN
ejpam-97	26	52	such	such	ADJ
ejpam-97	26	53	that	that	PRON
ejpam-97	26	54	for	for	ADP
ejpam-97	26	55	each	each	DET
ejpam-97	26	56	a	a	DET
ejpam-97	26	57	∈	∈	PROPN
ejpam-97	26	58	a	a	PRON
ejpam-97	26	59	and	and	CCONJ
ejpam-97	26	60	s	s	NOUN
ejpam-97	26	61	∈	∈	PROPN
ejpam-97	26	62	s	s	PROPN
ejpam-97	26	63	,	,	PUNCT
ejpam-97	26	64	f	f	X
ejpam-97	26	65	(	(	PUNCT
ejpam-97	26	66	as	as	ADP
ejpam-97	26	67	)	)	PUNCT
ejpam-97	26	68	=	=	SYM
ejpam-97	26	69	f	f	PROPN
ejpam-97	26	70	(	(	PUNCT
ejpam-97	26	71	a)s	a)s	X
ejpam-97	26	72	.	.	PUNCT
ejpam-97	27	1	since	since	SCONJ
ejpam-97	27	2	ida	ida	PROPN
ejpam-97	27	3	and	and	CCONJ
ejpam-97	27	4	the	the	DET
ejpam-97	27	5	composition	composition	NOUN
ejpam-97	27	6	of	of	ADP
ejpam-97	27	7	two	two	NUM
ejpam-97	27	8	equivariant	equivariant	ADJ
ejpam-97	27	9	maps	map	NOUN
ejpam-97	27	10	are	be	AUX
ejpam-97	27	11	equivariant	equivariant	ADJ
ejpam-97	27	12	,	,	PUNCT
ejpam-97	27	13	we	we	PRON
ejpam-97	27	14	have	have	VERB
ejpam-97	27	15	the	the	DET
ejpam-97	27	16	category	category	NOUN
ejpam-97	27	17	act	act	NOUN
ejpam-97	27	18	-	-	PUNCT
ejpam-97	27	19	s	s	PROPN
ejpam-97	27	20	of	of	ADP
ejpam-97	27	21	all	all	PRON
ejpam-97	27	22	(	(	PUNCT
ejpam-97	27	23	right	right	ADJ
ejpam-97	27	24	)	)	PUNCT
ejpam-97	27	25	s	s	NOUN
ejpam-97	27	26	-	-	PUNCT
ejpam-97	27	27	sets	set	NOUN
ejpam-97	27	28	and	and	CCONJ
ejpam-97	27	29	s	s	NOUN
ejpam-97	27	30	-	-	NOUN
ejpam-97	27	31	maps	map	NOUN
ejpam-97	27	32	between	between	ADP
ejpam-97	27	33	them	they	PRON
ejpam-97	27	34	.	.	PUNCT
ejpam-97	28	1	recall	recall	VERB
ejpam-97	28	2	that	that	PRON
ejpam-97	28	3	to	to	ADP
ejpam-97	28	4	every	every	DET
ejpam-97	28	5	semigroup	semigroup	NOUN
ejpam-97	28	6	s	s	PRON
ejpam-97	28	7	without	without	ADP
ejpam-97	28	8	an	an	DET
ejpam-97	28	9	identity	identity	NOUN
ejpam-97	28	10	one	one	NOUN
ejpam-97	28	11	can	can	AUX
ejpam-97	28	12	adjoin	adjoin	VERB
ejpam-97	28	13	an	an	DET
ejpam-97	28	14	identity	identity	NOUN
ejpam-97	28	15	1	1	NUM
ejpam-97	28	16	by	by	ADP
ejpam-97	28	17	setting	set	VERB
ejpam-97	28	18	1s	1	NOUN
ejpam-97	28	19	=	=	SYM
ejpam-97	28	20	s	s	PART
ejpam-97	28	21	=	=	NOUN
ejpam-97	28	22	s1	s1	NOUN
ejpam-97	28	23	for	for	ADP
ejpam-97	28	24	all	all	DET
ejpam-97	28	25	s	s	PART
ejpam-97	28	26	∈	∈	PROPN
ejpam-97	28	27	s	s	NOUN
ejpam-97	28	28	and	and	CCONJ
ejpam-97	28	29	get	get	VERB
ejpam-97	28	30	an	an	DET
ejpam-97	28	31	s	s	NOUN
ejpam-97	28	32	-	-	PUNCT
ejpam-97	28	33	act	act	NOUN
ejpam-97	28	34	denoted	denote	VERB
ejpam-97	28	35	by	by	ADP
ejpam-97	28	36	s1	s1	PROPN
ejpam-97	28	37	.	.	PUNCT
ejpam-97	29	1	as	as	ADP
ejpam-97	29	2	a	a	DET
ejpam-97	29	3	very	very	ADV
ejpam-97	29	4	interesting	interesting	ADJ
ejpam-97	29	5	example	example	NOUN
ejpam-97	29	6	,	,	PUNCT
ejpam-97	29	7	used	use	VERB
ejpam-97	29	8	in	in	ADP
ejpam-97	29	9	computer	computer	NOUN
ejpam-97	29	10	sciences	science	NOUN
ejpam-97	29	11	as	as	ADP
ejpam-97	29	12	a	a	DET
ejpam-97	29	13	convenient	convenient	ADJ
ejpam-97	29	14	means	mean	NOUN
ejpam-97	29	15	of	of	ADP
ejpam-97	29	16	algebraic	algebraic	ADJ
ejpam-97	29	17	specification	specification	NOUN
ejpam-97	29	18	of	of	ADP
ejpam-97	29	19	process	process	NOUN
ejpam-97	29	20	algebras	algebra	NOUN
ejpam-97	29	21	(	(	PUNCT
ejpam-97	29	22	see	see	VERB
ejpam-97	29	23	[	[	X
ejpam-97	29	24	7	7	NUM
ejpam-97	29	25	,	,	PUNCT
ejpam-97	29	26	8	8	NUM
ejpam-97	29	27	]	]	NUM
ejpam-97	29	28	)	)	PUNCT
ejpam-97	29	29	,	,	PUNCT
ejpam-97	29	30	consider	consider	VERB
ejpam-97	29	31	the	the	DET
ejpam-97	29	32	monoid	monoid	NOUN
ejpam-97	29	33	(	(	PUNCT
ejpam-97	29	34	n∞	n∞	PROPN
ejpam-97	29	35	,	,	PUNCT
ejpam-97	29	36	·	·	PUNCT
ejpam-97	29	37	)	)	PUNCT
ejpam-97	29	38	,	,	PUNCT
ejpam-97	29	39	where	where	SCONJ
ejpam-97	29	40	n	n	PRON
ejpam-97	29	41	is	be	AUX
ejpam-97	29	42	the	the	DET
ejpam-97	29	43	set	set	NOUN
ejpam-97	29	44	of	of	ADP
ejpam-97	29	45	natural	natural	ADJ
ejpam-97	29	46	numbers	number	NOUN
ejpam-97	29	47	and	and	CCONJ
ejpam-97	29	48	n∞	n∞	NOUN
ejpam-97	29	49	=	=	SYM
ejpam-97	29	50	n	n	CCONJ
ejpam-97	29	51	∪	∪	X
ejpam-97	29	52	{	{	PUNCT
ejpam-97	29	53	∞	∞	NOUN
ejpam-97	29	54	}	}	PUNCT
ejpam-97	29	55	with	with	ADP
ejpam-97	29	56	n	n	X
ejpam-97	29	57	<	<	X
ejpam-97	29	58	∞,∀n	∞,∀n	PROPN
ejpam-97	29	59	∈	∈	PROPN
ejpam-97	29	60	n	n	NOUN
ejpam-97	29	61	and	and	CCONJ
ejpam-97	29	62	m	m	PROPN
ejpam-97	29	63	·	·	PUNCT
ejpam-97	29	64	n	n	X
ejpam-97	29	65	=	=	SYM
ejpam-97	29	66	min{m	min{m	PROPN
ejpam-97	29	67	,	,	PUNCT
ejpam-97	29	68	n	n	CCONJ
ejpam-97	29	69	}	}	PUNCT
ejpam-97	29	70	for	for	ADP
ejpam-97	29	71	m	m	PROPN
ejpam-97	29	72	,	,	PUNCT
ejpam-97	29	73	n	n	PRON
ejpam-97	29	74	∈	∈	NOUN
ejpam-97	30	1	n∞.	n∞.	NOUN
ejpam-97	30	2	then	then	ADV
ejpam-97	30	3	an	an	DET
ejpam-97	30	4	n∞-act	n∞-act	PROPN
ejpam-97	30	5	is	be	AUX
ejpam-97	30	6	called	call	VERB
ejpam-97	30	7	a	a	DET
ejpam-97	30	8	projection	projection	NOUN
ejpam-97	30	9	algebra	algebra	NOUN
ejpam-97	30	10	or	or	CCONJ
ejpam-97	30	11	a	a	DET
ejpam-97	30	12	projection	projection	NOUN
ejpam-97	30	13	space	space	NOUN
ejpam-97	30	14	(	(	PUNCT
ejpam-97	30	15	see	see	VERB
ejpam-97	30	16	also	also	ADV
ejpam-97	30	17	[	[	X
ejpam-97	30	18	11,14	11,14	NUM
ejpam-97	30	19	]	]	PUNCT
ejpam-97	30	20	)	)	PUNCT
ejpam-97	30	21	.	.	PUNCT
ejpam-97	31	1	1.2	1.2	NUM
ejpam-97	31	2	.	.	PUNCT
ejpam-97	32	1	some	some	DET
ejpam-97	32	2	ingredients	ingredient	NOUN
ejpam-97	32	3	of	of	ADP
ejpam-97	32	4	the	the	DET
ejpam-97	32	5	category	category	NOUN
ejpam-97	32	6	act	act	NOUN
ejpam-97	32	7	-	-	PUNCT
ejpam-97	32	8	s	s	PROPN
ejpam-97	32	9	in	in	ADP
ejpam-97	32	10	this	this	DET
ejpam-97	32	11	subsection	subsection	NOUN
ejpam-97	32	12	we	we	PRON
ejpam-97	32	13	give	give	VERB
ejpam-97	32	14	some	some	DET
ejpam-97	32	15	categorical	categorical	ADJ
ejpam-97	32	16	and	and	CCONJ
ejpam-97	32	17	algebraic	algebraic	ADJ
ejpam-97	32	18	ingredients	ingredient	NOUN
ejpam-97	32	19	of	of	ADP
ejpam-97	32	20	act	act	PROPN
ejpam-97	32	21	-	-	PUNCT
ejpam-97	32	22	s	s	VERB
ejpam-97	32	23	needed	need	VERB
ejpam-97	32	24	in	in	ADP
ejpam-97	32	25	the	the	DET
ejpam-97	32	26	sequel	sequel	NOUN
ejpam-97	32	27	.	.	PUNCT
ejpam-97	33	1	since	since	SCONJ
ejpam-97	33	2	the	the	DET
ejpam-97	33	3	class	class	NOUN
ejpam-97	33	4	of	of	ADP
ejpam-97	33	5	s	s	NOUN
ejpam-97	33	6	-	-	PUNCT
ejpam-97	33	7	acts	act	NOUN
ejpam-97	33	8	is	be	AUX
ejpam-97	33	9	an	an	DET
ejpam-97	33	10	equational	equational	ADJ
ejpam-97	33	11	class	class	NOUN
ejpam-97	33	12	,	,	PUNCT
ejpam-97	33	13	the	the	DET
ejpam-97	33	14	category	category	NOUN
ejpam-97	33	15	act	act	NOUN
ejpam-97	33	16	-	-	PUNCT
ejpam-97	33	17	s	s	PART
ejpam-97	33	18	is	be	AUX
ejpam-97	33	19	complete	complete	ADJ
ejpam-97	33	20	(	(	PUNCT
ejpam-97	33	21	has	have	AUX
ejpam-97	33	22	all	all	DET
ejpam-97	33	23	products	product	NOUN
ejpam-97	33	24	and	and	CCONJ
ejpam-97	33	25	equalizers	equalizer	NOUN
ejpam-97	33	26	)	)	PUNCT
ejpam-97	33	27	.	.	PUNCT
ejpam-97	34	1	in	in	ADP
ejpam-97	34	2	fact	fact	NOUN
ejpam-97	34	3	,	,	PUNCT
ejpam-97	34	4	limits	limit	NOUN
ejpam-97	34	5	in	in	ADP
ejpam-97	34	6	this	this	DET
ejpam-97	34	7	category	category	NOUN
ejpam-97	34	8	are	be	AUX
ejpam-97	34	9	computed	compute	VERB
ejpam-97	34	10	as	as	ADP
ejpam-97	34	11	in	in	ADP
ejpam-97	34	12	the	the	DET
ejpam-97	34	13	category	category	NOUN
ejpam-97	34	14	set	set	VERB
ejpam-97	34	15	of	of	ADP
ejpam-97	34	16	sets	set	NOUN
ejpam-97	34	17	and	and	CCONJ
ejpam-97	34	18	equipped	equip	VERB
ejpam-97	34	19	with	with	ADP
ejpam-97	34	20	a	a	DET
ejpam-97	34	21	natural	natural	ADJ
ejpam-97	34	22	action	action	NOUN
ejpam-97	34	23	.	.	PUNCT
ejpam-97	35	1	in	in	ADP
ejpam-97	35	2	particular	particular	ADJ
ejpam-97	35	3	,	,	PUNCT
ejpam-97	35	4	the	the	DET
ejpam-97	35	5	terminal	terminal	ADJ
ejpam-97	35	6	object	object	NOUN
ejpam-97	35	7	of	of	ADP
ejpam-97	35	8	act	act	NOUN
ejpam-97	35	9	-	-	PUNCT
ejpam-97	35	10	s	s	PART
ejpam-97	35	11	is	be	AUX
ejpam-97	35	12	the	the	DET
ejpam-97	35	13	singleton	singleton	NOUN
ejpam-97	35	14	{	{	PUNCT
ejpam-97	35	15	0	0	NUM
ejpam-97	35	16	}	}	PUNCT
ejpam-97	35	17	,	,	PUNCT
ejpam-97	35	18	with	with	ADP
ejpam-97	35	19	the	the	DET
ejpam-97	35	20	obvious	obvious	ADJ
ejpam-97	35	21	s	s	NOUN
ejpam-97	35	22	-	-	NOUN
ejpam-97	35	23	action	action	NOUN
ejpam-97	35	24	.	.	PUNCT
ejpam-97	36	1	also	also	ADV
ejpam-97	36	2	,	,	PUNCT
ejpam-97	36	3	for	for	ADP
ejpam-97	36	4	s	s	NOUN
ejpam-97	36	5	-	-	PUNCT
ejpam-97	36	6	acts	act	VERB
ejpam-97	36	7	a	a	DET
ejpam-97	36	8	,	,	PUNCT
ejpam-97	36	9	b	b	NOUN
ejpam-97	36	10	,	,	PUNCT
ejpam-97	36	11	their	their	PRON
ejpam-97	36	12	cartesian	cartesian	ADJ
ejpam-97	36	13	product	product	NOUN
ejpam-97	36	14	a×	a×	PROPN
ejpam-97	36	15	b	b	PROPN
ejpam-97	36	16	with	with	ADP
ejpam-97	36	17	the	the	DET
ejpam-97	36	18	s	s	NOUN
ejpam-97	36	19	-	-	PUNCT
ejpam-97	36	20	action	action	NOUN
ejpam-97	36	21	defined	define	VERB
ejpam-97	36	22	by	by	ADP
ejpam-97	36	23	(	(	PUNCT
ejpam-97	36	24	a	a	PRON
ejpam-97	36	25	,	,	PUNCT
ejpam-97	36	26	b)s	b)s	X
ejpam-97	36	27	=	=	SYM
ejpam-97	36	28	(	(	PUNCT
ejpam-97	36	29	as	as	SCONJ
ejpam-97	36	30	,	,	PUNCT
ejpam-97	36	31	bs	bs	NOUN
ejpam-97	36	32	)	)	PUNCT
ejpam-97	36	33	is	be	AUX
ejpam-97	36	34	the	the	DET
ejpam-97	36	35	product	product	NOUN
ejpam-97	36	36	of	of	ADP
ejpam-97	36	37	a	a	PRON
ejpam-97	36	38	and	and	CCONJ
ejpam-97	36	39	b	b	NOUN
ejpam-97	36	40	in	in	ADP
ejpam-97	36	41	act	act	PROPN
ejpam-97	36	42	-	-	PUNCT
ejpam-97	36	43	s.	s.	PROPN
ejpam-97	36	44	recall	recall	VERB
ejpam-97	36	45	that	that	PRON
ejpam-97	36	46	for	for	ADP
ejpam-97	36	47	a	a	DET
ejpam-97	36	48	family	family	NOUN
ejpam-97	36	49	{	{	PUNCT
ejpam-97	36	50	aα	aα	NOUN
ejpam-97	36	51	:	:	PUNCT
ejpam-97	36	52	α	α	PROPN
ejpam-97	36	53	∈	∈	PROPN
ejpam-97	37	1	i	i	X
ejpam-97	37	2	}	}	PUNCT
ejpam-97	37	3	of	of	ADP
ejpam-97	37	4	s	s	NOUN
ejpam-97	37	5	-	-	PUNCT
ejpam-97	37	6	acts	act	VERB
ejpam-97	37	7	each	each	PRON
ejpam-97	37	8	with	with	ADP
ejpam-97	37	9	a	a	DET
ejpam-97	37	10	unique	unique	ADJ
ejpam-97	37	11	fixed	fix	VERB
ejpam-97	37	12	element	element	NOUN
ejpam-97	37	13	0	0	NUM
ejpam-97	37	14	,	,	PUNCT
ejpam-97	37	15	the	the	DET
ejpam-97	37	16	direct	direct	ADJ
ejpam-97	37	17	sum	sum	NOUN
ejpam-97	37	18	⊕	⊕	PROPN
ejpam-97	37	19	α∈i	α∈i	NUM
ejpam-97	37	20	aα	aα	NOUN
ejpam-97	37	21	is	be	AUX
ejpam-97	37	22	defined	define	VERB
ejpam-97	37	23	to	to	PART
ejpam-97	37	24	be	be	AUX
ejpam-97	37	25	the	the	DET
ejpam-97	37	26	subact	subact	NOUN
ejpam-97	37	27	of	of	ADP
ejpam-97	37	28	the	the	DET
ejpam-97	37	29	product	product	NOUN
ejpam-97	37	30	∏	∏	NUM
ejpam-97	38	1	α∈i	α∈i	NUM
ejpam-97	38	2	aα	aα	NOUN
ejpam-97	38	3	consisting	consist	VERB
ejpam-97	38	4	of	of	ADP
ejpam-97	38	5	all	all	PRON
ejpam-97	38	6	(	(	PUNCT
ejpam-97	38	7	aα)α∈i	aα)α∈i	NUM
ejpam-97	38	8	such	such	ADJ
ejpam-97	38	9	that	that	DET
ejpam-97	38	10	aα	aα	NOUN
ejpam-97	39	1	=	=	NOUN
ejpam-97	39	2	0	0	NUM
ejpam-97	39	3	for	for	ADP
ejpam-97	39	4	all	all	DET
ejpam-97	39	5	α	α	NOUN
ejpam-97	39	6	∈	∈	NOUN
ejpam-97	40	1	i	i	PRON
ejpam-97	40	2	except	except	SCONJ
ejpam-97	40	3	a	a	DET
ejpam-97	40	4	finite	finite	ADJ
ejpam-97	40	5	number	number	NOUN
ejpam-97	40	6	of	of	ADP
ejpam-97	40	7	indices	index	NOUN
ejpam-97	40	8	.	.	PUNCT
ejpam-97	41	1	the	the	DET
ejpam-97	41	2	pullback	pullback	NOUN
ejpam-97	41	3	of	of	ADP
ejpam-97	41	4	a	a	DET
ejpam-97	41	5	given	give	VERB
ejpam-97	41	6	diagram	diagram	NOUN
ejpam-97	41	7	a	a	DET
ejpam-97	41	8	↓	↓	NOUN
ejpam-97	41	9	f	f	PROPN
ejpam-97	41	10	c	c	PROPN
ejpam-97	41	11	g	g	PROPN
ejpam-97	41	12	→	→	SYM
ejpam-97	41	13	b	b	PROPN
ejpam-97	41	14	in	in	ADP
ejpam-97	41	15	act	act	PROPN
ejpam-97	41	16	-	-	PUNCT
ejpam-97	41	17	s	s	PART
ejpam-97	41	18	is	be	AUX
ejpam-97	41	19	the	the	DET
ejpam-97	41	20	subact	subact	NOUN
ejpam-97	41	21	p	p	NOUN
ejpam-97	41	22	=	=	PUNCT
ejpam-97	41	23	{	{	PUNCT
ejpam-97	41	24	(	(	PUNCT
ejpam-97	41	25	c	c	NOUN
ejpam-97	41	26	,	,	PUNCT
ejpam-97	41	27	a	a	NOUN
ejpam-97	41	28	)	)	PUNCT
ejpam-97	41	29	:	:	PUNCT
ejpam-97	41	30	c	c	X
ejpam-97	41	31	∈	∈	PROPN
ejpam-97	41	32	c	c	PROPN
ejpam-97	41	33	,	,	PUNCT
ejpam-97	41	34	a	a	DET
ejpam-97	41	35	∈	∈	PROPN
ejpam-97	41	36	a	a	DET
ejpam-97	41	37	,	,	PUNCT
ejpam-97	41	38	g(c	g(c	NOUN
ejpam-97	41	39	)	)	PUNCT
ejpam-97	41	40	=	=	SYM
ejpam-97	42	1	f	f	X
ejpam-97	42	2	(	(	PUNCT
ejpam-97	42	3	a	a	NOUN
ejpam-97	42	4	)	)	PUNCT
ejpam-97	42	5	}	}	PUNCT
ejpam-97	42	6	of	of	ADP
ejpam-97	42	7	c	c	PROPN
ejpam-97	42	8	×	×	NOUN
ejpam-97	42	9	a	a	NOUN
ejpam-97	42	10	,	,	PUNCT
ejpam-97	42	11	and	and	CCONJ
ejpam-97	42	12	pullback	pullback	NOUN
ejpam-97	42	13	maps	map	NOUN
ejpam-97	42	14	pc	pc	NOUN
ejpam-97	42	15	:	:	PUNCT
ejpam-97	42	16	p	p	X
ejpam-97	42	17	→	→	SYM
ejpam-97	42	18	c	c	PROPN
ejpam-97	42	19	,	,	PUNCT
ejpam-97	42	20	pa	pa	PROPN
ejpam-97	42	21	:	:	PUNCT
ejpam-97	42	22	p	p	X
ejpam-97	42	23	→	→	PUNCT
ejpam-97	42	24	a	a	PRON
ejpam-97	42	25	are	be	AUX
ejpam-97	42	26	restrictions	restriction	NOUN
ejpam-97	42	27	of	of	ADP
ejpam-97	42	28	projection	projection	NOUN
ejpam-97	42	29	maps	map	NOUN
ejpam-97	42	30	.	.	PUNCT
ejpam-97	43	1	notice	notice	VERB
ejpam-97	43	2	that	that	SCONJ
ejpam-97	43	3	for	for	ADP
ejpam-97	43	4	the	the	DET
ejpam-97	43	5	case	case	NOUN
ejpam-97	43	6	where	where	SCONJ
ejpam-97	43	7	g	g	PROPN
ejpam-97	43	8	is	be	AUX
ejpam-97	43	9	a	a	DET
ejpam-97	43	10	monomorphism	monomorphism	NOUN
ejpam-97	43	11	,	,	PUNCT
ejpam-97	43	12	p	p	NOUN
ejpam-97	43	13	can	can	AUX
ejpam-97	43	14	be	be	AUX
ejpam-97	43	15	taken	take	VERB
ejpam-97	43	16	as	as	ADP
ejpam-97	43	17	(	(	PUNCT
ejpam-97	43	18	isomorphic	isomorphic	ADJ
ejpam-97	43	19	to	to	ADP
ejpam-97	43	20	)	)	PUNCT
ejpam-97	43	21	f	f	PROPN
ejpam-97	43	22	−1(c	−1(c	PROPN
ejpam-97	43	23	)	)	PUNCT
ejpam-97	43	24	.	.	PUNCT
ejpam-97	44	1	all	all	DET
ejpam-97	44	2	colimits	colimit	NOUN
ejpam-97	44	3	in	in	ADP
ejpam-97	44	4	act	act	PROPN
ejpam-97	44	5	-	-	PUNCT
ejpam-97	44	6	s	s	NOUN
ejpam-97	44	7	exist	exist	NOUN
ejpam-97	44	8	and	and	CCONJ
ejpam-97	44	9	are	be	AUX
ejpam-97	44	10	calculated	calculate	VERB
ejpam-97	44	11	as	as	ADP
ejpam-97	44	12	in	in	ADP
ejpam-97	44	13	set	set	NOUN
ejpam-97	44	14	with	with	ADP
ejpam-97	44	15	a	a	DET
ejpam-97	44	16	natural	natural	ADJ
ejpam-97	44	17	action	action	NOUN
ejpam-97	44	18	of	of	ADP
ejpam-97	44	19	s	s	PRON
ejpam-97	44	20	on	on	ADP
ejpam-97	44	21	them	they	PRON
ejpam-97	44	22	.	.	PUNCT
ejpam-97	45	1	in	in	ADP
ejpam-97	45	2	particular	particular	ADJ
ejpam-97	45	3	,	,	PUNCT
ejpam-97	45	4	;	;	PUNCT
ejpam-97	45	5	with	with	ADP
ejpam-97	45	6	the	the	DET
ejpam-97	45	7	empty	empty	ADJ
ejpam-97	45	8	action	action	NOUN
ejpam-97	45	9	of	of	ADP
ejpam-97	45	10	s	s	PRON
ejpam-97	45	11	on	on	ADP
ejpam-97	45	12	it	it	PRON
ejpam-97	45	13	is	be	AUX
ejpam-97	45	14	the	the	DET
ejpam-97	45	15	initial	initial	ADJ
ejpam-97	45	16	object	object	NOUN
ejpam-97	45	17	of	of	ADP
ejpam-97	45	18	act	act	PROPN
ejpam-97	45	19	-	-	PUNCT
ejpam-97	45	20	s.	s.	PROPN
ejpam-97	45	21	also	also	ADV
ejpam-97	45	22	,	,	PUNCT
ejpam-97	45	23	the	the	DET
ejpam-97	45	24	coproduct	coproduct	NOUN
ejpam-97	45	25	of	of	ADP
ejpam-97	45	26	two	two	NUM
ejpam-97	45	27	s	s	NOUN
ejpam-97	45	28	-	-	PUNCT
ejpam-97	45	29	acts	act	VERB
ejpam-97	45	30	a	a	PRON
ejpam-97	45	31	,	,	PUNCT
ejpam-97	45	32	b	b	PROPN
ejpam-97	45	33	is	be	AUX
ejpam-97	45	34	their	their	PRON
ejpam-97	45	35	disjoint	disjoint	NOUN
ejpam-97	45	36	union	union	NOUN
ejpam-97	45	37	at	at	ADP
ejpam-97	45	38	b	b	PROPN
ejpam-97	45	39	=	=	PUNCT
ejpam-97	45	40	(	(	PUNCT
ejpam-97	45	41	a×	a×	X
ejpam-97	45	42	{	{	PUNCT
ejpam-97	45	43	1})∪	1})∪	X
ejpam-97	45	44	(	(	PUNCT
ejpam-97	45	45	b×	b×	NOUN
ejpam-97	45	46	{	{	PUNCT
ejpam-97	45	47	2	2	NUM
ejpam-97	45	48	}	}	PUNCT
ejpam-97	45	49	)	)	PUNCT
ejpam-97	45	50	with	with	ADP
ejpam-97	45	51	the	the	DET
ejpam-97	45	52	action	action	NOUN
ejpam-97	45	53	of	of	ADP
ejpam-97	45	54	s	s	PRON
ejpam-97	45	55	on	on	ADP
ejpam-97	45	56	h.	h.	PROPN
ejpam-97	45	57	barzegar	barzegar	PROPN
ejpam-97	45	58	and	and	CCONJ
ejpam-97	45	59	m.m	m.m	PROPN
ejpam-97	45	60	.	.	PROPN
ejpam-97	45	61	ebrahimi	ebrahimi	PROPN
ejpam-97	45	62	/	/	SYM
ejpam-97	45	63	eur	eur	PROPN
ejpam-97	45	64	.	.	PUNCT
ejpam-97	46	1	j.	j.	PROPN
ejpam-97	46	2	pure	pure	PROPN
ejpam-97	46	3	appl	appl	PROPN
ejpam-97	46	4	.	.	PROPN
ejpam-97	46	5	math	math	PROPN
ejpam-97	46	6	,	,	PUNCT
ejpam-97	46	7	1	1	NUM
ejpam-97	46	8	(	(	PUNCT
ejpam-97	46	9	2008	2008	NUM
ejpam-97	46	10	)	)	PUNCT
ejpam-97	46	11	,	,	PUNCT
ejpam-97	46	12	(	(	PUNCT
ejpam-97	46	13	41	41	NUM
ejpam-97	46	14	-	-	SYM
ejpam-97	46	15	55	55	NUM
ejpam-97	46	16	)	)	PUNCT
ejpam-97	46	17	43	43	NUM
ejpam-97	46	18	at	at	ADP
ejpam-97	46	19	b	b	NOUN
ejpam-97	46	20	defined	define	VERB
ejpam-97	46	21	by	by	ADP
ejpam-97	46	22	(	(	PUNCT
ejpam-97	46	23	a	a	PRON
ejpam-97	46	24	,	,	PUNCT
ejpam-97	46	25	1)s	1)s	NUM
ejpam-97	46	26	=	=	SYM
ejpam-97	46	27	(	(	PUNCT
ejpam-97	46	28	as	as	ADP
ejpam-97	46	29	,	,	PUNCT
ejpam-97	46	30	1	1	NUM
ejpam-97	46	31	)	)	PUNCT
ejpam-97	46	32	,	,	PUNCT
ejpam-97	46	33	(	(	PUNCT
ejpam-97	46	34	b	b	X
ejpam-97	46	35	,	,	PUNCT
ejpam-97	46	36	2)s	2)s	NOUN
ejpam-97	46	37	=	=	SYM
ejpam-97	46	38	(	(	PUNCT
ejpam-97	46	39	bs	bs	NOUN
ejpam-97	46	40	,	,	PUNCT
ejpam-97	46	41	2	2	NUM
ejpam-97	46	42	)	)	PUNCT
ejpam-97	46	43	for	for	ADP
ejpam-97	46	44	s	s	PROPN
ejpam-97	46	45	∈	∈	PROPN
ejpam-97	46	46	s	s	PROPN
ejpam-97	46	47	,	,	PUNCT
ejpam-97	46	48	a	a	DET
ejpam-97	46	49	∈	∈	PROPN
ejpam-97	46	50	a	a	DET
ejpam-97	46	51	,	,	PUNCT
ejpam-97	46	52	b	b	PROPN
ejpam-97	46	53	∈	∈	PROPN
ejpam-97	46	54	b.	b.	PROPN
ejpam-97	47	1	the	the	DET
ejpam-97	47	2	coproduct	coproduct	NOUN
ejpam-97	47	3	at	at	ADP
ejpam-97	47	4	{	{	PUNCT
ejpam-97	47	5	0	0	NUM
ejpam-97	47	6	}	}	PUNCT
ejpam-97	47	7	is	be	AUX
ejpam-97	47	8	denoted	denote	VERB
ejpam-97	47	9	by	by	ADP
ejpam-97	47	10	a0	a0	PROPN
ejpam-97	47	11	.	.	PUNCT
ejpam-97	48	1	definition	definition	NOUN
ejpam-97	48	2	1.1	1.1	NUM
ejpam-97	48	3	.	.	PUNCT
ejpam-97	49	1	let	let	VERB
ejpam-97	49	2	a	a	DET
ejpam-97	49	3	be	be	AUX
ejpam-97	49	4	an	an	DET
ejpam-97	49	5	s	s	NOUN
ejpam-97	49	6	-	-	NOUN
ejpam-97	49	7	act	act	NOUN
ejpam-97	49	8	.	.	PUNCT
ejpam-97	50	1	an	an	DET
ejpam-97	50	2	equivalence	equivalence	NOUN
ejpam-97	50	3	relation	relation	NOUN
ejpam-97	50	4	ρ	ρ	NOUN
ejpam-97	50	5	on	on	ADP
ejpam-97	50	6	a	a	PRON
ejpam-97	50	7	is	be	AUX
ejpam-97	50	8	called	call	VERB
ejpam-97	50	9	an	an	DET
ejpam-97	50	10	s	s	NOUN
ejpam-97	50	11	-	-	PUNCT
ejpam-97	50	12	act	act	NOUN
ejpam-97	50	13	congruence	congruence	NOUN
ejpam-97	50	14	on	on	ADP
ejpam-97	50	15	a	a	PRON
ejpam-97	50	16	if	if	SCONJ
ejpam-97	50	17	aρa′	aρa′	PRON
ejpam-97	50	18	implies	imply	VERB
ejpam-97	50	19	asρa′s	asρa′s	PROPN
ejpam-97	50	20	for	for	ADP
ejpam-97	50	21	a	a	PRON
ejpam-97	50	22	,	,	PUNCT
ejpam-97	50	23	a′	a′	PROPN
ejpam-97	50	24	∈	∈	PROPN
ejpam-97	50	25	a	a	PRON
ejpam-97	50	26	,	,	PUNCT
ejpam-97	50	27	s	s	VERB
ejpam-97	50	28	∈	∈	PROPN
ejpam-97	50	29	s.	s.	PROPN
ejpam-97	50	30	the	the	DET
ejpam-97	50	31	right	right	ADJ
ejpam-97	50	32	action	action	NOUN
ejpam-97	50	33	making	make	VERB
ejpam-97	50	34	a	a	DET
ejpam-97	50	35	/	/	SYM
ejpam-97	50	36	ρ	ρ	PROPN
ejpam-97	50	37	an	an	DET
ejpam-97	50	38	s	s	NOUN
ejpam-97	50	39	-	-	PUNCT
ejpam-97	50	40	act	act	NOUN
ejpam-97	50	41	is	be	AUX
ejpam-97	50	42	defined	define	VERB
ejpam-97	50	43	by	by	ADP
ejpam-97	50	44	[	[	X
ejpam-97	50	45	a]s	a]s	ADJ
ejpam-97	51	1	=	=	PUNCT
ejpam-97	52	1	[	[	X
ejpam-97	52	2	as	as	ADP
ejpam-97	52	3	]	]	PUNCT
ejpam-97	52	4	.	.	PUNCT
ejpam-97	53	1	for	for	ADP
ejpam-97	53	2	h	h	NOUN
ejpam-97	53	3	⊆	⊆	NUM
ejpam-97	53	4	a×	a×	PROPN
ejpam-97	53	5	a	a	X
ejpam-97	53	6	,	,	PUNCT
ejpam-97	53	7	the	the	DET
ejpam-97	53	8	congruence	congruence	NOUN
ejpam-97	53	9	generated	generate	VERB
ejpam-97	53	10	by	by	ADP
ejpam-97	53	11	h	h	PROPN
ejpam-97	53	12	,	,	PUNCT
ejpam-97	53	13	that	that	PRON
ejpam-97	53	14	is	be	AUX
ejpam-97	53	15	the	the	DET
ejpam-97	53	16	smallest	small	ADJ
ejpam-97	53	17	congruence	congruence	NOUN
ejpam-97	53	18	on	on	ADP
ejpam-97	53	19	a	a	DET
ejpam-97	53	20	containing	contain	VERB
ejpam-97	53	21	h	h	NOUN
ejpam-97	53	22	,	,	PUNCT
ejpam-97	53	23	is	be	AUX
ejpam-97	53	24	denoted	denote	VERB
ejpam-97	53	25	by	by	ADP
ejpam-97	53	26	ρ(h	ρ(h	NOUN
ejpam-97	53	27	)	)	PUNCT
ejpam-97	53	28	.	.	PUNCT
ejpam-97	54	1	for	for	ADP
ejpam-97	54	2	a	a	DET
ejpam-97	54	3	subset	subset	ADJ
ejpam-97	54	4	h	h	NOUN
ejpam-97	54	5	of	of	ADP
ejpam-97	54	6	a×	a×	PROPN
ejpam-97	54	7	a	a	DET
ejpam-97	54	8	let	let	NOUN
ejpam-97	54	9	h	h	NOUN
ejpam-97	54	10	e	e	AUX
ejpam-97	54	11	be	be	AUX
ejpam-97	54	12	the	the	DET
ejpam-97	54	13	equivalence	equivalence	NOUN
ejpam-97	54	14	relation	relation	NOUN
ejpam-97	54	15	generated	generate	VERB
ejpam-97	54	16	by	by	ADP
ejpam-97	54	17	h	h	PROPN
ejpam-97	54	18	and	and	CCONJ
ejpam-97	54	19	h	h	NOUN
ejpam-97	54	20	c	c	NOUN
ejpam-97	55	1	=	=	PRON
ejpam-97	55	2	{	{	PUNCT
ejpam-97	55	3	(	(	PUNCT
ejpam-97	55	4	as	as	ADP
ejpam-97	55	5	,	,	PUNCT
ejpam-97	55	6	bs	bs	NOUN
ejpam-97	55	7	)	)	PUNCT
ejpam-97	55	8	:	:	PUNCT
ejpam-97	55	9	(	(	PUNCT
ejpam-97	55	10	a	a	PRON
ejpam-97	55	11	,	,	PUNCT
ejpam-97	55	12	b	b	NOUN
ejpam-97	55	13	)	)	PUNCT
ejpam-97	55	14	∈	∈	PROPN
ejpam-97	55	15	h	h	NOUN
ejpam-97	55	16	,	,	PUNCT
ejpam-97	55	17	s	s	AUX
ejpam-97	55	18	∈	∈	PROPN
ejpam-97	55	19	s	s	AUX
ejpam-97	55	20	}	}	PUNCT
ejpam-97	55	21	then	then	ADV
ejpam-97	55	22	we	we	PRON
ejpam-97	55	23	have	have	VERB
ejpam-97	55	24	:	:	PUNCT
ejpam-97	55	25	lemma	lemma	PROPN
ejpam-97	55	26	1.1	1.1	NUM
ejpam-97	55	27	.	.	PUNCT
ejpam-97	56	1	let	let	VERB
ejpam-97	56	2	a	a	DET
ejpam-97	56	3	be	be	AUX
ejpam-97	56	4	an	an	DET
ejpam-97	56	5	act	act	NOUN
ejpam-97	56	6	over	over	ADP
ejpam-97	56	7	a	a	DET
ejpam-97	56	8	semigroup	semigroup	NOUN
ejpam-97	56	9	s	s	NOUN
ejpam-97	56	10	and	and	CCONJ
ejpam-97	56	11	h	h	NOUN
ejpam-97	56	12	⊆	⊆	NUM
ejpam-97	56	13	a×	a×	NOUN
ejpam-97	56	14	a.	a.	NOUN
ejpam-97	56	15	then	then	ADV
ejpam-97	56	16	ρ(h	ρ(h	X
ejpam-97	56	17	)	)	PUNCT
ejpam-97	57	1	=	=	PUNCT
ejpam-97	57	2	(	(	PUNCT
ejpam-97	57	3	h	h	NOUN
ejpam-97	57	4	∪h	∪h	NUM
ejpam-97	57	5	c)e	c)e	ADJ
ejpam-97	57	6	.	.	PUNCT
ejpam-97	58	1	proof	proof	NOUN
ejpam-97	58	2	.	.	PUNCT
ejpam-97	59	1	it	it	PRON
ejpam-97	59	2	is	be	AUX
ejpam-97	59	3	enough	enough	ADJ
ejpam-97	59	4	to	to	PART
ejpam-97	59	5	show	show	VERB
ejpam-97	59	6	that	that	SCONJ
ejpam-97	59	7	the	the	DET
ejpam-97	59	8	equivalence	equivalence	NOUN
ejpam-97	59	9	relation	relation	NOUN
ejpam-97	59	10	(	(	PUNCT
ejpam-97	59	11	h	h	NOUN
ejpam-97	59	12	∪	∪	NOUN
ejpam-97	59	13	h	h	PROPN
ejpam-97	59	14	c)e	c)e	ADJ
ejpam-97	59	15	is	be	AUX
ejpam-97	59	16	a	a	DET
ejpam-97	59	17	congruence	congruence	NOUN
ejpam-97	59	18	.	.	PUNCT
ejpam-97	60	1	suppose	suppose	VERB
ejpam-97	60	2	that	that	SCONJ
ejpam-97	60	3	x(h	x(h	PROPN
ejpam-97	60	4	∪h	∪h	X
ejpam-97	60	5	c)e	c)e	ADJ
ejpam-97	60	6	y	y	NOUN
ejpam-97	60	7	and	and	CCONJ
ejpam-97	60	8	s	s	PROPN
ejpam-97	60	9	∈	∈	PROPN
ejpam-97	60	10	s.	s.	PROPN
ejpam-97	60	11	then	then	ADV
ejpam-97	60	12	x	x	X
ejpam-97	60	13	=	=	SYM
ejpam-97	60	14	y	y	PROPN
ejpam-97	60	15	,	,	PUNCT
ejpam-97	60	16	and	and	CCONJ
ejpam-97	60	17	so	so	ADV
ejpam-97	60	18	xs	xs	PROPN
ejpam-97	60	19	=	=	SYM
ejpam-97	60	20	ys	ys	PROPN
ejpam-97	60	21	,	,	PUNCT
ejpam-97	60	22	or	or	CCONJ
ejpam-97	60	23	there	there	PRON
ejpam-97	60	24	exist	exist	VERB
ejpam-97	60	25	z1	z1	NOUN
ejpam-97	60	26	,	,	PUNCT
ejpam-97	60	27	...	...	PUNCT
ejpam-97	60	28	,	,	PUNCT
ejpam-97	60	29	zn	zn	PROPN
ejpam-97	60	30	∈	∈	PROPN
ejpam-97	60	31	a	a	DET
ejpam-97	60	32	such	such	ADJ
ejpam-97	60	33	that	that	SCONJ
ejpam-97	60	34	x	x	X
ejpam-97	60	35	=	=	SYM
ejpam-97	60	36	z1	z1	PROPN
ejpam-97	60	37	,	,	PUNCT
ejpam-97	60	38	y	y	PROPN
ejpam-97	60	39	=	=	SYM
ejpam-97	60	40	zn	zn	PROPN
ejpam-97	60	41	and	and	CCONJ
ejpam-97	60	42	(	(	PUNCT
ejpam-97	60	43	zi	zi	PROPN
ejpam-97	60	44	,	,	PUNCT
ejpam-97	60	45	zi+1	zi+1	X
ejpam-97	60	46	)	)	PUNCT
ejpam-97	60	47	∈	∈	PROPN
ejpam-97	60	48	(	(	PUNCT
ejpam-97	60	49	h	h	NOUN
ejpam-97	60	50	∪	∪	NOUN
ejpam-97	60	51	h	h	NOUN
ejpam-97	60	52	c	c	NOUN
ejpam-97	60	53	)	)	PUNCT
ejpam-97	60	54	∪	∪	NOUN
ejpam-97	60	55	(	(	PUNCT
ejpam-97	60	56	h	h	NOUN
ejpam-97	60	57	∪	∪	PROPN
ejpam-97	60	58	h	h	PROPN
ejpam-97	60	59	c)−1	c)−1	PROPN
ejpam-97	60	60	.	.	PUNCT
ejpam-97	61	1	then	then	ADV
ejpam-97	61	2	we	we	PRON
ejpam-97	61	3	also	also	ADV
ejpam-97	61	4	have	have	VERB
ejpam-97	61	5	(	(	PUNCT
ejpam-97	61	6	zis	zi	NOUN
ejpam-97	61	7	,	,	PUNCT
ejpam-97	61	8	zi+1s	zi+1s	NOUN
ejpam-97	61	9	)	)	PUNCT
ejpam-97	61	10	∈	∈	PROPN
ejpam-97	61	11	(	(	PUNCT
ejpam-97	61	12	h	h	NOUN
ejpam-97	61	13	∪h	∪h	NUM
ejpam-97	61	14	c)∪	c)∪	NOUN
ejpam-97	61	15	(	(	PUNCT
ejpam-97	61	16	h	h	PROPN
ejpam-97	61	17	∪h	∪h	NUM
ejpam-97	61	18	c)−1	c)−1	PROPN
ejpam-97	61	19	.	.	PUNCT
ejpam-97	62	1	corollary	corollary	ADJ
ejpam-97	62	2	1.1	1.1	NUM
ejpam-97	62	3	.	.	PUNCT
ejpam-97	63	1	let	let	VERB
ejpam-97	63	2	h	h	PRON
ejpam-97	63	3	⊆	⊆	SYM
ejpam-97	63	4	a	a	DET
ejpam-97	63	5	×	×	NOUN
ejpam-97	63	6	a	a	PRON
ejpam-97	63	7	and	and	CCONJ
ejpam-97	63	8	ρ	ρ	NOUN
ejpam-97	63	9	=	=	SYM
ejpam-97	63	10	ρ(h	ρ(h	NOUN
ejpam-97	63	11	)	)	PUNCT
ejpam-97	63	12	.	.	PUNCT
ejpam-97	64	1	then	then	ADV
ejpam-97	64	2	,	,	PUNCT
ejpam-97	64	3	for	for	ADP
ejpam-97	64	4	a	a	PRON
ejpam-97	64	5	,	,	PUNCT
ejpam-97	64	6	b	b	PROPN
ejpam-97	64	7	∈	∈	PROPN
ejpam-97	64	8	a	a	PRON
ejpam-97	64	9	,	,	PUNCT
ejpam-97	64	10	one	one	NOUN
ejpam-97	64	11	has	have	AUX
ejpam-97	64	12	aρb	aρb	VERB
ejpam-97	64	13	if	if	SCONJ
ejpam-97	64	14	and	and	CCONJ
ejpam-97	64	15	only	only	ADV
ejpam-97	64	16	if	if	SCONJ
ejpam-97	64	17	either	either	CCONJ
ejpam-97	64	18	a	a	DET
ejpam-97	64	19	=	=	SYM
ejpam-97	64	20	b	b	NOUN
ejpam-97	64	21	or	or	CCONJ
ejpam-97	64	22	there	there	ADV
ejpam-97	64	23	exist	exist	VERB
ejpam-97	64	24	p1	p1	NOUN
ejpam-97	64	25	,	,	PUNCT
ejpam-97	64	26	p2	p2	NOUN
ejpam-97	64	27	,	,	PUNCT
ejpam-97	64	28	...	...	PUNCT
ejpam-97	64	29	,	,	PUNCT
ejpam-97	64	30	pn	pn	PROPN
ejpam-97	64	31	,	,	PUNCT
ejpam-97	64	32	q1	q1	PROPN
ejpam-97	64	33	,	,	PUNCT
ejpam-97	64	34	q2	q2	NOUN
ejpam-97	64	35	,	,	PUNCT
ejpam-97	64	36	...	...	PUNCT
ejpam-97	64	37	,	,	PUNCT
ejpam-97	64	38	qn	qn	NOUN
ejpam-97	64	39	∈	∈	PROPN
ejpam-97	64	40	a	a	DET
ejpam-97	64	41	,	,	PUNCT
ejpam-97	64	42	s1	s1	NOUN
ejpam-97	64	43	,	,	PUNCT
ejpam-97	64	44	s2	s2	PROPN
ejpam-97	64	45	,	,	PUNCT
ejpam-97	64	46	...	...	PUNCT
ejpam-97	64	47	,	,	PUNCT
ejpam-97	64	48	sn	sn	PROPN
ejpam-97	64	49	∈	∈	PROPN
ejpam-97	64	50	s1	s1	NOUN
ejpam-97	64	51	where	where	SCONJ
ejpam-97	64	52	for	for	ADP
ejpam-97	64	53	i	i	PROPN
ejpam-97	64	54	=	=	NOUN
ejpam-97	64	55	1	1	NUM
ejpam-97	64	56	,	,	PUNCT
ejpam-97	64	57	...	...	PUNCT
ejpam-97	64	58	,	,	PUNCT
ejpam-97	64	59	n	n	CCONJ
ejpam-97	64	60	,	,	PUNCT
ejpam-97	64	61	(	(	PUNCT
ejpam-97	64	62	pi	pi	NOUN
ejpam-97	64	63	,	,	PUNCT
ejpam-97	64	64	qi	qi	PROPN
ejpam-97	64	65	)	)	PUNCT
ejpam-97	64	66	∈	∈	PROPN
ejpam-97	64	67	h	h	NOUN
ejpam-97	64	68	∪h−1	∪h−1	NOUN
ejpam-97	64	69	,	,	PUNCT
ejpam-97	64	70	such	such	ADJ
ejpam-97	64	71	that	that	SCONJ
ejpam-97	64	72	a	a	DET
ejpam-97	64	73	=	=	X
ejpam-97	64	74	p1s1	p1s1	NOUN
ejpam-97	64	75	,	,	PUNCT
ejpam-97	64	76	q1s1	q1s1	NOUN
ejpam-97	64	77	=	=	SYM
ejpam-97	64	78	p2s2	p2s2	PROPN
ejpam-97	64	79	,	,	PUNCT
ejpam-97	64	80	q2s2	q2s2	PROPN
ejpam-97	64	81	=	=	SYM
ejpam-97	64	82	p3s3	p3s3	NOUN
ejpam-97	64	83	,	,	PUNCT
ejpam-97	64	84	...	...	PUNCT
ejpam-97	64	85	,	,	PUNCT
ejpam-97	64	86	qnsn	qnsn	X
ejpam-97	64	87	=	=	SYM
ejpam-97	64	88	b.	b.	PROPN
ejpam-97	64	89	the	the	DET
ejpam-97	64	90	pushout	pushout	NOUN
ejpam-97	64	91	of	of	ADP
ejpam-97	64	92	a	a	DET
ejpam-97	64	93	given	give	VERB
ejpam-97	64	94	diagram	diagram	NOUN
ejpam-97	64	95	a	a	PRON
ejpam-97	64	96	f	f	PROPN
ejpam-97	64	97	→	→	SYM
ejpam-97	64	98	b	b	PROPN
ejpam-97	64	99	g	g	PROPN
ejpam-97	64	100	↓	↓	PROPN
ejpam-97	64	101	c	c	PROPN
ejpam-97	64	102	in	in	ADP
ejpam-97	64	103	act	act	PROPN
ejpam-97	64	104	-	-	PUNCT
ejpam-97	64	105	s	s	PART
ejpam-97	64	106	is	be	AUX
ejpam-97	64	107	the	the	DET
ejpam-97	64	108	factor	factor	NOUN
ejpam-97	64	109	act	act	NOUN
ejpam-97	64	110	q	q	X
ejpam-97	64	111	=	=	PUNCT
ejpam-97	64	112	(	(	PUNCT
ejpam-97	64	113	btc)/θ	btc)/θ	X
ejpam-97	64	114	where	where	SCONJ
ejpam-97	64	115	θ	θ	PROPN
ejpam-97	64	116	=	=	SYM
ejpam-97	64	117	ρ(h	ρ(h	X
ejpam-97	64	118	)	)	PUNCT
ejpam-97	64	119	and	and	CCONJ
ejpam-97	64	120	h	h	NOUN
ejpam-97	64	121	consists	consist	VERB
ejpam-97	64	122	of	of	ADP
ejpam-97	64	123	all	all	DET
ejpam-97	64	124	pairs	pair	NOUN
ejpam-97	64	125	(	(	PUNCT
ejpam-97	64	126	ub	ub	INTJ
ejpam-97	64	127	f	f	X
ejpam-97	64	128	(	(	PUNCT
ejpam-97	64	129	a	a	PROPN
ejpam-97	64	130	)	)	PUNCT
ejpam-97	64	131	,	,	PUNCT
ejpam-97	64	132	uc	uc	PROPN
ejpam-97	64	133	g(a	g(a	PROPN
ejpam-97	64	134	)	)	PUNCT
ejpam-97	64	135	)	)	PUNCT
ejpam-97	64	136	,	,	PUNCT
ejpam-97	64	137	a	a	DET
ejpam-97	64	138	∈	∈	PROPN
ejpam-97	64	139	a	a	PRON
ejpam-97	64	140	,	,	PUNCT
ejpam-97	64	141	where	where	SCONJ
ejpam-97	64	142	ub	ub	ADV
ejpam-97	64	143	:	:	PUNCT
ejpam-97	64	144	b→	b→	PROPN
ejpam-97	64	145	btc	btc	PROPN
ejpam-97	64	146	,	,	PUNCT
ejpam-97	64	147	uc	uc	INTJ
ejpam-97	64	148	:	:	PUNCT
ejpam-97	64	149	c	c	X
ejpam-97	64	150	→	→	SYM
ejpam-97	64	151	btc	btc	PROPN
ejpam-97	64	152	are	be	AUX
ejpam-97	64	153	coproduct	coproduct	NOUN
ejpam-97	64	154	injections	injection	NOUN
ejpam-97	64	155	.	.	PUNCT
ejpam-97	65	1	also	also	ADV
ejpam-97	65	2	,	,	PUNCT
ejpam-97	65	3	the	the	DET
ejpam-97	65	4	pushout	pushout	NOUN
ejpam-97	65	5	maps	map	NOUN
ejpam-97	65	6	are	be	AUX
ejpam-97	65	7	given	give	VERB
ejpam-97	65	8	as	as	ADP
ejpam-97	65	9	q1	q1	NOUN
ejpam-97	65	10	=	=	SYM
ejpam-97	65	11	πuc	πuc	NOUN
ejpam-97	65	12	:	:	PUNCT
ejpam-97	65	13	c	c	X
ejpam-97	65	14	→	→	PUNCT
ejpam-97	65	15	(	(	PUNCT
ejpam-97	65	16	btc)/θ	btc)/θ	X
ejpam-97	65	17	,	,	PUNCT
ejpam-97	65	18	q2	q2	NOUN
ejpam-97	65	19	=	=	SYM
ejpam-97	65	20	πub	πub	PROPN
ejpam-97	65	21	:	:	PUNCT
ejpam-97	65	22	b→	b→	PROPN
ejpam-97	65	23	(	(	PUNCT
ejpam-97	65	24	btc)/θ	btc)/θ	X
ejpam-97	65	25	,	,	PUNCT
ejpam-97	65	26	where	where	SCONJ
ejpam-97	65	27	π	π	NOUN
ejpam-97	65	28	:	:	PUNCT
ejpam-97	65	29	btc	btc	PROPN
ejpam-97	65	30	→	→	SYM
ejpam-97	65	31	(	(	PUNCT
ejpam-97	65	32	btc)/θ	btc)/θ	X
ejpam-97	65	33	is	be	AUX
ejpam-97	65	34	the	the	DET
ejpam-97	65	35	canonical	canonical	ADJ
ejpam-97	65	36	epimorphism	epimorphism	NOUN
ejpam-97	65	37	.	.	PUNCT
ejpam-97	66	1	multiple	multiple	ADJ
ejpam-97	66	2	pushouts	pushout	NOUN
ejpam-97	66	3	in	in	ADP
ejpam-97	66	4	act	act	PROPN
ejpam-97	66	5	-	-	PUNCT
ejpam-97	66	6	s	s	NOUN
ejpam-97	66	7	are	be	AUX
ejpam-97	66	8	constructed	construct	VERB
ejpam-97	66	9	analogously	analogously	ADV
ejpam-97	66	10	.	.	PUNCT
ejpam-97	67	1	recall	recall	VERB
ejpam-97	67	2	that	that	SCONJ
ejpam-97	67	3	a	a	DET
ejpam-97	67	4	directed	direct	VERB
ejpam-97	67	5	system	system	NOUN
ejpam-97	67	6	of	of	ADP
ejpam-97	67	7	s	s	NOUN
ejpam-97	67	8	-	-	PUNCT
ejpam-97	67	9	acts	act	NOUN
ejpam-97	67	10	and	and	CCONJ
ejpam-97	67	11	s	s	NOUN
ejpam-97	67	12	-	-	NOUN
ejpam-97	67	13	maps	map	NOUN
ejpam-97	67	14	is	be	AUX
ejpam-97	67	15	a	a	DET
ejpam-97	67	16	family	family	NOUN
ejpam-97	67	17	(	(	PUNCT
ejpam-97	67	18	bα)α∈i	bα)α∈i	NOUN
ejpam-97	67	19	of	of	ADP
ejpam-97	67	20	s	s	NOUN
ejpam-97	67	21	-	-	PUNCT
ejpam-97	67	22	acts	act	NOUN
ejpam-97	67	23	indexed	index	VERB
ejpam-97	67	24	by	by	ADP
ejpam-97	67	25	an	an	DET
ejpam-97	67	26	updirected	updirected	ADJ
ejpam-97	67	27	set	set	NOUN
ejpam-97	67	28	i	i	PRON
ejpam-97	67	29	endowed	endow	VERB
ejpam-97	67	30	by	by	ADP
ejpam-97	67	31	a	a	DET
ejpam-97	67	32	family	family	NOUN
ejpam-97	67	33	(	(	PUNCT
ejpam-97	67	34	gαβ	gαβ	NOUN
ejpam-97	67	35	:	:	PUNCT
ejpam-97	67	36	bα	bα	PROPN
ejpam-97	67	37	→	→	SYM
ejpam-97	67	38	bβ)α≤β∈i	bβ)α≤β∈i	PROPN
ejpam-97	67	39	of	of	ADP
ejpam-97	67	40	s	s	NOUN
ejpam-97	67	41	-	-	PUNCT
ejpam-97	67	42	maps	map	NOUN
ejpam-97	67	43	such	such	ADJ
ejpam-97	67	44	that	that	SCONJ
ejpam-97	67	45	given	give	VERB
ejpam-97	67	46	α	α	NOUN
ejpam-97	67	47	≤	≤	NOUN
ejpam-97	67	48	β	β	NOUN
ejpam-97	67	49	≤	≤	NUM
ejpam-97	67	50	γ	γ	X
ejpam-97	67	51	∈	∈	PROPN
ejpam-97	67	52	i	i	PRON
ejpam-97	67	53	we	we	PRON
ejpam-97	67	54	have	have	VERB
ejpam-97	67	55	gβγgαβ	gβγgαβ	NOUN
ejpam-97	67	56	=	=	SYM
ejpam-97	67	57	gαγ	gαγ	ADJ
ejpam-97	67	58	,	,	PUNCT
ejpam-97	67	59	also	also	ADV
ejpam-97	67	60	gαα	gαα	VERB
ejpam-97	67	61	=	=	SYM
ejpam-97	68	1	i	i	PRON
ejpam-97	68	2	d.	d.	PROPN
ejpam-97	68	3	note	note	VERB
ejpam-97	68	4	that	that	SCONJ
ejpam-97	68	5	the	the	DET
ejpam-97	68	6	direct	direct	ADJ
ejpam-97	68	7	limit	limit	NOUN
ejpam-97	68	8	(	(	PUNCT
ejpam-97	68	9	directed	direct	VERB
ejpam-97	68	10	colimit	colimit	NOUN
ejpam-97	68	11	)	)	PUNCT
ejpam-97	68	12	of	of	ADP
ejpam-97	68	13	a	a	DET
ejpam-97	68	14	directed	direct	VERB
ejpam-97	68	15	system	system	NOUN
ejpam-97	68	16	(	(	PUNCT
ejpam-97	68	17	(	(	PUNCT
ejpam-97	68	18	bα)α∈i	bα)α∈i	X
ejpam-97	68	19	,	,	PUNCT
ejpam-97	68	20	(	(	PUNCT
ejpam-97	68	21	gαβ)α≤β∈i	gαβ)α≤β∈i	X
ejpam-97	68	22	)	)	PUNCT
ejpam-97	68	23	in	in	ADP
ejpam-97	68	24	act	act	PROPN
ejpam-97	68	25	-	-	PUNCT
ejpam-97	68	26	s	s	PART
ejpam-97	68	27	is	be	AUX
ejpam-97	68	28	given	give	VERB
ejpam-97	68	29	as	as	ADP
ejpam-97	68	30	l	l	NOUN
ejpam-97	68	31	im−→αbα	im−→αbα	NOUN
ejpam-97	68	32	=	=	SYM
ejpam-97	68	33	∐	∐	X
ejpam-97	68	34	α	α	PROPN
ejpam-97	68	35	bα	bα	PROPN
ejpam-97	68	36	/	/	SYM
ejpam-97	68	37	ρ	ρ	PROPN
ejpam-97	68	38	where	where	SCONJ
ejpam-97	68	39	the	the	DET
ejpam-97	68	40	congruence	congruence	NOUN
ejpam-97	68	41	ρ	ρ	NOUN
ejpam-97	68	42	is	be	AUX
ejpam-97	68	43	given	give	VERB
ejpam-97	68	44	by	by	ADP
ejpam-97	68	45	bαρbβ	bαρbβ	PROPN
ejpam-97	69	1	if	if	SCONJ
ejpam-97	69	2	and	and	CCONJ
ejpam-97	69	3	only	only	ADV
ejpam-97	69	4	if	if	SCONJ
ejpam-97	69	5	there	there	PRON
ejpam-97	69	6	exists	exist	VERB
ejpam-97	69	7	γ	γ	PROPN
ejpam-97	69	8	≥	≥	PROPN
ejpam-97	69	9	α	α	X
ejpam-97	69	10	,	,	PUNCT
ejpam-97	69	11	β	β	PROPN
ejpam-97	69	12	such	such	ADJ
ejpam-97	69	13	that	that	DET
ejpam-97	69	14	uγgαγ(bα	uγgαγ(bα	NOUN
ejpam-97	69	15	)	)	PUNCT
ejpam-97	69	16	=	=	SYM
ejpam-97	69	17	uγgβγ(bβ	uγgβγ(bβ	PROPN
ejpam-97	69	18	)	)	PUNCT
ejpam-97	69	19	,	,	PUNCT
ejpam-97	69	20	in	in	ADP
ejpam-97	69	21	which	which	PRON
ejpam-97	69	22	each	each	DET
ejpam-97	69	23	uα	uα	X
ejpam-97	69	24	:	:	PUNCT
ejpam-97	70	1	bα→	bα→	NOUN
ejpam-97	70	2	∐	∐	X
ejpam-97	71	1	α	α	DET
ejpam-97	71	2	bα	bα	PROPN
ejpam-97	71	3	is	be	AUX
ejpam-97	71	4	an	an	DET
ejpam-97	71	5	injection	injection	NOUN
ejpam-97	71	6	map	map	NOUN
ejpam-97	71	7	of	of	ADP
ejpam-97	71	8	the	the	DET
ejpam-97	71	9	coproduct	coproduct	NOUN
ejpam-97	71	10	.	.	PUNCT
ejpam-97	72	1	notice	notice	VERB
ejpam-97	72	2	that	that	SCONJ
ejpam-97	72	3	the	the	DET
ejpam-97	72	4	family	family	NOUN
ejpam-97	72	5	gα	gα	NOUN
ejpam-97	72	6	=	=	PUNCT
ejpam-97	72	7	πuα	πuα	NOUN
ejpam-97	72	8	:	:	PUNCT
ejpam-97	72	9	bα	bα	PROPN
ejpam-97	72	10	→	→	SYM
ejpam-97	72	11	l	l	NOUN
ejpam-97	72	12	im−→αbα	im−→αbα	NOUN
ejpam-97	72	13	of	of	ADP
ejpam-97	72	14	s	s	NOUN
ejpam-97	72	15	-	-	PUNCT
ejpam-97	72	16	maps	map	NOUN
ejpam-97	72	17	satisfies	satisfie	NOUN
ejpam-97	72	18	gβ	gβ	ADP
ejpam-97	72	19	gαβ	gαβ	PROPN
ejpam-97	72	20	=	=	PUNCT
ejpam-97	73	1	gα	gα	NOUN
ejpam-97	73	2	for	for	ADP
ejpam-97	73	3	α	α	NOUN
ejpam-97	73	4	≤	≤	NOUN
ejpam-97	73	5	β	β	NOUN
ejpam-97	73	6	,	,	PUNCT
ejpam-97	73	7	where	where	SCONJ
ejpam-97	73	8	π	π	X
ejpam-97	73	9	:	:	PUNCT
ejpam-97	73	10	∐	∐	X
ejpam-97	73	11	α	α	X
ejpam-97	73	12	bα→	bα→	X
ejpam-97	73	13	l	l	NOUN
ejpam-97	73	14	im−→αbα	im−→αbα	NOUN
ejpam-97	73	15	is	be	AUX
ejpam-97	73	16	the	the	DET
ejpam-97	73	17	natural	natural	ADJ
ejpam-97	73	18	s	s	NOUN
ejpam-97	73	19	-	-	NOUN
ejpam-97	73	20	map	map	NOUN
ejpam-97	73	21	.	.	PUNCT
ejpam-97	74	1	h.	h.	PROPN
ejpam-97	74	2	barzegar	barzegar	PROPN
ejpam-97	74	3	and	and	CCONJ
ejpam-97	74	4	m.m	m.m	PROPN
ejpam-97	74	5	.	.	PROPN
ejpam-97	74	6	ebrahimi	ebrahimi	PROPN
ejpam-97	74	7	/	/	SYM
ejpam-97	74	8	eur	eur	PROPN
ejpam-97	74	9	.	.	PUNCT
ejpam-97	75	1	j.	j.	PROPN
ejpam-97	75	2	pure	pure	PROPN
ejpam-97	75	3	appl	appl	PROPN
ejpam-97	75	4	.	.	PROPN
ejpam-97	75	5	math	math	PROPN
ejpam-97	75	6	,	,	PUNCT
ejpam-97	75	7	1	1	NUM
ejpam-97	75	8	(	(	PUNCT
ejpam-97	75	9	2008	2008	NUM
ejpam-97	75	10	)	)	PUNCT
ejpam-97	75	11	,	,	PUNCT
ejpam-97	75	12	(	(	PUNCT
ejpam-97	75	13	41	41	NUM
ejpam-97	75	14	-	-	SYM
ejpam-97	75	15	55	55	NUM
ejpam-97	75	16	)	)	PUNCT
ejpam-97	75	17	44	44	NUM
ejpam-97	75	18	the	the	DET
ejpam-97	75	19	left	left	NOUN
ejpam-97	75	20	and	and	CCONJ
ejpam-97	75	21	the	the	DET
ejpam-97	75	22	right	right	ADJ
ejpam-97	75	23	adjoints	adjoint	NOUN
ejpam-97	75	24	f	f	NOUN
ejpam-97	75	25	and	and	CCONJ
ejpam-97	75	26	h	h	NOUN
ejpam-97	75	27	,	,	PUNCT
ejpam-97	75	28	respectively	respectively	ADV
ejpam-97	75	29	,	,	PUNCT
ejpam-97	75	30	of	of	ADP
ejpam-97	75	31	the	the	DET
ejpam-97	75	32	forgetful	forgetful	ADJ
ejpam-97	75	33	functor	functor	PROPN
ejpam-97	75	34	u	u	NOUN
ejpam-97	75	35	:	:	PUNCT
ejpam-97	75	36	act	act	PROPN
ejpam-97	75	37	-	-	PUNCT
ejpam-97	75	38	s	s	X
ejpam-97	75	39	→	→	PUNCT
ejpam-97	75	40	set	set	NOUN
ejpam-97	75	41	exist	exist	VERB
ejpam-97	75	42	and	and	CCONJ
ejpam-97	75	43	are	be	AUX
ejpam-97	75	44	defined	define	VERB
ejpam-97	75	45	as	as	SCONJ
ejpam-97	75	46	follows	follow	VERB
ejpam-97	75	47	:	:	PUNCT
ejpam-97	75	48	the	the	DET
ejpam-97	75	49	free	free	ADJ
ejpam-97	75	50	functor	functor	PROPN
ejpam-97	75	51	f	f	PROPN
ejpam-97	75	52	:	:	PUNCT
ejpam-97	75	53	set	set	PROPN
ejpam-97	75	54	→	→	SYM
ejpam-97	75	55	act	act	NOUN
ejpam-97	75	56	-	-	PUNCT
ejpam-97	75	57	s	s	PART
ejpam-97	75	58	is	be	AUX
ejpam-97	75	59	defined	define	VERB
ejpam-97	75	60	by	by	ADP
ejpam-97	75	61	:	:	PUNCT
ejpam-97	75	62	f(x	f(x	PROPN
ejpam-97	75	63	)	)	PUNCT
ejpam-97	76	1	=	=	PUNCT
ejpam-97	77	1	x	x	SYM
ejpam-97	77	2	×	×	NOUN
ejpam-97	77	3	s1	s1	NOUN
ejpam-97	77	4	with	with	ADP
ejpam-97	77	5	the	the	DET
ejpam-97	77	6	s	s	NOUN
ejpam-97	77	7	-	-	NOUN
ejpam-97	77	8	action	action	NOUN
ejpam-97	77	9	given	give	VERB
ejpam-97	77	10	by	by	ADP
ejpam-97	77	11	(	(	PUNCT
ejpam-97	77	12	x	x	INTJ
ejpam-97	77	13	,	,	PUNCT
ejpam-97	77	14	t)s	t)s	ADJ
ejpam-97	77	15	=	=	SYM
ejpam-97	77	16	(	(	PUNCT
ejpam-97	77	17	x	x	INTJ
ejpam-97	77	18	,	,	PUNCT
ejpam-97	77	19	ts	ts	PROPN
ejpam-97	77	20	)	)	PUNCT
ejpam-97	77	21	,	,	PUNCT
ejpam-97	77	22	for	for	ADP
ejpam-97	77	23	t	t	PROPN
ejpam-97	77	24	∈	∈	PROPN
ejpam-97	77	25	s1	s1	NOUN
ejpam-97	77	26	,	,	PUNCT
ejpam-97	77	27	s	s	PART
ejpam-97	77	28	∈	∈	PROPN
ejpam-97	77	29	s	s	NOUN
ejpam-97	77	30	,	,	PUNCT
ejpam-97	77	31	x	x	SYM
ejpam-97	77	32	∈	∈	NOUN
ejpam-97	77	33	x	x	X
ejpam-97	77	34	,	,	PUNCT
ejpam-97	77	35	and	and	CCONJ
ejpam-97	77	36	for	for	ADP
ejpam-97	77	37	every	every	DET
ejpam-97	77	38	map	map	NOUN
ejpam-97	77	39	f	f	X
ejpam-97	77	40	:	:	PUNCT
ejpam-97	77	41	x	x	X
ejpam-97	77	42	→	→	SYM
ejpam-97	77	43	y	y	PROPN
ejpam-97	77	44	in	in	ADP
ejpam-97	77	45	set	set	PROPN
ejpam-97	77	46	,	,	PUNCT
ejpam-97	77	47	f	f	X
ejpam-97	77	48	(	(	PUNCT
ejpam-97	77	49	f	f	PROPN
ejpam-97	77	50	)	)	PUNCT
ejpam-97	78	1	=	=	PUNCT
ejpam-97	79	1	f	f	X
ejpam-97	79	2	×	×	NOUN
ejpam-97	80	1	i	i	NOUN
ejpam-97	80	2	d	d	NOUN
ejpam-97	80	3	:	:	PUNCT
ejpam-97	80	4	x	x	SYM
ejpam-97	80	5	×	×	NOUN
ejpam-97	80	6	s1→	s1→	NOUN
ejpam-97	80	7	y	y	PROPN
ejpam-97	80	8	×	×	PROPN
ejpam-97	80	9	s1	s1	PROPN
ejpam-97	80	10	.	.	PUNCT
ejpam-97	81	1	the	the	DET
ejpam-97	81	2	existence	existence	NOUN
ejpam-97	81	3	of	of	ADP
ejpam-97	81	4	free	free	ADJ
ejpam-97	81	5	s	s	NOUN
ejpam-97	81	6	-	-	PUNCT
ejpam-97	81	7	acts	act	NOUN
ejpam-97	81	8	,	,	PUNCT
ejpam-97	81	9	in	in	ADP
ejpam-97	81	10	particular	particular	ADJ
ejpam-97	81	11	on	on	ADP
ejpam-97	81	12	the	the	DET
ejpam-97	81	13	singleton	singleton	PROPN
ejpam-97	81	14	set	set	NOUN
ejpam-97	81	15	,	,	PUNCT
ejpam-97	81	16	shows	show	VERB
ejpam-97	81	17	that	that	SCONJ
ejpam-97	81	18	an	an	DET
ejpam-97	81	19	s	s	NOUN
ejpam-97	81	20	-	-	PUNCT
ejpam-97	81	21	map	map	NOUN
ejpam-97	81	22	is	be	AUX
ejpam-97	81	23	a	a	DET
ejpam-97	81	24	monomorphism	monomorphism	NOUN
ejpam-97	81	25	if	if	SCONJ
ejpam-97	81	26	and	and	CCONJ
ejpam-97	81	27	only	only	ADV
ejpam-97	81	28	if	if	SCONJ
ejpam-97	81	29	it	it	PRON
ejpam-97	81	30	is	be	AUX
ejpam-97	81	31	one	one	NUM
ejpam-97	81	32	-	-	PUNCT
ejpam-97	81	33	one	one	NUM
ejpam-97	81	34	.	.	PUNCT
ejpam-97	82	1	therefore	therefore	ADV
ejpam-97	82	2	,	,	PUNCT
ejpam-97	82	3	we	we	PRON
ejpam-97	82	4	do	do	AUX
ejpam-97	82	5	not	not	PART
ejpam-97	82	6	distinguish	distinguish	VERB
ejpam-97	82	7	between	between	ADP
ejpam-97	82	8	monomorphisms	monomorphism	NOUN
ejpam-97	82	9	of	of	ADP
ejpam-97	82	10	acts	act	NOUN
ejpam-97	82	11	and	and	CCONJ
ejpam-97	82	12	inclusions	inclusion	NOUN
ejpam-97	82	13	.	.	PUNCT
ejpam-97	83	1	the	the	DET
ejpam-97	83	2	cofree	cofree	ADJ
ejpam-97	83	3	functor	functor	PROPN
ejpam-97	83	4	h	h	PROPN
ejpam-97	83	5	:	:	PUNCT
ejpam-97	83	6	set	set	PROPN
ejpam-97	83	7	→	→	SYM
ejpam-97	83	8	act	act	PROPN
ejpam-97	83	9	-	-	PUNCT
ejpam-97	83	10	s	s	PART
ejpam-97	83	11	is	be	AUX
ejpam-97	83	12	defined	define	VERB
ejpam-97	83	13	by	by	ADP
ejpam-97	83	14	hx	hx	PROPN
ejpam-97	83	15	=	=	SYM
ejpam-97	83	16	x	x	PROPN
ejpam-97	83	17	s1	s1	PROPN
ejpam-97	83	18	,	,	PUNCT
ejpam-97	83	19	the	the	DET
ejpam-97	83	20	set	set	NOUN
ejpam-97	83	21	of	of	ADP
ejpam-97	83	22	all	all	DET
ejpam-97	83	23	functions	function	NOUN
ejpam-97	83	24	from	from	ADP
ejpam-97	83	25	s1	s1	NOUN
ejpam-97	83	26	to	to	ADP
ejpam-97	83	27	the	the	DET
ejpam-97	83	28	set	set	NOUN
ejpam-97	83	29	x	x	INTJ
ejpam-97	83	30	,	,	PUNCT
ejpam-97	83	31	with	with	ADP
ejpam-97	83	32	the	the	DET
ejpam-97	83	33	action	action	NOUN
ejpam-97	83	34	of	of	ADP
ejpam-97	83	35	s	s	PRON
ejpam-97	83	36	on	on	ADP
ejpam-97	83	37	x	x	PROPN
ejpam-97	83	38	s1	s1	NOUN
ejpam-97	83	39	given	give	VERB
ejpam-97	83	40	by	by	ADP
ejpam-97	83	41	(	(	PUNCT
ejpam-97	83	42	f	f	PROPN
ejpam-97	83	43	s)(t	s)(t	PROPN
ejpam-97	83	44	)	)	PUNCT
ejpam-97	84	1	=	=	SYM
ejpam-97	84	2	f	f	PROPN
ejpam-97	84	3	(	(	PUNCT
ejpam-97	84	4	st	st	PROPN
ejpam-97	84	5	)	)	PUNCT
ejpam-97	84	6	for	for	ADP
ejpam-97	84	7	f	f	PROPN
ejpam-97	84	8	∈	∈	PROPN
ejpam-97	84	9	x	x	SYM
ejpam-97	84	10	s1	s1	NOUN
ejpam-97	84	11	,	,	PUNCT
ejpam-97	84	12	s	s	NOUN
ejpam-97	84	13	∈	∈	PROPN
ejpam-97	84	14	s	s	NOUN
ejpam-97	84	15	,	,	PUNCT
ejpam-97	84	16	and	and	CCONJ
ejpam-97	84	17	t	t	PROPN
ejpam-97	84	18	∈	∈	PROPN
ejpam-97	84	19	s1	s1	PROPN
ejpam-97	84	20	.	.	PUNCT
ejpam-97	85	1	also	also	ADV
ejpam-97	85	2	,	,	PUNCT
ejpam-97	85	3	for	for	ADP
ejpam-97	85	4	a	a	DET
ejpam-97	85	5	function	function	NOUN
ejpam-97	85	6	h	h	NOUN
ejpam-97	85	7	:	:	PUNCT
ejpam-97	85	8	x	x	X
ejpam-97	85	9	→	→	SYM
ejpam-97	85	10	y	y	PROPN
ejpam-97	85	11	,	,	PUNCT
ejpam-97	85	12	h(h	h(h	X
ejpam-97	85	13	)	)	PUNCT
ejpam-97	85	14	:	:	PUNCT
ejpam-97	85	15	x	x	X
ejpam-97	85	16	s1	s1	PROPN
ejpam-97	85	17	→	→	SYM
ejpam-97	85	18	y	y	PROPN
ejpam-97	85	19	s1	s1	PROPN
ejpam-97	85	20	is	be	AUX
ejpam-97	85	21	defined	define	VERB
ejpam-97	85	22	by	by	ADP
ejpam-97	85	23	(	(	PUNCT
ejpam-97	85	24	hh	hh	PROPN
ejpam-97	85	25	)	)	PUNCT
ejpam-97	85	26	(	(	PUNCT
ejpam-97	85	27	f	f	PROPN
ejpam-97	85	28	)	)	PUNCT
ejpam-97	86	1	=	=	SYM
ejpam-97	86	2	hf	hf	NOUN
ejpam-97	86	3	for	for	ADP
ejpam-97	86	4	f	f	PROPN
ejpam-97	86	5	∈	∈	PROPN
ejpam-97	86	6	x	x	PROPN
ejpam-97	86	7	s1	s1	PROPN
ejpam-97	86	8	.	.	PUNCT
ejpam-97	87	1	since	since	SCONJ
ejpam-97	87	2	a	a	DET
ejpam-97	87	3	left	left	ADJ
ejpam-97	87	4	adjoint	adjoint	NOUN
ejpam-97	87	5	preserves	preserve	NOUN
ejpam-97	87	6	colimits	colimit	NOUN
ejpam-97	87	7	,	,	PUNCT
ejpam-97	87	8	the	the	DET
ejpam-97	87	9	functor	functor	PROPN
ejpam-97	87	10	u	u	PROPN
ejpam-97	87	11	preserves	preserve	VERB
ejpam-97	87	12	epimorphisms	epimorphism	NOUN
ejpam-97	87	13	.	.	PUNCT
ejpam-97	88	1	so	so	ADV
ejpam-97	88	2	,	,	PUNCT
ejpam-97	88	3	epimorphisms	epimorphism	NOUN
ejpam-97	88	4	in	in	ADP
ejpam-97	88	5	act	act	PROPN
ejpam-97	88	6	-	-	PUNCT
ejpam-97	88	7	s	s	NOUN
ejpam-97	88	8	are	be	AUX
ejpam-97	88	9	exactly	exactly	ADV
ejpam-97	88	10	onto	onto	ADP
ejpam-97	88	11	s	s	NOUN
ejpam-97	88	12	-	-	NOUN
ejpam-97	88	13	maps	map	NOUN
ejpam-97	88	14	.	.	PUNCT
ejpam-97	89	1	2	2	X
ejpam-97	89	2	.	.	X
ejpam-97	89	3	sequentially	sequentially	ADV
ejpam-97	89	4	pure	pure	ADJ
ejpam-97	89	5	monomorphisms	monomorphism	NOUN
ejpam-97	89	6	any	any	DET
ejpam-97	89	7	notion	notion	NOUN
ejpam-97	89	8	of	of	ADP
ejpam-97	89	9	pure	pure	ADJ
ejpam-97	89	10	monomorphisms	monomorphism	NOUN
ejpam-97	89	11	is	be	AUX
ejpam-97	89	12	normally	normally	ADV
ejpam-97	89	13	defined	define	VERB
ejpam-97	89	14	in	in	ADP
ejpam-97	89	15	terms	term	NOUN
ejpam-97	89	16	of	of	ADP
ejpam-97	89	17	solvability	solvability	NOUN
ejpam-97	89	18	of	of	ADP
ejpam-97	89	19	some	some	DET
ejpam-97	89	20	set	set	NOUN
ejpam-97	89	21	of	of	ADP
ejpam-97	89	22	equations	equation	NOUN
ejpam-97	89	23	.	.	PUNCT
ejpam-97	90	1	in	in	ADP
ejpam-97	90	2	the	the	DET
ejpam-97	90	3	following	following	NOUN
ejpam-97	90	4	we	we	PRON
ejpam-97	90	5	first	first	ADV
ejpam-97	90	6	consider	consider	VERB
ejpam-97	90	7	this	this	DET
ejpam-97	90	8	point	point	NOUN
ejpam-97	90	9	of	of	ADP
ejpam-97	90	10	view	view	NOUN
ejpam-97	90	11	to	to	PART
ejpam-97	90	12	define	define	VERB
ejpam-97	90	13	a	a	DET
ejpam-97	90	14	kind	kind	NOUN
ejpam-97	90	15	of	of	ADP
ejpam-97	90	16	pure	pure	ADJ
ejpam-97	90	17	monomorphisms	monomorphism	NOUN
ejpam-97	90	18	,	,	PUNCT
ejpam-97	90	19	which	which	PRON
ejpam-97	90	20	is	be	AUX
ejpam-97	90	21	also	also	ADV
ejpam-97	90	22	of	of	ADP
ejpam-97	90	23	interest	interest	NOUN
ejpam-97	90	24	to	to	ADP
ejpam-97	90	25	computer	computer	NOUN
ejpam-97	90	26	scientists	scientist	NOUN
ejpam-97	90	27	,	,	PUNCT
ejpam-97	90	28	which	which	PRON
ejpam-97	90	29	we	we	PRON
ejpam-97	90	30	are	be	AUX
ejpam-97	90	31	going	go	VERB
ejpam-97	90	32	to	to	PART
ejpam-97	90	33	study	study	VERB
ejpam-97	90	34	their	their	PRON
ejpam-97	90	35	behaviour	behaviour	NOUN
ejpam-97	90	36	in	in	ADP
ejpam-97	90	37	this	this	DET
ejpam-97	90	38	paper	paper	NOUN
ejpam-97	90	39	,	,	PUNCT
ejpam-97	90	40	and	and	CCONJ
ejpam-97	90	41	then	then	ADV
ejpam-97	90	42	show	show	VERB
ejpam-97	90	43	that	that	SCONJ
ejpam-97	90	44	they	they	PRON
ejpam-97	90	45	are	be	AUX
ejpam-97	90	46	actually	actually	ADV
ejpam-97	90	47	equivalent	equivalent	ADJ
ejpam-97	90	48	to	to	ADP
ejpam-97	90	49	c	c	PROPN
ejpam-97	90	50	p	p	ADJ
ejpam-97	90	51	-	-	PUNCT
ejpam-97	90	52	pure	pure	ADJ
ejpam-97	90	53	monomorphisms	monomorphism	NOUN
ejpam-97	90	54	resulting	result	VERB
ejpam-97	90	55	from	from	ADP
ejpam-97	90	56	a	a	DET
ejpam-97	90	57	closure	closure	NOUN
ejpam-97	90	58	operator	operator	NOUN
ejpam-97	90	59	on	on	ADP
ejpam-97	90	60	the	the	DET
ejpam-97	90	61	category	category	NOUN
ejpam-97	90	62	act	act	PROPN
ejpam-97	90	63	-	-	PUNCT
ejpam-97	90	64	s.	s.	PROPN
ejpam-97	90	65	2.1	2.1	NUM
ejpam-97	90	66	.	.	PUNCT
ejpam-97	91	1	sequentially	sequentially	ADV
ejpam-97	91	2	pure	pure	ADJ
ejpam-97	91	3	monomorphisms	monomorphism	NOUN
ejpam-97	91	4	in	in	ADP
ejpam-97	91	5	[	[	X
ejpam-97	91	6	10	10	NUM
ejpam-97	91	7	,	,	PUNCT
ejpam-97	91	8	14	14	NUM
ejpam-97	91	9	,	,	PUNCT
ejpam-97	91	10	16	16	NUM
ejpam-97	91	11	]	]	PUNCT
ejpam-97	91	12	,	,	PUNCT
ejpam-97	91	13	it	it	PRON
ejpam-97	91	14	is	be	AUX
ejpam-97	91	15	shown	show	VERB
ejpam-97	91	16	that	that	SCONJ
ejpam-97	91	17	the	the	DET
ejpam-97	91	18	equations	equation	NOUN
ejpam-97	91	19	with	with	ADP
ejpam-97	91	20	constants	constant	NOUN
ejpam-97	91	21	from	from	ADP
ejpam-97	91	22	an	an	DET
ejpam-97	91	23	s	s	PROPN
ejpam-97	91	24	-	-	PUNCT
ejpam-97	91	25	act	act	NOUN
ejpam-97	91	26	a	a	DET
ejpam-97	91	27	are	be	AUX
ejpam-97	91	28	of	of	ADP
ejpam-97	91	29	one	one	NUM
ejpam-97	91	30	the	the	DET
ejpam-97	91	31	following	follow	VERB
ejpam-97	91	32	three	three	NUM
ejpam-97	91	33	types	type	NOUN
ejpam-97	91	34	:	:	PUNCT
ejpam-97	91	35	xs	xs	PROPN
ejpam-97	91	36	=	=	PUNCT
ejpam-97	91	37	y	y	PROPN
ejpam-97	91	38	t	t	PROPN
ejpam-97	91	39	,	,	PUNCT
ejpam-97	91	40	xs	xs	PROPN
ejpam-97	92	1	=	=	PUNCT
ejpam-97	92	2	x	x	SYM
ejpam-97	92	3	t	t	PROPN
ejpam-97	92	4	,	,	PUNCT
ejpam-97	92	5	xs	xs	PROPN
ejpam-97	92	6	=	=	PUNCT
ejpam-97	93	1	a	a	PRON
ejpam-97	93	2	where	where	SCONJ
ejpam-97	93	3	s	s	X
ejpam-97	93	4	,	,	PUNCT
ejpam-97	93	5	t	t	PROPN
ejpam-97	93	6	∈	∈	PROPN
ejpam-97	93	7	s	s	PROPN
ejpam-97	93	8	,	,	PUNCT
ejpam-97	93	9	a	a	DET
ejpam-97	93	10	∈	∈	NOUN
ejpam-97	93	11	a.	a.	NOUN
ejpam-97	93	12	here	here	ADV
ejpam-97	93	13	we	we	PRON
ejpam-97	93	14	are	be	AUX
ejpam-97	93	15	concerned	concerned	ADJ
ejpam-97	93	16	with	with	ADP
ejpam-97	93	17	the	the	DET
ejpam-97	93	18	equations	equation	NOUN
ejpam-97	93	19	of	of	ADP
ejpam-97	93	20	the	the	DET
ejpam-97	93	21	type	type	NOUN
ejpam-97	93	22	xs	xs	PROPN
ejpam-97	93	23	=	=	PUNCT
ejpam-97	93	24	a	a	DET
ejpam-97	93	25	only	only	ADJ
ejpam-97	93	26	.	.	PUNCT
ejpam-97	94	1	gould	gould	PROPN
ejpam-97	94	2	in	in	ADP
ejpam-97	94	3	[	[	X
ejpam-97	94	4	10	10	NUM
ejpam-97	94	5	]	]	PUNCT
ejpam-97	94	6	defines	define	VERB
ejpam-97	94	7	an	an	DET
ejpam-97	94	8	α	α	NOUN
ejpam-97	94	9	-	-	PUNCT
ejpam-97	94	10	system	system	NOUN
ejpam-97	94	11	of	of	ADP
ejpam-97	94	12	equations	equation	NOUN
ejpam-97	94	13	on	on	ADP
ejpam-97	94	14	an	an	DET
ejpam-97	94	15	s	s	PROPN
ejpam-97	94	16	-	-	NOUN
ejpam-97	94	17	act	act	NOUN
ejpam-97	94	18	a	a	PRON
ejpam-97	94	19	to	to	PART
ejpam-97	94	20	be	be	AUX
ejpam-97	94	21	σ	σ	NOUN
ejpam-97	94	22	=	=	PUNCT
ejpam-97	94	23	{	{	PUNCT
ejpam-97	94	24	xs	xs	PROPN
ejpam-97	94	25	j	j	PROPN
ejpam-97	94	26	=	=	PUNCT
ejpam-97	94	27	a	a	DET
ejpam-97	94	28	j	j	PROPN
ejpam-97	94	29	:	:	PUNCT
ejpam-97	95	1	j	j	PROPN
ejpam-97	95	2	∈	∈	PROPN
ejpam-97	95	3	j	j	PROPN
ejpam-97	95	4	,	,	PUNCT
ejpam-97	95	5	|j	|j	NOUN
ejpam-97	95	6	|	|	ADV
ejpam-97	95	7	<	<	X
ejpam-97	95	8	α	α	PROPN
ejpam-97	95	9	,	,	PUNCT
ejpam-97	95	10	s	s	PART
ejpam-97	95	11	j	j	PROPN
ejpam-97	95	12	∈	∈	PROPN
ejpam-97	95	13	s	s	PROPN
ejpam-97	95	14	,	,	PUNCT
ejpam-97	95	15	a	a	DET
ejpam-97	95	16	j	j	PROPN
ejpam-97	95	17	∈	∈	PROPN
ejpam-97	95	18	a	a	X
ejpam-97	95	19	}	}	PUNCT
ejpam-97	95	20	in	in	ADP
ejpam-97	95	21	which	which	PRON
ejpam-97	95	22	si	si	NOUN
ejpam-97	95	23	=	=	SYM
ejpam-97	95	24	s	s	PART
ejpam-97	95	25	j	j	NOUN
ejpam-97	95	26	need	need	AUX
ejpam-97	95	27	not	not	PART
ejpam-97	95	28	imply	imply	VERB
ejpam-97	95	29	ai	ai	VERB
ejpam-97	95	30	=	=	PROPN
ejpam-97	95	31	a	a	DET
ejpam-97	95	32	j	j	PROPN
ejpam-97	95	33	.	.	PUNCT
ejpam-97	96	1	but	but	CCONJ
ejpam-97	96	2	,	,	PUNCT
ejpam-97	96	3	note	note	VERB
ejpam-97	96	4	that	that	SCONJ
ejpam-97	96	5	if	if	SCONJ
ejpam-97	96	6	for	for	ADP
ejpam-97	96	7	any	any	DET
ejpam-97	96	8	s	s	X
ejpam-97	96	9	∈	∈	NOUN
ejpam-97	96	10	s	s	VERB
ejpam-97	96	11	there	there	PRON
ejpam-97	96	12	exist	exist	VERB
ejpam-97	96	13	two	two	NUM
ejpam-97	96	14	equations	equation	NOUN
ejpam-97	96	15	of	of	ADP
ejpam-97	96	16	the	the	DET
ejpam-97	96	17	form	form	NOUN
ejpam-97	96	18	xs	xs	PROPN
ejpam-97	96	19	=	=	PUNCT
ejpam-97	96	20	a1	a1	PROPN
ejpam-97	96	21	,	,	PUNCT
ejpam-97	96	22	xs	xs	PROPN
ejpam-97	96	23	=	=	PROPN
ejpam-97	96	24	a2	a2	PROPN
ejpam-97	96	25	in	in	ADP
ejpam-97	96	26	σ	σ	PROPN
ejpam-97	96	27	and	and	CCONJ
ejpam-97	96	28	σ	σ	PROPN
ejpam-97	96	29	has	have	VERB
ejpam-97	96	30	a	a	DET
ejpam-97	96	31	solution	solution	NOUN
ejpam-97	96	32	b	b	NOUN
ejpam-97	96	33	in	in	ADP
ejpam-97	96	34	some	some	DET
ejpam-97	96	35	extension	extension	NOUN
ejpam-97	96	36	b	b	PROPN
ejpam-97	96	37	of	of	ADP
ejpam-97	96	38	a	a	DET
ejpam-97	96	39	,	,	PUNCT
ejpam-97	96	40	then	then	ADV
ejpam-97	96	41	a1	a1	PROPN
ejpam-97	96	42	=	=	PROPN
ejpam-97	96	43	a2	a2	PROPN
ejpam-97	96	44	.	.	PUNCT
ejpam-97	97	1	so	so	ADV
ejpam-97	97	2	,	,	PUNCT
ejpam-97	97	3	for	for	SCONJ
ejpam-97	97	4	a	a	DET
ejpam-97	97	5	system	system	NOUN
ejpam-97	97	6	σ	σ	NOUN
ejpam-97	97	7	of	of	ADP
ejpam-97	97	8	equations	equation	NOUN
ejpam-97	97	9	to	to	PART
ejpam-97	97	10	have	have	VERB
ejpam-97	97	11	a	a	DET
ejpam-97	97	12	solution	solution	NOUN
ejpam-97	97	13	there	there	PRON
ejpam-97	97	14	can	can	AUX
ejpam-97	97	15	only	only	ADV
ejpam-97	97	16	be	be	AUX
ejpam-97	97	17	at	at	ADP
ejpam-97	97	18	most	most	ADV
ejpam-97	97	19	one	one	NUM
ejpam-97	97	20	equation	equation	NOUN
ejpam-97	97	21	xs	xs	NOUN
ejpam-97	98	1	=	=	PUNCT
ejpam-97	99	1	a	a	PRON
ejpam-97	99	2	in	in	ADP
ejpam-97	99	3	σ	σ	NOUN
ejpam-97	99	4	for	for	ADP
ejpam-97	99	5	each	each	DET
ejpam-97	99	6	s	s	PROPN
ejpam-97	99	7	∈	∈	PROPN
ejpam-97	99	8	s.	s.	PROPN
ejpam-97	99	9	therefore	therefore	ADV
ejpam-97	99	10	,	,	PUNCT
ejpam-97	99	11	σ	σ	PROPN
ejpam-97	99	12	should	should	AUX
ejpam-97	99	13	actually	actually	ADV
ejpam-97	99	14	be	be	AUX
ejpam-97	99	15	taken	take	VERB
ejpam-97	99	16	of	of	ADP
ejpam-97	99	17	the	the	DET
ejpam-97	99	18	form	form	NOUN
ejpam-97	99	19	σt	σt	ADP
ejpam-97	99	20	=	=	PUNCT
ejpam-97	99	21	{	{	PUNCT
ejpam-97	99	22	xs	xs	NOUN
ejpam-97	99	23	=	=	PUNCT
ejpam-97	99	24	at	at	ADP
ejpam-97	99	25	:	:	PUNCT
ejpam-97	99	26	t	t	PROPN
ejpam-97	99	27	∈	∈	PROPN
ejpam-97	99	28	t	t	PROPN
ejpam-97	99	29	,	,	PUNCT
ejpam-97	99	30	at	at	ADP
ejpam-97	99	31	∈	∈	PROPN
ejpam-97	99	32	a	a	PRON
ejpam-97	99	33	}	}	PUNCT
ejpam-97	99	34	for	for	ADP
ejpam-97	99	35	some	some	DET
ejpam-97	99	36	t	t	NOUN
ejpam-97	99	37	⊆	⊆	NUM
ejpam-97	99	38	s.	s.	PROPN
ejpam-97	99	39	hence	hence	ADV
ejpam-97	99	40	,	,	PUNCT
ejpam-97	99	41	for	for	ADP
ejpam-97	99	42	any	any	DET
ejpam-97	99	43	fixed	fix	VERB
ejpam-97	99	44	t	t	NOUN
ejpam-97	99	45	⊆	⊆	NUM
ejpam-97	99	46	s	s	NOUN
ejpam-97	99	47	,	,	PUNCT
ejpam-97	99	48	there	there	PRON
ejpam-97	99	49	is	be	VERB
ejpam-97	99	50	a	a	DET
ejpam-97	99	51	one	one	NUM
ejpam-97	99	52	to	to	ADP
ejpam-97	99	53	one	one	NUM
ejpam-97	99	54	correspondence	correspondence	NOUN
ejpam-97	99	55	between	between	ADP
ejpam-97	99	56	the	the	DET
ejpam-97	99	57	set	set	NOUN
ejpam-97	99	58	of	of	ADP
ejpam-97	99	59	all	all	DET
ejpam-97	99	60	systems	system	NOUN
ejpam-97	99	61	of	of	ADP
ejpam-97	99	62	equations	equation	NOUN
ejpam-97	99	63	of	of	ADP
ejpam-97	99	64	the	the	DET
ejpam-97	99	65	above	above	ADJ
ejpam-97	99	66	form	form	NOUN
ejpam-97	99	67	on	on	ADP
ejpam-97	99	68	an	an	DET
ejpam-97	99	69	s	s	NOUN
ejpam-97	99	70	-	-	NOUN
ejpam-97	99	71	act	act	NOUN
ejpam-97	99	72	a	a	PRON
ejpam-97	99	73	and	and	CCONJ
ejpam-97	99	74	the	the	DET
ejpam-97	99	75	set	set	NOUN
ejpam-97	99	76	of	of	ADP
ejpam-97	99	77	all	all	DET
ejpam-97	99	78	functions	function	NOUN
ejpam-97	99	79	k	k	X
ejpam-97	99	80	:	:	PUNCT
ejpam-97	99	81	t	t	PROPN
ejpam-97	99	82	→	→	SYM
ejpam-97	99	83	a.	a.	NOUN
ejpam-97	99	84	in	in	ADP
ejpam-97	99	85	fact	fact	NOUN
ejpam-97	99	86	,	,	PUNCT
ejpam-97	99	87	to	to	ADP
ejpam-97	99	88	each	each	DET
ejpam-97	99	89	system	system	NOUN
ejpam-97	99	90	of	of	ADP
ejpam-97	99	91	equations	equation	NOUN
ejpam-97	99	92	σt	σt	SCONJ
ejpam-97	99	93	we	we	PRON
ejpam-97	99	94	get	get	VERB
ejpam-97	99	95	the	the	DET
ejpam-97	99	96	function	function	NOUN
ejpam-97	99	97	kς	kς	PROPN
ejpam-97	99	98	:	:	PUNCT
ejpam-97	99	99	t	t	PROPN
ejpam-97	99	100	→	→	PUNCT
ejpam-97	99	101	a	a	DET
ejpam-97	99	102	given	give	VERB
ejpam-97	99	103	by	by	ADP
ejpam-97	99	104	k(t	k(t	NOUN
ejpam-97	99	105	)	)	PUNCT
ejpam-97	100	1	=	=	SYM
ejpam-97	100	2	at	at	ADP
ejpam-97	100	3	and	and	CCONJ
ejpam-97	100	4	conversely	conversely	ADV
ejpam-97	100	5	,	,	PUNCT
ejpam-97	100	6	for	for	ADP
ejpam-97	100	7	any	any	DET
ejpam-97	100	8	function	function	NOUN
ejpam-97	100	9	k	k	PROPN
ejpam-97	100	10	:	:	PUNCT
ejpam-97	100	11	t	t	PROPN
ejpam-97	100	12	→	→	PUNCT
ejpam-97	100	13	a	a	DET
ejpam-97	100	14	one	one	NOUN
ejpam-97	100	15	has	have	VERB
ejpam-97	100	16	the	the	DET
ejpam-97	100	17	system	system	NOUN
ejpam-97	100	18	of	of	ADP
ejpam-97	100	19	equations	equation	NOUN
ejpam-97	100	20	σk	σk	ADV
ejpam-97	100	21	=	=	PUNCT
ejpam-97	100	22	{	{	PUNCT
ejpam-97	100	23	x	x	X
ejpam-97	100	24	t	t	NOUN
ejpam-97	100	25	=	=	PUNCT
ejpam-97	100	26	k(t	k(t	NOUN
ejpam-97	100	27	)	)	PUNCT
ejpam-97	101	1	|	|	ADV
ejpam-97	101	2	t	t	PROPN
ejpam-97	101	3	∈	∈	PROPN
ejpam-97	101	4	t	t	PROPN
ejpam-97	101	5	}	}	PUNCT
ejpam-97	101	6	on	on	ADP
ejpam-97	101	7	a.	a.	NOUN
ejpam-97	101	8	thus	thus	ADV
ejpam-97	101	9	we	we	PRON
ejpam-97	101	10	have	have	VERB
ejpam-97	101	11	the	the	DET
ejpam-97	101	12	following	follow	VERB
ejpam-97	101	13	definition	definition	NOUN
ejpam-97	101	14	.	.	PUNCT
ejpam-97	102	1	h.	h.	PROPN
ejpam-97	102	2	barzegar	barzegar	PROPN
ejpam-97	102	3	and	and	CCONJ
ejpam-97	102	4	m.m	m.m	PROPN
ejpam-97	102	5	.	.	PROPN
ejpam-97	102	6	ebrahimi	ebrahimi	PROPN
ejpam-97	102	7	/	/	SYM
ejpam-97	102	8	eur	eur	PROPN
ejpam-97	102	9	.	.	PUNCT
ejpam-97	103	1	j.	j.	PROPN
ejpam-97	103	2	pure	pure	PROPN
ejpam-97	103	3	appl	appl	PROPN
ejpam-97	103	4	.	.	PROPN
ejpam-97	103	5	math	math	PROPN
ejpam-97	103	6	,	,	PUNCT
ejpam-97	103	7	1	1	NUM
ejpam-97	103	8	(	(	PUNCT
ejpam-97	103	9	2008	2008	NUM
ejpam-97	103	10	)	)	PUNCT
ejpam-97	103	11	,	,	PUNCT
ejpam-97	103	12	(	(	PUNCT
ejpam-97	103	13	41	41	NUM
ejpam-97	103	14	-	-	SYM
ejpam-97	103	15	55	55	NUM
ejpam-97	103	16	)	)	PUNCT
ejpam-97	103	17	45	45	NUM
ejpam-97	103	18	definition	definition	NOUN
ejpam-97	103	19	2.1	2.1	NUM
ejpam-97	103	20	.	.	PUNCT
ejpam-97	104	1	(	(	PUNCT
ejpam-97	104	2	1	1	X
ejpam-97	104	3	)	)	PUNCT
ejpam-97	104	4	let	let	VERB
ejpam-97	104	5	t	t	NOUN
ejpam-97	104	6	be	be	AUX
ejpam-97	104	7	a	a	DET
ejpam-97	104	8	subset	subset	NOUN
ejpam-97	104	9	of	of	ADP
ejpam-97	104	10	s	s	PRON
ejpam-97	104	11	and	and	CCONJ
ejpam-97	104	12	a	a	DET
ejpam-97	104	13	be	be	AUX
ejpam-97	104	14	an	an	DET
ejpam-97	104	15	s	s	NOUN
ejpam-97	104	16	-	-	NOUN
ejpam-97	104	17	act	act	NOUN
ejpam-97	104	18	.	.	PUNCT
ejpam-97	105	1	any	any	PRON
ejpam-97	105	2	σt	σt	ADP
ejpam-97	105	3	=	=	PUNCT
ejpam-97	105	4	{	{	PUNCT
ejpam-97	105	5	xs	xs	NOUN
ejpam-97	105	6	=	=	PUNCT
ejpam-97	105	7	at	at	ADP
ejpam-97	105	8	:	:	PUNCT
ejpam-97	105	9	t	t	PROPN
ejpam-97	105	10	∈	∈	PROPN
ejpam-97	105	11	t	t	PROPN
ejpam-97	105	12	,	,	PUNCT
ejpam-97	105	13	at	at	ADP
ejpam-97	105	14	∈	∈	PROPN
ejpam-97	105	15	a	a	PRON
ejpam-97	105	16	}	}	PUNCT
ejpam-97	105	17	(	(	PUNCT
ejpam-97	105	18	or	or	CCONJ
ejpam-97	105	19	,	,	PUNCT
ejpam-97	105	20	equivalently	equivalently	ADV
ejpam-97	105	21	,	,	PUNCT
ejpam-97	105	22	a	a	DET
ejpam-97	105	23	map	map	NOUN
ejpam-97	106	1	k	k	X
ejpam-97	106	2	:	:	PUNCT
ejpam-97	106	3	t	t	PROPN
ejpam-97	106	4	→	→	SYM
ejpam-97	106	5	a	a	X
ejpam-97	106	6	)	)	PUNCT
ejpam-97	106	7	will	will	AUX
ejpam-97	106	8	be	be	AUX
ejpam-97	106	9	called	call	VERB
ejpam-97	106	10	a	a	DET
ejpam-97	106	11	t	t	NOUN
ejpam-97	106	12	-system	-system	NOUN
ejpam-97	106	13	of	of	ADP
ejpam-97	106	14	equations	equation	NOUN
ejpam-97	106	15	(	(	PUNCT
ejpam-97	106	16	or	or	CCONJ
ejpam-97	106	17	a	a	DET
ejpam-97	106	18	t	t	NOUN
ejpam-97	106	19	-sequence	-sequence	NOUN
ejpam-97	106	20	)	)	PUNCT
ejpam-97	106	21	on	on	ADP
ejpam-97	106	22	a.	a.	NOUN
ejpam-97	106	23	(	(	PUNCT
ejpam-97	106	24	2	2	X
ejpam-97	106	25	)	)	PUNCT
ejpam-97	106	26	we	we	PRON
ejpam-97	106	27	say	say	VERB
ejpam-97	106	28	that	that	SCONJ
ejpam-97	106	29	a	a	DET
ejpam-97	106	30	system	system	NOUN
ejpam-97	106	31	σt	σt	ADP
ejpam-97	106	32	(	(	PUNCT
ejpam-97	106	33	or	or	CCONJ
ejpam-97	106	34	k	k	ADJ
ejpam-97	106	35	:	:	PUNCT
ejpam-97	106	36	t	t	PROPN
ejpam-97	106	37	→	→	SYM
ejpam-97	106	38	a	a	X
ejpam-97	106	39	)	)	PUNCT
ejpam-97	106	40	is	be	AUX
ejpam-97	106	41	solvable	solvable	ADJ
ejpam-97	106	42	in	in	ADP
ejpam-97	106	43	an	an	DET
ejpam-97	106	44	extension	extension	NOUN
ejpam-97	106	45	b	b	NOUN
ejpam-97	106	46	of	of	ADP
ejpam-97	106	47	a	a	PRON
ejpam-97	106	48	if	if	SCONJ
ejpam-97	106	49	there	there	PRON
ejpam-97	106	50	is	be	VERB
ejpam-97	106	51	some	some	DET
ejpam-97	106	52	b	b	NOUN
ejpam-97	106	53	∈	∈	NOUN
ejpam-97	106	54	b	b	NOUN
ejpam-97	106	55	such	such	ADJ
ejpam-97	107	1	that	that	DET
ejpam-97	107	2	bt	bt	NOUN
ejpam-97	107	3	=	=	SYM
ejpam-97	107	4	at	at	ADP
ejpam-97	107	5	(	(	PUNCT
ejpam-97	107	6	or	or	CCONJ
ejpam-97	107	7	k(t	k(t	PROPN
ejpam-97	107	8	)	)	PUNCT
ejpam-97	107	9	=	=	SYM
ejpam-97	107	10	bt	bt	NOUN
ejpam-97	107	11	)	)	PUNCT
ejpam-97	107	12	for	for	ADP
ejpam-97	107	13	all	all	DET
ejpam-97	107	14	t	t	NOUN
ejpam-97	107	15	∈	∈	PROPN
ejpam-97	107	16	t	t	NOUN
ejpam-97	107	17	;	;	PUNCT
ejpam-97	107	18	that	that	PRON
ejpam-97	107	19	is	is	ADV
ejpam-97	107	20	,	,	PUNCT
ejpam-97	107	21	k	k	PROPN
ejpam-97	108	1	=	=	PUNCT
ejpam-97	108	2	λb	λb	PROPN
ejpam-97	108	3	,	,	PUNCT
ejpam-97	108	4	where	where	SCONJ
ejpam-97	108	5	λb(t	λb(t	PUNCT
ejpam-97	108	6	)	)	PUNCT
ejpam-97	108	7	=	=	SYM
ejpam-97	109	1	bt	bt	PROPN
ejpam-97	109	2	.	.	PUNCT
ejpam-97	110	1	(	(	PUNCT
ejpam-97	110	2	3	3	X
ejpam-97	110	3	)	)	PUNCT
ejpam-97	110	4	we	we	PRON
ejpam-97	110	5	say	say	VERB
ejpam-97	110	6	that	that	SCONJ
ejpam-97	110	7	a	a	DET
ejpam-97	110	8	system	system	NOUN
ejpam-97	110	9	σt	σt	ADP
ejpam-97	110	10	(	(	PUNCT
ejpam-97	110	11	or	or	CCONJ
ejpam-97	110	12	k	k	ADJ
ejpam-97	110	13	:	:	PUNCT
ejpam-97	110	14	t	t	PROPN
ejpam-97	110	15	→	→	SYM
ejpam-97	110	16	a	a	X
ejpam-97	110	17	)	)	PUNCT
ejpam-97	110	18	is	be	AUX
ejpam-97	110	19	consistent	consistent	ADJ
ejpam-97	110	20	if	if	SCONJ
ejpam-97	110	21	it	it	PRON
ejpam-97	110	22	has	have	VERB
ejpam-97	110	23	a	a	DET
ejpam-97	110	24	solution	solution	NOUN
ejpam-97	110	25	in	in	ADP
ejpam-97	110	26	some	some	DET
ejpam-97	110	27	extension	extension	NOUN
ejpam-97	110	28	b	b	PROPN
ejpam-97	110	29	of	of	ADP
ejpam-97	110	30	a.	a.	NOUN
ejpam-97	110	31	now	now	ADV
ejpam-97	110	32	,	,	PUNCT
ejpam-97	110	33	we	we	PRON
ejpam-97	110	34	are	be	AUX
ejpam-97	110	35	going	go	VERB
ejpam-97	110	36	to	to	PART
ejpam-97	110	37	show	show	VERB
ejpam-97	110	38	that	that	SCONJ
ejpam-97	110	39	we	we	PRON
ejpam-97	110	40	should	should	AUX
ejpam-97	110	41	actually	actually	ADV
ejpam-97	110	42	only	only	ADV
ejpam-97	110	43	consider	consider	VERB
ejpam-97	110	44	just	just	ADV
ejpam-97	110	45	i	i	PRON
ejpam-97	110	46	-sequences	-sequence	VERB
ejpam-97	110	47	for	for	ADP
ejpam-97	110	48	an	an	DET
ejpam-97	110	49	ideal	ideal	ADJ
ejpam-97	110	50	i	i	PRON
ejpam-97	110	51	of	of	ADP
ejpam-97	110	52	s	s	PRON
ejpam-97	110	53	rather	rather	ADV
ejpam-97	110	54	than	than	ADP
ejpam-97	110	55	any	any	DET
ejpam-97	110	56	t	t	NOUN
ejpam-97	110	57	-sequence	-sequence	NOUN
ejpam-97	110	58	for	for	ADP
ejpam-97	110	59	any	any	DET
ejpam-97	110	60	subset	subset	NOUN
ejpam-97	110	61	t	t	PROPN
ejpam-97	110	62	of	of	ADP
ejpam-97	110	63	s.	s.	PROPN
ejpam-97	110	64	note	note	VERB
ejpam-97	110	65	that	that	SCONJ
ejpam-97	110	66	,	,	PUNCT
ejpam-97	110	67	although	although	SCONJ
ejpam-97	110	68	an	an	DET
ejpam-97	110	69	i	i	NOUN
ejpam-97	110	70	-sequence	-sequence	PROPN
ejpam-97	111	1	k	k	NOUN
ejpam-97	111	2	:	:	PUNCT
ejpam-97	111	3	i	i	PRON
ejpam-97	111	4	→	→	PUNCT
ejpam-97	111	5	a	a	PRON
ejpam-97	111	6	is	be	AUX
ejpam-97	111	7	just	just	ADV
ejpam-97	111	8	a	a	DET
ejpam-97	111	9	function	function	NOUN
ejpam-97	111	10	and	and	CCONJ
ejpam-97	111	11	not	not	PART
ejpam-97	111	12	necessarily	necessarily	ADV
ejpam-97	111	13	a	a	DET
ejpam-97	111	14	homomorphism	homomorphism	NOUN
ejpam-97	111	15	,	,	PUNCT
ejpam-97	111	16	we	we	PRON
ejpam-97	111	17	have	have	VERB
ejpam-97	111	18	the	the	DET
ejpam-97	111	19	following	following	NOUN
ejpam-97	111	20	:	:	PUNCT
ejpam-97	111	21	theorem	theorem	VERB
ejpam-97	111	22	2.1	2.1	NUM
ejpam-97	111	23	.	.	PUNCT
ejpam-97	112	1	let	let	VERB
ejpam-97	112	2	i	i	PRON
ejpam-97	112	3	be	be	AUX
ejpam-97	112	4	an	an	DET
ejpam-97	112	5	ideal	ideal	NOUN
ejpam-97	112	6	of	of	ADP
ejpam-97	112	7	s	s	PRON
ejpam-97	112	8	and	and	CCONJ
ejpam-97	112	9	a	a	DET
ejpam-97	112	10	be	be	AUX
ejpam-97	112	11	an	an	DET
ejpam-97	112	12	s	s	NOUN
ejpam-97	112	13	-	-	NOUN
ejpam-97	112	14	act	act	NOUN
ejpam-97	112	15	.	.	PUNCT
ejpam-97	113	1	then	then	ADV
ejpam-97	113	2	the	the	DET
ejpam-97	113	3	following	follow	VERB
ejpam-97	113	4	are	be	AUX
ejpam-97	113	5	equivalent	equivalent	ADJ
ejpam-97	113	6	for	for	ADP
ejpam-97	113	7	an	an	DET
ejpam-97	113	8	i	i	NOUN
ejpam-97	113	9	-	-	PUNCT
ejpam-97	113	10	sequence	sequence	NOUN
ejpam-97	113	11	k	k	NOUN
ejpam-97	113	12	:	:	PUNCT
ejpam-97	113	13	i	i	PRON
ejpam-97	113	14	→	→	SYM
ejpam-97	113	15	a	a	X
ejpam-97	113	16	:	:	PUNCT
ejpam-97	113	17	(	(	PUNCT
ejpam-97	113	18	1	1	X
ejpam-97	113	19	)	)	PUNCT
ejpam-97	113	20	k	k	NOUN
ejpam-97	113	21	:	:	PUNCT
ejpam-97	114	1	i	i	PRON
ejpam-97	114	2	→	→	PUNCT
ejpam-97	114	3	a	a	PRON
ejpam-97	114	4	is	be	AUX
ejpam-97	114	5	a	a	DET
ejpam-97	114	6	homomorphism	homomorphism	NOUN
ejpam-97	114	7	.	.	PUNCT
ejpam-97	115	1	(	(	PUNCT
ejpam-97	115	2	2	2	X
ejpam-97	115	3	)	)	PUNCT
ejpam-97	115	4	k	k	NOUN
ejpam-97	115	5	:	:	PUNCT
ejpam-97	116	1	i	i	PRON
ejpam-97	116	2	→	→	PUNCT
ejpam-97	116	3	a	a	PRON
ejpam-97	116	4	is	be	AUX
ejpam-97	116	5	a	a	DET
ejpam-97	116	6	consistent	consistent	ADJ
ejpam-97	116	7	map	map	NOUN
ejpam-97	116	8	.	.	PUNCT
ejpam-97	117	1	(	(	PUNCT
ejpam-97	117	2	3	3	X
ejpam-97	117	3	)	)	PUNCT
ejpam-97	117	4	the	the	DET
ejpam-97	117	5	system	system	NOUN
ejpam-97	117	6	σ	σ	NOUN
ejpam-97	117	7	=	=	SYM
ejpam-97	117	8	{	{	PUNCT
ejpam-97	117	9	xs	xs	NOUN
ejpam-97	117	10	=	=	PUNCT
ejpam-97	117	11	k(s)|	k(s)|	X
ejpam-97	117	12	s	s	X
ejpam-97	117	13	∈	∈	PROPN
ejpam-97	118	1	i	i	PRON
ejpam-97	118	2	}	}	PUNCT
ejpam-97	118	3	is	be	AUX
ejpam-97	118	4	a	a	DET
ejpam-97	118	5	consistent	consistent	ADJ
ejpam-97	118	6	system	system	NOUN
ejpam-97	118	7	.	.	PUNCT
ejpam-97	119	1	proof	proof	NOUN
ejpam-97	119	2	.	.	PUNCT
ejpam-97	120	1	(	(	PUNCT
ejpam-97	120	2	1)⇒(2	1)⇒(2	X
ejpam-97	120	3	)	)	PUNCT
ejpam-97	120	4	let	let	VERB
ejpam-97	120	5	k	k	NOUN
ejpam-97	120	6	:	:	PUNCT
ejpam-97	121	1	i	i	PRON
ejpam-97	121	2	→	→	PUNCT
ejpam-97	121	3	a	a	DET
ejpam-97	121	4	be	be	AUX
ejpam-97	121	5	a	a	DET
ejpam-97	121	6	homomorphism	homomorphism	NOUN
ejpam-97	121	7	.	.	PUNCT
ejpam-97	122	1	let	let	VERB
ejpam-97	122	2	e	e	PRON
ejpam-97	122	3	be	be	AUX
ejpam-97	122	4	an	an	DET
ejpam-97	122	5	injective	injective	ADJ
ejpam-97	122	6	s	s	NOUN
ejpam-97	122	7	-	-	PUNCT
ejpam-97	122	8	act	act	NOUN
ejpam-97	122	9	containing	contain	VERB
ejpam-97	122	10	a	a	PRON
ejpam-97	122	11	(	(	PUNCT
ejpam-97	122	12	see	see	VERB
ejpam-97	122	13	[	[	X
ejpam-97	122	14	13	13	NUM
ejpam-97	122	15	]	]	NUM
ejpam-97	122	16	)	)	PUNCT
ejpam-97	122	17	.	.	PUNCT
ejpam-97	123	1	considering	consider	VERB
ejpam-97	123	2	the	the	DET
ejpam-97	123	3	extension	extension	NOUN
ejpam-97	123	4	i1	i1	PROPN
ejpam-97	123	5	of	of	ADP
ejpam-97	123	6	i	i	PRON
ejpam-97	123	7	,	,	PUNCT
ejpam-97	123	8	k	k	PROPN
ejpam-97	123	9	can	can	AUX
ejpam-97	123	10	be	be	AUX
ejpam-97	123	11	lifted	lift	VERB
ejpam-97	123	12	to	to	PART
ejpam-97	123	13	k̄	k̄	VERB
ejpam-97	123	14	:	:	PUNCT
ejpam-97	123	15	i1→	i1→	AUX
ejpam-97	123	16	e.	e.	PROPN
ejpam-97	123	17	now	now	ADV
ejpam-97	123	18	it	it	PRON
ejpam-97	123	19	is	be	AUX
ejpam-97	123	20	easily	easily	ADV
ejpam-97	123	21	seen	see	VERB
ejpam-97	123	22	that	that	SCONJ
ejpam-97	123	23	k	k	PROPN
ejpam-97	123	24	=	=	PUNCT
ejpam-97	123	25	λx	λx	PROPN
ejpam-97	123	26	where	where	SCONJ
ejpam-97	123	27	x	x	SYM
ejpam-97	123	28	=	=	SYM
ejpam-97	123	29	k(1	k(1	PROPN
ejpam-97	123	30	)	)	PUNCT
ejpam-97	123	31	∈	∈	PROPN
ejpam-97	123	32	e	e	NOUN
ejpam-97	123	33	,	,	PUNCT
ejpam-97	123	34	and	and	CCONJ
ejpam-97	123	35	so	so	ADV
ejpam-97	123	36	k	k	PROPN
ejpam-97	123	37	is	be	AUX
ejpam-97	123	38	consistent	consistent	ADJ
ejpam-97	123	39	.	.	PUNCT
ejpam-97	124	1	(	(	PUNCT
ejpam-97	124	2	2)⇒(1	2)⇒(1	NOUN
ejpam-97	124	3	)	)	PUNCT
ejpam-97	124	4	let	let	VERB
ejpam-97	124	5	k	k	PRON
ejpam-97	124	6	be	be	AUX
ejpam-97	124	7	a	a	DET
ejpam-97	124	8	consistent	consistent	ADJ
ejpam-97	124	9	map	map	NOUN
ejpam-97	124	10	.	.	PUNCT
ejpam-97	125	1	so	so	ADV
ejpam-97	125	2	,	,	PUNCT
ejpam-97	125	3	there	there	PRON
ejpam-97	125	4	exist	exist	VERB
ejpam-97	125	5	an	an	DET
ejpam-97	125	6	extension	extension	NOUN
ejpam-97	125	7	b	b	NOUN
ejpam-97	125	8	of	of	ADP
ejpam-97	125	9	a	a	PRON
ejpam-97	125	10	and	and	CCONJ
ejpam-97	125	11	b	b	NOUN
ejpam-97	125	12	∈	∈	PROPN
ejpam-97	125	13	b	b	NOUN
ejpam-97	125	14	such	such	ADJ
ejpam-97	125	15	that	that	PRON
ejpam-97	125	16	k	k	PROPN
ejpam-97	125	17	=	=	PUNCT
ejpam-97	125	18	λb	λb	X
ejpam-97	125	19	which	which	PRON
ejpam-97	125	20	is	be	AUX
ejpam-97	125	21	in	in	ADP
ejpam-97	125	22	fact	fact	NOUN
ejpam-97	125	23	a	a	DET
ejpam-97	125	24	homomorphism	homomorphism	NOUN
ejpam-97	125	25	.	.	PUNCT
ejpam-97	126	1	the	the	DET
ejpam-97	126	2	equivalence	equivalence	NOUN
ejpam-97	126	3	of	of	ADP
ejpam-97	126	4	(	(	PUNCT
ejpam-97	126	5	3	3	NUM
ejpam-97	126	6	)	)	PUNCT
ejpam-97	126	7	and	and	CCONJ
ejpam-97	126	8	(	(	PUNCT
ejpam-97	126	9	2	2	X
ejpam-97	126	10	)	)	PUNCT
ejpam-97	126	11	follows	follow	VERB
ejpam-97	126	12	just	just	ADV
ejpam-97	126	13	from	from	ADP
ejpam-97	126	14	the	the	DET
ejpam-97	126	15	definition	definition	NOUN
ejpam-97	126	16	.	.	PUNCT
ejpam-97	127	1	corollary	corollary	ADJ
ejpam-97	127	2	2.1	2.1	NUM
ejpam-97	127	3	.	.	PUNCT
ejpam-97	128	1	a	a	DET
ejpam-97	128	2	t	t	NOUN
ejpam-97	128	3	-	-	PUNCT
ejpam-97	128	4	system	system	NOUN
ejpam-97	128	5	σt	σt	ADP
ejpam-97	128	6	=	=	PUNCT
ejpam-97	128	7	{	{	PUNCT
ejpam-97	128	8	x	x	X
ejpam-97	128	9	t	t	NOUN
ejpam-97	128	10	=	=	PUNCT
ejpam-97	128	11	at	at	ADP
ejpam-97	128	12	|	|	ADV
ejpam-97	128	13	t	t	PROPN
ejpam-97	128	14	∈	∈	PROPN
ejpam-97	128	15	t	t	PROPN
ejpam-97	128	16	}	}	PUNCT
ejpam-97	128	17	(	(	PUNCT
ejpam-97	128	18	or	or	CCONJ
ejpam-97	128	19	a	a	DET
ejpam-97	128	20	t	t	NOUN
ejpam-97	128	21	-	-	PUNCT
ejpam-97	128	22	sequence	sequence	NOUN
ejpam-97	128	23	k	k	NOUN
ejpam-97	128	24	:	:	PUNCT
ejpam-97	128	25	t	t	PROPN
ejpam-97	128	26	→	→	SYM
ejpam-97	128	27	a	a	X
ejpam-97	128	28	)	)	PUNCT
ejpam-97	128	29	is	be	AUX
ejpam-97	128	30	consistent	consistent	ADJ
ejpam-97	128	31	if	if	SCONJ
ejpam-97	128	32	and	and	CCONJ
ejpam-97	128	33	only	only	ADV
ejpam-97	128	34	if	if	SCONJ
ejpam-97	128	35	k̂	k̂	PROPN
ejpam-97	128	36	:	:	PUNCT
ejpam-97	128	37	ts1	ts1	PROPN
ejpam-97	128	38	→	→	PUNCT
ejpam-97	129	1	a	a	PRON
ejpam-97	129	2	defined	define	VERB
ejpam-97	129	3	by	by	ADP
ejpam-97	129	4	k̂(ts	k̂(ts	PROPN
ejpam-97	129	5	)	)	PUNCT
ejpam-97	129	6	=	=	SYM
ejpam-97	129	7	ats	ats	PROPN
ejpam-97	129	8	for	for	ADP
ejpam-97	129	9	t	t	PROPN
ejpam-97	129	10	∈	∈	PROPN
ejpam-97	129	11	t	t	PROPN
ejpam-97	129	12	,	,	PUNCT
ejpam-97	129	13	s	s	PART
ejpam-97	129	14	∈	∈	PROPN
ejpam-97	129	15	s1	s1	NOUN
ejpam-97	129	16	is	be	AUX
ejpam-97	129	17	a	a	DET
ejpam-97	129	18	“	"	PUNCT
ejpam-97	129	19	well	well	ADV
ejpam-97	129	20	defined	define	VERB
ejpam-97	129	21	"	"	PUNCT
ejpam-97	129	22	equivariant	equivariant	ADJ
ejpam-97	129	23	map	map	NOUN
ejpam-97	129	24	.	.	PUNCT
ejpam-97	130	1	proof	proof	NOUN
ejpam-97	130	2	.	.	PUNCT
ejpam-97	131	1	clearly	clearly	ADV
ejpam-97	131	2	σt	σt	ADP
ejpam-97	131	3	=	=	PUNCT
ejpam-97	131	4	{	{	PUNCT
ejpam-97	131	5	x	x	X
ejpam-97	131	6	t	t	NOUN
ejpam-97	131	7	=	=	PUNCT
ejpam-97	131	8	at	at	ADP
ejpam-97	131	9	|	|	ADV
ejpam-97	131	10	t	t	PROPN
ejpam-97	131	11	∈	∈	PROPN
ejpam-97	131	12	t	t	PROPN
ejpam-97	131	13	}	}	PUNCT
ejpam-97	131	14	is	be	AUX
ejpam-97	131	15	consistent	consistent	ADJ
ejpam-97	131	16	if	if	SCONJ
ejpam-97	131	17	and	and	CCONJ
ejpam-97	131	18	only	only	ADV
ejpam-97	131	19	if	if	SCONJ
ejpam-97	131	20	σ1	σ1	PROPN
ejpam-97	131	21	=	=	SYM
ejpam-97	131	22	{	{	PUNCT
ejpam-97	131	23	x(ts	x(ts	PROPN
ejpam-97	131	24	)	)	PUNCT
ejpam-97	131	25	=	=	SYM
ejpam-97	131	26	ats|	ats|	PROPN
ejpam-97	131	27	t	t	PROPN
ejpam-97	131	28	∈	∈	PROPN
ejpam-97	131	29	t	t	PROPN
ejpam-97	131	30	,	,	PUNCT
ejpam-97	131	31	s	s	PART
ejpam-97	131	32	∈	∈	PROPN
ejpam-97	131	33	s1	s1	NOUN
ejpam-97	131	34	}	}	PUNCT
ejpam-97	131	35	is	be	AUX
ejpam-97	131	36	consistent	consistent	ADJ
ejpam-97	131	37	.	.	PUNCT
ejpam-97	132	1	now	now	ADV
ejpam-97	132	2	,	,	PUNCT
ejpam-97	132	3	since	since	SCONJ
ejpam-97	132	4	ts1	ts1	PROPN
ejpam-97	132	5	is	be	AUX
ejpam-97	132	6	a	a	DET
ejpam-97	132	7	right	right	ADJ
ejpam-97	132	8	ideal	ideal	NOUN
ejpam-97	132	9	of	of	ADP
ejpam-97	132	10	s	s	PROPN
ejpam-97	132	11	,	,	PUNCT
ejpam-97	132	12	the	the	DET
ejpam-97	132	13	latter	latter	ADJ
ejpam-97	132	14	is	be	AUX
ejpam-97	132	15	true	true	ADJ
ejpam-97	132	16	by	by	ADP
ejpam-97	132	17	the	the	DET
ejpam-97	132	18	above	above	ADJ
ejpam-97	132	19	theorem	theorem	NOUN
ejpam-97	132	20	if	if	SCONJ
ejpam-97	132	21	and	and	CCONJ
ejpam-97	132	22	only	only	ADV
ejpam-97	132	23	if	if	SCONJ
ejpam-97	132	24	k̂	k̂	PROPN
ejpam-97	132	25	:	:	PUNCT
ejpam-97	132	26	ts1→	ts1→	NOUN
ejpam-97	132	27	a	a	PRON
ejpam-97	132	28	with	with	ADP
ejpam-97	132	29	k̂(ts	k̂(ts	PROPN
ejpam-97	132	30	)	)	PUNCT
ejpam-97	132	31	=	=	SYM
ejpam-97	132	32	ats	ats	PROPN
ejpam-97	132	33	is	be	AUX
ejpam-97	132	34	a	a	DET
ejpam-97	132	35	homomorphism	homomorphism	NOUN
ejpam-97	132	36	.	.	PUNCT
ejpam-97	133	1	the	the	DET
ejpam-97	133	2	above	above	ADJ
ejpam-97	133	3	corollary	corollary	NOUN
ejpam-97	133	4	shows	show	NOUN
ejpam-97	133	5	that	that	SCONJ
ejpam-97	133	6	,	,	PUNCT
ejpam-97	133	7	as	as	ADV
ejpam-97	133	8	long	long	ADV
ejpam-97	133	9	as	as	SCONJ
ejpam-97	133	10	consistent	consistent	ADJ
ejpam-97	133	11	systems	system	NOUN
ejpam-97	133	12	of	of	ADP
ejpam-97	133	13	equations	equation	NOUN
ejpam-97	133	14	are	be	AUX
ejpam-97	133	15	concerned	concern	VERB
ejpam-97	133	16	,	,	PUNCT
ejpam-97	133	17	we	we	PRON
ejpam-97	133	18	may	may	AUX
ejpam-97	133	19	as	as	ADV
ejpam-97	133	20	well	well	ADV
ejpam-97	133	21	consider	consider	VERB
ejpam-97	133	22	only	only	ADV
ejpam-97	133	23	equivariant	equivariant	ADJ
ejpam-97	133	24	maps	map	NOUN
ejpam-97	134	1	k	k	PROPN
ejpam-97	134	2	:	:	PUNCT
ejpam-97	134	3	i	i	PRON
ejpam-97	134	4	→	→	PUNCT
ejpam-97	134	5	a	a	PRON
ejpam-97	134	6	from	from	ADP
ejpam-97	134	7	a	a	DET
ejpam-97	134	8	right	right	ADJ
ejpam-97	134	9	ideal	ideal	NOUN
ejpam-97	134	10	i	i	PRON
ejpam-97	134	11	of	of	ADP
ejpam-97	134	12	s	s	PRON
ejpam-97	134	13	to	to	ADP
ejpam-97	134	14	a	a	DET
ejpam-97	134	15	rather	rather	ADV
ejpam-97	134	16	than	than	ADP
ejpam-97	134	17	functions	function	NOUN
ejpam-97	134	18	from	from	ADP
ejpam-97	134	19	an	an	DET
ejpam-97	134	20	arbitrary	arbitrary	ADJ
ejpam-97	134	21	set	set	VERB
ejpam-97	134	22	t	t	PROPN
ejpam-97	134	23	to	to	PART
ejpam-97	134	24	a.	a.	VERB
ejpam-97	134	25	in	in	ADP
ejpam-97	134	26	particular	particular	ADJ
ejpam-97	134	27	,	,	PUNCT
ejpam-97	134	28	we	we	PRON
ejpam-97	134	29	take	take	VERB
ejpam-97	134	30	i	i	PRON
ejpam-97	134	31	to	to	PART
ejpam-97	134	32	be	be	AUX
ejpam-97	134	33	s	s	PRON
ejpam-97	134	34	itself	itself	PRON
ejpam-97	134	35	and	and	CCONJ
ejpam-97	134	36	have	have	VERB
ejpam-97	134	37	the	the	DET
ejpam-97	134	38	following	following	NOUN
ejpam-97	134	39	:	:	PUNCT
ejpam-97	134	40	definition	definition	NOUN
ejpam-97	134	41	2.2	2.2	NUM
ejpam-97	134	42	.	.	PUNCT
ejpam-97	135	1	let	let	VERB
ejpam-97	135	2	a	a	DET
ejpam-97	135	3	be	be	AUX
ejpam-97	135	4	a	a	DET
ejpam-97	135	5	subact	subact	NOUN
ejpam-97	135	6	of	of	ADP
ejpam-97	135	7	b.	b.	PROPN
ejpam-97	136	1	we	we	PRON
ejpam-97	136	2	say	say	VERB
ejpam-97	136	3	that	that	SCONJ
ejpam-97	136	4	a	a	PRON
ejpam-97	136	5	is	be	AUX
ejpam-97	136	6	sequentially	sequentially	ADV
ejpam-97	136	7	pure	pure	ADJ
ejpam-97	136	8	or	or	CCONJ
ejpam-97	136	9	s	s	NOUN
ejpam-97	136	10	-	-	NOUN
ejpam-97	136	11	pure	pure	ADJ
ejpam-97	136	12	in	in	ADP
ejpam-97	136	13	b	b	NOUN
ejpam-97	136	14	if	if	SCONJ
ejpam-97	136	15	any	any	DET
ejpam-97	136	16	one	one	NUM
ejpam-97	136	17	of	of	ADP
ejpam-97	136	18	the	the	DET
ejpam-97	136	19	following	follow	VERB
ejpam-97	136	20	equivalent	equivalent	ADJ
ejpam-97	136	21	conditions	condition	NOUN
ejpam-97	136	22	hold	hold	VERB
ejpam-97	136	23	:	:	PUNCT
ejpam-97	136	24	(	(	PUNCT
ejpam-97	136	25	1	1	X
ejpam-97	136	26	)	)	PUNCT
ejpam-97	136	27	every	every	DET
ejpam-97	136	28	σ	σ	NOUN
ejpam-97	136	29	=	=	PUNCT
ejpam-97	136	30	{	{	PUNCT
ejpam-97	136	31	xs	xs	NOUN
ejpam-97	136	32	=	=	PUNCT
ejpam-97	136	33	as	as	ADP
ejpam-97	136	34	:	:	PUNCT
ejpam-97	136	35	s	s	VERB
ejpam-97	136	36	∈	∈	PROPN
ejpam-97	136	37	s	s	NOUN
ejpam-97	136	38	,	,	PUNCT
ejpam-97	136	39	as	as	SCONJ
ejpam-97	136	40	∈	∈	PROPN
ejpam-97	136	41	a	a	PRON
ejpam-97	136	42	}	}	PUNCT
ejpam-97	136	43	is	be	AUX
ejpam-97	136	44	solvable	solvable	ADJ
ejpam-97	136	45	in	in	ADP
ejpam-97	136	46	a	a	PRON
ejpam-97	136	47	whenever	whenever	SCONJ
ejpam-97	136	48	it	it	PRON
ejpam-97	136	49	is	be	AUX
ejpam-97	136	50	solvable	solvable	ADJ
ejpam-97	136	51	in	in	ADP
ejpam-97	136	52	b.	b.	PROPN
ejpam-97	136	53	(	(	PUNCT
ejpam-97	136	54	2	2	NUM
ejpam-97	136	55	)	)	PUNCT
ejpam-97	136	56	for	for	ADP
ejpam-97	136	57	every	every	DET
ejpam-97	136	58	b	b	PROPN
ejpam-97	136	59	∈	∈	PROPN
ejpam-97	136	60	b	b	PROPN
ejpam-97	136	61	with	with	ADP
ejpam-97	136	62	bs	bs	PROPN
ejpam-97	136	63	⊆	⊆	PROPN
ejpam-97	136	64	a	a	PRON
ejpam-97	136	65	there	there	PRON
ejpam-97	136	66	is	be	VERB
ejpam-97	136	67	an	an	DET
ejpam-97	136	68	element	element	NOUN
ejpam-97	136	69	a	a	DET
ejpam-97	136	70	∈	∈	PROPN
ejpam-97	136	71	a	a	DET
ejpam-97	136	72	such	such	ADJ
ejpam-97	136	73	that	that	DET
ejpam-97	136	74	λb	λb	PROPN
ejpam-97	136	75	=	=	SYM
ejpam-97	136	76	λa	λa	PROPN
ejpam-97	136	77	;	;	PUNCT
ejpam-97	136	78	in	in	ADP
ejpam-97	136	79	the	the	DET
ejpam-97	136	80	sense	sense	NOUN
ejpam-97	136	81	that	that	SCONJ
ejpam-97	136	82	bs	bs	NOUN
ejpam-97	136	83	=	=	PUNCT
ejpam-97	136	84	as	as	ADP
ejpam-97	136	85	for	for	ADP
ejpam-97	136	86	each	each	DET
ejpam-97	136	87	s	s	PROPN
ejpam-97	136	88	∈	∈	PROPN
ejpam-97	136	89	s.	s.	PROPN
ejpam-97	136	90	(	(	PUNCT
ejpam-97	136	91	3	3	X
ejpam-97	136	92	)	)	PUNCT
ejpam-97	136	93	every	every	DET
ejpam-97	136	94	homomorphism	homomorphism	NOUN
ejpam-97	136	95	k	k	X
ejpam-97	136	96	:	:	PUNCT
ejpam-97	136	97	s→	s→	X
ejpam-97	137	1	a	a	PRON
ejpam-97	137	2	is	be	AUX
ejpam-97	137	3	of	of	ADP
ejpam-97	137	4	the	the	DET
ejpam-97	137	5	form	form	NOUN
ejpam-97	137	6	λa	λa	INTJ
ejpam-97	137	7	for	for	ADP
ejpam-97	137	8	some	some	PRON
ejpam-97	137	9	a	a	DET
ejpam-97	137	10	∈	∈	NOUN
ejpam-97	137	11	a	a	PRON
ejpam-97	137	12	whenever	whenever	SCONJ
ejpam-97	137	13	it	it	PRON
ejpam-97	137	14	is	be	AUX
ejpam-97	137	15	of	of	ADP
ejpam-97	137	16	the	the	DET
ejpam-97	137	17	form	form	NOUN
ejpam-97	137	18	λb	λb	ADV
ejpam-97	137	19	for	for	ADP
ejpam-97	137	20	some	some	DET
ejpam-97	137	21	b	b	PROPN
ejpam-97	137	22	∈	∈	PROPN
ejpam-97	137	23	b.	b.	PROPN
ejpam-97	138	1	a	a	DET
ejpam-97	138	2	monomorphism	monomorphism	NOUN
ejpam-97	138	3	f	f	X
ejpam-97	138	4	:	:	PUNCT
ejpam-97	138	5	a→	a→	PROPN
ejpam-97	138	6	b	b	NOUN
ejpam-97	138	7	is	be	AUX
ejpam-97	138	8	said	say	VERB
ejpam-97	138	9	to	to	PART
ejpam-97	138	10	be	be	AUX
ejpam-97	138	11	s	s	NOUN
ejpam-97	138	12	-	-	ADJ
ejpam-97	138	13	pure	pure	ADJ
ejpam-97	138	14	if	if	SCONJ
ejpam-97	138	15	f	f	PROPN
ejpam-97	138	16	(	(	PUNCT
ejpam-97	138	17	a	a	NOUN
ejpam-97	138	18	)	)	PUNCT
ejpam-97	138	19	is	be	AUX
ejpam-97	138	20	s	s	NOUN
ejpam-97	138	21	-	-	ADJ
ejpam-97	138	22	pure	pure	ADJ
ejpam-97	138	23	in	in	ADP
ejpam-97	138	24	b.	b.	PROPN
ejpam-97	138	25	h.	h.	PROPN
ejpam-97	138	26	barzegar	barzegar	PROPN
ejpam-97	138	27	and	and	CCONJ
ejpam-97	138	28	m.m	m.m	PROPN
ejpam-97	138	29	.	.	PROPN
ejpam-97	138	30	ebrahimi	ebrahimi	PROPN
ejpam-97	138	31	/	/	SYM
ejpam-97	138	32	eur	eur	PROPN
ejpam-97	138	33	.	.	PUNCT
ejpam-97	139	1	j.	j.	PROPN
ejpam-97	139	2	pure	pure	PROPN
ejpam-97	139	3	appl	appl	PROPN
ejpam-97	139	4	.	.	PROPN
ejpam-97	139	5	math	math	PROPN
ejpam-97	139	6	,	,	PUNCT
ejpam-97	139	7	1	1	NUM
ejpam-97	139	8	(	(	PUNCT
ejpam-97	139	9	2008	2008	NUM
ejpam-97	139	10	)	)	PUNCT
ejpam-97	139	11	,	,	PUNCT
ejpam-97	139	12	(	(	PUNCT
ejpam-97	139	13	41	41	NUM
ejpam-97	139	14	-	-	SYM
ejpam-97	139	15	55	55	NUM
ejpam-97	139	16	)	)	PUNCT
ejpam-97	139	17	46	46	NUM
ejpam-97	139	18	the	the	DET
ejpam-97	139	19	following	following	NOUN
ejpam-97	139	20	is	be	AUX
ejpam-97	139	21	a	a	DET
ejpam-97	139	22	simple	simple	ADJ
ejpam-97	139	23	fact	fact	NOUN
ejpam-97	139	24	which	which	PRON
ejpam-97	139	25	will	will	AUX
ejpam-97	139	26	be	be	AUX
ejpam-97	139	27	used	use	VERB
ejpam-97	139	28	later	later	ADV
ejpam-97	139	29	:	:	PUNCT
ejpam-97	139	30	lemma	lemma	PROPN
ejpam-97	139	31	2.1	2.1	NUM
ejpam-97	139	32	.	.	PUNCT
ejpam-97	140	1	for	for	ADP
ejpam-97	140	2	every	every	DET
ejpam-97	140	3	s	s	NOUN
ejpam-97	140	4	-	-	PUNCT
ejpam-97	140	5	acts	act	VERB
ejpam-97	140	6	a	a	PRON
ejpam-97	140	7	and	and	CCONJ
ejpam-97	140	8	b	b	NOUN
ejpam-97	140	9	,	,	PUNCT
ejpam-97	140	10	we	we	PRON
ejpam-97	140	11	have	have	VERB
ejpam-97	140	12	:	:	PUNCT
ejpam-97	140	13	(	(	PUNCT
ejpam-97	140	14	1	1	X
ejpam-97	140	15	)	)	PUNCT
ejpam-97	140	16	a	a	PRON
ejpam-97	140	17	is	be	AUX
ejpam-97	140	18	s	s	NOUN
ejpam-97	140	19	-	-	NOUN
ejpam-97	140	20	pure	pure	ADJ
ejpam-97	140	21	in	in	ADP
ejpam-97	140	22	at	at	ADP
ejpam-97	140	23	b.	b.	PROPN
ejpam-97	140	24	(	(	PUNCT
ejpam-97	140	25	2	2	NUM
ejpam-97	140	26	)	)	PUNCT
ejpam-97	140	27	a	a	PRON
ejpam-97	140	28	is	be	AUX
ejpam-97	140	29	s	s	NOUN
ejpam-97	140	30	-	-	ADJ
ejpam-97	140	31	pure	pure	ADJ
ejpam-97	140	32	in	in	ADP
ejpam-97	140	33	a0	a0	PROPN
ejpam-97	140	34	.	.	PROPN
ejpam-97	141	1	remark	remark	PROPN
ejpam-97	141	2	2.1	2.1	NUM
ejpam-97	141	3	.	.	PUNCT
ejpam-97	142	1	note	note	VERB
ejpam-97	142	2	that	that	SCONJ
ejpam-97	142	3	one	one	PRON
ejpam-97	142	4	may	may	AUX
ejpam-97	142	5	say	say	VERB
ejpam-97	142	6	that	that	SCONJ
ejpam-97	142	7	a	a	DET
ejpam-97	142	8	subact	subact	NOUN
ejpam-97	142	9	a	a	PRON
ejpam-97	142	10	of	of	ADP
ejpam-97	142	11	an	an	DET
ejpam-97	142	12	act	act	NOUN
ejpam-97	142	13	b	b	NOUN
ejpam-97	142	14	is	be	AUX
ejpam-97	142	15	finitely	finitely	ADV
ejpam-97	142	16	pure	pure	ADJ
ejpam-97	142	17	in	in	ADP
ejpam-97	142	18	b	b	NOUN
ejpam-97	142	19	if	if	SCONJ
ejpam-97	142	20	for	for	SCONJ
ejpam-97	142	21	every	every	DET
ejpam-97	142	22	finite	finite	NOUN
ejpam-97	142	23	subset	subset	VERB
ejpam-97	142	24	t	t	PROPN
ejpam-97	142	25	⊆	⊆	NUM
ejpam-97	142	26	s	s	NOUN
ejpam-97	142	27	,	,	PUNCT
ejpam-97	142	28	the	the	DET
ejpam-97	142	29	system	system	NOUN
ejpam-97	142	30	σt	σt	VERB
ejpam-97	142	31	with	with	ADP
ejpam-97	142	32	constants	constant	NOUN
ejpam-97	142	33	from	from	ADP
ejpam-97	142	34	a	a	PRON
ejpam-97	142	35	has	have	VERB
ejpam-97	142	36	a	a	DET
ejpam-97	142	37	solution	solution	NOUN
ejpam-97	142	38	in	in	ADP
ejpam-97	142	39	a	a	PRON
ejpam-97	142	40	whenever	whenever	SCONJ
ejpam-97	142	41	it	it	PRON
ejpam-97	142	42	has	have	VERB
ejpam-97	142	43	a	a	DET
ejpam-97	142	44	solution	solution	NOUN
ejpam-97	142	45	in	in	ADP
ejpam-97	142	46	b.	b.	PROPN
ejpam-97	142	47	clearly	clearly	ADV
ejpam-97	142	48	,	,	PUNCT
ejpam-97	142	49	if	if	SCONJ
ejpam-97	142	50	s	s	NOUN
ejpam-97	142	51	is	be	AUX
ejpam-97	142	52	finitely	finitely	ADV
ejpam-97	142	53	generated	generate	VERB
ejpam-97	142	54	,	,	PUNCT
ejpam-97	142	55	say	say	INTJ
ejpam-97	142	56	by	by	ADP
ejpam-97	142	57	t	t	PROPN
ejpam-97	142	58	,	,	PUNCT
ejpam-97	142	59	then	then	ADV
ejpam-97	142	60	by	by	ADP
ejpam-97	142	61	corollary	corollary	ADJ
ejpam-97	142	62	2.1	2.1	NUM
ejpam-97	142	63	,	,	PUNCT
ejpam-97	142	64	finite	finite	NOUN
ejpam-97	142	65	(	(	PUNCT
ejpam-97	142	66	or	or	CCONJ
ejpam-97	142	67	even	even	ADV
ejpam-97	142	68	t	t	PROPN
ejpam-97	142	69	-	-	PUNCT
ejpam-97	142	70	)	)	PUNCT
ejpam-97	142	71	purity	purity	NOUN
ejpam-97	142	72	implies	imply	VERB
ejpam-97	142	73	s	s	NOUN
ejpam-97	142	74	-	-	NOUN
ejpam-97	142	75	purity	purity	NOUN
ejpam-97	142	76	.	.	PUNCT
ejpam-97	143	1	but	but	CCONJ
ejpam-97	143	2	,	,	PUNCT
ejpam-97	143	3	the	the	DET
ejpam-97	143	4	converse	converse	NOUN
ejpam-97	143	5	is	be	AUX
ejpam-97	143	6	not	not	PART
ejpam-97	143	7	true	true	ADJ
ejpam-97	143	8	:	:	PUNCT
ejpam-97	143	9	consider	consider	VERB
ejpam-97	143	10	the	the	DET
ejpam-97	143	11	semigroup	semigroup	NOUN
ejpam-97	143	12	s	s	PART
ejpam-97	143	13	=	=	PUNCT
ejpam-97	143	14	{	{	PUNCT
ejpam-97	143	15	1	1	NUM
ejpam-97	143	16	,	,	PUNCT
ejpam-97	143	17	a	a	DET
ejpam-97	143	18	,	,	PUNCT
ejpam-97	143	19	b	b	NOUN
ejpam-97	143	20	}	}	PUNCT
ejpam-97	143	21	in	in	ADP
ejpam-97	143	22	which	which	PRON
ejpam-97	143	23	1	1	NUM
ejpam-97	143	24	is	be	AUX
ejpam-97	143	25	a	a	DET
ejpam-97	143	26	left	left	ADJ
ejpam-97	143	27	identity	identity	NOUN
ejpam-97	143	28	and	and	CCONJ
ejpam-97	143	29	a	a	DET
ejpam-97	143	30	,	,	PUNCT
ejpam-97	143	31	b	b	NOUN
ejpam-97	143	32	are	be	AUX
ejpam-97	143	33	zero	zero	NUM
ejpam-97	143	34	elements	element	NOUN
ejpam-97	143	35	.	.	PUNCT
ejpam-97	144	1	then	then	ADV
ejpam-97	144	2	a	a	PRON
ejpam-97	144	3	=	=	X
ejpam-97	144	4	{	{	PUNCT
ejpam-97	144	5	a	a	PROPN
ejpam-97	144	6	,	,	PUNCT
ejpam-97	144	7	b	b	NOUN
ejpam-97	144	8	}	}	PUNCT
ejpam-97	144	9	is	be	AUX
ejpam-97	144	10	an	an	DET
ejpam-97	144	11	s	s	NOUN
ejpam-97	144	12	-	-	ADJ
ejpam-97	144	13	pure	pure	ADJ
ejpam-97	144	14	subact	subact	NOUN
ejpam-97	144	15	of	of	ADP
ejpam-97	144	16	s	s	PROPN
ejpam-97	144	17	,	,	PUNCT
ejpam-97	144	18	but	but	CCONJ
ejpam-97	144	19	the	the	DET
ejpam-97	144	20	finite	finite	ADJ
ejpam-97	144	21	system	system	NOUN
ejpam-97	144	22	σ	σ	PROPN
ejpam-97	144	23	=	=	SYM
ejpam-97	144	24	{	{	PUNCT
ejpam-97	144	25	xa	xa	PROPN
ejpam-97	144	26	=	=	SYM
ejpam-97	144	27	a	a	PROPN
ejpam-97	144	28	,	,	PUNCT
ejpam-97	144	29	x	x	PROPN
ejpam-97	144	30	b	b	X
ejpam-97	144	31	=	=	SYM
ejpam-97	144	32	b	b	AUX
ejpam-97	144	33	}	}	PUNCT
ejpam-97	144	34	having	have	VERB
ejpam-97	144	35	solution	solution	NOUN
ejpam-97	144	36	1	1	NUM
ejpam-97	144	37	in	in	ADP
ejpam-97	144	38	s	s	PRON
ejpam-97	144	39	does	do	AUX
ejpam-97	144	40	not	not	PART
ejpam-97	144	41	have	have	VERB
ejpam-97	144	42	any	any	DET
ejpam-97	144	43	solution	solution	NOUN
ejpam-97	144	44	in	in	ADP
ejpam-97	144	45	a.	a.	NOUN
ejpam-97	144	46	2.2	2.2	NUM
ejpam-97	144	47	.	.	PUNCT
ejpam-97	145	1	sequential	sequential	ADJ
ejpam-97	145	2	purity	purity	NOUN
ejpam-97	145	3	versus	versus	ADP
ejpam-97	145	4	c	c	NOUN
ejpam-97	145	5	p	p	NOUN
ejpam-97	145	6	-	-	PUNCT
ejpam-97	145	7	purity	purity	NOUN
ejpam-97	145	8	in	in	ADP
ejpam-97	145	9	this	this	DET
ejpam-97	145	10	subsection	subsection	NOUN
ejpam-97	145	11	we	we	PRON
ejpam-97	145	12	introduce	introduce	VERB
ejpam-97	145	13	a	a	DET
ejpam-97	145	14	closure	closure	NOUN
ejpam-97	145	15	operator	operator	NOUN
ejpam-97	145	16	which	which	PRON
ejpam-97	145	17	is	be	AUX
ejpam-97	145	18	closely	closely	ADV
ejpam-97	145	19	related	relate	VERB
ejpam-97	145	20	to	to	ADP
ejpam-97	145	21	sequential	sequential	ADJ
ejpam-97	145	22	purity	purity	NOUN
ejpam-97	145	23	defined	define	VERB
ejpam-97	145	24	above	above	ADV
ejpam-97	145	25	.	.	PUNCT
ejpam-97	146	1	we	we	PRON
ejpam-97	146	2	are	be	AUX
ejpam-97	146	3	not	not	PART
ejpam-97	146	4	going	go	VERB
ejpam-97	146	5	to	to	PART
ejpam-97	146	6	fully	fully	ADV
ejpam-97	146	7	investigate	investigate	VERB
ejpam-97	146	8	the	the	DET
ejpam-97	146	9	properties	property	NOUN
ejpam-97	146	10	of	of	ADP
ejpam-97	146	11	this	this	DET
ejpam-97	146	12	closure	closure	NOUN
ejpam-97	146	13	operator	operator	NOUN
ejpam-97	146	14	as	as	ADP
ejpam-97	146	15	in	in	ADP
ejpam-97	146	16	[	[	X
ejpam-97	146	17	4	4	NUM
ejpam-97	146	18	]	]	PUNCT
ejpam-97	146	19	.	.	PUNCT
ejpam-97	147	1	first	first	ADV
ejpam-97	147	2	recall	recall	VERB
ejpam-97	147	3	the	the	DET
ejpam-97	147	4	following	follow	VERB
ejpam-97	147	5	definition	definition	NOUN
ejpam-97	147	6	of	of	ADP
ejpam-97	147	7	a	a	DET
ejpam-97	147	8	categorical	categorical	ADJ
ejpam-97	147	9	closure	closure	NOUN
ejpam-97	147	10	operator	operator	NOUN
ejpam-97	147	11	from	from	ADP
ejpam-97	147	12	[	[	X
ejpam-97	147	13	3	3	NUM
ejpam-97	147	14	]	]	PUNCT
ejpam-97	147	15	.	.	PUNCT
ejpam-97	148	1	denoting	denote	VERB
ejpam-97	148	2	the	the	DET
ejpam-97	148	3	lattice	lattice	NOUN
ejpam-97	148	4	of	of	ADP
ejpam-97	148	5	all	all	DET
ejpam-97	148	6	subacts	subact	NOUN
ejpam-97	148	7	of	of	ADP
ejpam-97	148	8	an	an	DET
ejpam-97	148	9	s	s	NOUN
ejpam-97	148	10	-	-	PUNCT
ejpam-97	148	11	act	act	NOUN
ejpam-97	148	12	b	b	NUM
ejpam-97	148	13	by	by	ADP
ejpam-97	148	14	sub(b	sub(b	NOUN
ejpam-97	148	15	)	)	PUNCT
ejpam-97	148	16	,	,	PUNCT
ejpam-97	148	17	we	we	PRON
ejpam-97	148	18	have	have	VERB
ejpam-97	148	19	:	:	PUNCT
ejpam-97	148	20	definition	definition	NOUN
ejpam-97	148	21	2.3	2.3	NUM
ejpam-97	148	22	.	.	PUNCT
ejpam-97	149	1	a	a	DET
ejpam-97	149	2	family	family	NOUN
ejpam-97	149	3	c	c	NOUN
ejpam-97	149	4	=	=	SYM
ejpam-97	149	5	(	(	PUNCT
ejpam-97	149	6	cb)b∈act−s	cb)b∈act−	NOUN
ejpam-97	149	7	,	,	PUNCT
ejpam-97	149	8	with	with	ADP
ejpam-97	149	9	cb	cb	PROPN
ejpam-97	149	10	:	:	PUNCT
ejpam-97	149	11	sub(b	sub(b	X
ejpam-97	149	12	)	)	PUNCT
ejpam-97	149	13	→	→	SYM
ejpam-97	149	14	sub(b	sub(b	NOUN
ejpam-97	149	15	)	)	PUNCT
ejpam-97	149	16	,	,	PUNCT
ejpam-97	149	17	taking	take	VERB
ejpam-97	149	18	any	any	DET
ejpam-97	149	19	subact	subact	NOUN
ejpam-97	149	20	a≤	a≤	ADP
ejpam-97	149	21	b	b	X
ejpam-97	149	22	to	to	ADP
ejpam-97	149	23	a	a	DET
ejpam-97	149	24	subact	subact	NOUN
ejpam-97	149	25	cb(a	cb(a	NOUN
ejpam-97	149	26	)	)	PUNCT
ejpam-97	149	27	(	(	PUNCT
ejpam-97	149	28	or	or	CCONJ
ejpam-97	149	29	c(a	c(a	ADV
ejpam-97	149	30	)	)	PUNCT
ejpam-97	149	31	,	,	PUNCT
ejpam-97	149	32	if	if	SCONJ
ejpam-97	149	33	no	no	DET
ejpam-97	149	34	confusion	confusion	NOUN
ejpam-97	149	35	arises	arise	VERB
ejpam-97	149	36	)	)	PUNCT
ejpam-97	149	37	is	be	AUX
ejpam-97	149	38	called	call	VERB
ejpam-97	149	39	a	a	DET
ejpam-97	149	40	closure	closure	NOUN
ejpam-97	149	41	operator	operator	NOUN
ejpam-97	149	42	on	on	ADP
ejpam-97	149	43	act	act	PROPN
ejpam-97	149	44	-	-	PUNCT
ejpam-97	149	45	s	s	PRON
ejpam-97	149	46	if	if	SCONJ
ejpam-97	149	47	it	it	PRON
ejpam-97	149	48	satisfies	satisfy	VERB
ejpam-97	149	49	the	the	DET
ejpam-97	149	50	following	following	NOUN
ejpam-97	149	51	:	:	PUNCT
ejpam-97	149	52	(	(	PUNCT
ejpam-97	149	53	c1	c1	NOUN
ejpam-97	149	54	)	)	PUNCT
ejpam-97	149	55	(	(	PUNCT
ejpam-97	149	56	extension	extension	NOUN
ejpam-97	149	57	)	)	PUNCT
ejpam-97	149	58	a≤	a≤	PRON
ejpam-97	149	59	c(a	c(a	PROPN
ejpam-97	149	60	)	)	PUNCT
ejpam-97	149	61	,	,	PUNCT
ejpam-97	149	62	(	(	PUNCT
ejpam-97	149	63	c2	c2	PROPN
ejpam-97	149	64	)	)	PUNCT
ejpam-97	149	65	(	(	PUNCT
ejpam-97	149	66	monotonicity	monotonicity	NOUN
ejpam-97	149	67	)	)	PUNCT
ejpam-97	149	68	a1	a1	NOUN
ejpam-97	149	69	≤	≤	NUM
ejpam-97	149	70	a2	a2	PROPN
ejpam-97	149	71	≤	≤	PROPN
ejpam-97	149	72	b	b	PROPN
ejpam-97	149	73	implies	imply	VERB
ejpam-97	149	74	c(a1)≤	c(a1)≤	PROPN
ejpam-97	149	75	c(a2	c(a2	NOUN
ejpam-97	149	76	)	)	PUNCT
ejpam-97	149	77	,	,	PUNCT
ejpam-97	149	78	(	(	PUNCT
ejpam-97	149	79	c3	c3	PROPN
ejpam-97	149	80	)	)	PUNCT
ejpam-97	149	81	(	(	PUNCT
ejpam-97	149	82	continuity	continuity	NOUN
ejpam-97	149	83	)	)	PUNCT
ejpam-97	149	84	f	f	NOUN
ejpam-97	149	85	(	(	PUNCT
ejpam-97	149	86	cb(a))≤	cb(a))≤	PROPN
ejpam-97	149	87	cc	cc	PROPN
ejpam-97	149	88	(	(	PUNCT
ejpam-97	149	89	f	f	PROPN
ejpam-97	149	90	(	(	PUNCT
ejpam-97	149	91	a	a	NOUN
ejpam-97	149	92	)	)	PUNCT
ejpam-97	149	93	)	)	PUNCT
ejpam-97	149	94	for	for	ADP
ejpam-97	149	95	all	all	DET
ejpam-97	149	96	morphisms	morphism	NOUN
ejpam-97	149	97	f	f	NOUN
ejpam-97	149	98	:	:	PUNCT
ejpam-97	149	99	b→	b→	PROPN
ejpam-97	149	100	c	c	PROPN
ejpam-97	149	101	.	.	PUNCT
ejpam-97	150	1	now	now	ADV
ejpam-97	150	2	,	,	PUNCT
ejpam-97	150	3	one	one	PRON
ejpam-97	150	4	has	have	VERB
ejpam-97	150	5	the	the	DET
ejpam-97	150	6	usual	usual	ADJ
ejpam-97	150	7	two	two	NUM
ejpam-97	150	8	classes	class	NOUN
ejpam-97	150	9	of	of	ADP
ejpam-97	150	10	monomorphisms	monomorphism	NOUN
ejpam-97	150	11	related	relate	VERB
ejpam-97	150	12	to	to	ADP
ejpam-97	150	13	any	any	DET
ejpam-97	150	14	closure	closure	NOUN
ejpam-97	150	15	operator	operator	NOUN
ejpam-97	150	16	as	as	SCONJ
ejpam-97	150	17	follows	follow	VERB
ejpam-97	150	18	:	:	PUNCT
ejpam-97	150	19	definition	definition	NOUN
ejpam-97	150	20	2.4	2.4	NUM
ejpam-97	150	21	.	.	PUNCT
ejpam-97	151	1	let	let	VERB
ejpam-97	151	2	a	a	DET
ejpam-97	151	3	≤	≤	NUM
ejpam-97	151	4	b	b	NOUN
ejpam-97	151	5	be	be	AUX
ejpam-97	151	6	in	in	ADP
ejpam-97	151	7	act	act	PROPN
ejpam-97	151	8	-	-	PUNCT
ejpam-97	151	9	s.	s.	PROPN
ejpam-97	151	10	we	we	PRON
ejpam-97	151	11	say	say	VERB
ejpam-97	151	12	that	that	SCONJ
ejpam-97	151	13	a	a	PRON
ejpam-97	151	14	is	be	AUX
ejpam-97	151	15	c	c	NOUN
ejpam-97	151	16	-	-	PUNCT
ejpam-97	151	17	closed	closed	ADJ
ejpam-97	151	18	in	in	ADP
ejpam-97	151	19	b	b	NOUN
ejpam-97	151	20	if	if	SCONJ
ejpam-97	151	21	c(a	c(a	ADV
ejpam-97	151	22	)	)	PUNCT
ejpam-97	151	23	=	=	SYM
ejpam-97	151	24	a	a	NOUN
ejpam-97	151	25	,	,	PUNCT
ejpam-97	151	26	and	and	CCONJ
ejpam-97	151	27	it	it	PRON
ejpam-97	151	28	is	be	AUX
ejpam-97	151	29	c	c	NOUN
ejpam-97	151	30	-	-	PUNCT
ejpam-97	151	31	dense	dense	ADJ
ejpam-97	151	32	in	in	ADP
ejpam-97	151	33	b	b	NOUN
ejpam-97	151	34	if	if	SCONJ
ejpam-97	151	35	c(a	c(a	ADV
ejpam-97	151	36	)	)	PUNCT
ejpam-97	151	37	=	=	SYM
ejpam-97	151	38	b.	b.	PROPN
ejpam-97	151	39	also	also	ADV
ejpam-97	151	40	,	,	PUNCT
ejpam-97	151	41	an	an	DET
ejpam-97	151	42	s	s	NOUN
ejpam-97	151	43	-	-	PUNCT
ejpam-97	151	44	map	map	NOUN
ejpam-97	151	45	f	f	X
ejpam-97	151	46	:	:	PUNCT
ejpam-97	151	47	a→	a→	PROPN
ejpam-97	151	48	b	b	NOUN
ejpam-97	151	49	is	be	AUX
ejpam-97	151	50	said	say	VERB
ejpam-97	151	51	to	to	PART
ejpam-97	151	52	be	be	AUX
ejpam-97	151	53	c	c	NOUN
ejpam-97	151	54	-	-	PUNCT
ejpam-97	151	55	dense	dense	ADJ
ejpam-97	151	56	(	(	PUNCT
ejpam-97	151	57	c	c	NOUN
ejpam-97	151	58	-	-	PUNCT
ejpam-97	151	59	closed	closed	ADJ
ejpam-97	151	60	)	)	PUNCT
ejpam-97	151	61	if	if	SCONJ
ejpam-97	151	62	f	f	PROPN
ejpam-97	151	63	(	(	PUNCT
ejpam-97	151	64	a	a	NOUN
ejpam-97	151	65	)	)	PUNCT
ejpam-97	151	66	is	be	AUX
ejpam-97	151	67	a	a	DET
ejpam-97	151	68	c	c	NOUN
ejpam-97	151	69	-	-	PUNCT
ejpam-97	151	70	dense	dense	ADJ
ejpam-97	151	71	(	(	PUNCT
ejpam-97	151	72	c	c	NOUN
ejpam-97	151	73	-	-	PUNCT
ejpam-97	151	74	closed	closed	ADJ
ejpam-97	151	75	)	)	PUNCT
ejpam-97	151	76	subact	subact	NOUN
ejpam-97	151	77	of	of	ADP
ejpam-97	151	78	b.	b.	PROPN
ejpam-97	152	1	now	now	ADV
ejpam-97	152	2	we	we	PRON
ejpam-97	152	3	recall	recall	VERB
ejpam-97	152	4	the	the	DET
ejpam-97	152	5	following	follow	VERB
ejpam-97	152	6	closure	closure	NOUN
ejpam-97	152	7	operator	operator	NOUN
ejpam-97	152	8	needed	need	VERB
ejpam-97	152	9	in	in	ADP
ejpam-97	152	10	the	the	DET
ejpam-97	152	11	sequel	sequel	NOUN
ejpam-97	152	12	and	and	CCONJ
ejpam-97	152	13	has	have	AUX
ejpam-97	152	14	been	be	AUX
ejpam-97	152	15	studied	study	VERB
ejpam-97	152	16	in	in	ADP
ejpam-97	152	17	[	[	X
ejpam-97	152	18	4	4	NUM
ejpam-97	152	19	]	]	PUNCT
ejpam-97	152	20	and	and	CCONJ
ejpam-97	152	21	used	use	VERB
ejpam-97	152	22	in	in	ADP
ejpam-97	152	23	[	[	X
ejpam-97	152	24	6,9,14	6,9,14	NUM
ejpam-97	152	25	]	]	PUNCT
ejpam-97	152	26	to	to	PART
ejpam-97	152	27	study	study	VERB
ejpam-97	152	28	a	a	DET
ejpam-97	152	29	kind	kind	NOUN
ejpam-97	152	30	of	of	ADP
ejpam-97	152	31	injectivity	injectivity	NOUN
ejpam-97	152	32	.	.	PUNCT
ejpam-97	153	1	definition	definition	NOUN
ejpam-97	153	2	2.5	2.5	NUM
ejpam-97	153	3	.	.	PUNCT
ejpam-97	154	1	for	for	ADP
ejpam-97	154	2	any	any	DET
ejpam-97	154	3	subact	subact	NOUN
ejpam-97	154	4	a	a	PRON
ejpam-97	154	5	of	of	ADP
ejpam-97	154	6	an	an	DET
ejpam-97	154	7	s	s	NOUN
ejpam-97	154	8	-	-	PUNCT
ejpam-97	154	9	act	act	NOUN
ejpam-97	154	10	b	b	NOUN
ejpam-97	154	11	,	,	PUNCT
ejpam-97	154	12	define	define	VERB
ejpam-97	154	13	a	a	DET
ejpam-97	154	14	closure	closure	NOUN
ejpam-97	154	15	operatorcd	operatorcd	NOUN
ejpam-97	154	16	by	by	ADP
ejpam-97	154	17	cd(a	cd(a	NOUN
ejpam-97	154	18	)	)	PUNCT
ejpam-97	155	1	=	=	SYM
ejpam-97	155	2	{	{	PUNCT
ejpam-97	155	3	b	b	PROPN
ejpam-97	155	4	∈	∈	PROPN
ejpam-97	155	5	b	b	NOUN
ejpam-97	155	6	:	:	PUNCT
ejpam-97	155	7	bs	bs	PROPN
ejpam-97	155	8	⊆	⊆	X
ejpam-97	155	9	a	a	PRON
ejpam-97	155	10	}	}	PUNCT
ejpam-97	155	11	now	now	ADV
ejpam-97	155	12	,	,	PUNCT
ejpam-97	155	13	note	note	VERB
ejpam-97	155	14	that	that	SCONJ
ejpam-97	155	15	a	a	PRON
ejpam-97	155	16	is	be	AUX
ejpam-97	155	17	cd	cd	NOUN
ejpam-97	155	18	-dense	-dense	NOUN
ejpam-97	155	19	(	(	PUNCT
ejpam-97	155	20	or	or	CCONJ
ejpam-97	155	21	simply	simply	ADV
ejpam-97	155	22	s	s	NOUN
ejpam-97	155	23	-	-	PUNCT
ejpam-97	155	24	dense	dense	ADJ
ejpam-97	155	25	)	)	PUNCT
ejpam-97	155	26	in	in	ADP
ejpam-97	155	27	an	an	DET
ejpam-97	155	28	extension	extension	NOUN
ejpam-97	155	29	b	b	NOUN
ejpam-97	155	30	of	of	ADP
ejpam-97	155	31	a	a	DET
ejpam-97	155	32	if	if	SCONJ
ejpam-97	155	33	cd(a	cd(a	PRON
ejpam-97	155	34	)	)	PUNCT
ejpam-97	155	35	=	=	SYM
ejpam-97	155	36	b	b	X
ejpam-97	155	37	,	,	PUNCT
ejpam-97	155	38	that	that	ADV
ejpam-97	155	39	is	is	ADV
ejpam-97	155	40	,	,	PUNCT
ejpam-97	155	41	for	for	ADP
ejpam-97	155	42	every	every	DET
ejpam-97	155	43	b	b	PROPN
ejpam-97	155	44	∈	∈	PROPN
ejpam-97	155	45	b	b	PROPN
ejpam-97	155	46	,	,	PUNCT
ejpam-97	155	47	bs	bs	PROPN
ejpam-97	155	48	⊆	⊆	NUM
ejpam-97	155	49	a.	a.	NOUN
ejpam-97	155	50	notice	notice	NOUN
ejpam-97	155	51	that	that	SCONJ
ejpam-97	155	52	in	in	ADP
ejpam-97	155	53	the	the	DET
ejpam-97	155	54	case	case	NOUN
ejpam-97	155	55	where	where	SCONJ
ejpam-97	155	56	s	s	VERB
ejpam-97	155	57	is	be	AUX
ejpam-97	155	58	a	a	DET
ejpam-97	155	59	monoid	monoid	NOUN
ejpam-97	155	60	,	,	PUNCT
ejpam-97	155	61	cd(a	cd(a	X
ejpam-97	155	62	)	)	PUNCT
ejpam-97	155	63	=	=	SYM
ejpam-97	155	64	a	a	PRON
ejpam-97	155	65	for	for	ADP
ejpam-97	155	66	every	every	DET
ejpam-97	155	67	a	a	DET
ejpam-97	155	68	≤	≤	NUM
ejpam-97	155	69	b.	b.	NOUN
ejpam-97	155	70	so	so	ADV
ejpam-97	155	71	,	,	PUNCT
ejpam-97	155	72	it	it	PRON
ejpam-97	155	73	is	be	AUX
ejpam-97	155	74	more	more	ADV
ejpam-97	155	75	interesting	interesting	ADJ
ejpam-97	155	76	to	to	PART
ejpam-97	155	77	consider	consider	VERB
ejpam-97	155	78	the	the	DET
ejpam-97	155	79	closure	closure	NOUN
ejpam-97	155	80	operator	operator	NOUN
ejpam-97	155	81	cd	cd	NOUN
ejpam-97	155	82	only	only	ADV
ejpam-97	155	83	for	for	ADP
ejpam-97	155	84	semigroups	semigroup	NOUN
ejpam-97	155	85	,	,	PUNCT
ejpam-97	155	86	or	or	CCONJ
ejpam-97	155	87	for	for	ADP
ejpam-97	155	88	semigroup	semigroup	PROPN
ejpam-97	155	89	part	part	NOUN
ejpam-97	155	90	s	s	PROPN
ejpam-97	155	91	of	of	ADP
ejpam-97	155	92	monoids	monoid	NOUN
ejpam-97	155	93	of	of	ADP
ejpam-97	155	94	the	the	DET
ejpam-97	155	95	form	form	NOUN
ejpam-97	155	96	t	t	NOUN
ejpam-97	155	97	=	=	SYM
ejpam-97	155	98	s1	s1	PROPN
ejpam-97	155	99	.	.	PUNCT
ejpam-97	156	1	we	we	PRON
ejpam-97	156	2	now	now	ADV
ejpam-97	156	3	introduce	introduce	VERB
ejpam-97	156	4	and	and	CCONJ
ejpam-97	156	5	study	study	VERB
ejpam-97	156	6	another	another	DET
ejpam-97	156	7	closure	closure	NOUN
ejpam-97	156	8	operator	operator	NOUN
ejpam-97	156	9	on	on	ADP
ejpam-97	156	10	act	act	PROPN
ejpam-97	156	11	-	-	PUNCT
ejpam-97	156	12	s	s	PROPN
ejpam-97	156	13	which	which	PRON
ejpam-97	156	14	will	will	AUX
ejpam-97	156	15	be	be	AUX
ejpam-97	156	16	shown	show	VERB
ejpam-97	156	17	to	to	PART
ejpam-97	156	18	be	be	AUX
ejpam-97	156	19	closely	closely	ADV
ejpam-97	156	20	related	relate	VERB
ejpam-97	156	21	to	to	ADP
ejpam-97	156	22	sequential	sequential	ADJ
ejpam-97	156	23	purity	purity	NOUN
ejpam-97	156	24	.	.	PUNCT
ejpam-97	157	1	h.	h.	PROPN
ejpam-97	157	2	barzegar	barzegar	PROPN
ejpam-97	157	3	and	and	CCONJ
ejpam-97	157	4	m.m	m.m	PROPN
ejpam-97	157	5	.	.	PROPN
ejpam-97	157	6	ebrahimi	ebrahimi	PROPN
ejpam-97	157	7	/	/	SYM
ejpam-97	157	8	eur	eur	PROPN
ejpam-97	157	9	.	.	PUNCT
ejpam-97	158	1	j.	j.	PROPN
ejpam-97	158	2	pure	pure	PROPN
ejpam-97	158	3	appl	appl	PROPN
ejpam-97	158	4	.	.	PROPN
ejpam-97	158	5	math	math	PROPN
ejpam-97	158	6	,	,	PUNCT
ejpam-97	158	7	1	1	NUM
ejpam-97	158	8	(	(	PUNCT
ejpam-97	158	9	2008	2008	NUM
ejpam-97	158	10	)	)	PUNCT
ejpam-97	158	11	,	,	PUNCT
ejpam-97	158	12	(	(	PUNCT
ejpam-97	158	13	41	41	NUM
ejpam-97	158	14	-	-	SYM
ejpam-97	158	15	55	55	NUM
ejpam-97	158	16	)	)	PUNCT
ejpam-97	158	17	47	47	NUM
ejpam-97	158	18	definition	definition	NOUN
ejpam-97	158	19	2.6	2.6	NUM
ejpam-97	158	20	.	.	PUNCT
ejpam-97	159	1	the	the	DET
ejpam-97	159	2	sequential	sequential	ADJ
ejpam-97	159	3	pure	pure	ADJ
ejpam-97	159	4	closure	closure	NOUN
ejpam-97	159	5	operator	operator	NOUN
ejpam-97	159	6	c	c	PROPN
ejpam-97	159	7	p	p	NOUN
ejpam-97	159	8	on	on	ADP
ejpam-97	159	9	act	act	PROPN
ejpam-97	159	10	-	-	PUNCT
ejpam-97	159	11	s	s	PART
ejpam-97	159	12	is	be	AUX
ejpam-97	159	13	defined	define	VERB
ejpam-97	159	14	as	as	ADP
ejpam-97	159	15	c	c	PROPN
ejpam-97	159	16	p(a	p(a	PROPN
ejpam-97	159	17	)	)	PUNCT
ejpam-97	160	1	=	=	PRON
ejpam-97	160	2	{	{	PUNCT
ejpam-97	160	3	b	b	PROPN
ejpam-97	160	4	∈	∈	PROPN
ejpam-97	160	5	b	b	PROPN
ejpam-97	160	6	:	:	PUNCT
ejpam-97	160	7	∃a	∃a	NOUN
ejpam-97	160	8	∈	∈	PROPN
ejpam-97	160	9	a	a	PRON
ejpam-97	160	10	,	,	PUNCT
ejpam-97	160	11	λb	λb	NOUN
ejpam-97	160	12	=	=	PUNCT
ejpam-97	160	13	λa	λa	NOUN
ejpam-97	160	14	}	}	PUNCT
ejpam-97	160	15	where	where	SCONJ
ejpam-97	160	16	λx	λx	NOUN
ejpam-97	160	17	:	:	PUNCT
ejpam-97	160	18	s→	s→	X
ejpam-97	161	1	a	a	PRON
ejpam-97	161	2	is	be	AUX
ejpam-97	161	3	defined	define	VERB
ejpam-97	161	4	by	by	ADP
ejpam-97	161	5	λx(s	λx(s	PRON
ejpam-97	161	6	)	)	PUNCT
ejpam-97	161	7	=	=	SYM
ejpam-97	161	8	xs	xs	PROPN
ejpam-97	161	9	.	.	PUNCT
ejpam-97	162	1	now	now	ADV
ejpam-97	162	2	,	,	PUNCT
ejpam-97	162	3	note	note	VERB
ejpam-97	162	4	that	that	SCONJ
ejpam-97	162	5	a	a	PRON
ejpam-97	162	6	is	be	AUX
ejpam-97	162	7	c	c	NOUN
ejpam-97	162	8	p	p	NOUN
ejpam-97	162	9	-	-	PUNCT
ejpam-97	162	10	dense	dense	ADJ
ejpam-97	162	11	in	in	ADP
ejpam-97	162	12	an	an	DET
ejpam-97	162	13	extension	extension	NOUN
ejpam-97	162	14	b	b	NOUN
ejpam-97	162	15	of	of	ADP
ejpam-97	162	16	a	a	DET
ejpam-97	162	17	if	if	SCONJ
ejpam-97	162	18	c	c	PROPN
ejpam-97	162	19	p(a	p(a	PROPN
ejpam-97	162	20	)	)	PUNCT
ejpam-97	162	21	=	=	SYM
ejpam-97	162	22	b	b	X
ejpam-97	162	23	(	(	PUNCT
ejpam-97	162	24	this	this	PRON
ejpam-97	162	25	means	mean	VERB
ejpam-97	162	26	that	that	SCONJ
ejpam-97	162	27	for	for	ADP
ejpam-97	162	28	every	every	DET
ejpam-97	162	29	b	b	PROPN
ejpam-97	162	30	∈	∈	PROPN
ejpam-97	162	31	b	b	NOUN
ejpam-97	162	32	there	there	PRON
ejpam-97	162	33	is	be	VERB
ejpam-97	162	34	an	an	DET
ejpam-97	162	35	a	a	DET
ejpam-97	162	36	∈	∈	NOUN
ejpam-97	162	37	a	a	PRON
ejpam-97	162	38	with	with	ADP
ejpam-97	162	39	λb	λb	PROPN
ejpam-97	162	40	=	=	PUNCT
ejpam-97	162	41	λa	λa	PROPN
ejpam-97	162	42	;	;	PUNCT
ejpam-97	162	43	that	that	PRON
ejpam-97	162	44	is	is	ADV
ejpam-97	162	45	,	,	PUNCT
ejpam-97	162	46	bs	bs	NOUN
ejpam-97	162	47	=	=	PUNCT
ejpam-97	162	48	as	as	ADP
ejpam-97	162	49	for	for	ADP
ejpam-97	162	50	every	every	DET
ejpam-97	162	51	s	s	X
ejpam-97	162	52	∈	∈	PROPN
ejpam-97	162	53	s	s	NOUN
ejpam-97	162	54	)	)	PUNCT
ejpam-97	162	55	.	.	PUNCT
ejpam-97	163	1	and	and	CCONJ
ejpam-97	163	2	a	a	PRON
ejpam-97	163	3	is	be	AUX
ejpam-97	163	4	c	c	NOUN
ejpam-97	163	5	p	p	NOUN
ejpam-97	163	6	-	-	PUNCT
ejpam-97	163	7	closed	close	VERB
ejpam-97	163	8	in	in	ADP
ejpam-97	163	9	b	b	NOUN
ejpam-97	163	10	if	if	SCONJ
ejpam-97	163	11	c	c	PROPN
ejpam-97	163	12	p(a	p(a	PROPN
ejpam-97	163	13	)	)	PUNCT
ejpam-97	163	14	=	=	SYM
ejpam-97	164	1	a	a	PRON
ejpam-97	164	2	(	(	PUNCT
ejpam-97	164	3	that	that	PRON
ejpam-97	164	4	is	is	ADV
ejpam-97	164	5	,	,	PUNCT
ejpam-97	164	6	for	for	ADP
ejpam-97	164	7	every	every	DET
ejpam-97	164	8	b	b	PROPN
ejpam-97	164	9	∈	∈	PROPN
ejpam-97	164	10	b−	b−	NOUN
ejpam-97	164	11	a	a	NOUN
ejpam-97	164	12	and	and	CCONJ
ejpam-97	164	13	a	a	DET
ejpam-97	164	14	∈	∈	NOUN
ejpam-97	164	15	a	a	PRON
ejpam-97	164	16	there	there	PRON
ejpam-97	164	17	is	be	VERB
ejpam-97	164	18	an	an	DET
ejpam-97	164	19	s	s	X
ejpam-97	164	20	∈	∈	NOUN
ejpam-97	164	21	s	s	NOUN
ejpam-97	164	22	with	with	ADP
ejpam-97	164	23	bs	bs	NOUN
ejpam-97	164	24	6=	6=	PROPN
ejpam-97	164	25	as	as	ADP
ejpam-97	164	26	)	)	PUNCT
ejpam-97	164	27	.	.	PUNCT
ejpam-97	165	1	notice	notice	VERB
ejpam-97	165	2	that	that	SCONJ
ejpam-97	165	3	c	c	PROPN
ejpam-97	165	4	p	p	NOUN
ejpam-97	165	5	-	-	PUNCT
ejpam-97	165	6	closedness	closedness	NOUN
ejpam-97	165	7	is	be	AUX
ejpam-97	165	8	preserved	preserve	VERB
ejpam-97	165	9	by	by	ADP
ejpam-97	165	10	inverse	inverse	NOUN
ejpam-97	165	11	image	image	NOUN
ejpam-97	165	12	of	of	ADP
ejpam-97	165	13	s	s	NOUN
ejpam-97	165	14	-	-	PUNCT
ejpam-97	165	15	maps	map	NOUN
ejpam-97	165	16	and	and	CCONJ
ejpam-97	165	17	c	c	NOUN
ejpam-97	165	18	p	p	NOUN
ejpam-97	165	19	-	-	PUNCT
ejpam-97	165	20	denseness	denseness	NOUN
ejpam-97	165	21	is	be	AUX
ejpam-97	165	22	preserved	preserve	VERB
ejpam-97	165	23	by	by	ADP
ejpam-97	165	24	images	image	NOUN
ejpam-97	165	25	of	of	ADP
ejpam-97	165	26	onto	onto	ADP
ejpam-97	165	27	s	s	NOUN
ejpam-97	165	28	-	-	NOUN
ejpam-97	165	29	maps	map	NOUN
ejpam-97	165	30	.	.	PUNCT
ejpam-97	166	1	some	some	DET
ejpam-97	166	2	easily	easily	ADV
ejpam-97	166	3	proved	prove	VERB
ejpam-97	166	4	properties	property	NOUN
ejpam-97	166	5	of	of	ADP
ejpam-97	166	6	this	this	DET
ejpam-97	166	7	last	last	ADJ
ejpam-97	166	8	closure	closure	NOUN
ejpam-97	166	9	operator	operator	NOUN
ejpam-97	166	10	is	be	AUX
ejpam-97	166	11	stated	state	VERB
ejpam-97	166	12	in	in	ADP
ejpam-97	166	13	the	the	DET
ejpam-97	166	14	following	following	NOUN
ejpam-97	166	15	:	:	PUNCT
ejpam-97	166	16	lemma	lemma	PROPN
ejpam-97	166	17	2.2	2.2	NUM
ejpam-97	166	18	.	.	PUNCT
ejpam-97	167	1	c	c	PROPN
ejpam-97	167	2	p	p	NOUN
ejpam-97	167	3	is	be	AUX
ejpam-97	167	4	:	:	PUNCT
ejpam-97	167	5	(	(	PUNCT
ejpam-97	167	6	1	1	X
ejpam-97	167	7	)	)	PUNCT
ejpam-97	167	8	a	a	DET
ejpam-97	167	9	closure	closure	NOUN
ejpam-97	167	10	operator	operator	NOUN
ejpam-97	167	11	,	,	PUNCT
ejpam-97	167	12	(	(	PUNCT
ejpam-97	167	13	2	2	X
ejpam-97	167	14	)	)	PUNCT
ejpam-97	167	15	idempotent	idempotent	NOUN
ejpam-97	167	16	,	,	PUNCT
ejpam-97	167	17	(	(	PUNCT
ejpam-97	167	18	3	3	X
ejpam-97	167	19	)	)	PUNCT
ejpam-97	167	20	hereditary	hereditary	NOUN
ejpam-97	167	21	;	;	PUNCT
ejpam-97	167	22	for	for	ADP
ejpam-97	167	23	c	c	NOUN
ejpam-97	167	24	≤	≤	NOUN
ejpam-97	167	25	a	a	DET
ejpam-97	167	26	≤	≤	NUM
ejpam-97	167	27	b	b	NUM
ejpam-97	167	28	,	,	PUNCT
ejpam-97	167	29	c	c	PROPN
ejpam-97	167	30	p	p	PROPN
ejpam-97	167	31	b	b	PROPN
ejpam-97	167	32	(	(	PUNCT
ejpam-97	167	33	a	a	NOUN
ejpam-97	167	34	)	)	PUNCT
ejpam-97	167	35	=	=	PUNCT
ejpam-97	168	1	c	c	PROPN
ejpam-97	168	2	p	p	PROPN
ejpam-97	168	3	b	b	PROPN
ejpam-97	168	4	(	(	PUNCT
ejpam-97	168	5	c	c	NOUN
ejpam-97	168	6	)	)	PUNCT
ejpam-97	168	7	∩	∩	PROPN
ejpam-97	168	8	a	a	X
ejpam-97	168	9	,	,	PUNCT
ejpam-97	168	10	(	(	PUNCT
ejpam-97	168	11	4	4	X
ejpam-97	168	12	)	)	PUNCT
ejpam-97	168	13	weakly	weakly	ADV
ejpam-97	168	14	hereditary	hereditary	ADJ
ejpam-97	168	15	;	;	PUNCT
ejpam-97	168	16	every	every	DET
ejpam-97	168	17	a	a	DET
ejpam-97	168	18	≤	≤	NUM
ejpam-97	168	19	b	b	NOUN
ejpam-97	168	20	is	be	AUX
ejpam-97	168	21	c	c	NOUN
ejpam-97	168	22	p	p	NOUN
ejpam-97	168	23	-	-	PUNCT
ejpam-97	168	24	dense	dense	ADJ
ejpam-97	168	25	in	in	ADP
ejpam-97	168	26	c	c	PROPN
ejpam-97	168	27	p	p	PROPN
ejpam-97	168	28	b	b	PROPN
ejpam-97	168	29	(	(	PUNCT
ejpam-97	168	30	a	a	NOUN
ejpam-97	168	31	)	)	PUNCT
ejpam-97	168	32	,	,	PUNCT
ejpam-97	168	33	(	(	PUNCT
ejpam-97	168	34	5	5	X
ejpam-97	168	35	)	)	PUNCT
ejpam-97	168	36	grounded	ground	VERB
ejpam-97	168	37	;	;	PUNCT
ejpam-97	168	38	c	c	PROPN
ejpam-97	168	39	p	p	X
ejpam-97	168	40	(;	(;	X
ejpam-97	168	41	)	)	PUNCT
ejpam-97	168	42	=	=	SYM
ejpam-97	169	1	;	;	PUNCT
ejpam-97	169	2	,	,	PUNCT
ejpam-97	169	3	(	(	PUNCT
ejpam-97	169	4	6	6	X
ejpam-97	169	5	)	)	PUNCT
ejpam-97	169	6	additive	additive	NOUN
ejpam-97	169	7	;	;	PUNCT
ejpam-97	169	8	c	c	PROPN
ejpam-97	169	9	p(a∪c	p(a∪c	PROPN
ejpam-97	169	10	)	)	PUNCT
ejpam-97	170	1	=	=	PUNCT
ejpam-97	171	1	c	c	NOUN
ejpam-97	171	2	p(a)∪c	p(a)∪c	VERB
ejpam-97	171	3	p(c	p(c	NOUN
ejpam-97	171	4	)	)	PUNCT
ejpam-97	171	5	,	,	PUNCT
ejpam-97	171	6	(	(	PUNCT
ejpam-97	171	7	7	7	X
ejpam-97	171	8	)	)	PUNCT
ejpam-97	171	9	fully	fully	ADV
ejpam-97	171	10	additive	additive	ADJ
ejpam-97	171	11	;	;	PUNCT
ejpam-97	171	12	c	c	PROPN
ejpam-97	171	13	p	p	X
ejpam-97	171	14	(	(	PUNCT
ejpam-97	171	15	⋃	⋃	PROPN
ejpam-97	171	16	i∈i	i∈i	ADJ
ejpam-97	171	17	ai	ai	VERB
ejpam-97	171	18	)	)	PUNCT
ejpam-97	172	1	=	=	PUNCT
ejpam-97	172	2	⋃	⋃	ADP
ejpam-97	172	3	i∈i	i∈i	NOUN
ejpam-97	172	4	c	c	NOUN
ejpam-97	172	5	p(ai	p(ai	NOUN
ejpam-97	172	6	)	)	PUNCT
ejpam-97	172	7	,	,	PUNCT
ejpam-97	172	8	(	(	PUNCT
ejpam-97	172	9	8)	8)	NUM
ejpam-97	172	10	c	c	NOUN
ejpam-97	172	11	p	p	NOUN
ejpam-97	172	12	a	a	PRON
ejpam-97	172	13	(	(	PUNCT
ejpam-97	172	14	⋂	⋂	PROPN
ejpam-97	172	15	ai	ai	NOUN
ejpam-97	172	16	)	)	PUNCT
ejpam-97	172	17	⊆	⊆	NUM
ejpam-97	172	18	⋂	⋂	PROPN
ejpam-97	172	19	c	c	NOUN
ejpam-97	172	20	p	p	NOUN
ejpam-97	172	21	a	a	DET
ejpam-97	172	22	(	(	PUNCT
ejpam-97	172	23	ai	ai	NOUN
ejpam-97	172	24	)	)	PUNCT
ejpam-97	172	25	,	,	PUNCT
ejpam-97	172	26	(	(	PUNCT
ejpam-97	172	27	9	9	X
ejpam-97	172	28	)	)	PUNCT
ejpam-97	172	29	productive	productive	NOUN
ejpam-97	172	30	;	;	PUNCT
ejpam-97	172	31	for	for	ADP
ejpam-97	172	32	every	every	DET
ejpam-97	172	33	family	family	NOUN
ejpam-97	172	34	of	of	ADP
ejpam-97	172	35	subacts	subact	NOUN
ejpam-97	172	36	ai	ai	VERB
ejpam-97	172	37	of	of	ADP
ejpam-97	172	38	bi	bi	NOUN
ejpam-97	172	39	,	,	PUNCT
ejpam-97	172	40	taking	take	VERB
ejpam-97	172	41	a=	a=	ADV
ejpam-97	172	42	∏	∏	X
ejpam-97	173	1	i	i	PRON
ejpam-97	173	2	ai	ai	VERB
ejpam-97	173	3	and	and	CCONJ
ejpam-97	173	4	b	b	X
ejpam-97	173	5	=	=	SYM
ejpam-97	173	6	∏	∏	PROPN
ejpam-97	174	1	i	i	NOUN
ejpam-97	174	2	bi	bi	NOUN
ejpam-97	174	3	,	,	PUNCT
ejpam-97	174	4	c	c	PROPN
ejpam-97	174	5	p	p	PROPN
ejpam-97	174	6	b	b	PROPN
ejpam-97	174	7	(	(	PUNCT
ejpam-97	174	8	a	a	NOUN
ejpam-97	174	9	)	)	PUNCT
ejpam-97	174	10	=	=	SYM
ejpam-97	174	11	∏	∏	NUM
ejpam-97	175	1	i	i	INTJ
ejpam-97	175	2	c	c	NOUN
ejpam-97	176	1	p	p	ADJ
ejpam-97	176	2	bi	bi	NOUN
ejpam-97	176	3	(	(	PUNCT
ejpam-97	176	4	ai	ai	NOUN
ejpam-97	176	5	)	)	PUNCT
ejpam-97	176	6	.	.	PUNCT
ejpam-97	177	1	and	and	CCONJ
ejpam-97	177	2	,	,	PUNCT
ejpam-97	177	3	some	some	PRON
ejpam-97	177	4	of	of	ADP
ejpam-97	177	5	the	the	DET
ejpam-97	177	6	properties	property	NOUN
ejpam-97	177	7	that	that	PRON
ejpam-97	177	8	c	c	PROPN
ejpam-97	177	9	p	p	NOUN
ejpam-97	177	10	does	do	AUX
ejpam-97	177	11	not	not	PART
ejpam-97	177	12	satisfy	satisfy	VERB
ejpam-97	177	13	in	in	ADP
ejpam-97	177	14	general	general	ADJ
ejpam-97	177	15	are	be	AUX
ejpam-97	177	16	:	:	PUNCT
ejpam-97	177	17	lemma	lemma	PROPN
ejpam-97	177	18	2.3	2.3	NUM
ejpam-97	177	19	.	.	PUNCT
ejpam-97	178	1	for	for	ADP
ejpam-97	178	2	any	any	DET
ejpam-97	178	3	semigroup	semigroup	NOUN
ejpam-97	178	4	s	s	NOUN
ejpam-97	178	5	,	,	PUNCT
ejpam-97	178	6	c	c	PROPN
ejpam-97	178	7	p	p	NOUN
ejpam-97	178	8	is	be	AUX
ejpam-97	178	9	not	not	PART
ejpam-97	178	10	:	:	PUNCT
ejpam-97	178	11	(	(	PUNCT
ejpam-97	178	12	1	1	X
ejpam-97	178	13	)	)	PUNCT
ejpam-97	178	14	discrete	discrete	NOUN
ejpam-97	178	15	;	;	PUNCT
ejpam-97	178	16	c	c	PROPN
ejpam-97	178	17	p	p	PROPN
ejpam-97	178	18	b	b	PROPN
ejpam-97	178	19	(	(	PUNCT
ejpam-97	178	20	a	a	NOUN
ejpam-97	178	21	)	)	PUNCT
ejpam-97	178	22	=	=	NOUN
ejpam-97	178	23	a	a	PRON
ejpam-97	178	24	for	for	ADP
ejpam-97	178	25	every	every	DET
ejpam-97	178	26	s	s	NOUN
ejpam-97	178	27	-	-	PUNCT
ejpam-97	178	28	act	act	NOUN
ejpam-97	178	29	b	b	NOUN
ejpam-97	178	30	and	and	CCONJ
ejpam-97	178	31	every	every	DET
ejpam-97	178	32	a	a	DET
ejpam-97	178	33	≤	≤	NUM
ejpam-97	178	34	a	a	PRON
ejpam-97	178	35	,	,	PUNCT
ejpam-97	178	36	(	(	PUNCT
ejpam-97	178	37	2	2	NUM
ejpam-97	178	38	)	)	PUNCT
ejpam-97	178	39	trivial	trivial	ADJ
ejpam-97	178	40	;	;	PUNCT
ejpam-97	178	41	c	c	PROPN
ejpam-97	178	42	p	p	PROPN
ejpam-97	178	43	b	b	PROPN
ejpam-97	178	44	(	(	PUNCT
ejpam-97	178	45	a	a	NOUN
ejpam-97	178	46	)	)	PUNCT
ejpam-97	178	47	=	=	SYM
ejpam-97	178	48	b	b	NOUN
ejpam-97	178	49	for	for	ADP
ejpam-97	178	50	every	every	DET
ejpam-97	178	51	b	b	NOUN
ejpam-97	178	52	and	and	CCONJ
ejpam-97	178	53	every	every	DET
ejpam-97	178	54	a	a	DET
ejpam-97	178	55	≤	≤	NUM
ejpam-97	178	56	b	b	NOUN
ejpam-97	178	57	,	,	PUNCT
ejpam-97	178	58	(	(	PUNCT
ejpam-97	178	59	3	3	X
ejpam-97	178	60	)	)	PUNCT
ejpam-97	178	61	minimal	minimal	ADJ
ejpam-97	178	62	;	;	PUNCT
ejpam-97	178	63	for	for	ADP
ejpam-97	178	64	c	c	NOUN
ejpam-97	178	65	≤	≤	NOUN
ejpam-97	178	66	a	a	DET
ejpam-97	178	67	≤	≤	NUM
ejpam-97	178	68	b	b	NUM
ejpam-97	178	69	,	,	PUNCT
ejpam-97	178	70	c	c	PROPN
ejpam-97	178	71	p	p	PROPN
ejpam-97	178	72	b	b	PROPN
ejpam-97	178	73	(	(	PUNCT
ejpam-97	178	74	a	a	NOUN
ejpam-97	178	75	)	)	PUNCT
ejpam-97	178	76	=	=	PUNCT
ejpam-97	179	1	a∪	a∪	ADP
ejpam-97	179	2	c	c	NOUN
ejpam-97	179	3	p	p	PROPN
ejpam-97	179	4	b	b	PROPN
ejpam-97	179	5	(	(	PUNCT
ejpam-97	179	6	c	c	NOUN
ejpam-97	179	7	)	)	PUNCT
ejpam-97	179	8	.	.	PUNCT
ejpam-97	180	1	proof	proof	NOUN
ejpam-97	180	2	.	.	PUNCT
ejpam-97	181	1	let	let	VERB
ejpam-97	181	2	0	0	NUM
ejpam-97	181	3	∈	∈	PROPN
ejpam-97	181	4	a	a	DET
ejpam-97	181	5	be	be	AUX
ejpam-97	181	6	a	a	DET
ejpam-97	181	7	fixed	fix	VERB
ejpam-97	181	8	element	element	NOUN
ejpam-97	181	9	of	of	ADP
ejpam-97	181	10	a	a	PRON
ejpam-97	181	11	,	,	PUNCT
ejpam-97	181	12	and	and	CCONJ
ejpam-97	181	13	adjoin	adjoin	VERB
ejpam-97	181	14	two	two	NUM
ejpam-97	181	15	elements	element	NOUN
ejpam-97	181	16	θ	θ	PROPN
ejpam-97	181	17	,	,	PUNCT
ejpam-97	181	18	ω	ω	NUM
ejpam-97	181	19	to	to	ADP
ejpam-97	181	20	a	a	PRON
ejpam-97	181	21	with	with	ADP
ejpam-97	181	22	actions	action	NOUN
ejpam-97	181	23	ωs	ωs	PRON
ejpam-97	181	24	=	=	PROPN
ejpam-97	181	25	ω	ω	PROPN
ejpam-97	181	26	and	and	CCONJ
ejpam-97	181	27	θ	θ	PROPN
ejpam-97	181	28	s	s	PART
ejpam-97	181	29	=	=	ADJ
ejpam-97	181	30	0	0	PROPN
ejpam-97	181	31	.	.	PUNCT
ejpam-97	182	1	then	then	ADV
ejpam-97	182	2	c	c	PROPN
ejpam-97	182	3	p	p	PROPN
ejpam-97	182	4	b	b	PROPN
ejpam-97	182	5	(	(	PUNCT
ejpam-97	182	6	a	a	NOUN
ejpam-97	182	7	)	)	PUNCT
ejpam-97	182	8	=	=	SYM
ejpam-97	182	9	a∪{θ	a∪{θ	NOUN
ejpam-97	182	10	}	}	PUNCT
ejpam-97	182	11	where	where	SCONJ
ejpam-97	182	12	b	b	X
ejpam-97	182	13	=	=	SYM
ejpam-97	182	14	a∪	a∪	PROPN
ejpam-97	182	15	{	{	PUNCT
ejpam-97	182	16	θ	θ	PROPN
ejpam-97	182	17	,	,	PUNCT
ejpam-97	182	18	ω	ω	NOUN
ejpam-97	182	19	}	}	PUNCT
ejpam-97	182	20	.	.	PUNCT
ejpam-97	183	1	hence	hence	ADV
ejpam-97	183	2	c	c	PROPN
ejpam-97	183	3	p	p	NOUN
ejpam-97	183	4	is	be	AUX
ejpam-97	183	5	neither	neither	CCONJ
ejpam-97	183	6	discrete	discrete	ADJ
ejpam-97	183	7	nor	nor	CCONJ
ejpam-97	183	8	trivial	trivial	ADJ
ejpam-97	183	9	.	.	PUNCT
ejpam-97	184	1	also	also	ADV
ejpam-97	184	2	,	,	PUNCT
ejpam-97	184	3	it	it	PRON
ejpam-97	184	4	is	be	AUX
ejpam-97	184	5	not	not	PART
ejpam-97	184	6	minimal	minimal	ADJ
ejpam-97	184	7	.	.	PUNCT
ejpam-97	185	1	because	because	SCONJ
ejpam-97	185	2	,	,	PUNCT
ejpam-97	185	3	adjoining	adjoin	VERB
ejpam-97	185	4	two	two	NUM
ejpam-97	185	5	elements	element	NOUN
ejpam-97	185	6	θ	θ	PROPN
ejpam-97	185	7	,	,	PUNCT
ejpam-97	185	8	ω	ω	PROPN
ejpam-97	185	9	to	to	ADP
ejpam-97	185	10	an	an	DET
ejpam-97	185	11	s	s	NOUN
ejpam-97	185	12	-	-	PUNCT
ejpam-97	185	13	act	act	NOUN
ejpam-97	185	14	c	c	PROPN
ejpam-97	185	15	with	with	ADP
ejpam-97	185	16	actions	action	NOUN
ejpam-97	185	17	ωs	ωs	PRON
ejpam-97	185	18	=	=	SYM
ejpam-97	185	19	θ	θ	PROPN
ejpam-97	185	20	and	and	CCONJ
ejpam-97	185	21	θ	θ	PROPN
ejpam-97	185	22	s	s	PART
ejpam-97	185	23	=	=	SYM
ejpam-97	185	24	θ	θ	PROPN
ejpam-97	185	25	,	,	PUNCT
ejpam-97	185	26	and	and	CCONJ
ejpam-97	185	27	taking	take	VERB
ejpam-97	185	28	a=	a=	PROPN
ejpam-97	185	29	c	c	X
ejpam-97	185	30	∪	∪	X
ejpam-97	185	31	{	{	PUNCT
ejpam-97	185	32	θ	θ	NOUN
ejpam-97	185	33	}	}	PUNCT
ejpam-97	185	34	,	,	PUNCT
ejpam-97	185	35	b	b	X
ejpam-97	185	36	=	=	SYM
ejpam-97	185	37	c	c	NOUN
ejpam-97	185	38	∪	∪	X
ejpam-97	185	39	{	{	PUNCT
ejpam-97	185	40	θ	θ	PROPN
ejpam-97	185	41	,	,	PUNCT
ejpam-97	185	42	ω	ω	PROPN
ejpam-97	185	43	}	}	PUNCT
ejpam-97	185	44	,	,	PUNCT
ejpam-97	185	45	we	we	PRON
ejpam-97	185	46	get	get	VERB
ejpam-97	185	47	c	c	NOUN
ejpam-97	185	48	⊂	⊂	X
ejpam-97	185	49	a⊂	a⊂	NOUN
ejpam-97	185	50	b	b	NOUN
ejpam-97	185	51	,	,	PUNCT
ejpam-97	185	52	and	and	CCONJ
ejpam-97	185	53	c	c	PROPN
ejpam-97	185	54	p	p	PROPN
ejpam-97	185	55	b	b	PROPN
ejpam-97	185	56	(	(	PUNCT
ejpam-97	185	57	a	a	NOUN
ejpam-97	185	58	)	)	PUNCT
ejpam-97	185	59	=	=	SYM
ejpam-97	185	60	b	b	NOUN
ejpam-97	186	1	while	while	SCONJ
ejpam-97	186	2	c	c	PROPN
ejpam-97	186	3	p	p	PROPN
ejpam-97	186	4	b	b	PROPN
ejpam-97	186	5	(	(	PUNCT
ejpam-97	186	6	c	c	NOUN
ejpam-97	186	7	)	)	PUNCT
ejpam-97	186	8	=	=	SYM
ejpam-97	186	9	c	c	NOUN
ejpam-97	186	10	.	.	PUNCT
ejpam-97	187	1	another	another	DET
ejpam-97	187	2	monomorphism	monomorphism	NOUN
ejpam-97	187	3	which	which	PRON
ejpam-97	187	4	corresponds	correspond	VERB
ejpam-97	187	5	to	to	ADP
ejpam-97	187	6	this	this	DET
ejpam-97	187	7	closure	closure	NOUN
ejpam-97	187	8	operator	operator	NOUN
ejpam-97	187	9	,	,	PUNCT
ejpam-97	187	10	and	and	CCONJ
ejpam-97	187	11	is	be	AUX
ejpam-97	187	12	of	of	ADP
ejpam-97	187	13	main	main	ADJ
ejpam-97	187	14	interest	interest	NOUN
ejpam-97	187	15	in	in	ADP
ejpam-97	187	16	this	this	DET
ejpam-97	187	17	paper	paper	NOUN
ejpam-97	187	18	,	,	PUNCT
ejpam-97	187	19	is	be	AUX
ejpam-97	187	20	defined	define	VERB
ejpam-97	187	21	as	as	SCONJ
ejpam-97	187	22	follows	follow	VERB
ejpam-97	187	23	:	:	PUNCT
ejpam-97	187	24	definition	definition	NOUN
ejpam-97	187	25	2.7	2.7	NUM
ejpam-97	187	26	.	.	PUNCT
ejpam-97	188	1	an	an	DET
ejpam-97	188	2	s	s	NOUN
ejpam-97	188	3	-	-	PUNCT
ejpam-97	188	4	act	act	NOUN
ejpam-97	188	5	a	a	PRON
ejpam-97	188	6	is	be	AUX
ejpam-97	188	7	said	say	VERB
ejpam-97	188	8	to	to	PART
ejpam-97	188	9	be	be	AUX
ejpam-97	188	10	c	c	NOUN
ejpam-97	188	11	p	p	NOUN
ejpam-97	188	12	-	-	PUNCT
ejpam-97	188	13	pure	pure	ADJ
ejpam-97	188	14	in	in	ADP
ejpam-97	188	15	an	an	DET
ejpam-97	188	16	extension	extension	NOUN
ejpam-97	188	17	b	b	NOUN
ejpam-97	188	18	of	of	ADP
ejpam-97	188	19	a	a	DET
ejpam-97	188	20	if	if	SCONJ
ejpam-97	188	21	c	c	PROPN
ejpam-97	188	22	p(a	p(a	PROPN
ejpam-97	188	23	)	)	PUNCT
ejpam-97	188	24	=	=	PUNCT
ejpam-97	188	25	cd(a	cd(a	PROPN
ejpam-97	188	26	)	)	PUNCT
ejpam-97	188	27	.	.	PUNCT
ejpam-97	189	1	remark	remark	PROPN
ejpam-97	189	2	2.2	2.2	NUM
ejpam-97	189	3	.	.	PUNCT
ejpam-97	190	1	let	let	VERB
ejpam-97	190	2	ai	ai	AUX
ejpam-97	190	3	be	be	AUX
ejpam-97	190	4	a	a	DET
ejpam-97	190	5	family	family	NOUN
ejpam-97	190	6	of	of	ADP
ejpam-97	190	7	subacts	subact	NOUN
ejpam-97	190	8	of	of	ADP
ejpam-97	190	9	a	a	DET
ejpam-97	190	10	,	,	PUNCT
ejpam-97	190	11	(	(	PUNCT
ejpam-97	190	12	1	1	X
ejpam-97	190	13	)	)	PUNCT
ejpam-97	190	14	if	if	SCONJ
ejpam-97	190	15	⋂	⋂	PROPN
ejpam-97	190	16	ai	ai	VERB
ejpam-97	190	17	is	be	AUX
ejpam-97	190	18	s	s	NOUN
ejpam-97	190	19	-	-	ADJ
ejpam-97	190	20	pure	pure	ADJ
ejpam-97	190	21	in	in	ADP
ejpam-97	190	22	a	a	DET
ejpam-97	190	23	then	then	ADV
ejpam-97	191	1	c	c	PROPN
ejpam-97	191	2	p	p	PROPN
ejpam-97	191	3	a	a	PRON
ejpam-97	191	4	(	(	PUNCT
ejpam-97	191	5	⋂	⋂	PROPN
ejpam-97	191	6	ai	ai	NOUN
ejpam-97	191	7	)	)	PUNCT
ejpam-97	191	8	=	=	SYM
ejpam-97	192	1	⋂	⋂	PROPN
ejpam-97	192	2	c	c	NOUN
ejpam-97	192	3	p	p	NOUN
ejpam-97	192	4	a	a	DET
ejpam-97	192	5	(	(	PUNCT
ejpam-97	192	6	ai	ai	NOUN
ejpam-97	192	7	)	)	PUNCT
ejpam-97	192	8	.	.	PUNCT
ejpam-97	193	1	(	(	PUNCT
ejpam-97	193	2	2	2	X
ejpam-97	193	3	)	)	PUNCT
ejpam-97	193	4	if	if	SCONJ
ejpam-97	193	5	for	for	ADP
ejpam-97	193	6	every	every	DET
ejpam-97	193	7	i	i	NOUN
ejpam-97	193	8	∈	∈	PROPN
ejpam-97	194	1	i	i	PRON
ejpam-97	194	2	,	,	PUNCT
ejpam-97	194	3	ai	ai	VERB
ejpam-97	194	4	is	be	AUX
ejpam-97	194	5	s	s	NOUN
ejpam-97	194	6	-	-	ADJ
ejpam-97	194	7	pure	pure	ADJ
ejpam-97	194	8	in	in	ADP
ejpam-97	194	9	a	a	PRON
ejpam-97	194	10	and	and	CCONJ
ejpam-97	194	11	c	c	NOUN
ejpam-97	194	12	p	p	NOUN
ejpam-97	194	13	a	a	PRON
ejpam-97	194	14	(	(	PUNCT
ejpam-97	194	15	⋂	⋂	PROPN
ejpam-97	194	16	ai	ai	NOUN
ejpam-97	194	17	)	)	PUNCT
ejpam-97	194	18	=	=	SYM
ejpam-97	195	1	⋂	⋂	PROPN
ejpam-97	195	2	c	c	NOUN
ejpam-97	195	3	p	p	NOUN
ejpam-97	195	4	a	a	DET
ejpam-97	195	5	(	(	PUNCT
ejpam-97	195	6	ai	ai	NOUN
ejpam-97	195	7	)	)	PUNCT
ejpam-97	195	8	then	then	ADV
ejpam-97	195	9	⋂	⋂	PROPN
ejpam-97	195	10	ai	ai	VERB
ejpam-97	195	11	is	be	AUX
ejpam-97	195	12	s	s	NOUN
ejpam-97	195	13	-	-	ADJ
ejpam-97	195	14	pure	pure	ADJ
ejpam-97	195	15	in	in	ADP
ejpam-97	195	16	a.	a.	NOUN
ejpam-97	195	17	note	note	NOUN
ejpam-97	195	18	2.2	2.2	NUM
ejpam-97	195	19	.	.	PUNCT
ejpam-97	196	1	for	for	ADP
ejpam-97	196	2	a	a	DET
ejpam-97	196	3	≤	≤	NUM
ejpam-97	196	4	b	b	NOUN
ejpam-97	196	5	,	,	PUNCT
ejpam-97	196	6	we	we	PRON
ejpam-97	196	7	have	have	VERB
ejpam-97	196	8	a	a	DET
ejpam-97	196	9	≤	≤	NUM
ejpam-97	196	10	c	c	NOUN
ejpam-97	196	11	p(a	p(a	NOUN
ejpam-97	196	12	)	)	PUNCT
ejpam-97	196	13	≤	≤	NOUN
ejpam-97	196	14	cd(a	cd(a	PRON
ejpam-97	196	15	)	)	PUNCT
ejpam-97	196	16	≤	≤	NUM
ejpam-97	196	17	b.	b.	PROPN
ejpam-97	197	1	so	so	ADV
ejpam-97	197	2	,	,	PUNCT
ejpam-97	197	3	if	if	SCONJ
ejpam-97	197	4	a	a	PRON
ejpam-97	197	5	is	be	AUX
ejpam-97	197	6	c	c	NOUN
ejpam-97	197	7	p	p	NOUN
ejpam-97	197	8	-	-	PUNCT
ejpam-97	197	9	dense	dense	ADJ
ejpam-97	197	10	in	in	ADP
ejpam-97	197	11	b	b	NOUN
ejpam-97	197	12	,	,	PUNCT
ejpam-97	197	13	then	then	ADV
ejpam-97	197	14	c	c	PROPN
ejpam-97	197	15	p(a	p(a	PROPN
ejpam-97	197	16	)	)	PUNCT
ejpam-97	197	17	=	=	PUNCT
ejpam-97	197	18	cd(a	cd(a	X
ejpam-97	197	19	)	)	PUNCT
ejpam-97	198	1	=	=	SYM
ejpam-97	198	2	b	b	PROPN
ejpam-97	198	3	and	and	CCONJ
ejpam-97	198	4	so	so	ADV
ejpam-97	198	5	a	a	PRON
ejpam-97	198	6	is	be	AUX
ejpam-97	198	7	cd	cd	NOUN
ejpam-97	198	8	-dense	-dense	NOUN
ejpam-97	198	9	as	as	ADV
ejpam-97	198	10	well	well	ADV
ejpam-97	198	11	as	as	ADP
ejpam-97	198	12	c	c	NOUN
ejpam-97	198	13	p	p	NOUN
ejpam-97	198	14	-	-	PUNCT
ejpam-97	198	15	pure	pure	ADJ
ejpam-97	198	16	.	.	PUNCT
ejpam-97	199	1	similarly	similarly	ADV
ejpam-97	199	2	,	,	PUNCT
ejpam-97	199	3	if	if	SCONJ
ejpam-97	199	4	a	a	PRON
ejpam-97	199	5	is	is	ADV
ejpam-97	199	6	cd	cd	NOUN
ejpam-97	199	7	-closed	-close	VERB
ejpam-97	199	8	in	in	ADP
ejpam-97	199	9	b	b	NOUN
ejpam-97	199	10	,	,	PUNCT
ejpam-97	199	11	then	then	ADV
ejpam-97	199	12	a=	a=	PROPN
ejpam-97	199	13	c	c	X
ejpam-97	199	14	p(a	p(a	PROPN
ejpam-97	199	15	)	)	PUNCT
ejpam-97	199	16	=	=	PUNCT
ejpam-97	199	17	cd(a	cd(a	X
ejpam-97	199	18	)	)	PUNCT
ejpam-97	199	19	and	and	CCONJ
ejpam-97	199	20	hence	hence	ADV
ejpam-97	199	21	a	a	PRON
ejpam-97	199	22	is	be	AUX
ejpam-97	199	23	c	c	NOUN
ejpam-97	199	24	p	p	NOUN
ejpam-97	199	25	-	-	PUNCT
ejpam-97	199	26	closed	close	VERB
ejpam-97	199	27	as	as	ADV
ejpam-97	199	28	well	well	ADV
ejpam-97	199	29	as	as	ADP
ejpam-97	199	30	c	c	NOUN
ejpam-97	199	31	p	p	NOUN
ejpam-97	199	32	-	-	PUNCT
ejpam-97	199	33	pure	pure	ADJ
ejpam-97	199	34	.	.	PUNCT
ejpam-97	200	1	the	the	DET
ejpam-97	200	2	following	follow	VERB
ejpam-97	200	3	result	result	NOUN
ejpam-97	200	4	,	,	PUNCT
ejpam-97	200	5	the	the	DET
ejpam-97	200	6	proof	proof	NOUN
ejpam-97	200	7	of	of	ADP
ejpam-97	200	8	which	which	PRON
ejpam-97	200	9	is	be	AUX
ejpam-97	200	10	straightforward	straightforward	ADJ
ejpam-97	200	11	,	,	PUNCT
ejpam-97	200	12	is	be	AUX
ejpam-97	200	13	what	what	PRON
ejpam-97	200	14	we	we	PRON
ejpam-97	200	15	promised	promise	VERB
ejpam-97	200	16	in	in	ADP
ejpam-97	200	17	the	the	DET
ejpam-97	200	18	beginning	beginning	NOUN
ejpam-97	200	19	of	of	ADP
ejpam-97	200	20	this	this	DET
ejpam-97	200	21	section	section	NOUN
ejpam-97	200	22	.	.	PUNCT
ejpam-97	201	1	h.	h.	PROPN
ejpam-97	201	2	barzegar	barzegar	PROPN
ejpam-97	201	3	and	and	CCONJ
ejpam-97	201	4	m.m	m.m	PROPN
ejpam-97	201	5	.	.	PROPN
ejpam-97	201	6	ebrahimi	ebrahimi	PROPN
ejpam-97	201	7	/	/	SYM
ejpam-97	201	8	eur	eur	PROPN
ejpam-97	201	9	.	.	PUNCT
ejpam-97	202	1	j.	j.	PROPN
ejpam-97	202	2	pure	pure	PROPN
ejpam-97	202	3	appl	appl	PROPN
ejpam-97	202	4	.	.	PROPN
ejpam-97	202	5	math	math	PROPN
ejpam-97	202	6	,	,	PUNCT
ejpam-97	202	7	1	1	NUM
ejpam-97	202	8	(	(	PUNCT
ejpam-97	202	9	2008	2008	NUM
ejpam-97	202	10	)	)	PUNCT
ejpam-97	202	11	,	,	PUNCT
ejpam-97	202	12	(	(	PUNCT
ejpam-97	202	13	41	41	NUM
ejpam-97	202	14	-	-	SYM
ejpam-97	202	15	55	55	NUM
ejpam-97	202	16	)	)	PUNCT
ejpam-97	202	17	48	48	NUM
ejpam-97	202	18	theorem	theorem	VERB
ejpam-97	202	19	2.3	2.3	NUM
ejpam-97	202	20	.	.	PUNCT
ejpam-97	203	1	the	the	DET
ejpam-97	203	2	following	follow	VERB
ejpam-97	203	3	are	be	AUX
ejpam-97	203	4	equivalent	equivalent	ADJ
ejpam-97	203	5	:	:	PUNCT
ejpam-97	203	6	(	(	PUNCT
ejpam-97	203	7	1	1	X
ejpam-97	203	8	)	)	PUNCT
ejpam-97	203	9	a	a	PRON
ejpam-97	203	10	is	be	AUX
ejpam-97	203	11	s	s	NOUN
ejpam-97	203	12	-	-	ADJ
ejpam-97	203	13	pure	pure	ADJ
ejpam-97	203	14	in	in	ADP
ejpam-97	203	15	b.	b.	PROPN
ejpam-97	203	16	(	(	PUNCT
ejpam-97	203	17	2	2	NUM
ejpam-97	203	18	)	)	PUNCT
ejpam-97	203	19	a	a	PRON
ejpam-97	203	20	is	be	AUX
ejpam-97	203	21	c	c	NOUN
ejpam-97	203	22	p	p	NOUN
ejpam-97	203	23	-	-	PUNCT
ejpam-97	203	24	pure	pure	ADJ
ejpam-97	203	25	in	in	ADP
ejpam-97	203	26	b.	b.	PROPN
ejpam-97	203	27	lemma	lemma	PROPN
ejpam-97	203	28	2.4	2.4	NUM
ejpam-97	203	29	.	.	PUNCT
ejpam-97	204	1	(	(	PUNCT
ejpam-97	204	2	1	1	X
ejpam-97	204	3	)	)	PUNCT
ejpam-97	204	4	any	any	DET
ejpam-97	204	5	retraction	retraction	NOUN
ejpam-97	204	6	is	be	AUX
ejpam-97	204	7	s	s	NOUN
ejpam-97	204	8	-	-	ADJ
ejpam-97	204	9	pure	pure	ADJ
ejpam-97	204	10	.	.	PUNCT
ejpam-97	205	1	(	(	PUNCT
ejpam-97	205	2	2	2	X
ejpam-97	205	3	)	)	PUNCT
ejpam-97	205	4	any	any	DET
ejpam-97	205	5	c	c	NOUN
ejpam-97	205	6	p	p	NOUN
ejpam-97	205	7	-	-	PUNCT
ejpam-97	205	8	dense	dense	ADJ
ejpam-97	205	9	monomorphism	monomorphism	NOUN
ejpam-97	205	10	is	be	AUX
ejpam-97	205	11	a	a	DET
ejpam-97	205	12	retraction	retraction	NOUN
ejpam-97	205	13	.	.	PUNCT
ejpam-97	206	1	proof	proof	NOUN
ejpam-97	206	2	.	.	PUNCT
ejpam-97	207	1	:	:	PUNCT
ejpam-97	207	2	(	(	PUNCT
ejpam-97	207	3	1	1	X
ejpam-97	207	4	)	)	PUNCT
ejpam-97	207	5	let	let	VERB
ejpam-97	207	6	a	a	DET
ejpam-97	207	7	,	,	PUNCT
ejpam-97	207	8	→	→	SYM
ejpam-97	207	9	b	b	X
ejpam-97	207	10	π→	π→	PROPN
ejpam-97	207	11	a=	a=	PROPN
ejpam-97	207	12	ida	ida	PROPN
ejpam-97	207	13	be	be	AUX
ejpam-97	207	14	a	a	DET
ejpam-97	207	15	retraction	retraction	NOUN
ejpam-97	207	16	and	and	CCONJ
ejpam-97	207	17	s	s	NOUN
ejpam-97	207	18	k→	k→	X
ejpam-97	207	19	a	a	PRON
ejpam-97	207	20	,	,	PUNCT
ejpam-97	207	21	→	→	SYM
ejpam-97	207	22	b	b	X
ejpam-97	207	23	=	=	SYM
ejpam-97	207	24	λb	λb	NOUN
ejpam-97	207	25	for	for	ADP
ejpam-97	207	26	some	some	DET
ejpam-97	207	27	b	b	PROPN
ejpam-97	207	28	∈	∈	PROPN
ejpam-97	207	29	b.	b.	NOUN
ejpam-97	208	1	it	it	PRON
ejpam-97	208	2	is	be	AUX
ejpam-97	208	3	clear	clear	ADJ
ejpam-97	208	4	that	that	SCONJ
ejpam-97	208	5	k	k	PROPN
ejpam-97	208	6	=	=	X
ejpam-97	208	7	λπ(b	λπ(b	X
ejpam-97	208	8	)	)	PUNCT
ejpam-97	208	9	.	.	PUNCT
ejpam-97	209	1	(	(	PUNCT
ejpam-97	209	2	2	2	X
ejpam-97	209	3	)	)	PUNCT
ejpam-97	209	4	let	let	VERB
ejpam-97	209	5	a	a	PRON
ejpam-97	209	6	,	,	PUNCT
ejpam-97	209	7	→	→	SYM
ejpam-97	209	8	b	b	X
ejpam-97	209	9	be	be	AUX
ejpam-97	209	10	a	a	DET
ejpam-97	209	11	c	c	NOUN
ejpam-97	209	12	p	p	NOUN
ejpam-97	209	13	-	-	PUNCT
ejpam-97	209	14	dense	dense	ADJ
ejpam-97	209	15	subact	subact	NOUN
ejpam-97	209	16	.	.	PUNCT
ejpam-97	210	1	then	then	ADV
ejpam-97	210	2	,	,	PUNCT
ejpam-97	210	3	by	by	ADP
ejpam-97	210	4	?	?	PUNCT
ejpam-97	210	5	?	?	PUNCT
ejpam-97	211	1	it	it	PRON
ejpam-97	211	2	is	be	AUX
ejpam-97	211	3	c	c	NOUN
ejpam-97	211	4	p	p	NOUN
ejpam-97	211	5	-	-	PUNCT
ejpam-97	211	6	pure	pure	ADJ
ejpam-97	211	7	as	as	ADV
ejpam-97	211	8	well	well	ADV
ejpam-97	211	9	as	as	ADP
ejpam-97	211	10	cd	cd	PROPN
ejpam-97	211	11	-dense	-dense	PROPN
ejpam-97	211	12	subact	subact	NOUN
ejpam-97	211	13	.	.	PUNCT
ejpam-97	212	1	so	so	ADV
ejpam-97	212	2	,	,	PUNCT
ejpam-97	212	3	for	for	ADP
ejpam-97	212	4	every	every	DET
ejpam-97	212	5	b	b	PROPN
ejpam-97	212	6	∈	∈	PROPN
ejpam-97	212	7	b	b	NOUN
ejpam-97	212	8	there	there	PRON
ejpam-97	212	9	exists	exist	VERB
ejpam-97	212	10	ab	ab	PROPN
ejpam-97	212	11	∈	∈	PROPN
ejpam-97	212	12	a	a	DET
ejpam-97	212	13	such	such	ADJ
ejpam-97	212	14	that	that	DET
ejpam-97	212	15	λb	λb	PROPN
ejpam-97	212	16	=	=	PUNCT
ejpam-97	212	17	λab	λab	PROPN
ejpam-97	212	18	.	.	PUNCT
ejpam-97	213	1	now	now	ADV
ejpam-97	213	2	,	,	PUNCT
ejpam-97	213	3	for	for	ADP
ejpam-97	213	4	every	every	DET
ejpam-97	213	5	b	b	PROPN
ejpam-97	213	6	∈	∈	PROPN
ejpam-97	213	7	b	b	NOUN
ejpam-97	213	8	−	−	NOUN
ejpam-97	213	9	a	a	DET
ejpam-97	213	10	choose	choose	NOUN
ejpam-97	213	11	and	and	CCONJ
ejpam-97	213	12	fix	fix	VERB
ejpam-97	213	13	such	such	DET
ejpam-97	213	14	an	an	DET
ejpam-97	213	15	ab	ab	PROPN
ejpam-97	213	16	∈	∈	PROPN
ejpam-97	213	17	a.	a.	NOUN
ejpam-97	213	18	define	define	NOUN
ejpam-97	213	19	π	π	NOUN
ejpam-97	213	20	:	:	PUNCT
ejpam-97	214	1	b→	b→	PROPN
ejpam-97	214	2	a	a	X
ejpam-97	214	3	by	by	ADP
ejpam-97	214	4	π(x	π(x	NOUN
ejpam-97	214	5	)	)	PUNCT
ejpam-97	214	6	=	=	PUNCT
ejpam-97	215	1	¨	¨	NOUN
ejpam-97	215	2	x	x	X
ejpam-97	215	3	,	,	PUNCT
ejpam-97	215	4	if	if	SCONJ
ejpam-97	215	5	x	x	SYM
ejpam-97	215	6	∈	∈	PROPN
ejpam-97	215	7	a	a	DET
ejpam-97	215	8	ax	ax	NOUN
ejpam-97	215	9	,	,	PUNCT
ejpam-97	215	10	if	if	SCONJ
ejpam-97	215	11	x	x	PROPN
ejpam-97	215	12	6∈	6∈	PROPN
ejpam-97	215	13	a	a	PRON
ejpam-97	215	14	then	then	ADV
ejpam-97	215	15	,	,	PUNCT
ejpam-97	215	16	clearly	clearly	ADV
ejpam-97	215	17	π	π	PROPN
ejpam-97	215	18	is	be	AUX
ejpam-97	215	19	a	a	DET
ejpam-97	215	20	retraction	retraction	NOUN
ejpam-97	215	21	.	.	PUNCT
ejpam-97	216	1	it	it	PRON
ejpam-97	216	2	is	be	AUX
ejpam-97	216	3	a	a	DET
ejpam-97	216	4	homomorphism	homomorphism	NOUN
ejpam-97	216	5	because	because	SCONJ
ejpam-97	216	6	it	it	PRON
ejpam-97	216	7	is	be	AUX
ejpam-97	216	8	a	a	DET
ejpam-97	216	9	homomorphism	homomorphism	NOUN
ejpam-97	216	10	on	on	ADP
ejpam-97	216	11	a	a	PRON
ejpam-97	216	12	,	,	PUNCT
ejpam-97	216	13	and	and	CCONJ
ejpam-97	216	14	for	for	ADP
ejpam-97	216	15	x	x	PROPN
ejpam-97	216	16	∈	∈	PROPN
ejpam-97	216	17	b−	b−	PROPN
ejpam-97	216	18	a	a	PRON
ejpam-97	216	19	,	,	PUNCT
ejpam-97	216	20	s	s	NOUN
ejpam-97	216	21	∈	∈	PROPN
ejpam-97	216	22	s	s	PART
ejpam-97	216	23	,	,	PUNCT
ejpam-97	216	24	we	we	PRON
ejpam-97	216	25	have	have	VERB
ejpam-97	216	26	xs	xs	PROPN
ejpam-97	216	27	∈	∈	PROPN
ejpam-97	216	28	a	a	PRON
ejpam-97	216	29	and	and	CCONJ
ejpam-97	216	30	so	so	ADV
ejpam-97	216	31	π(xs	π(xs	NUM
ejpam-97	216	32	)	)	PUNCT
ejpam-97	216	33	=	=	SYM
ejpam-97	216	34	xs	xs	NOUN
ejpam-97	217	1	=	=	PUNCT
ejpam-97	218	1	ax	ax	NOUN
ejpam-97	218	2	s	s	X
ejpam-97	218	3	=	=	X
ejpam-97	218	4	π(x)s	π(x)s	PROPN
ejpam-97	218	5	.	.	PUNCT
ejpam-97	219	1	3	3	X
ejpam-97	219	2	.	.	X
ejpam-97	219	3	categorical	categorical	ADJ
ejpam-97	219	4	properties	property	NOUN
ejpam-97	219	5	of	of	ADP
ejpam-97	219	6	s	s	NOUN
ejpam-97	219	7	-	-	ADJ
ejpam-97	219	8	pure	pure	ADJ
ejpam-97	219	9	monomorphisms	monomorphism	NOUN
ejpam-97	219	10	in	in	ADP
ejpam-97	219	11	this	this	DET
ejpam-97	219	12	section	section	NOUN
ejpam-97	219	13	we	we	PRON
ejpam-97	219	14	investigate	investigate	VERB
ejpam-97	219	15	the	the	DET
ejpam-97	219	16	categorical	categorical	ADJ
ejpam-97	219	17	and	and	CCONJ
ejpam-97	219	18	algebraic	algebraic	ADJ
ejpam-97	219	19	properties	property	NOUN
ejpam-97	219	20	,	,	PUNCT
ejpam-97	219	21	regarding	regard	VERB
ejpam-97	219	22	composition	composition	NOUN
ejpam-97	219	23	,	,	PUNCT
ejpam-97	219	24	limits	limit	NOUN
ejpam-97	219	25	,	,	PUNCT
ejpam-97	219	26	and	and	CCONJ
ejpam-97	219	27	colimits	colimit	NOUN
ejpam-97	219	28	,	,	PUNCT
ejpam-97	219	29	of	of	ADP
ejpam-97	219	30	the	the	DET
ejpam-97	219	31	category	category	NOUN
ejpam-97	219	32	act	act	NOUN
ejpam-97	219	33	-	-	PUNCT
ejpam-97	219	34	s	s	PROPN
ejpam-97	219	35	with	with	ADP
ejpam-97	219	36	respect	respect	NOUN
ejpam-97	219	37	to	to	ADP
ejpam-97	219	38	the	the	DET
ejpam-97	219	39	classmp	classmp	NOUN
ejpam-97	219	40	of	of	ADP
ejpam-97	219	41	sequentially	sequentially	ADV
ejpam-97	219	42	pure	pure	ADJ
ejpam-97	219	43	monomorphisms	monomorphism	NOUN
ejpam-97	219	44	.	.	PUNCT
ejpam-97	220	1	we	we	PRON
ejpam-97	220	2	have	have	AUX
ejpam-97	220	3	divided	divide	VERB
ejpam-97	220	4	the	the	DET
ejpam-97	220	5	section	section	NOUN
ejpam-97	220	6	into	into	ADP
ejpam-97	220	7	three	three	NUM
ejpam-97	220	8	subsections	subsection	NOUN
ejpam-97	220	9	as	as	SCONJ
ejpam-97	220	10	follows	follow	VERB
ejpam-97	220	11	:	:	PUNCT
ejpam-97	220	12	3.1	3.1	NUM
ejpam-97	220	13	.	.	PUNCT
ejpam-97	220	14	composition	composition	NOUN
ejpam-97	220	15	properties	property	NOUN
ejpam-97	220	16	of	of	ADP
ejpam-97	220	17	s	s	NOUN
ejpam-97	220	18	-	-	ADJ
ejpam-97	220	19	pure	pure	ADJ
ejpam-97	220	20	monomorphisms	monomorphism	NOUN
ejpam-97	220	21	in	in	ADP
ejpam-97	220	22	this	this	DET
ejpam-97	220	23	subsection	subsection	NOUN
ejpam-97	220	24	we	we	PRON
ejpam-97	220	25	investigate	investigate	VERB
ejpam-97	220	26	some	some	DET
ejpam-97	220	27	properties	property	NOUN
ejpam-97	220	28	of	of	ADP
ejpam-97	220	29	the	the	DET
ejpam-97	220	30	classmp	classmp	NOUN
ejpam-97	220	31	which	which	PRON
ejpam-97	220	32	are	be	AUX
ejpam-97	220	33	mostly	mostly	ADV
ejpam-97	220	34	related	relate	VERB
ejpam-97	220	35	to	to	ADP
ejpam-97	220	36	the	the	DET
ejpam-97	220	37	composition	composition	NOUN
ejpam-97	220	38	of	of	ADP
ejpam-97	220	39	pure	pure	ADJ
ejpam-97	220	40	monomorphisms	monomorphism	NOUN
ejpam-97	220	41	.	.	PUNCT
ejpam-97	221	1	these	these	DET
ejpam-97	221	2	properties	property	NOUN
ejpam-97	221	3	and	and	CCONJ
ejpam-97	221	4	the	the	DET
ejpam-97	221	5	ones	one	NOUN
ejpam-97	221	6	given	give	VERB
ejpam-97	221	7	in	in	ADP
ejpam-97	221	8	the	the	DET
ejpam-97	221	9	next	next	ADJ
ejpam-97	221	10	two	two	NUM
ejpam-97	221	11	subsections	subsection	NOUN
ejpam-97	221	12	are	be	AUX
ejpam-97	221	13	what	what	PRON
ejpam-97	221	14	normally	normally	ADV
ejpam-97	221	15	used	use	VERB
ejpam-97	221	16	to	to	PART
ejpam-97	221	17	study	study	VERB
ejpam-97	221	18	injectivity	injectivity	NOUN
ejpam-97	221	19	with	with	ADP
ejpam-97	221	20	respect	respect	NOUN
ejpam-97	221	21	to	to	ADP
ejpam-97	221	22	a	a	DET
ejpam-97	221	23	class	class	NOUN
ejpam-97	221	24	of	of	ADP
ejpam-97	221	25	monomorphisms	monomorphism	NOUN
ejpam-97	221	26	(	(	PUNCT
ejpam-97	221	27	see	see	VERB
ejpam-97	221	28	[	[	X
ejpam-97	221	29	1,17	1,17	NUM
ejpam-97	221	30	]	]	PUNCT
ejpam-97	221	31	)	)	PUNCT
ejpam-97	221	32	lemma	lemma	PROPN
ejpam-97	221	33	3.1	3.1	NUM
ejpam-97	221	34	.	.	PUNCT
ejpam-97	222	1	the	the	DET
ejpam-97	222	2	classmp	classmp	PROPN
ejpam-97	222	3	is	be	AUX
ejpam-97	222	4	:	:	PUNCT
ejpam-97	222	5	(	(	PUNCT
ejpam-97	222	6	1	1	X
ejpam-97	222	7	)	)	PUNCT
ejpam-97	222	8	isomorphism	isomorphism	NOUN
ejpam-97	222	9	closed	close	VERB
ejpam-97	222	10	;	;	PUNCT
ejpam-97	222	11	that	that	PRON
ejpam-97	222	12	is	is	ADV
ejpam-97	222	13	,	,	PUNCT
ejpam-97	222	14	contains	contain	VERB
ejpam-97	222	15	all	all	DET
ejpam-97	222	16	isomorphisms	isomorphism	NOUN
ejpam-97	222	17	and	and	CCONJ
ejpam-97	222	18	is	be	AUX
ejpam-97	222	19	closed	close	VERB
ejpam-97	222	20	under	under	ADP
ejpam-97	222	21	composition	composition	NOUN
ejpam-97	222	22	with	with	ADP
ejpam-97	222	23	isomorphisms	isomorphism	NOUN
ejpam-97	222	24	.	.	PUNCT
ejpam-97	223	1	(	(	PUNCT
ejpam-97	223	2	2	2	X
ejpam-97	223	3	)	)	PUNCT
ejpam-97	223	4	composition	composition	NOUN
ejpam-97	223	5	closed	close	VERB
ejpam-97	223	6	;	;	PUNCT
ejpam-97	223	7	that	that	PRON
ejpam-97	223	8	is	is	ADV
ejpam-97	223	9	,	,	PUNCT
ejpam-97	223	10	if	if	SCONJ
ejpam-97	223	11	f	f	X
ejpam-97	223	12	:	:	PUNCT
ejpam-97	223	13	a→	a→	PROPN
ejpam-97	223	14	b	b	NOUN
ejpam-97	223	15	and	and	CCONJ
ejpam-97	223	16	g	g	NOUN
ejpam-97	223	17	:	:	PUNCT
ejpam-97	223	18	b	b	X
ejpam-97	223	19	→	→	SYM
ejpam-97	223	20	c	c	PROPN
ejpam-97	223	21	belong	belong	VERB
ejpam-97	223	22	to	to	ADP
ejpam-97	223	23	mp	mp	PROPN
ejpam-97	223	24	,	,	PUNCT
ejpam-97	223	25	then	then	ADV
ejpam-97	223	26	g	g	PROPN
ejpam-97	223	27	f	f	PROPN
ejpam-97	223	28	also	also	ADV
ejpam-97	223	29	belongs	belong	VERB
ejpam-97	223	30	tomp	tomp	PROPN
ejpam-97	223	31	.	.	PUNCT
ejpam-97	224	1	(	(	PUNCT
ejpam-97	224	2	3	3	X
ejpam-97	224	3	)	)	PUNCT
ejpam-97	224	4	left	leave	VERB
ejpam-97	224	5	cancellable	cancellable	ADJ
ejpam-97	224	6	;	;	PUNCT
ejpam-97	224	7	that	that	PRON
ejpam-97	224	8	is	is	ADV
ejpam-97	224	9	,	,	PUNCT
ejpam-97	224	10	if	if	SCONJ
ejpam-97	224	11	g	g	PROPN
ejpam-97	224	12	f	f	PROPN
ejpam-97	224	13	∈mp	∈mp	PROPN
ejpam-97	224	14	then	then	ADV
ejpam-97	224	15	f	f	PROPN
ejpam-97	224	16	∈mp	∈mp	NOUN
ejpam-97	224	17	.	.	PUNCT
ejpam-97	225	1	proof	proof	NOUN
ejpam-97	225	2	.	.	PUNCT
ejpam-97	226	1	we	we	PRON
ejpam-97	226	2	just	just	ADV
ejpam-97	226	3	prove	prove	VERB
ejpam-97	226	4	(	(	PUNCT
ejpam-97	226	5	2	2	NUM
ejpam-97	226	6	)	)	PUNCT
ejpam-97	226	7	,	,	PUNCT
ejpam-97	226	8	which	which	PRON
ejpam-97	226	9	may	may	AUX
ejpam-97	226	10	be	be	AUX
ejpam-97	226	11	less	less	ADV
ejpam-97	226	12	clear	clear	ADJ
ejpam-97	226	13	.	.	PUNCT
ejpam-97	227	1	for	for	ADP
ejpam-97	227	2	convenience	convenience	NOUN
ejpam-97	227	3	and	and	CCONJ
ejpam-97	227	4	without	without	ADP
ejpam-97	227	5	loss	loss	NOUN
ejpam-97	227	6	of	of	ADP
ejpam-97	227	7	generality	generality	NOUN
ejpam-97	227	8	,	,	PUNCT
ejpam-97	227	9	we	we	PRON
ejpam-97	227	10	consider	consider	VERB
ejpam-97	227	11	f	f	PROPN
ejpam-97	227	12	and	and	CCONJ
ejpam-97	227	13	g	g	PROPN
ejpam-97	227	14	to	to	PART
ejpam-97	227	15	be	be	AUX
ejpam-97	227	16	s	s	NOUN
ejpam-97	227	17	-	-	ADJ
ejpam-97	227	18	pure	pure	ADJ
ejpam-97	227	19	inclusions	inclusion	NOUN
ejpam-97	227	20	.	.	PUNCT
ejpam-97	228	1	let	let	VERB
ejpam-97	228	2	s	s	PRON
ejpam-97	228	3	k→	k→	VERB
ejpam-97	228	4	a	a	DET
ejpam-97	228	5	f	f	X
ejpam-97	228	6	,	,	PUNCT
ejpam-97	228	7	→	→	SYM
ejpam-97	228	8	b	b	X
ejpam-97	228	9	g	g	PROPN
ejpam-97	228	10	,	,	PUNCT
ejpam-97	228	11	→	→	SYM
ejpam-97	228	12	c	c	NOUN
ejpam-97	228	13	=	=	SYM
ejpam-97	228	14	λc	λc	NOUN
ejpam-97	228	15	,	,	PUNCT
ejpam-97	228	16	for	for	ADP
ejpam-97	228	17	some	some	DET
ejpam-97	228	18	c	c	NOUN
ejpam-97	228	19	∈	∈	PROPN
ejpam-97	228	20	c	c	NOUN
ejpam-97	228	21	.	.	PUNCT
ejpam-97	229	1	since	since	SCONJ
ejpam-97	229	2	g	g	PROPN
ejpam-97	229	3	is	be	AUX
ejpam-97	229	4	s	s	NOUN
ejpam-97	229	5	-	-	ADJ
ejpam-97	229	6	pure	pure	ADJ
ejpam-97	229	7	,	,	PUNCT
ejpam-97	229	8	there	there	PRON
ejpam-97	229	9	is	be	VERB
ejpam-97	229	10	an	an	DET
ejpam-97	229	11	element	element	NOUN
ejpam-97	229	12	b	b	PROPN
ejpam-97	229	13	∈	∈	PROPN
ejpam-97	229	14	b	b	NOUN
ejpam-97	229	15	such	such	ADJ
ejpam-97	229	16	that	that	SCONJ
ejpam-97	229	17	f	f	PROPN
ejpam-97	229	18	k	k	PROPN
ejpam-97	229	19	=	=	PUNCT
ejpam-97	229	20	λb	λb	PROPN
ejpam-97	229	21	.	.	PUNCT
ejpam-97	230	1	now	now	ADV
ejpam-97	230	2	,	,	PUNCT
ejpam-97	230	3	the	the	DET
ejpam-97	230	4	s	s	NOUN
ejpam-97	230	5	-	-	NOUN
ejpam-97	230	6	purity	purity	NOUN
ejpam-97	230	7	of	of	ADP
ejpam-97	230	8	f	f	PROPN
ejpam-97	230	9	provides	provide	VERB
ejpam-97	230	10	an	an	DET
ejpam-97	230	11	element	element	NOUN
ejpam-97	230	12	a	a	DET
ejpam-97	230	13	∈	∈	PROPN
ejpam-97	230	14	a	a	PRON
ejpam-97	230	15	with	with	ADP
ejpam-97	230	16	k	k	PROPN
ejpam-97	230	17	=	=	PUNCT
ejpam-97	230	18	λa	λa	PROPN
ejpam-97	230	19	.	.	PUNCT
ejpam-97	230	20	h.	h.	PROPN
ejpam-97	230	21	barzegar	barzegar	PROPN
ejpam-97	230	22	and	and	CCONJ
ejpam-97	230	23	m.m	m.m	PROPN
ejpam-97	230	24	.	.	PROPN
ejpam-97	230	25	ebrahimi	ebrahimi	PROPN
ejpam-97	230	26	/	/	SYM
ejpam-97	230	27	eur	eur	PROPN
ejpam-97	230	28	.	.	PUNCT
ejpam-97	231	1	j.	j.	PROPN
ejpam-97	231	2	pure	pure	PROPN
ejpam-97	231	3	appl	appl	PROPN
ejpam-97	231	4	.	.	PROPN
ejpam-97	231	5	math	math	PROPN
ejpam-97	231	6	,	,	PUNCT
ejpam-97	231	7	1	1	NUM
ejpam-97	231	8	(	(	PUNCT
ejpam-97	231	9	2008	2008	NUM
ejpam-97	231	10	)	)	PUNCT
ejpam-97	231	11	,	,	PUNCT
ejpam-97	231	12	(	(	PUNCT
ejpam-97	231	13	41	41	NUM
ejpam-97	231	14	-	-	SYM
ejpam-97	231	15	55	55	NUM
ejpam-97	231	16	)	)	PUNCT
ejpam-97	231	17	49	49	NUM
ejpam-97	231	18	theorem	theorem	VERB
ejpam-97	231	19	3.1	3.1	NUM
ejpam-97	231	20	.	.	PUNCT
ejpam-97	232	1	the	the	DET
ejpam-97	232	2	following	follow	VERB
ejpam-97	232	3	are	be	AUX
ejpam-97	232	4	equivalent	equivalent	ADJ
ejpam-97	232	5	:	:	PUNCT
ejpam-97	232	6	(	(	PUNCT
ejpam-97	232	7	1	1	X
ejpam-97	232	8	)	)	PUNCT
ejpam-97	232	9	s	s	AUX
ejpam-97	232	10	has	have	VERB
ejpam-97	232	11	a	a	DET
ejpam-97	232	12	left	left	ADJ
ejpam-97	232	13	identity	identity	NOUN
ejpam-97	232	14	.	.	PUNCT
ejpam-97	233	1	(	(	PUNCT
ejpam-97	233	2	2	2	X
ejpam-97	233	3	)	)	PUNCT
ejpam-97	233	4	every	every	DET
ejpam-97	233	5	monomorphism	monomorphism	NOUN
ejpam-97	233	6	is	be	AUX
ejpam-97	233	7	s	s	NOUN
ejpam-97	233	8	-	-	ADJ
ejpam-97	233	9	pure	pure	ADJ
ejpam-97	233	10	.	.	PUNCT
ejpam-97	234	1	(	(	PUNCT
ejpam-97	234	2	3	3	X
ejpam-97	234	3	)	)	PUNCT
ejpam-97	234	4	s	s	VERB
ejpam-97	234	5	is	be	AUX
ejpam-97	234	6	s	s	NOUN
ejpam-97	234	7	-	-	ADJ
ejpam-97	234	8	pure	pure	ADJ
ejpam-97	234	9	in	in	ADP
ejpam-97	234	10	s1	s1	NOUN
ejpam-97	234	11	.	.	PUNCT
ejpam-97	235	1	(	(	PUNCT
ejpam-97	235	2	4	4	X
ejpam-97	235	3	)	)	PUNCT
ejpam-97	235	4	mp	mp	NOUN
ejpam-97	235	5	is	be	AUX
ejpam-97	235	6	right	right	ADV
ejpam-97	235	7	cancellable	cancellable	ADJ
ejpam-97	235	8	;	;	PUNCT
ejpam-97	235	9	that	that	PRON
ejpam-97	235	10	is	is	ADV
ejpam-97	235	11	,	,	PUNCT
ejpam-97	235	12	for	for	ADP
ejpam-97	235	13	monomorphisms	monomorphism	NOUN
ejpam-97	235	14	f	f	NOUN
ejpam-97	235	15	and	and	CCONJ
ejpam-97	235	16	g	g	NOUN
ejpam-97	235	17	,	,	PUNCT
ejpam-97	235	18	if	if	SCONJ
ejpam-97	235	19	g	g	PROPN
ejpam-97	235	20	f	f	PROPN
ejpam-97	235	21	is	be	AUX
ejpam-97	235	22	s	s	NOUN
ejpam-97	235	23	-	-	ADJ
ejpam-97	235	24	pure	pure	ADJ
ejpam-97	235	25	then	then	ADV
ejpam-97	235	26	g	g	PROPN
ejpam-97	235	27	is	be	AUX
ejpam-97	235	28	s	s	NOUN
ejpam-97	235	29	-	-	ADJ
ejpam-97	235	30	pure	pure	ADJ
ejpam-97	235	31	.	.	PUNCT
ejpam-97	236	1	(	(	PUNCT
ejpam-97	236	2	5	5	NUM
ejpam-97	236	3	)	)	PUNCT
ejpam-97	236	4	for	for	ADP
ejpam-97	236	5	morphisms	morphisms	PROPN
ejpam-97	236	6	f	f	PROPN
ejpam-97	236	7	and	and	CCONJ
ejpam-97	236	8	g	g	NOUN
ejpam-97	236	9	,	,	PUNCT
ejpam-97	236	10	if	if	SCONJ
ejpam-97	236	11	f	f	PROPN
ejpam-97	236	12	is	be	AUX
ejpam-97	236	13	an	an	DET
ejpam-97	236	14	s	s	NOUN
ejpam-97	236	15	-	-	ADJ
ejpam-97	236	16	pure	pure	ADJ
ejpam-97	236	17	monomorphism	monomorphism	NOUN
ejpam-97	236	18	,	,	PUNCT
ejpam-97	236	19	g	g	PROPN
ejpam-97	236	20	is	be	AUX
ejpam-97	236	21	an	an	DET
ejpam-97	236	22	epimorphism	epimorphism	NOUN
ejpam-97	236	23	,	,	PUNCT
ejpam-97	236	24	and	and	CCONJ
ejpam-97	236	25	g	g	PROPN
ejpam-97	236	26	f	f	PROPN
ejpam-97	236	27	is	be	AUX
ejpam-97	236	28	a	a	DET
ejpam-97	236	29	monomorphism	monomorphism	NOUN
ejpam-97	236	30	,	,	PUNCT
ejpam-97	236	31	then	then	ADV
ejpam-97	236	32	g	g	PROPN
ejpam-97	236	33	f	f	PROPN
ejpam-97	236	34	is	be	AUX
ejpam-97	236	35	s	s	NOUN
ejpam-97	236	36	-	-	ADJ
ejpam-97	236	37	pure	pure	ADJ
ejpam-97	236	38	.	.	PUNCT
ejpam-97	237	1	categorical	categorical	ADJ
ejpam-97	237	2	properties	property	NOUN
ejpam-97	237	3	of	of	ADP
ejpam-97	237	4	proof	proof	NOUN
ejpam-97	237	5	.	.	PUNCT
ejpam-97	238	1	(	(	PUNCT
ejpam-97	238	2	1)⇒(2,3,4,5	1)⇒(2,3,4,5	NUM
ejpam-97	238	3	):	):	PUNCT
ejpam-97	238	4	clearly	clearly	ADV
ejpam-97	238	5	if	if	SCONJ
ejpam-97	238	6	s	s	PROPN
ejpam-97	238	7	has	have	VERB
ejpam-97	238	8	a	a	DET
ejpam-97	238	9	left	left	ADJ
ejpam-97	238	10	identity	identity	NOUN
ejpam-97	238	11	,	,	PUNCT
ejpam-97	238	12	then	then	ADV
ejpam-97	238	13	every	every	DET
ejpam-97	238	14	monomorphism	monomorphism	NOUN
ejpam-97	238	15	is	be	AUX
ejpam-97	238	16	s	s	NOUN
ejpam-97	238	17	-	-	ADJ
ejpam-97	238	18	pure	pure	ADJ
ejpam-97	238	19	.	.	PUNCT
ejpam-97	239	1	so	so	ADV
ejpam-97	239	2	,	,	PUNCT
ejpam-97	239	3	(	(	PUNCT
ejpam-97	239	4	1	1	X
ejpam-97	239	5	)	)	PUNCT
ejpam-97	239	6	implies	imply	VERB
ejpam-97	239	7	(	(	PUNCT
ejpam-97	239	8	2	2	NUM
ejpam-97	239	9	)	)	PUNCT
ejpam-97	239	10	,	,	PUNCT
ejpam-97	239	11	(	(	PUNCT
ejpam-97	239	12	3	3	NUM
ejpam-97	239	13	)	)	PUNCT
ejpam-97	239	14	,	,	PUNCT
ejpam-97	239	15	(	(	PUNCT
ejpam-97	239	16	4	4	NUM
ejpam-97	239	17	)	)	PUNCT
ejpam-97	239	18	,	,	PUNCT
ejpam-97	239	19	and	and	CCONJ
ejpam-97	239	20	(	(	PUNCT
ejpam-97	239	21	5	5	NUM
ejpam-97	239	22	)	)	PUNCT
ejpam-97	239	23	.	.	PUNCT
ejpam-97	240	1	(	(	PUNCT
ejpam-97	240	2	2)⇒(3	2)⇒(3	NUM
ejpam-97	240	3	)	)	PUNCT
ejpam-97	240	4	is	be	AUX
ejpam-97	240	5	clear	clear	ADJ
ejpam-97	240	6	.	.	PUNCT
ejpam-97	241	1	(	(	PUNCT
ejpam-97	241	2	3)⇒(1	3)⇒(1	NUM
ejpam-97	241	3	)	)	PUNCT
ejpam-97	241	4	since	since	SCONJ
ejpam-97	241	5	1	1	NUM
ejpam-97	241	6	∈	∈	PROPN
ejpam-97	241	7	cd	cd	NOUN
ejpam-97	241	8	s1(s	s1(s	PROPN
ejpam-97	241	9	)	)	PUNCT
ejpam-97	241	10	,	,	PUNCT
ejpam-97	241	11	there	there	PRON
ejpam-97	241	12	exists	exist	VERB
ejpam-97	241	13	e	e	X
ejpam-97	241	14	∈	∈	PROPN
ejpam-97	241	15	s	s	VERB
ejpam-97	241	16	with	with	ADP
ejpam-97	241	17	λe	λe	ADP
ejpam-97	241	18	=	=	SYM
ejpam-97	241	19	λ1	λ1	PROPN
ejpam-97	241	20	.	.	PUNCT
ejpam-97	242	1	this	this	PRON
ejpam-97	242	2	shows	show	VERB
ejpam-97	242	3	that	that	SCONJ
ejpam-97	242	4	e	e	NOUN
ejpam-97	242	5	is	be	AUX
ejpam-97	242	6	a	a	DET
ejpam-97	242	7	left	left	ADJ
ejpam-97	242	8	identity	identity	NOUN
ejpam-97	242	9	of	of	ADP
ejpam-97	242	10	s.	s.	PROPN
ejpam-97	242	11	(	(	PUNCT
ejpam-97	242	12	4)⇒(3	4)⇒(3	X
ejpam-97	242	13	)	)	PUNCT
ejpam-97	242	14	use	use	VERB
ejpam-97	242	15	the	the	DET
ejpam-97	242	16	fact	fact	NOUN
ejpam-97	242	17	that	that	SCONJ
ejpam-97	242	18	the	the	DET
ejpam-97	242	19	empty	empty	ADJ
ejpam-97	242	20	set	set	NOUN
ejpam-97	242	21	is	be	AUX
ejpam-97	242	22	s	s	NOUN
ejpam-97	242	23	-	-	ADJ
ejpam-97	242	24	pure	pure	ADJ
ejpam-97	242	25	in	in	ADP
ejpam-97	242	26	every	every	DET
ejpam-97	242	27	right	right	ADJ
ejpam-97	242	28	s	s	NOUN
ejpam-97	242	29	-	-	NOUN
ejpam-97	242	30	act	act	NOUN
ejpam-97	242	31	,	,	PUNCT
ejpam-97	242	32	and	and	CCONJ
ejpam-97	242	33	apply	apply	VERB
ejpam-97	242	34	(	(	PUNCT
ejpam-97	242	35	3	3	NUM
ejpam-97	242	36	)	)	PUNCT
ejpam-97	242	37	to	to	ADP
ejpam-97	242	38	;	;	PUNCT
ejpam-97	242	39	f	f	PROPN
ejpam-97	242	40	,	,	PUNCT
ejpam-97	242	41	→	→	SYM
ejpam-97	242	42	s	s	PART
ejpam-97	242	43	g	g	NOUN
ejpam-97	242	44	,	,	PUNCT
ejpam-97	242	45	→	→	SYM
ejpam-97	242	46	s1	s1	PROPN
ejpam-97	242	47	.	.	PUNCT
ejpam-97	243	1	(	(	PUNCT
ejpam-97	243	2	5)⇒(3	5)⇒(3	NOUN
ejpam-97	243	3	)	)	PUNCT
ejpam-97	243	4	consider	consider	VERB
ejpam-97	243	5	the	the	DET
ejpam-97	243	6	natural	natural	ADJ
ejpam-97	243	7	homomorphisms	homomorphism	NOUN
ejpam-97	243	8	s	s	PART
ejpam-97	243	9	τ→	τ→	SYM
ejpam-97	243	10	s	s	NOUN
ejpam-97	243	11	t	t	NOUN
ejpam-97	243	12	s1	s1	PROPN
ejpam-97	243	13	π→	π→	PROPN
ejpam-97	243	14	s1	s1	PROPN
ejpam-97	243	15	.	.	PUNCT
ejpam-97	244	1	by	by	ADP
ejpam-97	244	2	lemma	lemma	PROPN
ejpam-97	244	3	2.1	2.1	NUM
ejpam-97	244	4	,	,	PUNCT
ejpam-97	244	5	τ	τ	PROPN
ejpam-97	244	6	is	be	AUX
ejpam-97	244	7	s	s	NOUN
ejpam-97	244	8	-	-	NOUN
ejpam-97	244	9	pure	pure	ADJ
ejpam-97	244	10	.	.	PUNCT
ejpam-97	245	1	since	since	SCONJ
ejpam-97	245	2	π	π	PROPN
ejpam-97	245	3	is	be	AUX
ejpam-97	245	4	an	an	DET
ejpam-97	245	5	epimorphism	epimorphism	NOUN
ejpam-97	245	6	and	and	CCONJ
ejpam-97	245	7	πτ	πτ	NOUN
ejpam-97	245	8	(	(	PUNCT
ejpam-97	245	9	the	the	DET
ejpam-97	245	10	inclusion	inclusion	NOUN
ejpam-97	245	11	map	map	NOUN
ejpam-97	245	12	)	)	PUNCT
ejpam-97	245	13	is	be	AUX
ejpam-97	245	14	one	one	NUM
ejpam-97	245	15	-	-	PUNCT
ejpam-97	245	16	one	one	NUM
ejpam-97	245	17	,	,	PUNCT
ejpam-97	245	18	by	by	ADP
ejpam-97	245	19	(	(	PUNCT
ejpam-97	245	20	5	5	NUM
ejpam-97	245	21	)	)	PUNCT
ejpam-97	245	22	,	,	PUNCT
ejpam-97	245	23	πτ	πτ	X
ejpam-97	245	24	is	be	AUX
ejpam-97	245	25	s	s	NOUN
ejpam-97	245	26	-	-	ADJ
ejpam-97	245	27	pure	pure	ADJ
ejpam-97	245	28	.	.	PUNCT
ejpam-97	246	1	as	as	ADP
ejpam-97	246	2	the	the	DET
ejpam-97	246	3	above	above	ADJ
ejpam-97	246	4	theorem	theorem	ADJ
ejpam-97	246	5	shows	show	NOUN
ejpam-97	246	6	,	,	PUNCT
ejpam-97	246	7	mp	mp	PROPN
ejpam-97	246	8	is	be	AUX
ejpam-97	246	9	not	not	PART
ejpam-97	246	10	generally	generally	ADV
ejpam-97	246	11	right	right	ADJ
ejpam-97	246	12	cancellable	cancellable	ADJ
ejpam-97	246	13	.	.	PUNCT
ejpam-97	247	1	but	but	CCONJ
ejpam-97	247	2	for	for	ADP
ejpam-97	247	3	some	some	DET
ejpam-97	247	4	semigroups	semigroup	NOUN
ejpam-97	247	5	,	,	PUNCT
ejpam-97	247	6	regardless	regardless	ADV
ejpam-97	247	7	of	of	ADP
ejpam-97	247	8	having	have	VERB
ejpam-97	247	9	a	a	DET
ejpam-97	247	10	left	left	ADJ
ejpam-97	247	11	identity	identity	NOUN
ejpam-97	247	12	,	,	PUNCT
ejpam-97	247	13	some	some	DET
ejpam-97	247	14	special	special	ADJ
ejpam-97	247	15	monomorphisms	monomorphism	NOUN
ejpam-97	247	16	may	may	AUX
ejpam-97	247	17	be	be	AUX
ejpam-97	247	18	cancelled	cancel	VERB
ejpam-97	247	19	from	from	ADP
ejpam-97	247	20	the	the	DET
ejpam-97	247	21	right	right	NOUN
ejpam-97	247	22	.	.	PUNCT
ejpam-97	248	1	see	see	VERB
ejpam-97	248	2	the	the	DET
ejpam-97	248	3	following	following	NOUN
ejpam-97	248	4	:	:	PUNCT
ejpam-97	248	5	lemma	lemma	PROPN
ejpam-97	248	6	3.2	3.2	NUM
ejpam-97	248	7	.	.	PUNCT
ejpam-97	249	1	if	if	SCONJ
ejpam-97	249	2	s2	s2	VERB
ejpam-97	249	3	=	=	SYM
ejpam-97	249	4	s	s	PROPN
ejpam-97	249	5	,	,	PUNCT
ejpam-97	249	6	f	f	X
ejpam-97	249	7	:	:	PUNCT
ejpam-97	249	8	a	a	DET
ejpam-97	249	9	,	,	PUNCT
ejpam-97	249	10	→	→	SYM
ejpam-97	249	11	b	b	PROPN
ejpam-97	249	12	and	and	CCONJ
ejpam-97	249	13	g	g	PROPN
ejpam-97	249	14	:	:	PUNCT
ejpam-97	249	15	b	b	NOUN
ejpam-97	249	16	,	,	PUNCT
ejpam-97	249	17	→	→	SYM
ejpam-97	249	18	c	c	NOUN
ejpam-97	249	19	are	be	AUX
ejpam-97	249	20	monomorphisms	monomorphism	NOUN
ejpam-97	249	21	,	,	PUNCT
ejpam-97	249	22	f	f	PROPN
ejpam-97	249	23	is	be	AUX
ejpam-97	249	24	s	s	NOUN
ejpam-97	249	25	-	-	PUNCT
ejpam-97	249	26	dense	dense	ADJ
ejpam-97	249	27	,	,	PUNCT
ejpam-97	249	28	and	and	CCONJ
ejpam-97	249	29	g	g	PROPN
ejpam-97	249	30	f	f	PROPN
ejpam-97	249	31	is	be	AUX
ejpam-97	249	32	s	s	NOUN
ejpam-97	249	33	-	-	ADJ
ejpam-97	249	34	pure	pure	ADJ
ejpam-97	249	35	,	,	PUNCT
ejpam-97	249	36	then	then	ADV
ejpam-97	249	37	g	g	PROPN
ejpam-97	249	38	is	be	AUX
ejpam-97	249	39	s	s	NOUN
ejpam-97	249	40	-	-	ADJ
ejpam-97	249	41	pure	pure	ADJ
ejpam-97	249	42	.	.	PUNCT
ejpam-97	250	1	proof	proof	NOUN
ejpam-97	250	2	.	.	PUNCT
ejpam-97	251	1	without	without	ADP
ejpam-97	251	2	loss	loss	NOUN
ejpam-97	251	3	of	of	ADP
ejpam-97	251	4	generality	generality	NOUN
ejpam-97	251	5	,	,	PUNCT
ejpam-97	251	6	we	we	PRON
ejpam-97	251	7	again	again	ADV
ejpam-97	251	8	assume	assume	VERB
ejpam-97	251	9	that	that	SCONJ
ejpam-97	251	10	f	f	PROPN
ejpam-97	251	11	and	and	CCONJ
ejpam-97	251	12	g	g	PROPN
ejpam-97	251	13	are	be	AUX
ejpam-97	251	14	inclusions	inclusion	NOUN
ejpam-97	251	15	.	.	PUNCT
ejpam-97	252	1	let	let	VERB
ejpam-97	252	2	c	c	NOUN
ejpam-97	252	3	∈	∈	PROPN
ejpam-97	252	4	c	c	AUX
ejpam-97	252	5	be	be	AUX
ejpam-97	252	6	such	such	ADJ
ejpam-97	252	7	that	that	SCONJ
ejpam-97	252	8	cs	cs	PROPN
ejpam-97	252	9	⊆	⊆	NUM
ejpam-97	252	10	b.	b.	NOUN
ejpam-97	253	1	so	so	ADV
ejpam-97	253	2	,	,	PUNCT
ejpam-97	253	3	since	since	SCONJ
ejpam-97	253	4	f	f	PROPN
ejpam-97	253	5	is	be	AUX
ejpam-97	253	6	s	s	NOUN
ejpam-97	253	7	-	-	PUNCT
ejpam-97	253	8	dense	dense	ADJ
ejpam-97	253	9	,	,	PUNCT
ejpam-97	253	10	we	we	PRON
ejpam-97	253	11	get	get	VERB
ejpam-97	253	12	(	(	PUNCT
ejpam-97	253	13	cs)s	cs)s	PROPN
ejpam-97	253	14	⊆	⊆	NUM
ejpam-97	253	15	a.	a.	NOUN
ejpam-97	253	16	now	now	ADV
ejpam-97	253	17	,	,	PUNCT
ejpam-97	253	18	since	since	SCONJ
ejpam-97	253	19	s2	s2	VERB
ejpam-97	253	20	=	=	SYM
ejpam-97	253	21	s	s	PROPN
ejpam-97	253	22	and	and	CCONJ
ejpam-97	253	23	g	g	PROPN
ejpam-97	253	24	f	f	PROPN
ejpam-97	253	25	is	be	AUX
ejpam-97	253	26	s	s	NOUN
ejpam-97	253	27	-	-	ADJ
ejpam-97	253	28	pure	pure	ADJ
ejpam-97	253	29	,	,	PUNCT
ejpam-97	253	30	we	we	PRON
ejpam-97	253	31	get	get	VERB
ejpam-97	253	32	an	an	DET
ejpam-97	253	33	a	a	DET
ejpam-97	253	34	∈	∈	NOUN
ejpam-97	253	35	a⊆	a⊆	PROPN
ejpam-97	253	36	b	b	NOUN
ejpam-97	253	37	with	with	ADP
ejpam-97	253	38	λc	λc	X
ejpam-97	253	39	=	=	SYM
ejpam-97	253	40	λa	λa	PROPN
ejpam-97	253	41	,	,	PUNCT
ejpam-97	253	42	which	which	PRON
ejpam-97	253	43	proves	prove	VERB
ejpam-97	253	44	that	that	SCONJ
ejpam-97	253	45	g	g	PROPN
ejpam-97	253	46	is	be	AUX
ejpam-97	253	47	s	s	NOUN
ejpam-97	253	48	-	-	ADJ
ejpam-97	253	49	pure	pure	ADJ
ejpam-97	253	50	.	.	PUNCT
ejpam-97	254	1	definition	definition	NOUN
ejpam-97	254	2	3.1	3.1	NUM
ejpam-97	254	3	.	.	PUNCT
ejpam-97	255	1	let	let	VERB
ejpam-97	255	2	e	e	PRON
ejpam-97	255	3	be	be	AUX
ejpam-97	255	4	a	a	DET
ejpam-97	255	5	class	class	NOUN
ejpam-97	255	6	of	of	ADP
ejpam-97	255	7	homomorphisms	homomorphism	NOUN
ejpam-97	255	8	.	.	PUNCT
ejpam-97	256	1	we	we	PRON
ejpam-97	256	2	say	say	VERB
ejpam-97	256	3	that	that	DET
ejpam-97	256	4	act	act	NOUN
ejpam-97	256	5	-	-	PUNCT
ejpam-97	256	6	s	s	PART
ejpam-97	256	7	has	have	VERB
ejpam-97	256	8	(	(	PUNCT
ejpam-97	256	9	e	e	NOUN
ejpam-97	256	10	,	,	PUNCT
ejpam-97	256	11	mp	mp	PROPN
ejpam-97	256	12	)	)	PUNCT
ejpam-97	256	13	diagonalization	diagonalization	NOUN
ejpam-97	256	14	property	property	NOUN
ejpam-97	256	15	if	if	SCONJ
ejpam-97	256	16	for	for	ADP
ejpam-97	256	17	any	any	DET
ejpam-97	256	18	commutative	commutative	ADJ
ejpam-97	256	19	diagram	diagram	NOUN
ejpam-97	256	20	a	a	DET
ejpam-97	256	21	e−→	e−→	NOUN
ejpam-97	257	1	b	b	NOUN
ejpam-97	257	2	f	f	PROPN
ejpam-97	257	3	↓	↓	PROPN
ejpam-97	257	4	↓	↓	PROPN
ejpam-97	257	5	g	g	PROPN
ejpam-97	257	6	c	c	PROPN
ejpam-97	257	7	m−→	m−→	PROPN
ejpam-97	257	8	d	d	NOUN
ejpam-97	257	9	with	with	ADP
ejpam-97	257	10	e	e	PROPN
ejpam-97	257	11	∈	∈	PROPN
ejpam-97	257	12	e	e	X
ejpam-97	257	13	and	and	CCONJ
ejpam-97	257	14	m	m	PROPN
ejpam-97	257	15	∈mp	∈mp	NOUN
ejpam-97	257	16	there	there	ADV
ejpam-97	257	17	exists	exist	VERB
ejpam-97	257	18	a	a	DET
ejpam-97	257	19	unique	unique	ADJ
ejpam-97	257	20	diagonal	diagonal	ADJ
ejpam-97	257	21	s	s	NOUN
ejpam-97	257	22	-	-	PUNCT
ejpam-97	257	23	map	map	NOUN
ejpam-97	257	24	d	d	X
ejpam-97	257	25	:	:	PUNCT
ejpam-97	257	26	b→	b→	PROPN
ejpam-97	257	27	c	c	NOUN
ejpam-97	257	28	such	such	ADJ
ejpam-97	257	29	that	that	PRON
ejpam-97	257	30	de	de	PROPN
ejpam-97	257	31	=	=	SYM
ejpam-97	257	32	f	f	PROPN
ejpam-97	257	33	and	and	CCONJ
ejpam-97	257	34	md	md	PROPN
ejpam-97	257	35	=	=	PUNCT
ejpam-97	257	36	g.	g.	PROPN
ejpam-97	257	37	proposition	proposition	PROPN
ejpam-97	257	38	3.1	3.1	NUM
ejpam-97	257	39	.	.	PUNCT
ejpam-97	258	1	act	act	PROPN
ejpam-97	258	2	-	-	PUNCT
ejpam-97	258	3	s	s	PROPN
ejpam-97	258	4	has	have	VERB
ejpam-97	258	5	(	(	PUNCT
ejpam-97	258	6	e	e	NOUN
ejpam-97	258	7	,	,	PUNCT
ejpam-97	258	8	mp	mp	PROPN
ejpam-97	258	9	)	)	PUNCT
ejpam-97	258	10	diagonalization	diagonalization	NOUN
ejpam-97	258	11	property	property	NOUN
ejpam-97	258	12	,	,	PUNCT
ejpam-97	258	13	for	for	ADP
ejpam-97	258	14	e	e	NOUN
ejpam-97	258	15	the	the	DET
ejpam-97	258	16	class	class	NOUN
ejpam-97	258	17	of	of	ADP
ejpam-97	258	18	all	all	DET
ejpam-97	258	19	epimorphisms	epimorphism	NOUN
ejpam-97	258	20	.	.	PUNCT
ejpam-97	259	1	h.	h.	PROPN
ejpam-97	259	2	barzegar	barzegar	PROPN
ejpam-97	259	3	and	and	CCONJ
ejpam-97	259	4	m.m	m.m	PROPN
ejpam-97	259	5	.	.	PROPN
ejpam-97	259	6	ebrahimi	ebrahimi	PROPN
ejpam-97	259	7	/	/	SYM
ejpam-97	259	8	eur	eur	PROPN
ejpam-97	259	9	.	.	PUNCT
ejpam-97	260	1	j.	j.	PROPN
ejpam-97	260	2	pure	pure	PROPN
ejpam-97	260	3	appl	appl	PROPN
ejpam-97	260	4	.	.	PROPN
ejpam-97	260	5	math	math	PROPN
ejpam-97	260	6	,	,	PUNCT
ejpam-97	260	7	1	1	NUM
ejpam-97	260	8	(	(	PUNCT
ejpam-97	260	9	2008	2008	NUM
ejpam-97	260	10	)	)	PUNCT
ejpam-97	260	11	,	,	PUNCT
ejpam-97	260	12	(	(	PUNCT
ejpam-97	260	13	41	41	NUM
ejpam-97	260	14	-	-	SYM
ejpam-97	260	15	55	55	NUM
ejpam-97	260	16	)	)	PUNCT
ejpam-97	260	17	50	50	NUM
ejpam-97	260	18	proof	proof	NOUN
ejpam-97	260	19	.	.	PUNCT
ejpam-97	261	1	consider	consider	VERB
ejpam-97	261	2	the	the	DET
ejpam-97	261	3	diagram	diagram	NOUN
ejpam-97	261	4	given	give	VERB
ejpam-97	261	5	in	in	ADP
ejpam-97	261	6	the	the	DET
ejpam-97	261	7	above	above	ADJ
ejpam-97	261	8	definition	definition	NOUN
ejpam-97	261	9	.	.	PUNCT
ejpam-97	262	1	first	first	ADV
ejpam-97	262	2	,	,	PUNCT
ejpam-97	262	3	we	we	PRON
ejpam-97	262	4	see	see	VERB
ejpam-97	262	5	that	that	DET
ejpam-97	262	6	ker	ker	NOUN
ejpam-97	262	7	e	e	NOUN
ejpam-97	262	8	⊆	⊆	NUM
ejpam-97	262	9	ker	ker	NOUN
ejpam-97	262	10	f	f	X
ejpam-97	262	11	.	.	PUNCT
ejpam-97	263	1	let	let	VERB
ejpam-97	263	2	e(a	e(a	NOUN
ejpam-97	263	3	)	)	PUNCT
ejpam-97	263	4	=	=	SYM
ejpam-97	263	5	e(a′	e(a′	PROPN
ejpam-97	263	6	)	)	PUNCT
ejpam-97	263	7	and	and	CCONJ
ejpam-97	263	8	so	so	ADV
ejpam-97	263	9	ge(a	ge(a	X
ejpam-97	263	10	)	)	PUNCT
ejpam-97	264	1	=	=	SYM
ejpam-97	264	2	ge(a′	ge(a′	PROPN
ejpam-97	264	3	)	)	PUNCT
ejpam-97	264	4	.	.	PUNCT
ejpam-97	265	1	thus	thus	ADV
ejpam-97	265	2	,	,	PUNCT
ejpam-97	265	3	mf	mf	X
ejpam-97	265	4	(	(	PUNCT
ejpam-97	265	5	a	a	X
ejpam-97	265	6	)	)	PUNCT
ejpam-97	265	7	=	=	NOUN
ejpam-97	265	8	mf	mf	X
ejpam-97	265	9	(	(	PUNCT
ejpam-97	265	10	a′	a′	PROPN
ejpam-97	265	11	)	)	PUNCT
ejpam-97	265	12	,	,	PUNCT
ejpam-97	265	13	and	and	CCONJ
ejpam-97	265	14	so	so	ADV
ejpam-97	265	15	f	f	X
ejpam-97	265	16	(	(	PUNCT
ejpam-97	265	17	a	a	X
ejpam-97	265	18	)	)	PUNCT
ejpam-97	265	19	=	=	SYM
ejpam-97	265	20	f	f	PROPN
ejpam-97	265	21	(	(	PUNCT
ejpam-97	265	22	a′	a′	PROPN
ejpam-97	265	23	)	)	PUNCT
ejpam-97	265	24	,	,	PUNCT
ejpam-97	265	25	since	since	SCONJ
ejpam-97	265	26	m	m	PROPN
ejpam-97	265	27	is	be	AUX
ejpam-97	265	28	a	a	DET
ejpam-97	265	29	monomorphism	monomorphism	NOUN
ejpam-97	265	30	.	.	PUNCT
ejpam-97	266	1	then	then	ADV
ejpam-97	266	2	,	,	PUNCT
ejpam-97	266	3	by	by	ADP
ejpam-97	266	4	the	the	DET
ejpam-97	266	5	decomposition	decomposition	NOUN
ejpam-97	266	6	theorem	theorem	NOUN
ejpam-97	266	7	(	(	PUNCT
ejpam-97	266	8	which	which	PRON
ejpam-97	266	9	holds	hold	VERB
ejpam-97	266	10	since	since	SCONJ
ejpam-97	266	11	s	s	NOUN
ejpam-97	266	12	-	-	PUNCT
ejpam-97	266	13	acts	act	NOUN
ejpam-97	266	14	form	form	VERB
ejpam-97	266	15	an	an	DET
ejpam-97	266	16	equational	equational	ADJ
ejpam-97	266	17	class	class	NOUN
ejpam-97	266	18	)	)	PUNCT
ejpam-97	266	19	,	,	PUNCT
ejpam-97	266	20	there	there	PRON
ejpam-97	266	21	exists	exist	VERB
ejpam-97	266	22	a	a	DET
ejpam-97	266	23	unique	unique	ADJ
ejpam-97	266	24	s	s	NOUN
ejpam-97	266	25	-	-	NOUN
ejpam-97	266	26	map	map	NOUN
ejpam-97	266	27	d	d	X
ejpam-97	266	28	:	:	PUNCT
ejpam-97	266	29	b→	b→	PROPN
ejpam-97	266	30	c	c	NOUN
ejpam-97	266	31	with	with	ADP
ejpam-97	266	32	de	de	X
ejpam-97	266	33	=	=	PROPN
ejpam-97	266	34	f	f	PROPN
ejpam-97	266	35	(	(	PUNCT
ejpam-97	266	36	given	give	VERB
ejpam-97	266	37	by	by	ADP
ejpam-97	266	38	d(b	d(b	NOUN
ejpam-97	266	39	)	)	PUNCT
ejpam-97	267	1	=	=	SYM
ejpam-97	267	2	f	f	X
ejpam-97	267	3	(	(	PUNCT
ejpam-97	267	4	a	a	NOUN
ejpam-97	267	5	)	)	PUNCT
ejpam-97	267	6	,	,	PUNCT
ejpam-97	267	7	where	where	SCONJ
ejpam-97	267	8	e(a	e(a	NOUN
ejpam-97	267	9	)	)	PUNCT
ejpam-97	267	10	=	=	SYM
ejpam-97	267	11	b	b	X
ejpam-97	267	12	)	)	PUNCT
ejpam-97	267	13	.	.	PUNCT
ejpam-97	268	1	it	it	PRON
ejpam-97	268	2	is	be	AUX
ejpam-97	268	3	also	also	ADV
ejpam-97	268	4	easily	easily	ADV
ejpam-97	268	5	seen	see	VERB
ejpam-97	268	6	that	that	SCONJ
ejpam-97	268	7	md	md	PROPN
ejpam-97	268	8	=	=	SYM
ejpam-97	268	9	g.	g.	PROPN
ejpam-97	268	10	recall	recall	VERB
ejpam-97	268	11	that	that	SCONJ
ejpam-97	268	12	a	a	DET
ejpam-97	268	13	category	category	NOUN
ejpam-97	268	14	is	be	AUX
ejpam-97	268	15	said	say	VERB
ejpam-97	268	16	to	to	PART
ejpam-97	268	17	have	have	VERB
ejpam-97	268	18	unique	unique	ADJ
ejpam-97	268	19	(	(	PUNCT
ejpam-97	268	20	e	e	NOUN
ejpam-97	268	21	,	,	PUNCT
ejpam-97	268	22	m	m	NOUN
ejpam-97	268	23	)	)	PUNCT
ejpam-97	268	24	factorization	factorization	NOUN
ejpam-97	268	25	property	property	NOUN
ejpam-97	268	26	if	if	SCONJ
ejpam-97	268	27	every	every	DET
ejpam-97	268	28	morphism	morphism	NOUN
ejpam-97	268	29	f	f	PROPN
ejpam-97	268	30	can	can	AUX
ejpam-97	268	31	be	be	AUX
ejpam-97	268	32	uniquely	uniquely	ADV
ejpam-97	268	33	represented	represent	VERB
ejpam-97	268	34	as	as	ADP
ejpam-97	268	35	f	f	PROPN
ejpam-97	268	36	=	=	PROPN
ejpam-97	268	37	me	i	PRON
ejpam-97	268	38	with	with	ADP
ejpam-97	268	39	e	e	PROPN
ejpam-97	268	40	∈	∈	PROPN
ejpam-97	268	41	e	e	NOUN
ejpam-97	268	42	and	and	CCONJ
ejpam-97	268	43	m	m	PROPN
ejpam-97	268	44	∈	∈	PROPN
ejpam-97	268	45	m	m	NOUN
ejpam-97	268	46	,	,	PUNCT
ejpam-97	268	47	where	where	SCONJ
ejpam-97	268	48	e	e	X
ejpam-97	268	49	,	,	PUNCT
ejpam-97	268	50	m	m	VERB
ejpam-97	268	51	are	be	AUX
ejpam-97	268	52	some	some	DET
ejpam-97	268	53	classes	class	NOUN
ejpam-97	268	54	of	of	ADP
ejpam-97	268	55	morphisms	morphism	NOUN
ejpam-97	268	56	.	.	PUNCT
ejpam-97	269	1	remark	remark	PROPN
ejpam-97	269	2	3.1	3.1	NUM
ejpam-97	269	3	.	.	PUNCT
ejpam-97	270	1	act	act	PROPN
ejpam-97	270	2	-	-	PUNCT
ejpam-97	270	3	s	s	PART
ejpam-97	270	4	does	do	AUX
ejpam-97	270	5	not	not	PART
ejpam-97	270	6	generally	generally	ADV
ejpam-97	270	7	have	have	VERB
ejpam-97	270	8	unique	unique	ADJ
ejpam-97	270	9	(	(	PUNCT
ejpam-97	270	10	e	e	NOUN
ejpam-97	270	11	,	,	PUNCT
ejpam-97	270	12	mp	mp	PROPN
ejpam-97	270	13	)	)	PUNCT
ejpam-97	270	14	factorization	factorization	NOUN
ejpam-97	270	15	property	property	NOUN
ejpam-97	270	16	,	,	PUNCT
ejpam-97	270	17	where	where	SCONJ
ejpam-97	270	18	e	e	NOUN
ejpam-97	270	19	is	be	AUX
ejpam-97	270	20	the	the	DET
ejpam-97	270	21	class	class	NOUN
ejpam-97	270	22	of	of	ADP
ejpam-97	270	23	all	all	DET
ejpam-97	270	24	epimorphisms	epimorphism	NOUN
ejpam-97	270	25	.	.	PUNCT
ejpam-97	271	1	to	to	PART
ejpam-97	271	2	see	see	VERB
ejpam-97	271	3	this	this	PRON
ejpam-97	271	4	,	,	PUNCT
ejpam-97	271	5	let	let	VERB
ejpam-97	271	6	s	s	PRON
ejpam-97	271	7	be	be	AUX
ejpam-97	271	8	a	a	DET
ejpam-97	271	9	semigroup	semigroup	NOUN
ejpam-97	271	10	that	that	PRON
ejpam-97	271	11	does	do	AUX
ejpam-97	271	12	not	not	PART
ejpam-97	271	13	have	have	VERB
ejpam-97	271	14	a	a	DET
ejpam-97	271	15	left	left	ADJ
ejpam-97	271	16	identity	identity	NOUN
ejpam-97	271	17	.	.	PUNCT
ejpam-97	272	1	then	then	ADV
ejpam-97	272	2	,	,	PUNCT
ejpam-97	272	3	by	by	ADP
ejpam-97	272	4	theorem	theorem	NOUN
ejpam-97	272	5	3.1	3.1	NUM
ejpam-97	272	6	,	,	PUNCT
ejpam-97	272	7	s	s	PART
ejpam-97	272	8	is	be	AUX
ejpam-97	272	9	not	not	PART
ejpam-97	272	10	s	s	NOUN
ejpam-97	272	11	-	-	NOUN
ejpam-97	272	12	pure	pure	ADJ
ejpam-97	272	13	in	in	ADP
ejpam-97	272	14	s1	s1	NOUN
ejpam-97	272	15	.	.	PUNCT
ejpam-97	273	1	on	on	ADP
ejpam-97	273	2	the	the	DET
ejpam-97	273	3	contrary	contrary	NOUN
ejpam-97	273	4	,	,	PUNCT
ejpam-97	273	5	let	let	VERB
ejpam-97	273	6	the	the	DET
ejpam-97	273	7	inclusion	inclusion	NOUN
ejpam-97	273	8	morphism	morphism	NOUN
ejpam-97	273	9	τ	τ	PROPN
ejpam-97	273	10	:	:	PUNCT
ejpam-97	273	11	s	s	X
ejpam-97	273	12	→	→	PUNCT
ejpam-97	273	13	s1	s1	PROPN
ejpam-97	273	14	have	have	VERB
ejpam-97	273	15	an	an	DET
ejpam-97	273	16	(	(	PUNCT
ejpam-97	273	17	e	e	NOUN
ejpam-97	273	18	,	,	PUNCT
ejpam-97	273	19	mp)-factorization	mp)-factorization	NOUN
ejpam-97	273	20	s	s	PART
ejpam-97	273	21	e→	e→	NOUN
ejpam-97	273	22	a	a	DET
ejpam-97	273	23	m→	m→	NOUN
ejpam-97	273	24	s1	s1	NOUN
ejpam-97	273	25	.	.	PUNCT
ejpam-97	274	1	since	since	SCONJ
ejpam-97	274	2	me	i	PRON
ejpam-97	274	3	is	be	AUX
ejpam-97	274	4	a	a	DET
ejpam-97	274	5	monomorphism	monomorphism	NOUN
ejpam-97	274	6	,	,	PUNCT
ejpam-97	274	7	e	e	X
ejpam-97	274	8	is	be	AUX
ejpam-97	274	9	a	a	DET
ejpam-97	274	10	monomorphism	monomorphism	NOUN
ejpam-97	274	11	and	and	CCONJ
ejpam-97	274	12	hence	hence	ADV
ejpam-97	274	13	an	an	DET
ejpam-97	274	14	isomorphism	isomorphism	NOUN
ejpam-97	274	15	.	.	PUNCT
ejpam-97	275	1	thus	thus	ADV
ejpam-97	275	2	,	,	PUNCT
ejpam-97	275	3	τ=	τ=	PROPN
ejpam-97	275	4	m	m	VERB
ejpam-97	275	5	is	be	AUX
ejpam-97	275	6	s	s	NOUN
ejpam-97	275	7	-	-	ADJ
ejpam-97	275	8	pure	pure	ADJ
ejpam-97	275	9	which	which	PRON
ejpam-97	275	10	is	be	AUX
ejpam-97	275	11	a	a	DET
ejpam-97	275	12	contradiction	contradiction	NOUN
ejpam-97	275	13	.	.	PUNCT
ejpam-97	276	1	3.2	3.2	NUM
ejpam-97	276	2	.	.	PUNCT
ejpam-97	276	3	limits	limit	NOUN
ejpam-97	276	4	of	of	ADP
ejpam-97	276	5	s	s	NOUN
ejpam-97	276	6	-	-	ADJ
ejpam-97	276	7	pure	pure	ADJ
ejpam-97	276	8	monomorphisms	monomorphism	NOUN
ejpam-97	276	9	in	in	ADP
ejpam-97	276	10	this	this	DET
ejpam-97	276	11	subsection	subsection	NOUN
ejpam-97	276	12	some	some	PRON
ejpam-97	276	13	of	of	ADP
ejpam-97	276	14	the	the	DET
ejpam-97	276	15	categorical	categorical	ADJ
ejpam-97	276	16	properties	property	NOUN
ejpam-97	276	17	of	of	ADP
ejpam-97	276	18	s	s	NOUN
ejpam-97	276	19	-	-	ADJ
ejpam-97	276	20	pure	pure	ADJ
ejpam-97	276	21	monomorphisms	monomorphism	NOUN
ejpam-97	276	22	related	relate	VERB
ejpam-97	276	23	to	to	ADP
ejpam-97	276	24	limits	limit	NOUN
ejpam-97	276	25	are	be	AUX
ejpam-97	276	26	studied	study	VERB
ejpam-97	276	27	.	.	PUNCT
ejpam-97	277	1	the	the	DET
ejpam-97	277	2	proof	proof	NOUN
ejpam-97	277	3	of	of	ADP
ejpam-97	277	4	the	the	DET
ejpam-97	277	5	following	following	NOUN
ejpam-97	277	6	is	be	AUX
ejpam-97	277	7	straightforward	straightforward	ADJ
ejpam-97	277	8	.	.	PUNCT
ejpam-97	278	1	proposition	proposition	NOUN
ejpam-97	278	2	3.2	3.2	NUM
ejpam-97	278	3	.	.	PUNCT
ejpam-97	279	1	(	(	PUNCT
ejpam-97	279	2	1)mp	1)mp	NUM
ejpam-97	279	3	is	be	AUX
ejpam-97	279	4	closed	close	VERB
ejpam-97	279	5	under	under	ADP
ejpam-97	279	6	products	product	NOUN
ejpam-97	279	7	.	.	PUNCT
ejpam-97	280	1	(	(	PUNCT
ejpam-97	280	2	2	2	X
ejpam-97	280	3	)	)	PUNCT
ejpam-97	280	4	let	let	VERB
ejpam-97	280	5	{	{	PUNCT
ejpam-97	280	6	fα	fα	ADP
ejpam-97	280	7	:	:	PUNCT
ejpam-97	280	8	a	a	PRON
ejpam-97	280	9	→	→	X
ejpam-97	280	10	bα|α	bα|α	PRON
ejpam-97	280	11	∈	∈	PROPN
ejpam-97	281	1	i	i	PRON
ejpam-97	281	2	}	}	PUNCT
ejpam-97	281	3	be	be	VERB
ejpam-97	281	4	a	a	DET
ejpam-97	281	5	family	family	NOUN
ejpam-97	281	6	of	of	ADP
ejpam-97	281	7	s	s	NOUN
ejpam-97	281	8	-	-	ADJ
ejpam-97	281	9	pure	pure	ADJ
ejpam-97	281	10	monomorphisms	monomorphism	NOUN
ejpam-97	281	11	.	.	PUNCT
ejpam-97	282	1	then	then	ADV
ejpam-97	282	2	their	their	PRON
ejpam-97	282	3	product	product	NOUN
ejpam-97	282	4	homomorphism	homomorphism	NOUN
ejpam-97	282	5	h	h	NOUN
ejpam-97	282	6	:	:	PUNCT
ejpam-97	282	7	a→	a→	PUNCT
ejpam-97	282	8	∏	∏	X
ejpam-97	282	9	α∈i	α∈i	ADJ
ejpam-97	282	10	bα	bα	NOUN
ejpam-97	282	11	is	be	AUX
ejpam-97	282	12	also	also	ADV
ejpam-97	282	13	an	an	DET
ejpam-97	282	14	s	s	NOUN
ejpam-97	282	15	-	-	ADJ
ejpam-97	282	16	pure	pure	ADJ
ejpam-97	282	17	monomorphism	monomorphism	NOUN
ejpam-97	282	18	.	.	PUNCT
ejpam-97	283	1	note	note	VERB
ejpam-97	283	2	that	that	SCONJ
ejpam-97	283	3	the	the	DET
ejpam-97	283	4	above	above	ADJ
ejpam-97	283	5	result	result	NOUN
ejpam-97	283	6	(	(	PUNCT
ejpam-97	283	7	2	2	X
ejpam-97	283	8	)	)	PUNCT
ejpam-97	283	9	is	be	AUX
ejpam-97	283	10	also	also	ADV
ejpam-97	283	11	true	true	ADJ
ejpam-97	283	12	whenever	whenever	SCONJ
ejpam-97	283	13	for	for	ADP
ejpam-97	283	14	some	some	PRON
ejpam-97	283	15	(	(	PUNCT
ejpam-97	283	16	not	not	PART
ejpam-97	283	17	necessarily	necessarily	ADV
ejpam-97	283	18	all	all	PRON
ejpam-97	283	19	)	)	PUNCT
ejpam-97	284	1	α	α	PRON
ejpam-97	284	2	∈	∈	PROPN
ejpam-97	285	1	i	i	PRON
ejpam-97	285	2	,	,	PUNCT
ejpam-97	285	3	fα	fα	ADV
ejpam-97	285	4	is	be	AUX
ejpam-97	285	5	an	an	DET
ejpam-97	285	6	s	s	NOUN
ejpam-97	285	7	-	-	ADJ
ejpam-97	285	8	pure	pure	ADJ
ejpam-97	285	9	monomorphism	monomorphism	NOUN
ejpam-97	285	10	.	.	PUNCT
ejpam-97	286	1	lemma	lemma	PROPN
ejpam-97	286	2	3.3	3.3	NUM
ejpam-97	286	3	.	.	PUNCT
ejpam-97	287	1	in	in	ADP
ejpam-97	287	2	act	act	PROPN
ejpam-97	287	3	-	-	PUNCT
ejpam-97	287	4	s	s	PROPN
ejpam-97	287	5	,	,	PUNCT
ejpam-97	287	6	pullbacks	pullback	NOUN
ejpam-97	287	7	transfer	transfer	VERB
ejpam-97	287	8	s	s	NOUN
ejpam-97	287	9	-	-	ADJ
ejpam-97	287	10	pure	pure	ADJ
ejpam-97	287	11	monomorphisms	monomorphism	NOUN
ejpam-97	287	12	if	if	SCONJ
ejpam-97	287	13	and	and	CCONJ
ejpam-97	287	14	only	only	ADV
ejpam-97	287	15	if	if	SCONJ
ejpam-97	287	16	s	s	PROPN
ejpam-97	287	17	has	have	VERB
ejpam-97	287	18	a	a	DET
ejpam-97	287	19	left	left	ADJ
ejpam-97	287	20	identity	identity	NOUN
ejpam-97	287	21	.	.	PUNCT
ejpam-97	288	1	proof	proof	NOUN
ejpam-97	288	2	.	.	PUNCT
ejpam-97	289	1	necessity	necessity	NOUN
ejpam-97	289	2	:	:	PUNCT
ejpam-97	289	3	by	by	ADP
ejpam-97	289	4	theorem	theorem	NOUN
ejpam-97	289	5	3.1	3.1	NUM
ejpam-97	289	6	,	,	PUNCT
ejpam-97	289	7	it	it	PRON
ejpam-97	289	8	is	be	AUX
ejpam-97	289	9	enough	enough	ADJ
ejpam-97	289	10	to	to	PART
ejpam-97	289	11	show	show	VERB
ejpam-97	289	12	that	that	SCONJ
ejpam-97	289	13	s	s	VERB
ejpam-97	289	14	is	be	AUX
ejpam-97	289	15	s	s	NOUN
ejpam-97	289	16	-	-	ADJ
ejpam-97	289	17	pure	pure	ADJ
ejpam-97	289	18	in	in	ADP
ejpam-97	289	19	s1	s1	NOUN
ejpam-97	289	20	.	.	PUNCT
ejpam-97	290	1	let	let	VERB
ejpam-97	290	2	e	e	PRON
ejpam-97	290	3	be	be	AUX
ejpam-97	290	4	an	an	DET
ejpam-97	290	5	injective	injective	ADJ
ejpam-97	290	6	s	s	NOUN
ejpam-97	290	7	-	-	NOUN
ejpam-97	290	8	act	act	NOUN
ejpam-97	290	9	and	and	CCONJ
ejpam-97	290	10	0	0	NUM
ejpam-97	290	11	be	be	AUX
ejpam-97	290	12	a	a	DET
ejpam-97	290	13	zero	zero	NUM
ejpam-97	290	14	element	element	NOUN
ejpam-97	290	15	of	of	ADP
ejpam-97	290	16	e	e	PROPN
ejpam-97	290	17	(	(	PUNCT
ejpam-97	290	18	see	see	VERB
ejpam-97	290	19	[	[	X
ejpam-97	290	20	13	13	NUM
ejpam-97	290	21	]	]	PUNCT
ejpam-97	290	22	,	,	PUNCT
ejpam-97	290	23	lemma	lemma	PROPN
ejpam-97	290	24	iii.1.7	iii.1.7	PROPN
ejpam-97	290	25	)	)	PUNCT
ejpam-97	290	26	.	.	PUNCT
ejpam-97	291	1	adjoin	adjoin	VERB
ejpam-97	291	2	an	an	DET
ejpam-97	291	3	element	element	NOUN
ejpam-97	291	4	θ	θ	NOUN
ejpam-97	291	5	to	to	ADP
ejpam-97	291	6	e	e	NOUN
ejpam-97	291	7	and	and	CCONJ
ejpam-97	291	8	define	define	VERB
ejpam-97	291	9	θ	θ	PROPN
ejpam-97	291	10	s	s	PART
ejpam-97	291	11	=	=	NOUN
ejpam-97	291	12	0	0	NUM
ejpam-97	291	13	for	for	ADP
ejpam-97	291	14	all	all	PRON
ejpam-97	291	15	s	s	PROPN
ejpam-97	291	16	∈	∈	PROPN
ejpam-97	291	17	s.	s.	PROPN
ejpam-97	291	18	then	then	ADV
ejpam-97	291	19	,	,	PUNCT
ejpam-97	291	20	e	e	PROPN
ejpam-97	291	21	is	be	AUX
ejpam-97	291	22	clearly	clearly	ADV
ejpam-97	291	23	s	s	VERB
ejpam-97	291	24	-	-	ADJ
ejpam-97	291	25	pure	pure	ADJ
ejpam-97	291	26	in	in	ADP
ejpam-97	291	27	eθ	eθ	NOUN
ejpam-97	291	28	=	=	SYM
ejpam-97	291	29	e	e	X
ejpam-97	291	30	∪	∪	X
ejpam-97	291	31	{	{	PUNCT
ejpam-97	291	32	θ	θ	NOUN
ejpam-97	291	33	}	}	PUNCT
ejpam-97	291	34	.	.	PUNCT
ejpam-97	292	1	taking	take	VERB
ejpam-97	292	2	a	a	DET
ejpam-97	292	3	homomorphism	homomorphism	NOUN
ejpam-97	292	4	f	f	X
ejpam-97	292	5	:	:	PUNCT
ejpam-97	292	6	s1	s1	PROPN
ejpam-97	292	7	−→	−→	NOUN
ejpam-97	292	8	eθ	eθ	ADP
ejpam-97	292	9	given	give	VERB
ejpam-97	292	10	by	by	ADP
ejpam-97	292	11	f	f	PROPN
ejpam-97	292	12	(	(	PUNCT
ejpam-97	292	13	s	s	NOUN
ejpam-97	292	14	)	)	PUNCT
ejpam-97	292	15	=	=	SYM
ejpam-97	292	16	θ	θ	NOUN
ejpam-97	292	17	s	s	X
ejpam-97	292	18	(	(	PUNCT
ejpam-97	292	19	s	s	NOUN
ejpam-97	292	20	∈	∈	PROPN
ejpam-97	292	21	s1	s1	NOUN
ejpam-97	292	22	)	)	PUNCT
ejpam-97	292	23	we	we	PRON
ejpam-97	292	24	have	have	VERB
ejpam-97	292	25	the	the	DET
ejpam-97	292	26	pullback	pullback	NOUN
ejpam-97	292	27	diagram	diagram	NOUN
ejpam-97	292	28	:	:	PUNCT
ejpam-97	292	29	s	s	PART
ejpam-97	292	30	τ−→	τ−→	NUM
ejpam-97	292	31	s1	s1	PROPN
ejpam-97	292	32	f	f	PROPN
ejpam-97	292	33	↓	↓	PROPN
ejpam-97	292	34	↓	↓	PROPN
ejpam-97	292	35	f	f	PROPN
ejpam-97	292	36	e	e	PROPN
ejpam-97	292	37	τ′−→	τ′−→	X
ejpam-97	292	38	eθ	eθ	PROPN
ejpam-97	292	39	where	where	SCONJ
ejpam-97	292	40	τ	τ	X
ejpam-97	292	41	,	,	PUNCT
ejpam-97	292	42	τ′	τ′	PROPN
ejpam-97	292	43	are	be	AUX
ejpam-97	292	44	inclusion	inclusion	NOUN
ejpam-97	292	45	morphisms	morphism	NOUN
ejpam-97	292	46	.	.	PUNCT
ejpam-97	293	1	then	then	ADV
ejpam-97	293	2	,	,	PUNCT
ejpam-97	293	3	since	since	SCONJ
ejpam-97	293	4	τ′	τ′	X
ejpam-97	293	5	is	be	AUX
ejpam-97	293	6	s	s	NOUN
ejpam-97	293	7	-	-	ADJ
ejpam-97	293	8	pure	pure	ADJ
ejpam-97	293	9	,	,	PUNCT
ejpam-97	293	10	we	we	PRON
ejpam-97	293	11	get	get	VERB
ejpam-97	293	12	that	that	PRON
ejpam-97	293	13	s	s	NOUN
ejpam-97	293	14	is	be	AUX
ejpam-97	293	15	s	s	NOUN
ejpam-97	293	16	-	-	ADJ
ejpam-97	293	17	pure	pure	ADJ
ejpam-97	293	18	in	in	ADP
ejpam-97	293	19	s1	s1	NOUN
ejpam-97	293	20	,	,	PUNCT
ejpam-97	293	21	by	by	ADP
ejpam-97	293	22	the	the	DET
ejpam-97	293	23	hypothesis	hypothesis	NOUN
ejpam-97	293	24	.	.	PUNCT
ejpam-97	294	1	sufficiency	sufficiency	NOUN
ejpam-97	294	2	:	:	PUNCT
ejpam-97	294	3	let	let	VERB
ejpam-97	294	4	s	s	PRON
ejpam-97	294	5	have	have	VERB
ejpam-97	294	6	a	a	DET
ejpam-97	294	7	left	left	ADJ
ejpam-97	294	8	identity	identity	NOUN
ejpam-97	294	9	.	.	PUNCT
ejpam-97	295	1	in	in	ADP
ejpam-97	295	2	this	this	DET
ejpam-97	295	3	case	case	NOUN
ejpam-97	295	4	,	,	PUNCT
ejpam-97	295	5	by	by	ADP
ejpam-97	295	6	theorem	theorem	NOUN
ejpam-97	295	7	3.1	3.1	NUM
ejpam-97	295	8	,	,	PUNCT
ejpam-97	295	9	every	every	DET
ejpam-97	295	10	monomorphism	monomorphism	NOUN
ejpam-97	295	11	is	be	AUX
ejpam-97	295	12	s	s	NOUN
ejpam-97	295	13	-	-	ADJ
ejpam-97	295	14	pure	pure	ADJ
ejpam-97	295	15	and	and	CCONJ
ejpam-97	295	16	pullbacks	pullback	NOUN
ejpam-97	295	17	clearly	clearly	ADV
ejpam-97	295	18	preserve	preserve	VERB
ejpam-97	295	19	monomorphisms	monomorphism	NOUN
ejpam-97	295	20	.	.	PUNCT
ejpam-97	296	1	h.	h.	PROPN
ejpam-97	296	2	barzegar	barzegar	PROPN
ejpam-97	296	3	and	and	CCONJ
ejpam-97	296	4	m.m	m.m	PROPN
ejpam-97	296	5	.	.	PROPN
ejpam-97	296	6	ebrahimi	ebrahimi	PROPN
ejpam-97	296	7	/	/	SYM
ejpam-97	296	8	eur	eur	PROPN
ejpam-97	296	9	.	.	PUNCT
ejpam-97	297	1	j.	j.	PROPN
ejpam-97	297	2	pure	pure	PROPN
ejpam-97	297	3	appl	appl	PROPN
ejpam-97	297	4	.	.	PROPN
ejpam-97	297	5	math	math	PROPN
ejpam-97	297	6	,	,	PUNCT
ejpam-97	297	7	1	1	NUM
ejpam-97	297	8	(	(	PUNCT
ejpam-97	297	9	2008	2008	NUM
ejpam-97	297	10	)	)	PUNCT
ejpam-97	297	11	,	,	PUNCT
ejpam-97	297	12	(	(	PUNCT
ejpam-97	297	13	41	41	NUM
ejpam-97	297	14	-	-	SYM
ejpam-97	297	15	55	55	NUM
ejpam-97	297	16	)	)	PUNCT
ejpam-97	297	17	51	51	NUM
ejpam-97	297	18	proposition	proposition	NOUN
ejpam-97	297	19	3.3	3.3	NUM
ejpam-97	297	20	.	.	PUNCT
ejpam-97	298	1	let	let	VERB
ejpam-97	298	2	{	{	PUNCT
ejpam-97	298	3	fα	fα	PART
ejpam-97	298	4	:	:	PUNCT
ejpam-97	298	5	a→	a→	X
ejpam-97	298	6	bα|α	bα|α	X
ejpam-97	298	7	∈	∈	PROPN
ejpam-97	299	1	i	i	PRON
ejpam-97	299	2	}	}	PUNCT
ejpam-97	299	3	be	be	VERB
ejpam-97	299	4	a	a	DET
ejpam-97	299	5	source	source	NOUN
ejpam-97	299	6	of	of	ADP
ejpam-97	299	7	s	s	NOUN
ejpam-97	299	8	-	-	ADJ
ejpam-97	299	9	pure	pure	ADJ
ejpam-97	299	10	monomorphisms	monomorphism	NOUN
ejpam-97	299	11	.	.	PUNCT
ejpam-97	300	1	then	then	ADV
ejpam-97	300	2	the	the	DET
ejpam-97	300	3	homomorphism	homomorphism	PROPN
ejpam-97	300	4	f	f	X
ejpam-97	300	5	:	:	PUNCT
ejpam-97	300	6	a→	a→	PUNCT
ejpam-97	300	7	l	l	PROPN
ejpam-97	300	8	im←−bα	im←−bα	PROPN
ejpam-97	300	9	(	(	PUNCT
ejpam-97	300	10	existing	exist	VERB
ejpam-97	300	11	by	by	ADP
ejpam-97	300	12	the	the	DET
ejpam-97	300	13	universal	universal	ADJ
ejpam-97	300	14	property	property	NOUN
ejpam-97	300	15	of	of	ADP
ejpam-97	300	16	limits	limit	NOUN
ejpam-97	300	17	)	)	PUNCT
ejpam-97	300	18	is	be	AUX
ejpam-97	300	19	an	an	DET
ejpam-97	300	20	s	s	NOUN
ejpam-97	300	21	-	-	ADJ
ejpam-97	300	22	pure	pure	ADJ
ejpam-97	300	23	monomorphism	monomorphism	NOUN
ejpam-97	300	24	.	.	PUNCT
ejpam-97	301	1	proof	proof	NOUN
ejpam-97	301	2	.	.	PUNCT
ejpam-97	302	1	it	it	PRON
ejpam-97	302	2	is	be	AUX
ejpam-97	302	3	clear	clear	ADJ
ejpam-97	302	4	that	that	SCONJ
ejpam-97	302	5	f	f	PROPN
ejpam-97	302	6	is	be	AUX
ejpam-97	302	7	one	one	NUM
ejpam-97	302	8	-	-	PUNCT
ejpam-97	302	9	one	one	NUM
ejpam-97	302	10	,	,	PUNCT
ejpam-97	302	11	because	because	SCONJ
ejpam-97	302	12	so	so	ADV
ejpam-97	302	13	is	be	AUX
ejpam-97	302	14	every	every	DET
ejpam-97	302	15	fα	fα	NOUN
ejpam-97	302	16	.	.	PUNCT
ejpam-97	303	1	also	also	ADV
ejpam-97	303	2	,	,	PUNCT
ejpam-97	303	3	if	if	SCONJ
ejpam-97	303	4	k	k	X
ejpam-97	303	5	:	:	PUNCT
ejpam-97	303	6	s→	s→	X
ejpam-97	303	7	a	a	PRON
ejpam-97	303	8	is	be	AUX
ejpam-97	303	9	an	an	DET
ejpam-97	303	10	s	s	NOUN
ejpam-97	303	11	-	-	NOUN
ejpam-97	303	12	map	map	NOUN
ejpam-97	303	13	with	with	ADP
ejpam-97	303	14	f	f	PROPN
ejpam-97	303	15	k	k	PROPN
ejpam-97	303	16	=	=	PUNCT
ejpam-97	303	17	λx	λx	PROPN
ejpam-97	303	18	for	for	ADP
ejpam-97	303	19	some	some	DET
ejpam-97	303	20	x	x	SYM
ejpam-97	303	21	∈	∈	PROPN
ejpam-97	303	22	l	l	NOUN
ejpam-97	303	23	im←−bα	im←−bα	PROPN
ejpam-97	303	24	,	,	PUNCT
ejpam-97	303	25	then	then	ADV
ejpam-97	303	26	for	for	ADP
ejpam-97	303	27	every	every	DET
ejpam-97	303	28	α	α	DET
ejpam-97	303	29	fαk	fαk	PROPN
ejpam-97	303	30	=	=	SYM
ejpam-97	303	31	πα	πα	PROPN
ejpam-97	303	32	f	f	PROPN
ejpam-97	303	33	k	k	PROPN
ejpam-97	303	34	=	=	SYM
ejpam-97	303	35	λπα(x	λπα(x	PROPN
ejpam-97	303	36	)	)	PUNCT
ejpam-97	303	37	,	,	PUNCT
ejpam-97	303	38	where	where	SCONJ
ejpam-97	303	39	πα	πα	ADJ
ejpam-97	303	40	:	:	PUNCT
ejpam-97	303	41	l	l	X
ejpam-97	303	42	im←−bα→	im←−bα→	PROPN
ejpam-97	303	43	bα	bα	PROPN
ejpam-97	303	44	is	be	AUX
ejpam-97	303	45	a	a	DET
ejpam-97	303	46	limit	limit	NOUN
ejpam-97	303	47	morphism	morphism	NOUN
ejpam-97	303	48	.	.	PUNCT
ejpam-97	304	1	so	so	ADV
ejpam-97	304	2	,	,	PUNCT
ejpam-97	304	3	k	k	PROPN
ejpam-97	304	4	=	=	PUNCT
ejpam-97	304	5	λa	λa	X
ejpam-97	304	6	for	for	ADP
ejpam-97	304	7	some	some	DET
ejpam-97	304	8	a	a	DET
ejpam-97	304	9	∈	∈	PROPN
ejpam-97	304	10	a	a	PRON
ejpam-97	304	11	,	,	PUNCT
ejpam-97	304	12	since	since	SCONJ
ejpam-97	304	13	fα	fα	ADV
ejpam-97	304	14	is	be	AUX
ejpam-97	304	15	s	s	NOUN
ejpam-97	304	16	-	-	ADJ
ejpam-97	304	17	pure	pure	ADJ
ejpam-97	304	18	.	.	PUNCT
ejpam-97	305	1	note	note	VERB
ejpam-97	305	2	that	that	SCONJ
ejpam-97	305	3	,	,	PUNCT
ejpam-97	305	4	the	the	DET
ejpam-97	305	5	above	above	ADJ
ejpam-97	305	6	result	result	NOUN
ejpam-97	305	7	is	be	AUX
ejpam-97	305	8	also	also	ADV
ejpam-97	305	9	true	true	ADJ
ejpam-97	305	10	whenever	whenever	SCONJ
ejpam-97	305	11	for	for	ADP
ejpam-97	305	12	some	some	PRON
ejpam-97	305	13	(	(	PUNCT
ejpam-97	305	14	not	not	PART
ejpam-97	305	15	necessarily	necessarily	ADV
ejpam-97	305	16	all	all	PRON
ejpam-97	305	17	)	)	PUNCT
ejpam-97	306	1	α	α	PRON
ejpam-97	306	2	∈	∈	PROPN
ejpam-97	307	1	i	i	PRON
ejpam-97	307	2	,	,	PUNCT
ejpam-97	307	3	fα	fα	ADV
ejpam-97	307	4	is	be	AUX
ejpam-97	307	5	an	an	DET
ejpam-97	307	6	s	s	NOUN
ejpam-97	307	7	-	-	ADJ
ejpam-97	307	8	pure	pure	ADJ
ejpam-97	307	9	monomorphism	monomorphism	NOUN
ejpam-97	307	10	.	.	PUNCT
ejpam-97	308	1	3.3	3.3	NUM
ejpam-97	308	2	.	.	PUNCT
ejpam-97	308	3	colimits	colimit	NOUN
ejpam-97	308	4	of	of	ADP
ejpam-97	308	5	s	s	NOUN
ejpam-97	308	6	-	-	ADJ
ejpam-97	308	7	pure	pure	ADJ
ejpam-97	308	8	monomorphisms	monomorphism	NOUN
ejpam-97	308	9	in	in	ADP
ejpam-97	308	10	this	this	DET
ejpam-97	308	11	subsection	subsection	NOUN
ejpam-97	308	12	we	we	PRON
ejpam-97	308	13	investigate	investigate	VERB
ejpam-97	308	14	the	the	DET
ejpam-97	308	15	colimit	colimit	NOUN
ejpam-97	308	16	properties	property	NOUN
ejpam-97	308	17	of	of	ADP
ejpam-97	308	18	s	s	NOUN
ejpam-97	308	19	-	-	ADJ
ejpam-97	308	20	pure	pure	ADJ
ejpam-97	308	21	monomorphisms	monomorphism	NOUN
ejpam-97	308	22	.	.	PUNCT
ejpam-97	309	1	proposition	proposition	NOUN
ejpam-97	309	2	3.4	3.4	NUM
ejpam-97	309	3	.	.	PUNCT
ejpam-97	310	1	the	the	DET
ejpam-97	310	2	classmp	classmp	PROPN
ejpam-97	310	3	is	be	AUX
ejpam-97	310	4	closed	close	VERB
ejpam-97	310	5	under	under	ADP
ejpam-97	310	6	coproducts	coproduct	NOUN
ejpam-97	310	7	.	.	PUNCT
ejpam-97	311	1	proof	proof	NOUN
ejpam-97	311	2	.	.	PUNCT
ejpam-97	312	1	let	let	VERB
ejpam-97	312	2	{	{	PUNCT
ejpam-97	312	3	fα	fα	ADP
ejpam-97	312	4	:	:	PUNCT
ejpam-97	312	5	aα	aα	NOUN
ejpam-97	312	6	→	→	SYM
ejpam-97	312	7	bα|α	bα|α	PRON
ejpam-97	312	8	∈	∈	PROPN
ejpam-97	313	1	i	i	PRON
ejpam-97	313	2	}	}	PUNCT
ejpam-97	313	3	be	be	VERB
ejpam-97	313	4	a	a	DET
ejpam-97	313	5	family	family	NOUN
ejpam-97	313	6	of	of	ADP
ejpam-97	313	7	s	s	NOUN
ejpam-97	313	8	-	-	ADJ
ejpam-97	313	9	pure	pure	ADJ
ejpam-97	313	10	monomorphisms	monomorphism	NOUN
ejpam-97	313	11	and	and	CCONJ
ejpam-97	313	12	f	f	NOUN
ejpam-97	313	13	:	:	PUNCT
ejpam-97	313	14	∐	∐	PROPN
ejpam-97	313	15	aα	aα	PROPN
ejpam-97	313	16	→	→	SYM
ejpam-97	313	17	∐	∐	ADJ
ejpam-97	313	18	bα	bα	NOUN
ejpam-97	313	19	be	be	AUX
ejpam-97	313	20	the	the	DET
ejpam-97	313	21	coproduct	coproduct	NOUN
ejpam-97	313	22	(	(	PUNCT
ejpam-97	313	23	mono)morphism	mono)morphism	NOUN
ejpam-97	313	24	induced	induce	VERB
ejpam-97	313	25	by	by	ADP
ejpam-97	313	26	all	all	DET
ejpam-97	313	27	fα	fα	NOUN
ejpam-97	313	28	.	.	PUNCT
ejpam-97	314	1	let	let	VERB
ejpam-97	314	2	k	k	NOUN
ejpam-97	314	3	:	:	PUNCT
ejpam-97	314	4	s→	s→	PROPN
ejpam-97	314	5	∐	∐	PROPN
ejpam-97	314	6	aα	aα	PROPN
ejpam-97	314	7	be	be	AUX
ejpam-97	314	8	a	a	DET
ejpam-97	314	9	homomorphism	homomorphism	NOUN
ejpam-97	315	1	such	such	ADJ
ejpam-97	315	2	that	that	SCONJ
ejpam-97	315	3	f	f	PROPN
ejpam-97	315	4	k	k	NOUN
ejpam-97	315	5	=	=	PUNCT
ejpam-97	315	6	λb	λb	NOUN
ejpam-97	315	7	for	for	ADP
ejpam-97	315	8	some	some	DET
ejpam-97	315	9	b	b	NOUN
ejpam-97	315	10	∈	∈	PROPN
ejpam-97	315	11	∐	∐	X
ejpam-97	315	12	bα	bα	PROPN
ejpam-97	315	13	.	.	PUNCT
ejpam-97	316	1	since	since	SCONJ
ejpam-97	316	2	b	b	PROPN
ejpam-97	316	3	∈	∈	PROPN
ejpam-97	316	4	bα	bα	NOUN
ejpam-97	316	5	for	for	ADP
ejpam-97	316	6	some	some	DET
ejpam-97	316	7	α	α	NOUN
ejpam-97	316	8	∈	∈	NOUN
ejpam-97	317	1	i	i	PRON
ejpam-97	317	2	,	,	PUNCT
ejpam-97	317	3	k(s	k(s	PROPN
ejpam-97	317	4	)	)	PUNCT
ejpam-97	317	5	⊆	⊆	NUM
ejpam-97	317	6	bα	bα	NOUN
ejpam-97	317	7	,	,	PUNCT
ejpam-97	317	8	and	and	CCONJ
ejpam-97	317	9	so	so	ADV
ejpam-97	317	10	k(s)⊆	k(s)⊆	PROPN
ejpam-97	317	11	aα	aα	PROPN
ejpam-97	317	12	.	.	PUNCT
ejpam-97	318	1	since	since	SCONJ
ejpam-97	318	2	aα	aα	NOUN
ejpam-97	318	3	is	be	AUX
ejpam-97	318	4	s	s	NOUN
ejpam-97	318	5	-	-	ADJ
ejpam-97	318	6	pure	pure	ADJ
ejpam-97	318	7	in	in	ADP
ejpam-97	318	8	bα	bα	PROPN
ejpam-97	318	9	,	,	PUNCT
ejpam-97	318	10	k	k	PROPN
ejpam-97	318	11	=	=	PUNCT
ejpam-97	318	12	λaα	λaα	NOUN
ejpam-97	318	13	for	for	ADP
ejpam-97	318	14	some	some	DET
ejpam-97	318	15	aα	aα	NOUN
ejpam-97	318	16	∈	∈	PROPN
ejpam-97	318	17	aα	aα	NOUN
ejpam-97	318	18	,	,	PUNCT
ejpam-97	318	19	which	which	PRON
ejpam-97	318	20	proves	prove	VERB
ejpam-97	318	21	the	the	DET
ejpam-97	318	22	result	result	NOUN
ejpam-97	318	23	.	.	PUNCT
ejpam-97	319	1	in	in	ADP
ejpam-97	319	2	the	the	DET
ejpam-97	319	3	following	follow	VERB
ejpam-97	319	4	proposition	proposition	NOUN
ejpam-97	319	5	,	,	PUNCT
ejpam-97	319	6	suppose	suppose	VERB
ejpam-97	319	7	that	that	SCONJ
ejpam-97	319	8	every	every	DET
ejpam-97	319	9	aα	aα	NOUN
ejpam-97	319	10	has	have	VERB
ejpam-97	319	11	a	a	DET
ejpam-97	319	12	fixed	fix	VERB
ejpam-97	319	13	element	element	NOUN
ejpam-97	319	14	0	0	NUM
ejpam-97	319	15	.	.	PUNCT
ejpam-97	320	1	proposition	proposition	NOUN
ejpam-97	320	2	3.5	3.5	NUM
ejpam-97	320	3	.	.	PUNCT
ejpam-97	321	1	(	(	PUNCT
ejpam-97	321	2	1	1	X
ejpam-97	321	3	)	)	PUNCT
ejpam-97	321	4	the	the	DET
ejpam-97	321	5	classmp	classmp	PROPN
ejpam-97	321	6	is	be	AUX
ejpam-97	321	7	closed	close	VERB
ejpam-97	321	8	under	under	ADP
ejpam-97	321	9	direct	direct	ADJ
ejpam-97	321	10	sums	sum	NOUN
ejpam-97	321	11	.	.	PUNCT
ejpam-97	322	1	(	(	PUNCT
ejpam-97	322	2	2	2	X
ejpam-97	322	3	)	)	PUNCT
ejpam-97	322	4	if	if	SCONJ
ejpam-97	322	5	s	s	VERB
ejpam-97	322	6	is	be	AUX
ejpam-97	322	7	a	a	DET
ejpam-97	322	8	finitely	finitely	ADV
ejpam-97	322	9	generated	generate	VERB
ejpam-97	322	10	semigroup	semigroup	NOUN
ejpam-97	322	11	,	,	PUNCT
ejpam-97	322	12	then	then	ADV
ejpam-97	322	13	⊕α∈iaα	⊕α∈iaα	PROPN
ejpam-97	322	14	is	be	AUX
ejpam-97	322	15	s	s	NOUN
ejpam-97	322	16	-	-	ADJ
ejpam-97	322	17	pure	pure	ADJ
ejpam-97	322	18	in	in	ADP
ejpam-97	322	19	∏	∏	NUM
ejpam-97	322	20	α∈i	α∈i	NUM
ejpam-97	322	21	aα	aα	NOUN
ejpam-97	322	22	.	.	PUNCT
ejpam-97	323	1	proof	proof	NOUN
ejpam-97	323	2	.	.	PUNCT
ejpam-97	324	1	(	(	PUNCT
ejpam-97	324	2	1	1	X
ejpam-97	324	3	)	)	PUNCT
ejpam-97	324	4	let	let	VERB
ejpam-97	324	5	{	{	PUNCT
ejpam-97	324	6	fα	fα	ADP
ejpam-97	324	7	:	:	PUNCT
ejpam-97	324	8	aα	aα	NOUN
ejpam-97	324	9	→	→	SYM
ejpam-97	324	10	bα|α	bα|α	PRON
ejpam-97	324	11	∈	∈	PROPN
ejpam-97	325	1	i	i	PRON
ejpam-97	325	2	}	}	PUNCT
ejpam-97	325	3	be	be	VERB
ejpam-97	325	4	a	a	DET
ejpam-97	325	5	family	family	NOUN
ejpam-97	325	6	of	of	ADP
ejpam-97	325	7	s	s	NOUN
ejpam-97	325	8	-	-	ADJ
ejpam-97	325	9	pure	pure	ADJ
ejpam-97	325	10	monomorphisms	monomorphism	NOUN
ejpam-97	325	11	,	,	PUNCT
ejpam-97	325	12	and	and	CCONJ
ejpam-97	325	13	f	f	NOUN
ejpam-97	325	14	:	:	PUNCT
ejpam-97	325	15	⊕aα	⊕aα	NUM
ejpam-97	325	16	→	→	SYM
ejpam-97	325	17	⊕bα	⊕bα	PRON
ejpam-97	325	18	be	be	VERB
ejpam-97	325	19	the	the	DET
ejpam-97	325	20	monomorphism	monomorphism	NOUN
ejpam-97	325	21	induced	induce	VERB
ejpam-97	325	22	by	by	ADP
ejpam-97	325	23	the	the	DET
ejpam-97	325	24	product	product	NOUN
ejpam-97	325	25	of	of	ADP
ejpam-97	325	26	fα	fα	ADP
ejpam-97	325	27	,	,	PUNCT
ejpam-97	325	28	s.	s.	PROPN
ejpam-97	325	29	let	let	VERB
ejpam-97	325	30	k	k	NOUN
ejpam-97	325	31	:	:	PUNCT
ejpam-97	325	32	s	s	X
ejpam-97	325	33	→	→	PUNCT
ejpam-97	325	34	⊕aα	⊕aα	X
ejpam-97	325	35	be	be	AUX
ejpam-97	325	36	a	a	DET
ejpam-97	325	37	homomorphism	homomorphism	NOUN
ejpam-97	326	1	such	such	ADJ
ejpam-97	326	2	that	that	SCONJ
ejpam-97	326	3	k	k	PROPN
ejpam-97	326	4	=	=	PUNCT
ejpam-97	326	5	λb	λb	NOUN
ejpam-97	326	6	for	for	ADP
ejpam-97	326	7	some	some	DET
ejpam-97	326	8	b	b	NOUN
ejpam-97	326	9	=	=	SYM
ejpam-97	326	10	(	(	PUNCT
ejpam-97	326	11	bα)α∈i	bα)α∈i	X
ejpam-97	326	12	∈	∈	PROPN
ejpam-97	326	13	⊕bα	⊕bα	PROPN
ejpam-97	326	14	.	.	PUNCT
ejpam-97	327	1	let	let	VERB
ejpam-97	327	2	j	j	PROPN
ejpam-97	327	3	be	be	AUX
ejpam-97	327	4	a	a	DET
ejpam-97	327	5	finite	finite	NOUN
ejpam-97	327	6	subset	subset	NOUN
ejpam-97	327	7	of	of	ADP
ejpam-97	327	8	i	i	PRON
ejpam-97	327	9	such	such	ADJ
ejpam-97	327	10	that	that	PRON
ejpam-97	327	11	for	for	SCONJ
ejpam-97	327	12	all	all	DET
ejpam-97	327	13	α	α	DET
ejpam-97	327	14	6∈	6∈	PROPN
ejpam-97	327	15	j	j	PROPN
ejpam-97	327	16	,	,	PUNCT
ejpam-97	327	17	bα	bα	PROPN
ejpam-97	327	18	=	=	NOUN
ejpam-97	327	19	0	0	X
ejpam-97	327	20	.	.	PUNCT
ejpam-97	328	1	so	so	ADV
ejpam-97	328	2	,	,	PUNCT
ejpam-97	328	3	for	for	ADP
ejpam-97	328	4	every	every	DET
ejpam-97	328	5	β	β	PROPN
ejpam-97	328	6	∈	∈	PROPN
ejpam-97	328	7	j	j	PROPN
ejpam-97	328	8	,	,	PUNCT
ejpam-97	328	9	fβ	fβ	ADP
ejpam-97	328	10	pβk	pβk	NOUN
ejpam-97	328	11	=	=	SYM
ejpam-97	328	12	λbβ	λbβ	X
ejpam-97	328	13	,	,	PUNCT
ejpam-97	328	14	where	where	SCONJ
ejpam-97	328	15	pβ	pβ	ADV
ejpam-97	328	16	:	:	PUNCT
ejpam-97	328	17	∏	∏	PROPN
ejpam-97	328	18	aβ	aβ	INTJ
ejpam-97	328	19	→	→	PUNCT
ejpam-97	328	20	aβ	aβ	NOUN
ejpam-97	328	21	is	be	AUX
ejpam-97	328	22	the	the	DET
ejpam-97	328	23	projection	projection	NOUN
ejpam-97	328	24	map	map	NOUN
ejpam-97	328	25	.	.	PUNCT
ejpam-97	329	1	since	since	SCONJ
ejpam-97	329	2	each	each	DET
ejpam-97	329	3	fβ	fβ	NOUN
ejpam-97	329	4	is	be	AUX
ejpam-97	329	5	s	s	NOUN
ejpam-97	329	6	-	-	ADJ
ejpam-97	329	7	pure	pure	ADJ
ejpam-97	329	8	,	,	PUNCT
ejpam-97	329	9	there	there	PRON
ejpam-97	329	10	exists	exist	VERB
ejpam-97	329	11	aβ	aβ	PRON
ejpam-97	329	12	∈	∈	PROPN
ejpam-97	329	13	aβ	aβ	ADP
ejpam-97	329	14	such	such	ADJ
ejpam-97	329	15	that	that	DET
ejpam-97	329	16	pβk	pβk	NOUN
ejpam-97	329	17	=	=	X
ejpam-97	329	18	λaβ	λaβ	NOUN
ejpam-97	329	19	.	.	PUNCT
ejpam-97	330	1	thus	thus	ADV
ejpam-97	330	2	,	,	PUNCT
ejpam-97	330	3	k	k	PROPN
ejpam-97	330	4	=	=	X
ejpam-97	330	5	λ(aα)α∈i	λ(aα)α∈i	NOUN
ejpam-97	330	6	,	,	PUNCT
ejpam-97	330	7	where	where	SCONJ
ejpam-97	330	8	for	for	ADP
ejpam-97	330	9	all	all	DET
ejpam-97	330	10	α	α	NOUN
ejpam-97	330	11	/∈	/∈	PUNCT
ejpam-97	330	12	j	j	NOUN
ejpam-97	330	13	,	,	PUNCT
ejpam-97	330	14	aα	aα	NOUN
ejpam-97	330	15	=	=	NOUN
ejpam-97	330	16	0	0	NUM
ejpam-97	330	17	.	.	PUNCT
ejpam-97	331	1	(	(	PUNCT
ejpam-97	331	2	2	2	X
ejpam-97	331	3	)	)	PUNCT
ejpam-97	331	4	let	let	VERB
ejpam-97	331	5	k	k	NOUN
ejpam-97	331	6	:	:	PUNCT
ejpam-97	331	7	s	s	AUX
ejpam-97	331	8	→⊕aα	→⊕aα	PUNCT
ejpam-97	331	9	be	be	AUX
ejpam-97	331	10	a	a	DET
ejpam-97	331	11	homomorphism	homomorphism	NOUN
ejpam-97	331	12	with	with	ADP
ejpam-97	331	13	k	k	PROPN
ejpam-97	331	14	=	=	PUNCT
ejpam-97	331	15	λa	λa	NOUN
ejpam-97	331	16	for	for	ADP
ejpam-97	331	17	some	some	DET
ejpam-97	331	18	a	a	DET
ejpam-97	331	19	=	=	SYM
ejpam-97	331	20	(	(	PUNCT
ejpam-97	331	21	aα)α∈i	aα)α∈i	NUM
ejpam-97	331	22	∈	∈	PROPN
ejpam-97	331	23	∏	∏	NUM
ejpam-97	331	24	aα	aα	NOUN
ejpam-97	331	25	,	,	PUNCT
ejpam-97	331	26	and	and	CCONJ
ejpam-97	331	27	s	s	VERB
ejpam-97	331	28	=	=	PUNCT
ejpam-97	331	29	∪n	∪n	NUM
ejpam-97	331	30	i=1	i=1	PROPN
ejpam-97	331	31	t	t	PROPN
ejpam-97	331	32	is	be	AUX
ejpam-97	331	33	1	1	NUM
ejpam-97	331	34	.	.	PUNCT
ejpam-97	332	1	so	so	ADV
ejpam-97	332	2	,	,	PUNCT
ejpam-97	332	3	since	since	SCONJ
ejpam-97	332	4	k(t	k(t	PROPN
ejpam-97	332	5	i	i	PRON
ejpam-97	332	6	)	)	PUNCT
ejpam-97	332	7	∈	∈	PROPN
ejpam-97	332	8	⊕aα	⊕aα	PROPN
ejpam-97	332	9	,	,	PUNCT
ejpam-97	332	10	at	at	ADP
ejpam-97	332	11	i	i	PRON
ejpam-97	332	12	=	=	PUNCT
ejpam-97	332	13	(	(	PUNCT
ejpam-97	332	14	aα	aα	NOUN
ejpam-97	332	15	t	t	NOUN
ejpam-97	332	16	i)α∈i	i)α∈i	PROPN
ejpam-97	332	17	∈	∈	PROPN
ejpam-97	332	18	⊕aα	⊕aα	NOUN
ejpam-97	332	19	.	.	PUNCT
ejpam-97	333	1	thus	thus	ADV
ejpam-97	333	2	,	,	PUNCT
ejpam-97	333	3	for	for	ADP
ejpam-97	333	4	every	every	DET
ejpam-97	333	5	i	i	PRON
ejpam-97	333	6	there	there	PRON
ejpam-97	333	7	exists	exist	VERB
ejpam-97	333	8	a	a	DET
ejpam-97	333	9	finite	finite	NOUN
ejpam-97	333	10	subset	subset	VERB
ejpam-97	333	11	ji	ji	PROPN
ejpam-97	333	12	of	of	ADP
ejpam-97	333	13	i	i	PRON
ejpam-97	333	14	such	such	ADJ
ejpam-97	333	15	that	that	PRON
ejpam-97	333	16	for	for	ADP
ejpam-97	333	17	every	every	DET
ejpam-97	333	18	α	α	NOUN
ejpam-97	333	19	6∈	6∈	NOUN
ejpam-97	333	20	ji	ji	INTJ
ejpam-97	333	21	,	,	PUNCT
ejpam-97	333	22	aα	aα	NOUN
ejpam-97	333	23	t	t	NOUN
ejpam-97	333	24	i	i	PRON
ejpam-97	333	25	=	=	NOUN
ejpam-97	334	1	0	0	X
ejpam-97	334	2	.	.	PUNCT
ejpam-97	334	3	now	now	ADV
ejpam-97	334	4	considering	consider	VERB
ejpam-97	334	5	the	the	DET
ejpam-97	334	6	finite	finite	PROPN
ejpam-97	334	7	subset	subset	VERB
ejpam-97	334	8	j	j	PROPN
ejpam-97	334	9	=	=	SYM
ejpam-97	334	10	⋃n	⋃n	PROPN
ejpam-97	334	11	i=1	i=1	PROPN
ejpam-97	334	12	ji	ji	PROPN
ejpam-97	334	13	⊆	⊆	NUM
ejpam-97	334	14	i	i	PROPN
ejpam-97	334	15	and	and	CCONJ
ejpam-97	334	16	bα	bα	PROPN
ejpam-97	334	17	=	=	SYM
ejpam-97	334	18	¨	¨	NOUN
ejpam-97	334	19	aα	aα	NOUN
ejpam-97	334	20	,	,	PUNCT
ejpam-97	334	21	if	if	SCONJ
ejpam-97	334	22	α	α	PROPN
ejpam-97	334	23	∈	∈	PROPN
ejpam-97	334	24	j	j	PROPN
ejpam-97	334	25	0	0	NUM
ejpam-97	334	26	,	,	PUNCT
ejpam-97	334	27	if	if	SCONJ
ejpam-97	334	28	α	α	DET
ejpam-97	334	29	6∈	6∈	PROPN
ejpam-97	334	30	j	j	NOUN
ejpam-97	334	31	,	,	PUNCT
ejpam-97	334	32	it	it	PRON
ejpam-97	334	33	is	be	AUX
ejpam-97	334	34	clear	clear	ADJ
ejpam-97	334	35	that	that	SCONJ
ejpam-97	334	36	k	k	PROPN
ejpam-97	334	37	=	=	PUNCT
ejpam-97	334	38	λb	λb	PROPN
ejpam-97	334	39	for	for	ADP
ejpam-97	334	40	b	b	NOUN
ejpam-97	334	41	=	=	PUNCT
ejpam-97	334	42	(	(	PUNCT
ejpam-97	334	43	bα)α∈i	bα)α∈i	X
ejpam-97	334	44	.	.	PUNCT
ejpam-97	335	1	theorem	theorem	VERB
ejpam-97	335	2	3.2	3.2	NUM
ejpam-97	335	3	.	.	PUNCT
ejpam-97	336	1	for	for	ADP
ejpam-97	336	2	the	the	DET
ejpam-97	336	3	following	follow	VERB
ejpam-97	336	4	pushout	pushout	PROPN
ejpam-97	336	5	diagram	diagram	NOUN
ejpam-97	336	6	in	in	ADP
ejpam-97	336	7	act	act	PROPN
ejpam-97	336	8	-	-	PUNCT
ejpam-97	336	9	s	s	PROPN
ejpam-97	336	10	,	,	PUNCT
ejpam-97	336	11	we	we	PRON
ejpam-97	336	12	have	have	VERB
ejpam-97	336	13	:	:	PUNCT
ejpam-97	336	14	(	(	PUNCT
ejpam-97	336	15	1	1	X
ejpam-97	336	16	)	)	PUNCT
ejpam-97	336	17	if	if	SCONJ
ejpam-97	336	18	f	f	PROPN
ejpam-97	336	19	is	be	AUX
ejpam-97	336	20	a	a	DET
ejpam-97	336	21	monomorphism	monomorphism	NOUN
ejpam-97	336	22	then	then	ADV
ejpam-97	336	23	h	h	PROPN
ejpam-97	336	24	is	be	AUX
ejpam-97	336	25	a	a	DET
ejpam-97	336	26	monomorphism	monomorphism	NOUN
ejpam-97	336	27	.	.	PUNCT
ejpam-97	337	1	h.	h.	PROPN
ejpam-97	337	2	barzegar	barzegar	PROPN
ejpam-97	337	3	and	and	CCONJ
ejpam-97	337	4	m.m	m.m	PROPN
ejpam-97	337	5	.	.	PROPN
ejpam-97	337	6	ebrahimi	ebrahimi	PROPN
ejpam-97	337	7	/	/	SYM
ejpam-97	337	8	eur	eur	PROPN
ejpam-97	337	9	.	.	PUNCT
ejpam-97	338	1	j.	j.	PROPN
ejpam-97	338	2	pure	pure	PROPN
ejpam-97	338	3	appl	appl	PROPN
ejpam-97	338	4	.	.	PROPN
ejpam-97	338	5	math	math	PROPN
ejpam-97	338	6	,	,	PUNCT
ejpam-97	338	7	1	1	NUM
ejpam-97	338	8	(	(	PUNCT
ejpam-97	338	9	2008	2008	NUM
ejpam-97	338	10	)	)	PUNCT
ejpam-97	338	11	,	,	PUNCT
ejpam-97	338	12	(	(	PUNCT
ejpam-97	338	13	41	41	NUM
ejpam-97	338	14	-	-	SYM
ejpam-97	338	15	55	55	NUM
ejpam-97	338	16	)	)	PUNCT
ejpam-97	338	17	52	52	NUM
ejpam-97	338	18	(	(	PUNCT
ejpam-97	338	19	2	2	NUM
ejpam-97	338	20	)	)	PUNCT
ejpam-97	338	21	if	if	SCONJ
ejpam-97	338	22	f	f	PROPN
ejpam-97	338	23	is	be	AUX
ejpam-97	338	24	s	s	NOUN
ejpam-97	338	25	-	-	ADJ
ejpam-97	338	26	pure	pure	ADJ
ejpam-97	338	27	then	then	ADV
ejpam-97	338	28	h	h	NOUN
ejpam-97	338	29	is	be	AUX
ejpam-97	338	30	s	s	NOUN
ejpam-97	338	31	-	-	ADJ
ejpam-97	338	32	pure	pure	ADJ
ejpam-97	338	33	.	.	PUNCT
ejpam-97	339	1	a	a	DET
ejpam-97	339	2	f	f	NOUN
ejpam-97	339	3	−→	−→	NOUN
ejpam-97	339	4	b	b	NOUN
ejpam-97	339	5	g	g	PROPN
ejpam-97	339	6	↓	↓	PROPN
ejpam-97	339	7	↓	↓	PROPN
ejpam-97	339	8	h′	h′	PROPN
ejpam-97	339	9	c	c	PROPN
ejpam-97	339	10	h−→	h−→	PROPN
ejpam-97	339	11	q	q	ADJ
ejpam-97	339	12	proof	proof	NOUN
ejpam-97	339	13	.	.	PUNCT
ejpam-97	340	1	(	(	PUNCT
ejpam-97	340	2	1	1	X
ejpam-97	340	3	)	)	PUNCT
ejpam-97	340	4	recall	recall	NOUN
ejpam-97	340	5	that	that	PRON
ejpam-97	340	6	q	q	NOUN
ejpam-97	341	1	=	=	SYM
ejpam-97	341	2	(	(	PUNCT
ejpam-97	341	3	b	b	PROPN
ejpam-97	341	4	t	t	NOUN
ejpam-97	341	5	c)/θ	c)/θ	NOUN
ejpam-97	341	6	where	where	SCONJ
ejpam-97	341	7	θ	θ	PROPN
ejpam-97	341	8	=	=	SYM
ejpam-97	341	9	ρ(h	ρ(h	X
ejpam-97	341	10	)	)	PUNCT
ejpam-97	341	11	and	and	CCONJ
ejpam-97	341	12	h	h	NOUN
ejpam-97	341	13	consists	consist	VERB
ejpam-97	341	14	of	of	ADP
ejpam-97	341	15	all	all	DET
ejpam-97	341	16	pairs	pair	NOUN
ejpam-97	341	17	(	(	PUNCT
ejpam-97	341	18	ub	ub	INTJ
ejpam-97	341	19	f	f	X
ejpam-97	341	20	(	(	PUNCT
ejpam-97	341	21	a	a	PROPN
ejpam-97	341	22	)	)	PUNCT
ejpam-97	341	23	,	,	PUNCT
ejpam-97	341	24	uc	uc	PROPN
ejpam-97	341	25	g(a	g(a	PROPN
ejpam-97	341	26	)	)	PUNCT
ejpam-97	341	27	)	)	PUNCT
ejpam-97	341	28	,	,	PUNCT
ejpam-97	341	29	a	a	DET
ejpam-97	341	30	∈	∈	PROPN
ejpam-97	341	31	a	a	PRON
ejpam-97	341	32	,	,	PUNCT
ejpam-97	341	33	where	where	SCONJ
ejpam-97	341	34	ub	ub	ADP
ejpam-97	341	35	:	:	PUNCT
ejpam-97	341	36	b	b	X
ejpam-97	341	37	→	→	SYM
ejpam-97	341	38	b	b	PROPN
ejpam-97	341	39	t	t	PROPN
ejpam-97	341	40	c	c	NOUN
ejpam-97	341	41	,	,	PUNCT
ejpam-97	341	42	uc	uc	X
ejpam-97	341	43	:	:	PUNCT
ejpam-97	341	44	c	c	X
ejpam-97	341	45	→	→	SYM
ejpam-97	341	46	b	b	PROPN
ejpam-97	341	47	t	t	PROPN
ejpam-97	341	48	c	c	NOUN
ejpam-97	341	49	are	be	AUX
ejpam-97	341	50	coproduct	coproduct	NOUN
ejpam-97	341	51	injections	injection	NOUN
ejpam-97	341	52	.	.	PUNCT
ejpam-97	342	1	and	and	CCONJ
ejpam-97	342	2	h	h	NOUN
ejpam-97	342	3	=	=	NOUN
ejpam-97	342	4	πuc	πuc	NOUN
ejpam-97	342	5	:	:	PUNCT
ejpam-97	343	1	c	c	X
ejpam-97	343	2	→	→	PUNCT
ejpam-97	343	3	(	(	PUNCT
ejpam-97	343	4	b	b	PROPN
ejpam-97	343	5	t	t	NOUN
ejpam-97	343	6	c)/θ	c)/θ	NOUN
ejpam-97	343	7	,	,	PUNCT
ejpam-97	343	8	h′	h′	PROPN
ejpam-97	343	9	=	=	PUNCT
ejpam-97	343	10	πub	πub	PROPN
ejpam-97	343	11	:	:	PUNCT
ejpam-97	343	12	b	b	X
ejpam-97	343	13	→	→	SYM
ejpam-97	343	14	(	(	PUNCT
ejpam-97	343	15	b	b	PROPN
ejpam-97	343	16	t	t	NOUN
ejpam-97	343	17	c)/θ	c)/θ	NOUN
ejpam-97	343	18	,	,	PUNCT
ejpam-97	343	19	where	where	SCONJ
ejpam-97	343	20	π	π	X
ejpam-97	343	21	:	:	PUNCT
ejpam-97	343	22	b	b	X
ejpam-97	343	23	t	t	NOUN
ejpam-97	343	24	c	c	PROPN
ejpam-97	343	25	→	→	PUNCT
ejpam-97	343	26	(	(	PUNCT
ejpam-97	343	27	b	b	X
ejpam-97	343	28	t	t	PROPN
ejpam-97	343	29	c)/θ	c)/θ	PROPN
ejpam-97	343	30	is	be	AUX
ejpam-97	343	31	the	the	DET
ejpam-97	343	32	canonical	canonical	ADJ
ejpam-97	343	33	epimorphism	epimorphism	NOUN
ejpam-97	343	34	.	.	PUNCT
ejpam-97	344	1	let	let	VERB
ejpam-97	344	2	h(c	h(c	PROPN
ejpam-97	344	3	)	)	PUNCT
ejpam-97	345	1	=	=	SYM
ejpam-97	345	2	h(c′	h(c′	PROPN
ejpam-97	345	3	)	)	PUNCT
ejpam-97	345	4	,	,	PUNCT
ejpam-97	345	5	c	c	X
ejpam-97	345	6	,	,	PUNCT
ejpam-97	345	7	c′	c′	NOUN
ejpam-97	345	8	∈	∈	PROPN
ejpam-97	345	9	c	c	NOUN
ejpam-97	345	10	,	,	PUNCT
ejpam-97	345	11	and	and	CCONJ
ejpam-97	345	12	so	so	ADV
ejpam-97	345	13	uc(c)ρ(h)uc(c′	uc(c)ρ(h)uc(c′	ADJ
ejpam-97	345	14	)	)	PUNCT
ejpam-97	345	15	.	.	PUNCT
ejpam-97	346	1	thus	thus	ADV
ejpam-97	346	2	c	c	X
ejpam-97	346	3	=	=	SYM
ejpam-97	346	4	c′	c′	NOUN
ejpam-97	346	5	,	,	PUNCT
ejpam-97	346	6	and	and	CCONJ
ejpam-97	346	7	the	the	DET
ejpam-97	346	8	result	result	NOUN
ejpam-97	346	9	is	be	AUX
ejpam-97	346	10	proved	prove	VERB
ejpam-97	346	11	,	,	PUNCT
ejpam-97	346	12	or	or	CCONJ
ejpam-97	346	13	there	there	PRON
ejpam-97	346	14	exist	exist	VERB
ejpam-97	346	15	a1	a1	NOUN
ejpam-97	346	16	,	,	PUNCT
ejpam-97	346	17	a2	a2	PROPN
ejpam-97	346	18	,	,	PUNCT
ejpam-97	346	19	...	...	PUNCT
ejpam-97	346	20	an	an	DET
ejpam-97	346	21	∈	∈	PROPN
ejpam-97	346	22	a	a	DET
ejpam-97	346	23	,	,	PUNCT
ejpam-97	346	24	s1	s1	NOUN
ejpam-97	346	25	,	,	PUNCT
ejpam-97	346	26	s2	s2	PROPN
ejpam-97	346	27	,	,	PUNCT
ejpam-97	346	28	...	...	PUNCT
ejpam-97	346	29	,	,	PUNCT
ejpam-97	346	30	sn	sn	PROPN
ejpam-97	346	31	∈	∈	PROPN
ejpam-97	346	32	s1	s1	NOUN
ejpam-97	346	33	such	such	ADJ
ejpam-97	346	34	that	that	SCONJ
ejpam-97	346	35	c	c	NOUN
ejpam-97	346	36	=	=	SYM
ejpam-97	346	37	g(a1s1	g(a1s1	NOUN
ejpam-97	346	38	)	)	PUNCT
ejpam-97	346	39	,	,	PUNCT
ejpam-97	346	40	g(ansn	g(ansn	NOUN
ejpam-97	346	41	)	)	PUNCT
ejpam-97	346	42	=	=	SYM
ejpam-97	346	43	c′	c′	NOUN
ejpam-97	346	44	,	,	PUNCT
ejpam-97	346	45	and	and	CCONJ
ejpam-97	346	46	f	f	PROPN
ejpam-97	346	47	(	(	PUNCT
ejpam-97	346	48	a1s1	a1s1	NOUN
ejpam-97	346	49	)	)	PUNCT
ejpam-97	347	1	=	=	SYM
ejpam-97	347	2	f	f	PROPN
ejpam-97	347	3	(	(	PUNCT
ejpam-97	347	4	a2s2	a2s2	NOUN
ejpam-97	347	5	)	)	PUNCT
ejpam-97	347	6	·	·	PUNCT
ejpam-97	347	7	·	·	PUNCT
ejpam-97	347	8	·	·	PUNCT
ejpam-97	348	1	f	f	X
ejpam-97	348	2	(	(	PUNCT
ejpam-97	348	3	an−1sn−1	an−1sn−1	PROPN
ejpam-97	348	4	)	)	PUNCT
ejpam-97	348	5	=	=	SYM
ejpam-97	348	6	f	f	PROPN
ejpam-97	348	7	(	(	PUNCT
ejpam-97	348	8	ansn	ansn	PROPN
ejpam-97	348	9	)	)	PUNCT
ejpam-97	348	10	g(a2s2	g(a2s2	NOUN
ejpam-97	348	11	)	)	PUNCT
ejpam-97	348	12	=	=	SYM
ejpam-97	349	1	g(a3s3	g(a3s3	NOUN
ejpam-97	349	2	)	)	PUNCT
ejpam-97	349	3	·	·	PUNCT
ejpam-97	349	4	·	·	PUNCT
ejpam-97	349	5	·	·	PUNCT
ejpam-97	349	6	and	and	CCONJ
ejpam-97	349	7	then	then	ADV
ejpam-97	349	8	,	,	PUNCT
ejpam-97	349	9	the	the	DET
ejpam-97	349	10	fact	fact	NOUN
ejpam-97	349	11	that	that	SCONJ
ejpam-97	349	12	f	f	PROPN
ejpam-97	349	13	is	be	AUX
ejpam-97	349	14	a	a	DET
ejpam-97	349	15	monomorphism	monomorphism	NOUN
ejpam-97	349	16	gives	give	VERB
ejpam-97	349	17	a1s1	a1s1	X
ejpam-97	350	1	=	=	SYM
ejpam-97	350	2	a2s2	a2s2	PROPN
ejpam-97	350	3	,	,	PUNCT
ejpam-97	350	4	a3s3	a3s3	X
ejpam-97	350	5	=	=	PUNCT
ejpam-97	350	6	a4s4	a4s4	X
ejpam-97	350	7	,	,	PUNCT
ejpam-97	350	8	...	...	PUNCT
ejpam-97	350	9	,	,	PUNCT
ejpam-97	350	10	an−1sn−1	an−1sn−1	PROPN
ejpam-97	350	11	=	=	PUNCT
ejpam-97	350	12	ansn	ansn	NOUN
ejpam-97	350	13	.	.	PUNCT
ejpam-97	351	1	thus	thus	ADV
ejpam-97	351	2	,	,	PUNCT
ejpam-97	351	3	we	we	PRON
ejpam-97	351	4	get	get	VERB
ejpam-97	351	5	g(a1s1	g(a1s1	NOUN
ejpam-97	351	6	)	)	PUNCT
ejpam-97	351	7	=	=	SYM
ejpam-97	351	8	g(a2s2	g(a2s2	NOUN
ejpam-97	351	9	)	)	PUNCT
ejpam-97	351	10	=	=	SYM
ejpam-97	352	1	g(a3s3	g(a3s3	NOUN
ejpam-97	352	2	)	)	PUNCT
ejpam-97	352	3	=	=	SYM
ejpam-97	352	4	·	·	PUNCT
ejpam-97	352	5	·	·	PUNCT
ejpam-97	352	6	·	·	PUNCT
ejpam-97	352	7	=	=	SYM
ejpam-97	352	8	g(ansn	g(ansn	PROPN
ejpam-97	352	9	)	)	PUNCT
ejpam-97	352	10	and	and	CCONJ
ejpam-97	352	11	hence	hence	ADV
ejpam-97	352	12	c	c	X
ejpam-97	353	1	=	=	PUNCT
ejpam-97	353	2	c′.	c′.	X
ejpam-97	353	3	(	(	PUNCT
ejpam-97	353	4	2	2	X
ejpam-97	353	5	)	)	PUNCT
ejpam-97	353	6	let	let	VERB
ejpam-97	353	7	k	k	NOUN
ejpam-97	353	8	:	:	PUNCT
ejpam-97	353	9	s	s	X
ejpam-97	353	10	→	→	SYM
ejpam-97	353	11	c	c	AUX
ejpam-97	353	12	be	be	AUX
ejpam-97	353	13	a	a	DET
ejpam-97	353	14	homomorphism	homomorphism	NOUN
ejpam-97	353	15	such	such	ADJ
ejpam-97	353	16	that	that	DET
ejpam-97	353	17	hk	hk	PROPN
ejpam-97	353	18	=	=	PROPN
ejpam-97	353	19	λx	λx	PROPN
ejpam-97	353	20	for	for	ADP
ejpam-97	353	21	some	some	DET
ejpam-97	353	22	x	x	SYM
ejpam-97	353	23	∈	∈	PROPN
ejpam-97	353	24	q.	q.	NOUN
ejpam-97	353	25	two	two	NUM
ejpam-97	353	26	cases	case	NOUN
ejpam-97	353	27	may	may	AUX
ejpam-97	353	28	occur	occur	VERB
ejpam-97	353	29	:	:	PUNCT
ejpam-97	353	30	(	(	PUNCT
ejpam-97	353	31	i	i	NOUN
ejpam-97	353	32	)	)	PUNCT
ejpam-97	353	33	there	there	PRON
ejpam-97	353	34	exists	exist	VERB
ejpam-97	353	35	c	c	PROPN
ejpam-97	353	36	∈	∈	PROPN
ejpam-97	353	37	c	c	NOUN
ejpam-97	353	38	such	such	ADJ
ejpam-97	353	39	that	that	PRON
ejpam-97	353	40	x	x	X
ejpam-97	353	41	=	=	PUNCT
ejpam-97	354	1	[	[	X
ejpam-97	354	2	uc(c)]ρ(h	uc(c)]ρ(h	NOUN
ejpam-97	354	3	)	)	PUNCT
ejpam-97	354	4	.	.	PUNCT
ejpam-97	355	1	therefore	therefore	ADV
ejpam-97	355	2	,	,	PUNCT
ejpam-97	355	3	hk	hk	PROPN
ejpam-97	355	4	=	=	PUNCT
ejpam-97	355	5	λx	λx	PROPN
ejpam-97	355	6	=	=	PUNCT
ejpam-97	355	7	λh(c	λh(c	X
ejpam-97	355	8	)	)	PUNCT
ejpam-97	355	9	and	and	CCONJ
ejpam-97	355	10	hence	hence	ADV
ejpam-97	355	11	k	k	PROPN
ejpam-97	355	12	=	=	PUNCT
ejpam-97	355	13	λc	λc	INTJ
ejpam-97	355	14	,	,	PUNCT
ejpam-97	355	15	since	since	SCONJ
ejpam-97	355	16	h	h	NOUN
ejpam-97	355	17	is	be	AUX
ejpam-97	355	18	one	one	NUM
ejpam-97	355	19	-	-	PUNCT
ejpam-97	355	20	one	one	NUM
ejpam-97	355	21	.	.	PUNCT
ejpam-97	356	1	(	(	PUNCT
ejpam-97	356	2	ii	ii	NOUN
ejpam-97	356	3	)	)	PUNCT
ejpam-97	356	4	there	there	PRON
ejpam-97	356	5	exists	exist	VERB
ejpam-97	356	6	b	b	PROPN
ejpam-97	356	7	∈	∈	PROPN
ejpam-97	356	8	b	b	NOUN
ejpam-97	356	9	such	such	ADJ
ejpam-97	356	10	that	that	PRON
ejpam-97	356	11	x	x	X
ejpam-97	357	1	=	=	PUNCT
ejpam-97	358	1	[	[	X
ejpam-97	358	2	ub(b)]ρ(h	ub(b)]ρ(h	NOUN
ejpam-97	358	3	)	)	PUNCT
ejpam-97	358	4	.	.	PUNCT
ejpam-97	359	1	for	for	ADP
ejpam-97	359	2	every	every	DET
ejpam-97	359	3	s	s	X
ejpam-97	359	4	∈	∈	PROPN
ejpam-97	359	5	s	s	NOUN
ejpam-97	359	6	,	,	PUNCT
ejpam-97	359	7	[	[	X
ejpam-97	359	8	uc(k(s))]ρ(h	uc(k(s))]ρ(h	X
ejpam-97	359	9	)	)	PUNCT
ejpam-97	359	10	=	=	PUNCT
ejpam-97	360	1	[	[	X
ejpam-97	360	2	ub(bs)]ρ(h	ub(bs)]ρ(h	X
ejpam-97	360	3	)	)	PUNCT
ejpam-97	360	4	,	,	PUNCT
ejpam-97	360	5	and	and	CCONJ
ejpam-97	360	6	so	so	ADV
ejpam-97	360	7	there	there	PRON
ejpam-97	360	8	exist	exist	VERB
ejpam-97	360	9	elements	element	NOUN
ejpam-97	360	10	as	as	ADP
ejpam-97	360	11	1	1	NUM
ejpam-97	360	12	,	,	PUNCT
ejpam-97	360	13	·	·	PUNCT
ejpam-97	360	14	·	·	PUNCT
ejpam-97	360	15	·	·	PUNCT
ejpam-97	360	16	,	,	PUNCT
ejpam-97	360	17	as	as	ADP
ejpam-97	360	18	n	n	X
ejpam-97	360	19	in	in	ADP
ejpam-97	360	20	a	a	DET
ejpam-97	360	21	such	such	ADJ
ejpam-97	360	22	that	that	DET
ejpam-97	360	23	ub(bs	ub(b	NOUN
ejpam-97	360	24	)	)	PUNCT
ejpam-97	360	25	=	=	SYM
ejpam-97	361	1	ub	ub	INTJ
ejpam-97	361	2	f	f	X
ejpam-97	361	3	(	(	PUNCT
ejpam-97	361	4	as	as	ADP
ejpam-97	361	5	1	1	NUM
ejpam-97	361	6	)	)	PUNCT
ejpam-97	361	7	,	,	PUNCT
ejpam-97	361	8	uc	uc	INTJ
ejpam-97	361	9	g(as	g(as	PROPN
ejpam-97	361	10	1	1	X
ejpam-97	361	11	)	)	PUNCT
ejpam-97	361	12	=	=	VERB
ejpam-97	362	1	uc	uc	INTJ
ejpam-97	362	2	g(as	g(as	INTJ
ejpam-97	362	3	2	2	NUM
ejpam-97	362	4	)	)	PUNCT
ejpam-97	362	5	,	,	PUNCT
ejpam-97	362	6	ub	ub	PROPN
ejpam-97	362	7	f	f	X
ejpam-97	362	8	(	(	PUNCT
ejpam-97	362	9	as	as	ADP
ejpam-97	362	10	2	2	NUM
ejpam-97	362	11	)	)	PUNCT
ejpam-97	362	12	=	=	SYM
ejpam-97	363	1	ub	ub	INTJ
ejpam-97	363	2	f	f	X
ejpam-97	363	3	(	(	PUNCT
ejpam-97	363	4	as	as	ADP
ejpam-97	363	5	3	3	NUM
ejpam-97	363	6	)	)	PUNCT
ejpam-97	363	7	,	,	PUNCT
ejpam-97	363	8	·	·	PUNCT
ejpam-97	363	9	·	·	PUNCT
ejpam-97	363	10	·	·	PUNCT
ejpam-97	363	11	,	,	PUNCT
ejpam-97	363	12	uc	uc	INTJ
ejpam-97	363	13	g(as	g(as	INTJ
ejpam-97	363	14	n	n	CCONJ
ejpam-97	363	15	)	)	PUNCT
ejpam-97	363	16	=	=	SYM
ejpam-97	363	17	uc(k(s	uc(k(s	NOUN
ejpam-97	363	18	)	)	PUNCT
ejpam-97	363	19	)	)	PUNCT
ejpam-97	363	20	.	.	PUNCT
ejpam-97	364	1	then	then	ADV
ejpam-97	364	2	,	,	PUNCT
ejpam-97	364	3	since	since	SCONJ
ejpam-97	364	4	f	f	PROPN
ejpam-97	364	5	is	be	AUX
ejpam-97	364	6	a	a	DET
ejpam-97	364	7	monomorphism	monomorphism	NOUN
ejpam-97	364	8	,	,	PUNCT
ejpam-97	364	9	as	as	ADP
ejpam-97	364	10	2	2	NUM
ejpam-97	364	11	=	=	NOUN
ejpam-97	364	12	as	as	ADP
ejpam-97	364	13	3	3	NUM
ejpam-97	364	14	,	,	PUNCT
ejpam-97	364	15	as	as	ADP
ejpam-97	364	16	4	4	NUM
ejpam-97	364	17	=	=	NOUN
ejpam-97	364	18	as	as	ADP
ejpam-97	364	19	5	5	NUM
ejpam-97	364	20	,	,	PUNCT
ejpam-97	364	21	·	·	PUNCT
ejpam-97	364	22	·	·	PUNCT
ejpam-97	364	23	·	·	PUNCT
ejpam-97	364	24	,	,	PUNCT
ejpam-97	364	25	and	and	CCONJ
ejpam-97	364	26	hence	hence	ADV
ejpam-97	364	27	uc	uc	INTJ
ejpam-97	364	28	g(as	g(as	INTJ
ejpam-97	364	29	1	1	X
ejpam-97	364	30	)	)	PUNCT
ejpam-97	364	31	=	=	VERB
ejpam-97	365	1	uc	uc	PART
ejpam-97	365	2	g(as	g(as	INTJ
ejpam-97	365	3	2	2	X
ejpam-97	365	4	)	)	PUNCT
ejpam-97	365	5	=	=	VERB
ejpam-97	366	1	uc	uc	PART
ejpam-97	366	2	g(as	g(as	INTJ
ejpam-97	366	3	3	3	X
ejpam-97	366	4	)	)	PUNCT
ejpam-97	366	5	=	=	SYM
ejpam-97	366	6	·	·	PUNCT
ejpam-97	366	7	·	·	PUNCT
ejpam-97	366	8	·	·	PUNCT
ejpam-97	367	1	=	=	SYM
ejpam-97	367	2	uc	uc	X
ejpam-97	367	3	g(sn	g(sn	PROPN
ejpam-97	367	4	)	)	PUNCT
ejpam-97	367	5	=	=	SYM
ejpam-97	367	6	uc(k(s	uc(k(s	NOUN
ejpam-97	367	7	)	)	PUNCT
ejpam-97	367	8	)	)	PUNCT
ejpam-97	367	9	.	.	PUNCT
ejpam-97	368	1	now	now	ADV
ejpam-97	368	2	,	,	PUNCT
ejpam-97	368	3	for	for	ADP
ejpam-97	368	4	all	all	DET
ejpam-97	368	5	s	s	PART
ejpam-97	368	6	∈	∈	PROPN
ejpam-97	368	7	s	s	NOUN
ejpam-97	368	8	,	,	PUNCT
ejpam-97	368	9	bs	bs	NOUN
ejpam-97	368	10	=	=	SYM
ejpam-97	368	11	f	f	PROPN
ejpam-97	368	12	(	(	PUNCT
ejpam-97	368	13	as	as	ADP
ejpam-97	368	14	1	1	NUM
ejpam-97	368	15	)	)	PUNCT
ejpam-97	368	16	∈	∈	PROPN
ejpam-97	368	17	f	f	X
ejpam-97	368	18	(	(	PUNCT
ejpam-97	368	19	a	a	NOUN
ejpam-97	368	20	)	)	PUNCT
ejpam-97	368	21	,	,	PUNCT
ejpam-97	368	22	and	and	CCONJ
ejpam-97	368	23	thus	thus	ADV
ejpam-97	368	24	there	there	PRON
ejpam-97	368	25	exists	exist	VERB
ejpam-97	368	26	k1	k1	NOUN
ejpam-97	368	27	:	:	PUNCT
ejpam-97	368	28	s→	s→	X
ejpam-97	369	1	a	a	PRON
ejpam-97	369	2	with	with	ADP
ejpam-97	369	3	k1(s	k1(s	NOUN
ejpam-97	369	4	)	)	PUNCT
ejpam-97	369	5	=	=	PUNCT
ejpam-97	369	6	as	as	ADP
ejpam-97	369	7	1	1	NUM
ejpam-97	369	8	,	,	PUNCT
ejpam-97	369	9	and	and	CCONJ
ejpam-97	369	10	so	so	ADV
ejpam-97	369	11	f	f	PROPN
ejpam-97	369	12	k1	k1	PROPN
ejpam-97	369	13	=	=	SYM
ejpam-97	369	14	λb	λb	PROPN
ejpam-97	369	15	.	.	PUNCT
ejpam-97	370	1	then	then	ADV
ejpam-97	370	2	,	,	PUNCT
ejpam-97	370	3	since	since	SCONJ
ejpam-97	370	4	f	f	PROPN
ejpam-97	370	5	is	be	AUX
ejpam-97	370	6	s	s	NOUN
ejpam-97	370	7	-	-	ADJ
ejpam-97	370	8	pure	pure	ADJ
ejpam-97	370	9	,	,	PUNCT
ejpam-97	370	10	there	there	PRON
ejpam-97	370	11	is	be	VERB
ejpam-97	370	12	an	an	DET
ejpam-97	370	13	element	element	NOUN
ejpam-97	370	14	a	a	DET
ejpam-97	370	15	∈	∈	PROPN
ejpam-97	370	16	a	a	DET
ejpam-97	370	17	such	such	ADJ
ejpam-97	370	18	that	that	DET
ejpam-97	370	19	k1	k1	NOUN
ejpam-97	370	20	=	=	SYM
ejpam-97	370	21	λa	λa	PROPN
ejpam-97	370	22	.	.	PUNCT
ejpam-97	371	1	therefore	therefore	ADV
ejpam-97	371	2	,	,	PUNCT
ejpam-97	371	3	f	f	X
ejpam-97	371	4	(	(	PUNCT
ejpam-97	371	5	as	as	ADP
ejpam-97	371	6	1	1	NUM
ejpam-97	371	7	)	)	PUNCT
ejpam-97	371	8	=	=	SYM
ejpam-97	371	9	f	f	PROPN
ejpam-97	371	10	(	(	PUNCT
ejpam-97	371	11	k1(s	k1(s	PROPN
ejpam-97	371	12	)	)	PUNCT
ejpam-97	371	13	)	)	PUNCT
ejpam-97	372	1	=	=	SYM
ejpam-97	372	2	f	f	X
ejpam-97	372	3	(	(	PUNCT
ejpam-97	372	4	as	as	ADP
ejpam-97	372	5	)	)	PUNCT
ejpam-97	372	6	and	and	CCONJ
ejpam-97	372	7	so	so	ADV
ejpam-97	372	8	hg(as	hg(as	ADJ
ejpam-97	372	9	1	1	X
ejpam-97	372	10	)	)	PUNCT
ejpam-97	372	11	=	=	SYM
ejpam-97	372	12	h′	h′	PROPN
ejpam-97	372	13	f	f	X
ejpam-97	372	14	(	(	PUNCT
ejpam-97	372	15	as	as	ADP
ejpam-97	372	16	1	1	NUM
ejpam-97	372	17	)	)	PUNCT
ejpam-97	372	18	=	=	SYM
ejpam-97	372	19	h′	h′	PROPN
ejpam-97	372	20	f	f	X
ejpam-97	372	21	(	(	PUNCT
ejpam-97	372	22	as	as	ADP
ejpam-97	372	23	)	)	PUNCT
ejpam-97	372	24	=	=	SYM
ejpam-97	372	25	hg(as	hg(as	PROPN
ejpam-97	372	26	)	)	PUNCT
ejpam-97	372	27	which	which	PRON
ejpam-97	372	28	,	,	PUNCT
ejpam-97	372	29	since	since	SCONJ
ejpam-97	372	30	h	h	NOUN
ejpam-97	372	31	is	be	AUX
ejpam-97	372	32	a	a	DET
ejpam-97	372	33	monomorphism	monomorphism	NOUN
ejpam-97	372	34	,	,	PUNCT
ejpam-97	372	35	yields	yield	NOUN
ejpam-97	372	36	k(s	k(s	PROPN
ejpam-97	372	37	)	)	PUNCT
ejpam-97	373	1	=	=	PUNCT
ejpam-97	373	2	g(as	g(as	ADJ
ejpam-97	373	3	1	1	X
ejpam-97	373	4	)	)	PUNCT
ejpam-97	374	1	=	=	SYM
ejpam-97	374	2	g(as	g(as	ADJ
ejpam-97	374	3	)	)	PUNCT
ejpam-97	374	4	=	=	SYM
ejpam-97	374	5	g(a)s	g(a)s	NOUN
ejpam-97	374	6	,	,	PUNCT
ejpam-97	374	7	that	that	PRON
ejpam-97	374	8	is	be	AUX
ejpam-97	374	9	k	k	NOUN
ejpam-97	374	10	=	=	PUNCT
ejpam-97	374	11	λg(a	λg(a	X
ejpam-97	374	12	)	)	PUNCT
ejpam-97	374	13	,	,	PUNCT
ejpam-97	374	14	and	and	CCONJ
ejpam-97	374	15	h	h	NOUN
ejpam-97	374	16	is	be	AUX
ejpam-97	374	17	s	s	NOUN
ejpam-97	374	18	-	-	ADJ
ejpam-97	374	19	pure	pure	ADJ
ejpam-97	374	20	.	.	PUNCT
ejpam-97	375	1	theorem	theorem	VERB
ejpam-97	375	2	3.3	3.3	NUM
ejpam-97	375	3	.	.	PUNCT
ejpam-97	376	1	let	let	VERB
ejpam-97	376	2	i	i	PRON
ejpam-97	376	3	be	be	AUX
ejpam-97	376	4	a	a	DET
ejpam-97	376	5	directed	direct	VERB
ejpam-97	376	6	set	set	NOUN
ejpam-97	376	7	which	which	PRON
ejpam-97	376	8	has	have	VERB
ejpam-97	376	9	a	a	DET
ejpam-97	376	10	maximal	maximal	ADJ
ejpam-97	376	11	element	element	NOUN
ejpam-97	376	12	γ	γ	NOUN
ejpam-97	376	13	and	and	CCONJ
ejpam-97	376	14	{	{	PUNCT
ejpam-97	376	15	hα	hα	X
ejpam-97	376	16	:	:	PUNCT
ejpam-97	376	17	aα→	aα→	PROPN
ejpam-97	376	18	bα|	bα|	ADP
ejpam-97	376	19	α	α	PROPN
ejpam-97	376	20	∈	∈	PROPN
ejpam-97	377	1	i	i	PRON
ejpam-97	377	2	}	}	PUNCT
ejpam-97	377	3	be	be	VERB
ejpam-97	377	4	a	a	DET
ejpam-97	377	5	directed	direct	VERB
ejpam-97	377	6	family	family	NOUN
ejpam-97	377	7	of	of	ADP
ejpam-97	377	8	s	s	NOUN
ejpam-97	377	9	-	-	ADJ
ejpam-97	377	10	pure	pure	ADJ
ejpam-97	377	11	monomorphisms	monomorphism	NOUN
ejpam-97	377	12	.	.	PUNCT
ejpam-97	378	1	then	then	ADV
ejpam-97	378	2	,	,	PUNCT
ejpam-97	378	3	the	the	DET
ejpam-97	378	4	directed	direct	VERB
ejpam-97	378	5	colimit	colimit	NOUN
ejpam-97	378	6	homomorphism	homomorphism	NOUN
ejpam-97	378	7	induced	induce	VERB
ejpam-97	378	8	by	by	ADP
ejpam-97	378	9	h	h	NOUN
ejpam-97	378	10	:	:	PUNCT
ejpam-97	378	11	l	l	PROPN
ejpam-97	378	12	im−→aα→	im−→aα→	PROPN
ejpam-97	378	13	l	l	PROPN
ejpam-97	378	14	im−→bα	im−→bα	PROPN
ejpam-97	378	15	is	be	AUX
ejpam-97	378	16	s	s	NOUN
ejpam-97	378	17	-	-	ADJ
ejpam-97	378	18	pure	pure	ADJ
ejpam-97	378	19	.	.	PUNCT
ejpam-97	379	1	proof	proof	NOUN
ejpam-97	379	2	.	.	PUNCT
ejpam-97	380	1	let	let	VERB
ejpam-97	380	2	(	(	PUNCT
ejpam-97	380	3	l	l	NOUN
ejpam-97	380	4	im−→aα	im−→aα	NOUN
ejpam-97	380	5	,	,	PUNCT
ejpam-97	380	6	fα	fα	NOUN
ejpam-97	380	7	)	)	PUNCT
ejpam-97	380	8	,	,	PUNCT
ejpam-97	380	9	(	(	PUNCT
ejpam-97	380	10	l	l	PROPN
ejpam-97	380	11	im−→bα	im−→bα	PROPN
ejpam-97	380	12	,	,	PUNCT
ejpam-97	380	13	gα	gα	NOUN
ejpam-97	380	14	)	)	PUNCT
ejpam-97	380	15	be	be	AUX
ejpam-97	380	16	direct	direct	ADJ
ejpam-97	380	17	limits	limit	NOUN
ejpam-97	380	18	of	of	ADP
ejpam-97	380	19	the	the	DET
ejpam-97	380	20	directed	direct	VERB
ejpam-97	380	21	systems	system	NOUN
ejpam-97	380	22	(	(	PUNCT
ejpam-97	380	23	(	(	PUNCT
ejpam-97	380	24	aα	aα	NOUN
ejpam-97	380	25	)	)	PUNCT
ejpam-97	380	26	,	,	PUNCT
ejpam-97	380	27	(	(	PUNCT
ejpam-97	380	28	ψαβ))α≤β∈i	ψαβ))α≤β∈i	PUNCT
ejpam-97	380	29	and	and	CCONJ
ejpam-97	380	30	(	(	PUNCT
ejpam-97	380	31	(	(	PUNCT
ejpam-97	380	32	bα	bα	NOUN
ejpam-97	380	33	)	)	PUNCT
ejpam-97	380	34	,	,	PUNCT
ejpam-97	380	35	(	(	PUNCT
ejpam-97	380	36	ϕαβ))α≤β∈i	ϕαβ))α≤β∈i	NUM
ejpam-97	380	37	and	and	CCONJ
ejpam-97	380	38	suppose	suppose	VERB
ejpam-97	380	39	{	{	PUNCT
ejpam-97	380	40	hα	hα	X
ejpam-97	380	41	:	:	PUNCT
ejpam-97	380	42	aα	aα	PROPN
ejpam-97	380	43	→	→	SYM
ejpam-97	380	44	bα|	bα|	PROPN
ejpam-97	380	45	α	α	PROPN
ejpam-97	380	46	∈	∈	PROPN
ejpam-97	381	1	i	i	PRON
ejpam-97	381	2	}	}	PUNCT
ejpam-97	381	3	is	be	AUX
ejpam-97	381	4	a	a	DET
ejpam-97	381	5	directed	direct	VERB
ejpam-97	381	6	family	family	NOUN
ejpam-97	381	7	of	of	ADP
ejpam-97	381	8	s	s	NOUN
ejpam-97	381	9	-	-	ADJ
ejpam-97	381	10	pure	pure	ADJ
ejpam-97	381	11	monomorphisms	monomorphism	NOUN
ejpam-97	381	12	such	such	ADJ
ejpam-97	381	13	that	that	PRON
ejpam-97	381	14	for	for	ADP
ejpam-97	381	15	every	every	DET
ejpam-97	381	16	α	α	NOUN
ejpam-97	381	17	≤	≤	ADJ
ejpam-97	381	18	β	β	X
ejpam-97	381	19	,	,	PUNCT
ejpam-97	381	20	fβψαβ	fβψαβ	NOUN
ejpam-97	381	21	=	=	PUNCT
ejpam-97	381	22	fα	fα	NOUN
ejpam-97	381	23	and	and	CCONJ
ejpam-97	381	24	gβϕαβ	gβϕαβ	VERB
ejpam-97	381	25	=	=	PUNCT
ejpam-97	381	26	gα	gα	NOUN
ejpam-97	381	27	.	.	PUNCT
ejpam-97	382	1	then	then	ADV
ejpam-97	382	2	,	,	PUNCT
ejpam-97	382	3	for	for	ADP
ejpam-97	382	4	every	every	DET
ejpam-97	382	5	α	α	NOUN
ejpam-97	382	6	≤	≤	ADJ
ejpam-97	382	7	β	β	X
ejpam-97	382	8	,	,	PUNCT
ejpam-97	382	9	gβhβψαβ	gβhβψαβ	NOUN
ejpam-97	382	10	=	=	SYM
ejpam-97	382	11	gβϕαβhα	gβϕαβhα	NOUN
ejpam-97	382	12	=	=	SYM
ejpam-97	382	13	gαhα	gαhα	ADJ
ejpam-97	382	14	,	,	PUNCT
ejpam-97	382	15	so	so	ADV
ejpam-97	382	16	h	h	NOUN
ejpam-97	383	1	=	=	SYM
ejpam-97	384	1	l	l	NOUN
ejpam-97	385	1	im−→hα	im−→hα	NOUN
ejpam-97	385	2	exists	exist	VERB
ejpam-97	385	3	by	by	ADP
ejpam-97	385	4	the	the	DET
ejpam-97	385	5	universal	universal	ADJ
ejpam-97	385	6	property	property	NOUN
ejpam-97	385	7	of	of	ADP
ejpam-97	385	8	colimits	colimit	NOUN
ejpam-97	385	9	.	.	PUNCT
ejpam-97	386	1	consider	consider	VERB
ejpam-97	386	2	l	l	NOUN
ejpam-97	386	3	im−→aα	im−→aα	PROPN
ejpam-97	386	4	=	=	SYM
ejpam-97	386	5	aα	aα	PROPN
ejpam-97	386	6	/	/	SYM
ejpam-97	386	7	ρ	ρ	PROPN
ejpam-97	386	8	and	and	CCONJ
ejpam-97	386	9	l	l	PROPN
ejpam-97	386	10	im−→bα	im−→bα	PROPN
ejpam-97	386	11	=	=	ADJ
ejpam-97	386	12	bα	bα	PROPN
ejpam-97	386	13	/	/	SYM
ejpam-97	386	14	ρ	ρ	PROPN
ejpam-97	386	15	′	′	NUM
ejpam-97	386	16	as	as	SCONJ
ejpam-97	386	17	defined	define	VERB
ejpam-97	386	18	in	in	ADP
ejpam-97	386	19	section	section	NOUN
ejpam-97	386	20	1	1	NUM
ejpam-97	386	21	.	.	PUNCT
ejpam-97	387	1	let	let	VERB
ejpam-97	387	2	h.	h.	PROPN
ejpam-97	387	3	barzegar	barzegar	PROPN
ejpam-97	387	4	and	and	CCONJ
ejpam-97	387	5	m.m	m.m	PROPN
ejpam-97	387	6	.	.	PROPN
ejpam-97	387	7	ebrahimi	ebrahimi	PROPN
ejpam-97	387	8	/	/	SYM
ejpam-97	387	9	eur	eur	PROPN
ejpam-97	387	10	.	.	PUNCT
ejpam-97	388	1	j.	j.	PROPN
ejpam-97	388	2	pure	pure	PROPN
ejpam-97	388	3	appl	appl	PROPN
ejpam-97	388	4	.	.	PROPN
ejpam-97	388	5	math	math	PROPN
ejpam-97	388	6	,	,	PUNCT
ejpam-97	388	7	1	1	NUM
ejpam-97	388	8	(	(	PUNCT
ejpam-97	388	9	2008	2008	NUM
ejpam-97	388	10	)	)	PUNCT
ejpam-97	388	11	,	,	PUNCT
ejpam-97	388	12	(	(	PUNCT
ejpam-97	388	13	41	41	NUM
ejpam-97	388	14	-	-	SYM
ejpam-97	388	15	55	55	NUM
ejpam-97	388	16	)	)	PUNCT
ejpam-97	388	17	53	53	NUM
ejpam-97	388	18	h[aα]ρ	h[aα]ρ	NOUN
ejpam-97	388	19	=	=	PUNCT
ejpam-97	389	1	h[aβ]ρ	h[aβ]ρ	PROPN
ejpam-97	389	2	.	.	PUNCT
ejpam-97	390	1	then	then	ADV
ejpam-97	390	2	,	,	PUNCT
ejpam-97	390	3	[	[	X
ejpam-97	390	4	hα(aα)]ρ′	hα(aα)]ρ′	PROPN
ejpam-97	390	5	=	=	SYM
ejpam-97	390	6	gαhα(aα	gαhα(aα	PROPN
ejpam-97	390	7	)	)	PUNCT
ejpam-97	390	8	=	=	SYM
ejpam-97	390	9	gβhβ(aβ	gβhβ(aβ	PROPN
ejpam-97	390	10	)	)	PUNCT
ejpam-97	390	11	=	=	PUNCT
ejpam-97	391	1	[	[	X
ejpam-97	391	2	hβ(aβ)]ρ′	hβ(aβ)]ρ′	PROPN
ejpam-97	391	3	,	,	PUNCT
ejpam-97	391	4	and	and	CCONJ
ejpam-97	391	5	so	so	ADV
ejpam-97	391	6	there	there	PRON
ejpam-97	391	7	exists	exist	VERB
ejpam-97	391	8	γ	γ	PROPN
ejpam-97	391	9	∈	∈	PROPN
ejpam-97	391	10	i	i	PRON
ejpam-97	391	11	with	with	ADP
ejpam-97	391	12	γ	γ	PROPN
ejpam-97	391	13	≥	≥	PROPN
ejpam-97	391	14	α	α	X
ejpam-97	391	15	,	,	PUNCT
ejpam-97	391	16	β	β	X
ejpam-97	391	17	and	and	CCONJ
ejpam-97	391	18	ϕαγhα(aα	ϕαγhα(aα	ADJ
ejpam-97	391	19	)	)	PUNCT
ejpam-97	391	20	=	=	SYM
ejpam-97	391	21	ϕβγhβ(aβ	ϕβγhβ(aβ	PROPN
ejpam-97	391	22	)	)	PUNCT
ejpam-97	391	23	which	which	PRON
ejpam-97	391	24	implies	imply	VERB
ejpam-97	391	25	that	that	SCONJ
ejpam-97	392	1	[	[	X
ejpam-97	392	2	aα]ρ	aα]ρ	NOUN
ejpam-97	392	3	=	=	PUNCT
ejpam-97	393	1	[	[	X
ejpam-97	393	2	aβ]ρ	aβ]ρ	PROPN
ejpam-97	393	3	,	,	PUNCT
ejpam-97	393	4	and	and	CCONJ
ejpam-97	393	5	so	so	ADV
ejpam-97	393	6	h	h	NOUN
ejpam-97	393	7	is	be	AUX
ejpam-97	393	8	a	a	DET
ejpam-97	393	9	monomorphism	monomorphism	NOUN
ejpam-97	393	10	.	.	PUNCT
ejpam-97	394	1	now	now	ADV
ejpam-97	394	2	,	,	PUNCT
ejpam-97	394	3	let	let	VERB
ejpam-97	394	4	k	k	PRON
ejpam-97	394	5	:	:	PUNCT
ejpam-97	394	6	s	s	X
ejpam-97	394	7	→	→	SYM
ejpam-97	395	1	l	l	NOUN
ejpam-97	395	2	im−→aα	im−→aα	NOUN
ejpam-97	395	3	be	be	AUX
ejpam-97	395	4	a	a	DET
ejpam-97	395	5	homomorphism	homomorphism	NOUN
ejpam-97	395	6	such	such	ADJ
ejpam-97	395	7	that	that	DET
ejpam-97	395	8	hk	hk	PROPN
ejpam-97	395	9	=	=	PUNCT
ejpam-97	395	10	λ[bα]ρ′	λ[bα]ρ′	PROPN
ejpam-97	395	11	and	and	CCONJ
ejpam-97	395	12	for	for	ADP
ejpam-97	395	13	s	s	PROPN
ejpam-97	395	14	∈	∈	PROPN
ejpam-97	395	15	s	s	PROPN
ejpam-97	395	16	,	,	PUNCT
ejpam-97	395	17	k(s	k(s	PROPN
ejpam-97	395	18	)	)	PUNCT
ejpam-97	395	19	=	=	PUNCT
ejpam-97	396	1	[	[	X
ejpam-97	396	2	aαs	aαs	NOUN
ejpam-97	396	3	]	]	SYM
ejpam-97	396	4	ρ	ρ	NOUN
ejpam-97	396	5	,	,	PUNCT
ejpam-97	396	6	aαs	aαs	PROPN
ejpam-97	396	7	∈	∈	PROPN
ejpam-97	396	8	a.	a.	NOUN
ejpam-97	396	9	notice	notice	NOUN
ejpam-97	396	10	that	that	SCONJ
ejpam-97	396	11	γ	γ	PROPN
ejpam-97	396	12	≥	≥	NUM
ejpam-97	396	13	α	α	NOUN
ejpam-97	396	14	,	,	PUNCT
ejpam-97	396	15	αs	αs	PROPN
ejpam-97	396	16	,	,	PUNCT
ejpam-97	396	17	for	for	ADP
ejpam-97	396	18	s	s	PROPN
ejpam-97	396	19	∈	∈	PROPN
ejpam-97	396	20	s	s	NOUN
ejpam-97	396	21	,	,	PUNCT
ejpam-97	396	22	and	and	CCONJ
ejpam-97	396	23	define	define	VERB
ejpam-97	396	24	k1	k1	NOUN
ejpam-97	396	25	:	:	PUNCT
ejpam-97	396	26	s	s	X
ejpam-97	396	27	→	→	PUNCT
ejpam-97	396	28	aγ	aγ	NOUN
ejpam-97	396	29	by	by	ADP
ejpam-97	396	30	k1(s	k1(s	PROPN
ejpam-97	396	31	)	)	PUNCT
ejpam-97	396	32	=	=	SYM
ejpam-97	396	33	ψαsγ	ψαsγ	NOUN
ejpam-97	396	34	(	(	PUNCT
ejpam-97	396	35	aαs	aαs	NOUN
ejpam-97	396	36	)	)	PUNCT
ejpam-97	396	37	.	.	PUNCT
ejpam-97	397	1	then	then	ADV
ejpam-97	397	2	,	,	PUNCT
ejpam-97	397	3	since	since	SCONJ
ejpam-97	397	4	fγk1(s	fγk1(	NOUN
ejpam-97	397	5	)	)	PUNCT
ejpam-97	397	6	=	=	NOUN
ejpam-97	397	7	fγψαsγ	fγψαsγ	NOUN
ejpam-97	397	8	(	(	PUNCT
ejpam-97	397	9	aαs	aαs	NOUN
ejpam-97	397	10	)	)	PUNCT
ejpam-97	397	11	=	=	SYM
ejpam-97	397	12	fαs	fαs	PROPN
ejpam-97	397	13	(	(	PUNCT
ejpam-97	397	14	aαs	aαs	NOUN
ejpam-97	397	15	)	)	PUNCT
ejpam-97	397	16	=	=	PUNCT
ejpam-97	398	1	[	[	X
ejpam-97	398	2	aαs	aαs	NOUN
ejpam-97	398	3	]	]	PUNCT
ejpam-97	398	4	ρ	ρ	X
ejpam-97	398	5	=	=	SYM
ejpam-97	398	6	k(s	k(s	PROPN
ejpam-97	398	7	)	)	PUNCT
ejpam-97	398	8	and	and	CCONJ
ejpam-97	398	9	fγk1(st	fγk1(st	PROPN
ejpam-97	398	10	)	)	PUNCT
ejpam-97	398	11	=	=	SYM
ejpam-97	398	12	k(st	k(st	PROPN
ejpam-97	398	13	)	)	PUNCT
ejpam-97	398	14	=	=	SYM
ejpam-97	399	1	k(s)t	k(s)t	NOUN
ejpam-97	399	2	=	=	SYM
ejpam-97	399	3	fγk1(s)t	fγk1(s)t	PROPN
ejpam-97	399	4	,	,	PUNCT
ejpam-97	399	5	it	it	PRON
ejpam-97	399	6	follows	follow	VERB
ejpam-97	399	7	that	that	SCONJ
ejpam-97	399	8	k1	k1	PROPN
ejpam-97	399	9	is	be	AUX
ejpam-97	399	10	a	a	DET
ejpam-97	399	11	homomorphism	homomorphism	NOUN
ejpam-97	399	12	,	,	PUNCT
ejpam-97	399	13	since	since	SCONJ
ejpam-97	399	14	fγ	fγ	PROPN
ejpam-97	399	15	is	be	AUX
ejpam-97	399	16	a	a	DET
ejpam-97	399	17	monomorphism	monomorphism	NOUN
ejpam-97	399	18	.	.	PUNCT
ejpam-97	400	1	now	now	ADV
ejpam-97	400	2	,	,	PUNCT
ejpam-97	400	3	for	for	ADP
ejpam-97	400	4	every	every	DET
ejpam-97	400	5	s	s	X
ejpam-97	400	6	∈	∈	PROPN
ejpam-97	400	7	s	s	NOUN
ejpam-97	400	8	,	,	PUNCT
ejpam-97	400	9	gγhγk1(s	gγhγk1(s	NOUN
ejpam-97	400	10	)	)	PUNCT
ejpam-97	400	11	=	=	PUNCT
ejpam-97	400	12	hfγk1(s	hfγk1(	VERB
ejpam-97	400	13	)	)	PUNCT
ejpam-97	400	14	=	=	SYM
ejpam-97	400	15	hk(s	hk(s	X
ejpam-97	400	16	)	)	PUNCT
ejpam-97	400	17	=	=	NOUN
ejpam-97	401	1	[	[	X
ejpam-97	401	2	bα]s	bα]s	NOUN
ejpam-97	401	3	=	=	SYM
ejpam-97	401	4	gα(bα)s	gα(bα)s	X
ejpam-97	401	5	=	=	X
ejpam-97	401	6	gγϕαγ(bαs	gγϕαγ(bαs	PROPN
ejpam-97	401	7	)	)	PUNCT
ejpam-97	401	8	and	and	CCONJ
ejpam-97	401	9	then	then	ADV
ejpam-97	401	10	,	,	PUNCT
ejpam-97	401	11	since	since	SCONJ
ejpam-97	401	12	gγ	gγ	ADV
ejpam-97	401	13	is	be	VERB
ejpam-97	401	14	a	a	DET
ejpam-97	401	15	monomorphism	monomorphism	NOUN
ejpam-97	401	16	,	,	PUNCT
ejpam-97	401	17	we	we	PRON
ejpam-97	401	18	have	have	VERB
ejpam-97	401	19	hγk1	hγk1	ADJ
ejpam-97	401	20	=	=	SYM
ejpam-97	401	21	λϕαγ(bα	λϕαγ(bα	PROPN
ejpam-97	401	22	)	)	PUNCT
ejpam-97	401	23	.	.	PUNCT
ejpam-97	402	1	but	but	CCONJ
ejpam-97	402	2	,	,	PUNCT
ejpam-97	402	3	hγ	hγ	PRON
ejpam-97	402	4	is	be	AUX
ejpam-97	402	5	s	s	NOUN
ejpam-97	402	6	-	-	ADJ
ejpam-97	402	7	pure	pure	ADJ
ejpam-97	402	8	and	and	CCONJ
ejpam-97	402	9	so	so	ADV
ejpam-97	402	10	k1	k1	PROPN
ejpam-97	402	11	=	=	SYM
ejpam-97	402	12	λa	λa	NOUN
ejpam-97	402	13	for	for	ADP
ejpam-97	402	14	some	some	DET
ejpam-97	402	15	a	a	DET
ejpam-97	402	16	∈	∈	NOUN
ejpam-97	402	17	aγ	aγ	NOUN
ejpam-97	402	18	.	.	PUNCT
ejpam-97	403	1	hence	hence	ADV
ejpam-97	403	2	k	k	PROPN
ejpam-97	403	3	=	=	PUNCT
ejpam-97	403	4	λ	λ	NOUN
ejpam-97	403	5	fγ(a	fγ(a	NOUN
ejpam-97	403	6	)	)	PUNCT
ejpam-97	403	7	,	,	PUNCT
ejpam-97	403	8	because	because	SCONJ
ejpam-97	403	9	fγk1	fγk1	NOUN
ejpam-97	403	10	=	=	SYM
ejpam-97	403	11	k.	k.	PROPN
ejpam-97	403	12	corollary	corollary	PROPN
ejpam-97	403	13	3.1	3.1	NUM
ejpam-97	403	14	.	.	PUNCT
ejpam-97	404	1	let	let	VERB
ejpam-97	404	2	i	i	PRON
ejpam-97	404	3	be	be	AUX
ejpam-97	404	4	a	a	DET
ejpam-97	404	5	directed	direct	VERB
ejpam-97	404	6	set	set	NOUN
ejpam-97	404	7	which	which	PRON
ejpam-97	404	8	has	have	VERB
ejpam-97	404	9	a	a	DET
ejpam-97	404	10	maximal	maximal	ADJ
ejpam-97	404	11	element	element	NOUN
ejpam-97	404	12	γ	γ	NOUN
ejpam-97	404	13	and	and	CCONJ
ejpam-97	404	14	{	{	PUNCT
ejpam-97	404	15	hα	hα	X
ejpam-97	404	16	:	:	PUNCT
ejpam-97	404	17	a→	a→	X
ejpam-97	405	1	bα|α	bα|α	X
ejpam-97	405	2	∈	∈	PROPN
ejpam-97	406	1	i	i	PRON
ejpam-97	406	2	}	}	PUNCT
ejpam-97	406	3	be	be	VERB
ejpam-97	406	4	a	a	DET
ejpam-97	406	5	directed	direct	VERB
ejpam-97	406	6	family	family	NOUN
ejpam-97	406	7	of	of	ADP
ejpam-97	406	8	s	s	NOUN
ejpam-97	406	9	-	-	ADJ
ejpam-97	406	10	pure	pure	ADJ
ejpam-97	406	11	monomorphisms	monomorphism	NOUN
ejpam-97	406	12	.	.	PUNCT
ejpam-97	407	1	then	then	ADV
ejpam-97	407	2	,	,	PUNCT
ejpam-97	407	3	the	the	DET
ejpam-97	407	4	directed	direct	VERB
ejpam-97	407	5	limit	limit	NOUN
ejpam-97	407	6	(	(	PUNCT
ejpam-97	407	7	colimit	colimit	NOUN
ejpam-97	407	8	)	)	PUNCT
ejpam-97	407	9	of	of	ADP
ejpam-97	407	10	hα	hα	ADP
ejpam-97	407	11	,	,	PUNCT
ejpam-97	407	12	s	s	PART
ejpam-97	407	13	is	be	AUX
ejpam-97	407	14	s	s	NOUN
ejpam-97	407	15	-	-	ADJ
ejpam-97	407	16	pure	pure	ADJ
ejpam-97	407	17	.	.	PUNCT
ejpam-97	408	1	proof	proof	NOUN
ejpam-97	408	2	.	.	PUNCT
ejpam-97	409	1	let	let	VERB
ejpam-97	409	2	h	h	NOUN
ejpam-97	409	3	:	:	PUNCT
ejpam-97	409	4	a→	a→	PUNCT
ejpam-97	409	5	l	l	NOUN
ejpam-97	409	6	im−→αbα	im−→αbα	NOUN
ejpam-97	409	7	be	be	AUX
ejpam-97	409	8	a	a	DET
ejpam-97	409	9	direct	direct	ADJ
ejpam-97	409	10	limit	limit	NOUN
ejpam-97	409	11	in	in	ADP
ejpam-97	409	12	act	act	PROPN
ejpam-97	409	13	-	-	PUNCT
ejpam-97	409	14	s	s	PROPN
ejpam-97	409	15	of	of	ADP
ejpam-97	409	16	s	s	NOUN
ejpam-97	409	17	-	-	ADJ
ejpam-97	409	18	pure	pure	ADJ
ejpam-97	409	19	monomorphisms	monomorphism	NOUN
ejpam-97	409	20	hα	hα	X
ejpam-97	409	21	:	:	PUNCT
ejpam-97	409	22	a→	a→	PROPN
ejpam-97	409	23	bα	bα	PROPN
ejpam-97	409	24	,	,	PUNCT
ejpam-97	409	25	α	α	PROPN
ejpam-97	409	26	∈	∈	X
ejpam-97	410	1	i	i	PRON
ejpam-97	410	2	,	,	PUNCT
ejpam-97	410	3	and	and	CCONJ
ejpam-97	410	4	consider	consider	VERB
ejpam-97	410	5	gα	gα	ADP
ejpam-97	410	6	:	:	PUNCT
ejpam-97	410	7	bα	bα	PROPN
ejpam-97	410	8	→	→	SYM
ejpam-97	410	9	l	l	NOUN
ejpam-97	410	10	im−→αbα	im−→αbα	NOUN
ejpam-97	410	11	as	as	ADP
ejpam-97	410	12	in	in	ADP
ejpam-97	410	13	the	the	DET
ejpam-97	410	14	definition	definition	NOUN
ejpam-97	410	15	.	.	PUNCT
ejpam-97	411	1	recall	recall	VERB
ejpam-97	411	2	that	that	DET
ejpam-97	411	3	h	h	NOUN
ejpam-97	412	1	=	=	PUNCT
ejpam-97	412	2	l	l	NOUN
ejpam-97	412	3	im−→αhα	im−→αhα	NOUN
ejpam-97	412	4	=	=	SYM
ejpam-97	412	5	gγhγ	gγhγ	NOUN
ejpam-97	412	6	=	=	SYM
ejpam-97	412	7	gαhα	gαhα	ADJ
ejpam-97	412	8	=	=	SYM
ejpam-97	412	9	gβhβ	gβhβ	PROPN
ejpam-97	412	10	=	=	PUNCT
ejpam-97	412	11	.	.	PUNCT
ejpam-97	412	12	.	.	PUNCT
ejpam-97	412	13	.	.	PUNCT
ejpam-97	412	14	.	.	PUNCT
ejpam-97	413	1	it	it	PRON
ejpam-97	413	2	is	be	AUX
ejpam-97	413	3	clear	clear	ADJ
ejpam-97	413	4	that	that	SCONJ
ejpam-97	413	5	h	h	NOUN
ejpam-97	413	6	:	:	PUNCT
ejpam-97	413	7	a→	a→	PUNCT
ejpam-97	413	8	l	l	NOUN
ejpam-97	413	9	im−→αbα	im−→αbα	NOUN
ejpam-97	413	10	is	be	AUX
ejpam-97	413	11	a	a	DET
ejpam-97	413	12	directed	direct	VERB
ejpam-97	413	13	colimit	colimit	NOUN
ejpam-97	413	14	of	of	ADP
ejpam-97	413	15	the	the	DET
ejpam-97	413	16	directed	direct	VERB
ejpam-97	413	17	family	family	NOUN
ejpam-97	413	18	{	{	PUNCT
ejpam-97	413	19	hα	hα	X
ejpam-97	413	20	:	:	PUNCT
ejpam-97	414	1	i	i	PROPN
ejpam-97	414	2	d	d	PROPN
ejpam-97	414	3	:	:	PUNCT
ejpam-97	414	4	aα	aα	NOUN
ejpam-97	414	5	→	→	PUNCT
ejpam-97	414	6	aγ	aγ	NOUN
ejpam-97	415	1	|	|	ADV
ejpam-97	415	2	α	α	NOUN
ejpam-97	415	3	∈	∈	PROPN
ejpam-97	416	1	i	i	PRON
ejpam-97	416	2	−	−	PROPN
ejpam-97	416	3	{	{	PUNCT
ejpam-97	416	4	γ	γ	X
ejpam-97	416	5	}	}	PUNCT
ejpam-97	416	6	,	,	PUNCT
ejpam-97	416	7	aα	aα	NOUN
ejpam-97	416	8	=	=	NOUN
ejpam-97	416	9	a	a	X
ejpam-97	416	10	}	}	PUNCT
ejpam-97	416	11	.	.	PUNCT
ejpam-97	417	1	then	then	ADV
ejpam-97	417	2	,	,	PUNCT
ejpam-97	417	3	apply	apply	VERB
ejpam-97	417	4	the	the	DET
ejpam-97	417	5	above	above	ADJ
ejpam-97	417	6	theorem	theorem	NOUN
ejpam-97	417	7	to	to	PART
ejpam-97	417	8	complete	complete	VERB
ejpam-97	417	9	the	the	DET
ejpam-97	417	10	proof	proof	NOUN
ejpam-97	417	11	.	.	PUNCT
ejpam-97	418	1	another	another	DET
ejpam-97	418	2	condition	condition	NOUN
ejpam-97	418	3	which	which	PRON
ejpam-97	418	4	gives	give	VERB
ejpam-97	418	5	the	the	DET
ejpam-97	418	6	above	above	ADJ
ejpam-97	418	7	result	result	NOUN
ejpam-97	418	8	is	be	AUX
ejpam-97	418	9	finitely	finitely	ADV
ejpam-97	418	10	generatedness	generatedness	NOUN
ejpam-97	418	11	of	of	ADP
ejpam-97	418	12	semigroup	semigroup	NOUN
ejpam-97	418	13	:	:	PUNCT
ejpam-97	418	14	theorem	theorem	NOUN
ejpam-97	418	15	3.4	3.4	NUM
ejpam-97	418	16	.	.	PUNCT
ejpam-97	419	1	let	let	VERB
ejpam-97	419	2	i	i	PRON
ejpam-97	419	3	be	be	AUX
ejpam-97	419	4	a	a	DET
ejpam-97	419	5	directed	direct	VERB
ejpam-97	419	6	set	set	NOUN
ejpam-97	419	7	and	and	CCONJ
ejpam-97	419	8	s	s	AUX
ejpam-97	419	9	be	be	AUX
ejpam-97	419	10	a	a	DET
ejpam-97	419	11	finitely	finitely	ADV
ejpam-97	419	12	generated	generate	VERB
ejpam-97	419	13	semigroup	semigroup	NOUN
ejpam-97	419	14	.	.	PUNCT
ejpam-97	420	1	then	then	ADV
ejpam-97	420	2	,	,	PUNCT
ejpam-97	420	3	the	the	DET
ejpam-97	420	4	category	category	NOUN
ejpam-97	420	5	act	act	NOUN
ejpam-97	420	6	-	-	PUNCT
ejpam-97	420	7	s	s	PART
ejpam-97	420	8	hasmp	hasmp	ADJ
ejpam-97	420	9	-	-	PUNCT
ejpam-97	420	10	directed	direct	VERB
ejpam-97	420	11	colimits	colimit	NOUN
ejpam-97	420	12	.	.	PUNCT
ejpam-97	421	1	proof	proof	NOUN
ejpam-97	421	2	.	.	PUNCT
ejpam-97	422	1	let	let	VERB
ejpam-97	422	2	h	h	NOUN
ejpam-97	422	3	:	:	PUNCT
ejpam-97	422	4	a→	a→	PUNCT
ejpam-97	422	5	l	l	NOUN
ejpam-97	422	6	im−→αbα	im−→αbα	NOUN
ejpam-97	422	7	be	be	AUX
ejpam-97	422	8	a	a	DET
ejpam-97	422	9	direct	direct	ADJ
ejpam-97	422	10	limit	limit	NOUN
ejpam-97	422	11	in	in	ADP
ejpam-97	422	12	act	act	PROPN
ejpam-97	422	13	-	-	PUNCT
ejpam-97	422	14	s	s	PROPN
ejpam-97	422	15	of	of	ADP
ejpam-97	422	16	s	s	NOUN
ejpam-97	422	17	-	-	ADJ
ejpam-97	422	18	pure	pure	ADJ
ejpam-97	422	19	monomorphisms	monomorphism	NOUN
ejpam-97	422	20	hα	hα	X
ejpam-97	422	21	:	:	PUNCT
ejpam-97	422	22	a→	a→	PROPN
ejpam-97	422	23	bα	bα	PROPN
ejpam-97	422	24	,	,	PUNCT
ejpam-97	422	25	α	α	PROPN
ejpam-97	422	26	∈	∈	X
ejpam-97	423	1	i	i	PRON
ejpam-97	423	2	,	,	PUNCT
ejpam-97	423	3	and	and	CCONJ
ejpam-97	423	4	consider	consider	VERB
ejpam-97	423	5	gα	gα	ADP
ejpam-97	423	6	:	:	PUNCT
ejpam-97	423	7	bα	bα	PROPN
ejpam-97	423	8	→	→	SYM
ejpam-97	423	9	l	l	NOUN
ejpam-97	423	10	im−→αbα	im−→αbα	NOUN
ejpam-97	423	11	as	as	ADP
ejpam-97	423	12	in	in	ADP
ejpam-97	423	13	the	the	DET
ejpam-97	423	14	definition	definition	NOUN
ejpam-97	423	15	.	.	PUNCT
ejpam-97	424	1	recall	recall	VERB
ejpam-97	424	2	that	that	DET
ejpam-97	424	3	h	h	NOUN
ejpam-97	425	1	=	=	PUNCT
ejpam-97	425	2	l	l	NOUN
ejpam-97	425	3	im−→αhα	im−→αhα	NOUN
ejpam-97	425	4	=	=	SYM
ejpam-97	425	5	gγhγ	gγhγ	NOUN
ejpam-97	425	6	=	=	SYM
ejpam-97	425	7	gαhα	gαhα	ADJ
ejpam-97	425	8	=	=	SYM
ejpam-97	425	9	gβhβ	gβhβ	PROPN
ejpam-97	425	10	=	=	PUNCT
ejpam-97	425	11	.	.	PUNCT
ejpam-97	425	12	.	.	PUNCT
ejpam-97	425	13	.	.	PUNCT
ejpam-97	425	14	.	.	PUNCT
ejpam-97	426	1	let	let	VERB
ejpam-97	426	2	s	s	PRON
ejpam-97	426	3	=	=	PUNCT
ejpam-97	426	4	∪n	∪n	NUM
ejpam-97	426	5	i=1	i=1	PROPN
ejpam-97	426	6	t	t	PROPN
ejpam-97	426	7	is	be	AUX
ejpam-97	426	8	1	1	NUM
ejpam-97	426	9	and	and	CCONJ
ejpam-97	426	10	k	k	NOUN
ejpam-97	426	11	:	:	PUNCT
ejpam-97	426	12	s→	s→	X
ejpam-97	426	13	a	a	PRON
ejpam-97	426	14	be	be	AUX
ejpam-97	426	15	an	an	DET
ejpam-97	426	16	s	s	NOUN
ejpam-97	426	17	-	-	PUNCT
ejpam-97	426	18	map	map	NOUN
ejpam-97	427	1	such	such	ADJ
ejpam-97	427	2	that	that	DET
ejpam-97	427	3	hk	hk	PROPN
ejpam-97	427	4	=	=	PUNCT
ejpam-97	427	5	λ[bα	λ[bα	PROPN
ejpam-97	427	6	]	]	X
ejpam-97	427	7	.	.	PUNCT
ejpam-97	428	1	then	then	ADV
ejpam-97	428	2	,	,	PUNCT
ejpam-97	428	3	for	for	ADP
ejpam-97	428	4	every	every	DET
ejpam-97	428	5	1	1	NUM
ejpam-97	428	6	≤	≤	NUM
ejpam-97	428	7	i	i	NOUN
ejpam-97	428	8	≤	≤	NOUN
ejpam-97	428	9	n	n	CCONJ
ejpam-97	428	10	,	,	PUNCT
ejpam-97	428	11	[	[	X
ejpam-97	428	12	hαk(t	hαk(t	X
ejpam-97	428	13	i	i	PRON
ejpam-97	428	14	)	)	PUNCT
ejpam-97	428	15	]	]	PUNCT
ejpam-97	429	1	=	=	PUNCT
ejpam-97	430	1	[	[	X
ejpam-97	430	2	bα	bα	NOUN
ejpam-97	430	3	t	t	NOUN
ejpam-97	430	4	i	i	PRON
ejpam-97	430	5	]	]	X
ejpam-97	430	6	,	,	PUNCT
ejpam-97	430	7	and	and	CCONJ
ejpam-97	430	8	so	so	ADV
ejpam-97	430	9	there	there	PRON
ejpam-97	430	10	exist	exist	VERB
ejpam-97	430	11	γi	γi	ADP
ejpam-97	430	12	∈	∈	PROPN
ejpam-97	431	1	i	i	PRON
ejpam-97	431	2	such	such	ADJ
ejpam-97	431	3	that	that	DET
ejpam-97	431	4	ψαγi	ψαγi	NOUN
ejpam-97	431	5	(	(	PUNCT
ejpam-97	431	6	hαk(t	hαk(t	PROPN
ejpam-97	431	7	i	i	PRON
ejpam-97	431	8	)	)	PUNCT
ejpam-97	431	9	)	)	PUNCT
ejpam-97	432	1	=	=	SYM
ejpam-97	432	2	ψαγi	ψαγi	NOUN
ejpam-97	432	3	(	(	PUNCT
ejpam-97	432	4	bα	bα	NOUN
ejpam-97	432	5	t	t	PROPN
ejpam-97	432	6	i	i	PROPN
ejpam-97	432	7	)	)	PUNCT
ejpam-97	432	8	.	.	PUNCT
ejpam-97	433	1	now	now	ADV
ejpam-97	433	2	,	,	PUNCT
ejpam-97	433	3	let	let	VERB
ejpam-97	433	4	γ≥	γ≥	NOUN
ejpam-97	433	5	max{γ1	max{γ1	NOUN
ejpam-97	433	6	,	,	PUNCT
ejpam-97	433	7	·	·	PUNCT
ejpam-97	433	8	·	·	PUNCT
ejpam-97	433	9	·	·	PUNCT
ejpam-97	433	10	,	,	PUNCT
ejpam-97	433	11	γn	γn	X
ejpam-97	433	12	}	}	PUNCT
ejpam-97	433	13	and	and	CCONJ
ejpam-97	433	14	so	so	ADV
ejpam-97	433	15	for	for	ADP
ejpam-97	433	16	every	every	DET
ejpam-97	433	17	s	s	X
ejpam-97	433	18	∈	∈	PROPN
ejpam-97	433	19	s	s	NOUN
ejpam-97	433	20	,	,	PUNCT
ejpam-97	433	21	hγ(k(s	hγ(k(s	ADJ
ejpam-97	433	22	)	)	PUNCT
ejpam-97	433	23	)	)	PUNCT
ejpam-97	434	1	=	=	SYM
ejpam-97	434	2	ψαγ(bα)s	ψαγ(bα)s	PROPN
ejpam-97	434	3	.	.	PUNCT
ejpam-97	434	4	then	then	ADV
ejpam-97	434	5	,	,	PUNCT
ejpam-97	434	6	since	since	SCONJ
ejpam-97	434	7	hγ	hγ	PRON
ejpam-97	434	8	is	be	AUX
ejpam-97	434	9	s	s	NOUN
ejpam-97	434	10	-	-	ADJ
ejpam-97	434	11	pure	pure	ADJ
ejpam-97	434	12	,	,	PUNCT
ejpam-97	434	13	k	k	PROPN
ejpam-97	434	14	=	=	PUNCT
ejpam-97	434	15	λa	λa	X
ejpam-97	434	16	for	for	ADP
ejpam-97	434	17	some	some	PRON
ejpam-97	434	18	a	a	DET
ejpam-97	434	19	∈	∈	NOUN
ejpam-97	434	20	a.	a.	NOUN
ejpam-97	434	21	we	we	PRON
ejpam-97	434	22	say	say	VERB
ejpam-97	434	23	that	that	SCONJ
ejpam-97	434	24	mul	mul	PROPN
ejpam-97	434	25	tiple	tiple	NOUN
ejpam-97	434	26	pushouts	pushout	NOUN
ejpam-97	434	27	transfer	transfer	VERB
ejpam-97	434	28	s	s	NOUN
ejpam-97	434	29	-	-	ADJ
ejpam-97	434	30	pure	pure	ADJ
ejpam-97	434	31	monomorphisms	monomorphism	NOUN
ejpam-97	434	32	if	if	SCONJ
ejpam-97	434	33	in	in	ADP
ejpam-97	434	34	multiple	multiple	ADJ
ejpam-97	434	35	pushout	pushout	NOUN
ejpam-97	434	36	(	(	PUNCT
ejpam-97	434	37	p	p	NOUN
ejpam-97	434	38	,	,	PUNCT
ejpam-97	434	39	aα	aα	NOUN
ejpam-97	434	40	hα→	hα→	NOUN
ejpam-97	435	1	p	p	NOUN
ejpam-97	435	2	)	)	PUNCT
ejpam-97	435	3	of	of	ADP
ejpam-97	435	4	a	a	DET
ejpam-97	435	5	family	family	NOUN
ejpam-97	435	6	of	of	ADP
ejpam-97	435	7	s	s	NOUN
ejpam-97	435	8	-	-	ADJ
ejpam-97	435	9	pure	pure	ADJ
ejpam-97	435	10	monomorphisms	monomorphism	NOUN
ejpam-97	435	11	{	{	PUNCT
ejpam-97	435	12	fα	fα	ADP
ejpam-97	435	13	:	:	PUNCT
ejpam-97	435	14	a→	a→	X
ejpam-97	436	1	aα|α	aα|α	ADV
ejpam-97	436	2	∈	∈	PROPN
ejpam-97	436	3	i	i	PRON
ejpam-97	436	4	}	}	PUNCT
ejpam-97	436	5	,	,	PUNCT
ejpam-97	436	6	every	every	DET
ejpam-97	436	7	hα	hα	NOUN
ejpam-97	436	8	,	,	PUNCT
ejpam-97	436	9	α	α	PROPN
ejpam-97	436	10	∈	∈	X
ejpam-97	437	1	i	i	PRON
ejpam-97	437	2	,	,	PUNCT
ejpam-97	437	3	is	be	AUX
ejpam-97	437	4	an	an	DET
ejpam-97	437	5	s	s	NOUN
ejpam-97	437	6	-	-	ADJ
ejpam-97	437	7	pure	pure	ADJ
ejpam-97	437	8	monomorphism	monomorphism	NOUN
ejpam-97	437	9	.	.	PUNCT
ejpam-97	438	1	theorem	theorem	VERB
ejpam-97	438	2	3.5	3.5	NUM
ejpam-97	438	3	.	.	PUNCT
ejpam-97	439	1	multiple	multiple	ADJ
ejpam-97	439	2	pushouts	pushout	NOUN
ejpam-97	439	3	transfer	transfer	VERB
ejpam-97	439	4	s	s	NOUN
ejpam-97	439	5	-	-	ADJ
ejpam-97	439	6	pure	pure	ADJ
ejpam-97	439	7	monomorphisms	monomorphism	NOUN
ejpam-97	439	8	.	.	PUNCT
ejpam-97	440	1	proof	proof	NOUN
ejpam-97	440	2	.	.	PUNCT
ejpam-97	441	1	let	let	VERB
ejpam-97	441	2	(	(	PUNCT
ejpam-97	441	3	p	p	X
ejpam-97	441	4	,	,	PUNCT
ejpam-97	441	5	aα	aα	NOUN
ejpam-97	441	6	hα→	hα→	NOUN
ejpam-97	442	1	p	p	X
ejpam-97	442	2	)	)	PUNCT
ejpam-97	442	3	be	be	AUX
ejpam-97	442	4	the	the	DET
ejpam-97	442	5	multiple	multiple	ADJ
ejpam-97	442	6	pushout	pushout	NOUN
ejpam-97	442	7	of	of	ADP
ejpam-97	442	8	the	the	DET
ejpam-97	442	9	family	family	NOUN
ejpam-97	442	10	{	{	PUNCT
ejpam-97	442	11	fα	fα	ADP
ejpam-97	442	12	:	:	PUNCT
ejpam-97	442	13	a→	a→	X
ejpam-97	442	14	aα|α	aα|α	ADV
ejpam-97	442	15	∈	∈	PROPN
ejpam-97	442	16	i	i	PRON
ejpam-97	442	17	}	}	PUNCT
ejpam-97	442	18	of	of	ADP
ejpam-97	442	19	s	s	NOUN
ejpam-97	442	20	-	-	ADJ
ejpam-97	442	21	pure	pure	ADJ
ejpam-97	442	22	monomorphisms	monomorphism	NOUN
ejpam-97	442	23	.	.	PUNCT
ejpam-97	443	1	we	we	PRON
ejpam-97	443	2	know	know	VERB
ejpam-97	443	3	that	that	SCONJ
ejpam-97	443	4	p	p	X
ejpam-97	443	5	=	=	X
ejpam-97	443	6	∐	∐	ADJ
ejpam-97	443	7	aα	aα	NOUN
ejpam-97	443	8	/	/	SYM
ejpam-97	443	9	ρ(h	ρ(h	NOUN
ejpam-97	443	10	)	)	PUNCT
ejpam-97	443	11	where	where	SCONJ
ejpam-97	443	12	h	h	NOUN
ejpam-97	443	13	=	=	PRON
ejpam-97	443	14	{	{	PUNCT
ejpam-97	443	15	(	(	PUNCT
ejpam-97	443	16	fα(a	fα(a	NOUN
ejpam-97	443	17	)	)	PUNCT
ejpam-97	443	18	,	,	PUNCT
ejpam-97	443	19	fβ(a	fβ(a	PROPN
ejpam-97	443	20	)	)	PUNCT
ejpam-97	443	21	)	)	PUNCT
ejpam-97	444	1	|	|	ADV
ejpam-97	444	2	a	a	DET
ejpam-97	444	3	∈	∈	PROPN
ejpam-97	444	4	a	a	DET
ejpam-97	444	5	,	,	PUNCT
ejpam-97	444	6	α	α	X
ejpam-97	444	7	,	,	PUNCT
ejpam-97	444	8	β	β	X
ejpam-97	444	9	∈	∈	PROPN
ejpam-97	445	1	i	i	PRON
ejpam-97	445	2	}	}	PUNCT
ejpam-97	445	3	(	(	PUNCT
ejpam-97	445	4	we	we	PRON
ejpam-97	445	5	have	have	AUX
ejpam-97	445	6	taken	take	VERB
ejpam-97	445	7	the	the	DET
ejpam-97	445	8	image	image	NOUN
ejpam-97	445	9	of	of	ADP
ejpam-97	445	10	each	each	DET
ejpam-97	445	11	element	element	NOUN
ejpam-97	445	12	aα	aα	NOUN
ejpam-97	445	13	under	under	ADP
ejpam-97	445	14	coproduct	coproduct	NOUN
ejpam-97	445	15	morphisms	morphism	NOUN
ejpam-97	445	16	equal	equal	ADJ
ejpam-97	445	17	to	to	ADP
ejpam-97	445	18	itself	itself	PRON
ejpam-97	445	19	)	)	PUNCT
ejpam-97	445	20	.	.	PUNCT
ejpam-97	446	1	let	let	VERB
ejpam-97	446	2	hα(a	hα(a	NOUN
ejpam-97	446	3	)	)	PUNCT
ejpam-97	447	1	=	=	SYM
ejpam-97	447	2	hα(a′	hα(a′	NOUN
ejpam-97	447	3	)	)	PUNCT
ejpam-97	447	4	,	,	PUNCT
ejpam-97	447	5	a	a	PRON
ejpam-97	447	6	,	,	PUNCT
ejpam-97	447	7	a′	a′	PROPN
ejpam-97	447	8	∈	∈	PROPN
ejpam-97	447	9	aα	aα	NOUN
ejpam-97	447	10	,	,	PUNCT
ejpam-97	447	11	and	and	CCONJ
ejpam-97	447	12	so	so	ADV
ejpam-97	447	13	there	there	PRON
ejpam-97	447	14	exist	exist	VERB
ejpam-97	447	15	p1	p1	NOUN
ejpam-97	447	16	,	,	PUNCT
ejpam-97	447	17	p2	p2	NOUN
ejpam-97	447	18	,	,	PUNCT
ejpam-97	447	19	...	...	PUNCT
ejpam-97	447	20	,	,	PUNCT
ejpam-97	447	21	pn	pn	PROPN
ejpam-97	447	22	,	,	PUNCT
ejpam-97	447	23	q1	q1	PROPN
ejpam-97	447	24	,	,	PUNCT
ejpam-97	447	25	q2	q2	NOUN
ejpam-97	447	26	,	,	PUNCT
ejpam-97	447	27	...	...	PUNCT
ejpam-97	447	28	,	,	PUNCT
ejpam-97	447	29	qn	qn	NOUN
ejpam-97	447	30	∈	∈	PROPN
ejpam-97	447	31	a	a	DET
ejpam-97	447	32	,	,	PUNCT
ejpam-97	447	33	s1	s1	NOUN
ejpam-97	447	34	,	,	PUNCT
ejpam-97	447	35	s2	s2	PROPN
ejpam-97	447	36	,	,	PUNCT
ejpam-97	447	37	...	...	PUNCT
ejpam-97	447	38	,	,	PUNCT
ejpam-97	447	39	sn	sn	PROPN
ejpam-97	447	40	∈	∈	PROPN
ejpam-97	447	41	references	reference	VERB
ejpam-97	447	42	54	54	NUM
ejpam-97	447	43	s1	s1	NOUN
ejpam-97	447	44	where	where	SCONJ
ejpam-97	447	45	for	for	ADP
ejpam-97	447	46	i	i	PROPN
ejpam-97	447	47	=	=	NOUN
ejpam-97	447	48	1	1	NUM
ejpam-97	447	49	,	,	PUNCT
ejpam-97	447	50	...	...	PUNCT
ejpam-97	447	51	,	,	PUNCT
ejpam-97	447	52	n	n	CCONJ
ejpam-97	447	53	,	,	PUNCT
ejpam-97	447	54	(	(	PUNCT
ejpam-97	447	55	pi	pi	NOUN
ejpam-97	447	56	,	,	PUNCT
ejpam-97	447	57	qi	qi	PROPN
ejpam-97	447	58	)	)	PUNCT
ejpam-97	447	59	∈	∈	PROPN
ejpam-97	447	60	h	h	NOUN
ejpam-97	447	61	∪	∪	VERB
ejpam-97	447	62	h−1	h−1	PROPN
ejpam-97	447	63	and	and	CCONJ
ejpam-97	447	64	such	such	ADJ
ejpam-97	448	1	that	that	SCONJ
ejpam-97	448	2	a	a	DET
ejpam-97	448	3	=	=	X
ejpam-97	448	4	p1s1	p1s1	NOUN
ejpam-97	448	5	,	,	PUNCT
ejpam-97	448	6	q1s1	q1s1	NOUN
ejpam-97	448	7	=	=	SYM
ejpam-97	448	8	p2s2	p2s2	PROPN
ejpam-97	448	9	,	,	PUNCT
ejpam-97	448	10	q2s2	q2s2	PROPN
ejpam-97	448	11	=	=	SYM
ejpam-97	448	12	p3s3	p3s3	NOUN
ejpam-97	448	13	,	,	PUNCT
ejpam-97	448	14	...	...	PUNCT
ejpam-97	448	15	,	,	PUNCT
ejpam-97	448	16	qnsn	qnsn	NOUN
ejpam-97	448	17	=	=	SYM
ejpam-97	448	18	a′.	a′.	NOUN
ejpam-97	448	19	then	then	ADV
ejpam-97	448	20	,	,	PUNCT
ejpam-97	448	21	a	a	DET
ejpam-97	448	22	=	=	SYM
ejpam-97	448	23	fα(a1)s1	fα(a1)s1	NOUN
ejpam-97	448	24	and	and	CCONJ
ejpam-97	448	25	there	there	PRON
ejpam-97	448	26	exists	exist	VERB
ejpam-97	448	27	β	β	X
ejpam-97	448	28	∈	∈	PROPN
ejpam-97	448	29	i	i	PRON
ejpam-97	448	30	such	such	ADJ
ejpam-97	448	31	that	that	DET
ejpam-97	448	32	fβ(a1)s1	fβ(a1)s1	NOUN
ejpam-97	448	33	=	=	SYM
ejpam-97	448	34	fβ(a2)s2	fβ(a2)s2	PROPN
ejpam-97	448	35	.	.	PUNCT
ejpam-97	449	1	then	then	ADV
ejpam-97	449	2	,	,	PUNCT
ejpam-97	449	3	since	since	SCONJ
ejpam-97	449	4	fβ	fβ	NOUN
ejpam-97	449	5	is	be	VERB
ejpam-97	449	6	a	a	DET
ejpam-97	449	7	monomorphism	monomorphism	NOUN
ejpam-97	449	8	,	,	PUNCT
ejpam-97	449	9	a1s1	a1s1	X
ejpam-97	449	10	=	=	SYM
ejpam-97	449	11	a2s2	a2s2	NOUN
ejpam-97	449	12	.	.	PUNCT
ejpam-97	450	1	continuing	continue	VERB
ejpam-97	450	2	this	this	DET
ejpam-97	450	3	process	process	NOUN
ejpam-97	450	4	we	we	PRON
ejpam-97	450	5	get	get	VERB
ejpam-97	450	6	that	that	PRON
ejpam-97	450	7	a1s1	a1s1	PUNCT
ejpam-97	451	1	=	=	PUNCT
ejpam-97	451	2	a2s2	a2s2	PROPN
ejpam-97	451	3	=	=	SYM
ejpam-97	451	4	...	...	PUNCT
ejpam-97	452	1	=	=	NOUN
ejpam-97	452	2	ansn	ansn	NOUN
ejpam-97	452	3	,	,	PUNCT
ejpam-97	452	4	and	and	CCONJ
ejpam-97	452	5	therefore	therefore	ADV
ejpam-97	452	6	a	a	DET
ejpam-97	452	7	=	=	NOUN
ejpam-97	452	8	a′.	a′.	NOUN
ejpam-97	452	9	now	now	ADV
ejpam-97	452	10	,	,	PUNCT
ejpam-97	452	11	let	let	VERB
ejpam-97	452	12	k	k	PRON
ejpam-97	452	13	:	:	PUNCT
ejpam-97	452	14	s	s	X
ejpam-97	452	15	→	→	PUNCT
ejpam-97	452	16	aα	aα	NOUN
ejpam-97	452	17	be	be	AUX
ejpam-97	452	18	a	a	DET
ejpam-97	452	19	homomorphism	homomorphism	NOUN
ejpam-97	452	20	such	such	ADJ
ejpam-97	452	21	that	that	SCONJ
ejpam-97	452	22	hαk	hαk	PROPN
ejpam-97	452	23	=	=	SYM
ejpam-97	452	24	λ[p	λ[p	PROPN
ejpam-97	452	25	]	]	X
ejpam-97	452	26	.	.	PUNCT
ejpam-97	453	1	if	if	SCONJ
ejpam-97	453	2	p	p	PROPN
ejpam-97	453	3	∈	∈	PROPN
ejpam-97	453	4	aα	aα	NOUN
ejpam-97	453	5	then	then	ADV
ejpam-97	453	6	,	,	PUNCT
ejpam-97	453	7	since	since	SCONJ
ejpam-97	453	8	hα	hα	ADP
ejpam-97	453	9	is	be	AUX
ejpam-97	453	10	a	a	DET
ejpam-97	453	11	monomorphism	monomorphism	NOUN
ejpam-97	453	12	,	,	PUNCT
ejpam-97	453	13	k	k	PROPN
ejpam-97	453	14	=	=	PUNCT
ejpam-97	454	1	λp	λp	PROPN
ejpam-97	454	2	.	.	PUNCT
ejpam-97	455	1	if	if	SCONJ
ejpam-97	455	2	p	p	PROPN
ejpam-97	455	3	∈	∈	PROPN
ejpam-97	455	4	aβ	aβ	INTJ
ejpam-97	455	5	,	,	PUNCT
ejpam-97	455	6	β	β	PROPN
ejpam-97	455	7	6=	6=	ADP
ejpam-97	455	8	α	α	PROPN
ejpam-97	455	9	,	,	PUNCT
ejpam-97	455	10	then	then	ADV
ejpam-97	455	11	for	for	ADP
ejpam-97	455	12	every	every	DET
ejpam-97	455	13	s	s	X
ejpam-97	455	14	∈	∈	PROPN
ejpam-97	455	15	s	s	NOUN
ejpam-97	455	16	,	,	PUNCT
ejpam-97	455	17	ps	ps	PROPN
ejpam-97	455	18	=	=	SYM
ejpam-97	455	19	fβ(a1)s1	fβ(a1)s1	NOUN
ejpam-97	455	20	and	and	CCONJ
ejpam-97	455	21	thus	thus	ADV
ejpam-97	455	22	for	for	ADP
ejpam-97	455	23	every	every	DET
ejpam-97	455	24	s	s	X
ejpam-97	455	25	∈	∈	PROPN
ejpam-97	455	26	s	s	NOUN
ejpam-97	455	27	,	,	PUNCT
ejpam-97	455	28	ps	ps	PROPN
ejpam-97	455	29	∈	∈	PROPN
ejpam-97	455	30	fβ(a	fβ(a	NOUN
ejpam-97	455	31	)	)	PUNCT
ejpam-97	455	32	.	.	PUNCT
ejpam-97	456	1	so	so	ADV
ejpam-97	456	2	,	,	PUNCT
ejpam-97	456	3	there	there	PRON
ejpam-97	456	4	exists	exist	VERB
ejpam-97	456	5	a	a	DET
ejpam-97	456	6	∈	∈	NOUN
ejpam-97	456	7	a	a	DET
ejpam-97	456	8	such	such	ADJ
ejpam-97	456	9	that	that	PRON
ejpam-97	456	10	k	k	PROPN
ejpam-97	457	1	=	=	PUNCT
ejpam-97	457	2	λ	λ	X
ejpam-97	457	3	fβ	fβ	INTJ
ejpam-97	457	4	(	(	PUNCT
ejpam-97	457	5	a	a	NOUN
ejpam-97	457	6	)	)	PUNCT
ejpam-97	457	7	.	.	PUNCT
ejpam-97	458	1	corollary	corollary	ADJ
ejpam-97	458	2	3.2	3.2	NUM
ejpam-97	458	3	.	.	PUNCT
ejpam-97	459	1	every	every	DET
ejpam-97	459	2	multiple	multiple	ADJ
ejpam-97	459	3	pushout	pushout	NOUN
ejpam-97	459	4	of	of	ADP
ejpam-97	459	5	s	s	NOUN
ejpam-97	459	6	-	-	ADJ
ejpam-97	459	7	pure	pure	ADJ
ejpam-97	459	8	monomorphisms	monomorphism	NOUN
ejpam-97	459	9	(	(	PUNCT
ejpam-97	459	10	the	the	DET
ejpam-97	459	11	diagonal	diagonal	ADJ
ejpam-97	459	12	maps	map	NOUN
ejpam-97	459	13	on	on	ADP
ejpam-97	459	14	the	the	DET
ejpam-97	459	15	multiple	multiple	ADJ
ejpam-97	459	16	pushout	pushout	NOUN
ejpam-97	459	17	diagram	diagram	NOUN
ejpam-97	459	18	)	)	PUNCT
ejpam-97	459	19	is	be	AUX
ejpam-97	459	20	an	an	DET
ejpam-97	459	21	s	s	NOUN
ejpam-97	459	22	-	-	ADJ
ejpam-97	459	23	pure	pure	ADJ
ejpam-97	459	24	monomorphism	monomorphism	NOUN
ejpam-97	459	25	.	.	PUNCT
ejpam-97	460	1	proof	proof	NOUN
ejpam-97	460	2	.	.	PUNCT
ejpam-97	461	1	apply	apply	VERB
ejpam-97	461	2	lemma	lemma	PROPN
ejpam-97	461	3	3.1(2	3.1(2	NUM
ejpam-97	461	4	)	)	PUNCT
ejpam-97	461	5	and	and	CCONJ
ejpam-97	461	6	the	the	DET
ejpam-97	461	7	above	above	ADJ
ejpam-97	461	8	theorem	theorem	NOUN
ejpam-97	461	9	.	.	PROPN
ejpam-97	462	1	definition	definition	NOUN
ejpam-97	462	2	3.2	3.2	NUM
ejpam-97	462	3	.	.	PUNCT
ejpam-97	463	1	the	the	DET
ejpam-97	463	2	category	category	NOUN
ejpam-97	463	3	act	act	NOUN
ejpam-97	463	4	-	-	PUNCT
ejpam-97	463	5	s	s	PART
ejpam-97	463	6	has	have	AUX
ejpam-97	463	7	:	:	PUNCT
ejpam-97	463	8	(	(	PUNCT
ejpam-97	463	9	1)mp	1)mp	NUM
ejpam-97	463	10	-	-	PUNCT
ejpam-97	463	11	bounds	bound	NOUN
ejpam-97	463	12	if	if	SCONJ
ejpam-97	463	13	for	for	ADP
ejpam-97	463	14	any	any	DET
ejpam-97	463	15	small	small	ADJ
ejpam-97	463	16	(	(	PUNCT
ejpam-97	463	17	and	and	CCONJ
ejpam-97	463	18	non	non	ADJ
ejpam-97	463	19	-	-	ADJ
ejpam-97	463	20	empty	empty	ADJ
ejpam-97	463	21	)	)	PUNCT
ejpam-97	463	22	family	family	NOUN
ejpam-97	463	23	(	(	PUNCT
ejpam-97	463	24	hα	hα	NOUN
ejpam-97	463	25	:	:	PUNCT
ejpam-97	463	26	a→	a→	X
ejpam-97	463	27	bα)α∈i	bα)α∈i	VERB
ejpam-97	463	28	ofmp	ofmp	NOUN
ejpam-97	463	29	-	-	PUNCT
ejpam-97	463	30	morphisms	morphism	NOUN
ejpam-97	463	31	there	there	PRON
ejpam-97	463	32	is	be	VERB
ejpam-97	463	33	anmp	anmp	NOUN
ejpam-97	463	34	-	-	PUNCT
ejpam-97	463	35	morphism	morphism	NOUN
ejpam-97	463	36	h	h	NOUN
ejpam-97	463	37	:	:	PUNCT
ejpam-97	463	38	a→	a→	PROPN
ejpam-97	463	39	b	b	NOUN
ejpam-97	463	40	which	which	PRON
ejpam-97	463	41	factorizes	factorize	VERB
ejpam-97	463	42	through	through	ADP
ejpam-97	463	43	all	all	DET
ejpam-97	463	44	hα	hα	NOUN
ejpam-97	463	45	,	,	PUNCT
ejpam-97	463	46	s.	s.	PROPN
ejpam-97	463	47	(	(	PUNCT
ejpam-97	463	48	2)mp	2)mp	ADJ
ejpam-97	463	49	-	-	PUNCT
ejpam-97	463	50	amalgamation	amalgamation	NOUN
ejpam-97	463	51	property	property	NOUN
ejpam-97	463	52	if	if	SCONJ
ejpam-97	463	53	in	in	ADP
ejpam-97	463	54	(	(	PUNCT
ejpam-97	463	55	i	i	NOUN
ejpam-97	463	56	)	)	PUNCT
ejpam-97	463	57	h	h	NOUN
ejpam-97	463	58	factorizes	factorize	VERB
ejpam-97	463	59	through	through	ADP
ejpam-97	463	60	all	all	DET
ejpam-97	463	61	hα	hα	NOUN
ejpam-97	463	62	,	,	PUNCT
ejpam-97	463	63	s	s	PART
ejpam-97	463	64	bymp	bymp	PROPN
ejpam-97	463	65	maps	map	NOUN
ejpam-97	463	66	.	.	PUNCT
ejpam-97	464	1	the	the	DET
ejpam-97	464	2	above	above	ADJ
ejpam-97	464	3	corollary	corollary	NOUN
ejpam-97	464	4	gives	give	VERB
ejpam-97	464	5	that	that	PRON
ejpam-97	464	6	:	:	PUNCT
ejpam-97	464	7	proposition	proposition	NOUN
ejpam-97	464	8	3.6	3.6	NUM
ejpam-97	464	9	.	.	PUNCT
ejpam-97	465	1	act	act	PROPN
ejpam-97	465	2	-	-	PUNCT
ejpam-97	465	3	s	s	PART
ejpam-97	465	4	hasmp	hasmp	NOUN
ejpam-97	465	5	-	-	PUNCT
ejpam-97	465	6	amalgamation	amalgamation	NOUN
ejpam-97	465	7	property	property	NOUN
ejpam-97	465	8	and	and	CCONJ
ejpam-97	465	9	so	so	ADV
ejpam-97	465	10	also	also	ADV
ejpam-97	465	11	hasmp	hasmp	ADJ
ejpam-97	465	12	-	-	PUNCT
ejpam-97	465	13	bound	bind	VERB
ejpam-97	465	14	.	.	PUNCT
ejpam-97	466	1	references	reference	NOUN
ejpam-97	466	2	[	[	X
ejpam-97	466	3	1	1	NUM
ejpam-97	466	4	]	]	PUNCT
ejpam-97	466	5	banaschewski	banaschewski	PROPN
ejpam-97	466	6	,	,	PUNCT
ejpam-97	466	7	b.	b.	PROPN
ejpam-97	466	8	,	,	PUNCT
ejpam-97	466	9	injectivity	injectivity	NOUN
ejpam-97	466	10	and	and	CCONJ
ejpam-97	466	11	essential	essential	ADJ
ejpam-97	466	12	extensions	extension	NOUN
ejpam-97	466	13	in	in	ADP
ejpam-97	466	14	equational	equational	ADJ
ejpam-97	466	15	classes	class	NOUN
ejpam-97	466	16	of	of	ADP
ejpam-97	466	17	algebras	algebras	PROPN
ejpam-97	466	18	,	,	PUNCT
ejpam-97	466	19	queen	queen	PROPN
ejpam-97	466	20	’s	’s	PART
ejpam-97	466	21	papers	paper	NOUN
ejpam-97	466	22	in	in	ADP
ejpam-97	466	23	pure	pure	ADJ
ejpam-97	466	24	and	and	CCONJ
ejpam-97	466	25	appl	appl	NOUN
ejpam-97	466	26	.	.	PROPN
ejpam-97	466	27	math	math	PROPN
ejpam-97	466	28	.	.	PUNCT
ejpam-97	467	1	,	,	PUNCT
ejpam-97	467	2	25	25	NUM
ejpam-97	467	3	(	(	PUNCT
ejpam-97	467	4	1970	1970	NUM
ejpam-97	467	5	)	)	PUNCT
ejpam-97	467	6	,	,	PUNCT
ejpam-97	467	7	131	131	NUM
ejpam-97	467	8	-	-	SYM
ejpam-97	467	9	147	147	NUM
ejpam-97	467	10	.	.	PUNCT
ejpam-97	468	1	[	[	X
ejpam-97	468	2	2	2	NUM
ejpam-97	468	3	]	]	PUNCT
ejpam-97	468	4	berthiaume	berthiaume	NOUN
ejpam-97	468	5	,	,	PUNCT
ejpam-97	468	6	p.	p.	PROPN
ejpam-97	468	7	,	,	PUNCT
ejpam-97	468	8	the	the	DET
ejpam-97	468	9	injective	injective	ADJ
ejpam-97	468	10	envelope	envelope	NOUN
ejpam-97	468	11	of	of	ADP
ejpam-97	468	12	s	s	NOUN
ejpam-97	468	13	-	-	PUNCT
ejpam-97	468	14	sets	set	NOUN
ejpam-97	468	15	,	,	PUNCT
ejpam-97	468	16	canad	canad	PROPN
ejpam-97	468	17	.	.	PUNCT
ejpam-97	469	1	math	math	NOUN
ejpam-97	469	2	.	.	PUNCT
ejpam-97	470	1	bull	bull	PROPN
ejpam-97	470	2	.	.	PUNCT
ejpam-97	470	3	,	,	PUNCT
ejpam-97	470	4	10(2	10(2	NUM
ejpam-97	470	5	)	)	PUNCT
ejpam-97	470	6	(	(	PUNCT
ejpam-97	470	7	1967	1967	NUM
ejpam-97	470	8	)	)	PUNCT
ejpam-97	470	9	,	,	PUNCT
ejpam-97	470	10	261	261	NUM
ejpam-97	470	11	-	-	SYM
ejpam-97	470	12	273	273	NUM
ejpam-97	470	13	.	.	PUNCT
ejpam-97	471	1	[	[	X
ejpam-97	471	2	3	3	X
ejpam-97	471	3	]	]	PUNCT
ejpam-97	471	4	dikranjan	dikranjan	NOUN
ejpam-97	471	5	d.	d.	PROPN
ejpam-97	471	6	,	,	PUNCT
ejpam-97	471	7	tholen	tholen	VERB
ejpam-97	471	8	,	,	PUNCT
ejpam-97	471	9	w.	w.	PROPN
ejpam-97	471	10	,	,	PUNCT
ejpam-97	471	11	categorical	categorical	ADJ
ejpam-97	471	12	structure	structure	NOUN
ejpam-97	471	13	of	of	ADP
ejpam-97	471	14	closure	closure	NOUN
ejpam-97	471	15	operators	operator	NOUN
ejpam-97	471	16	,	,	PUNCT
ejpam-97	471	17	with	with	ADP
ejpam-97	471	18	applications	application	NOUN
ejpam-97	471	19	to	to	ADP
ejpam-97	471	20	topology	topology	NOUN
ejpam-97	471	21	,	,	PUNCT
ejpam-97	471	22	algebra	algebra	NOUN
ejpam-97	471	23	,	,	PUNCT
ejpam-97	471	24	and	and	CCONJ
ejpam-97	471	25	discrete	discrete	ADJ
ejpam-97	471	26	mathematics	mathematic	NOUN
ejpam-97	471	27	,	,	PUNCT
ejpam-97	471	28	mathematics	mathematic	NOUN
ejpam-97	471	29	and	and	CCONJ
ejpam-97	471	30	its	its	PRON
ejpam-97	471	31	applications	application	NOUN
ejpam-97	471	32	,	,	PUNCT
ejpam-97	471	33	kluwer	kluwer	NOUN
ejpam-97	471	34	academic	academic	ADJ
ejpam-97	471	35	publ	publ	PROPN
ejpam-97	471	36	.	.	PUNCT
ejpam-97	471	37	,	,	PUNCT
ejpam-97	471	38	1995	1995	NUM
ejpam-97	471	39	.	.	PUNCT
ejpam-97	472	1	[	[	X
ejpam-97	472	2	4	4	NUM
ejpam-97	472	3	]	]	X
ejpam-97	472	4	ebrahimi	ebrahimi	PROPN
ejpam-97	472	5	,	,	PUNCT
ejpam-97	472	6	m.m	m.m	PROPN
ejpam-97	472	7	.	.	PROPN
ejpam-97	472	8	,	,	PUNCT
ejpam-97	472	9	on	on	ADP
ejpam-97	472	10	ideal	ideal	ADJ
ejpam-97	472	11	closure	closure	NOUN
ejpam-97	472	12	operators	operator	NOUN
ejpam-97	472	13	of	of	ADP
ejpam-97	472	14	m	m	NOUN
ejpam-97	472	15	-	-	PUNCT
ejpam-97	472	16	sets	set	NOUN
ejpam-97	472	17	,	,	PUNCT
ejpam-97	472	18	southeast	southeast	ADJ
ejpam-97	472	19	asian	asian	ADJ
ejpam-97	472	20	bull	bull	NOUN
ejpam-97	472	21	.	.	PUNCT
ejpam-97	473	1	of	of	ADP
ejpam-97	473	2	math	math	NOUN
ejpam-97	473	3	.	.	PUNCT
ejpam-97	474	1	,	,	PUNCT
ejpam-97	474	2	30	30	NUM
ejpam-97	474	3	(	(	PUNCT
ejpam-97	474	4	2006	2006	NUM
ejpam-97	474	5	)	)	PUNCT
ejpam-97	474	6	,	,	PUNCT
ejpam-97	474	7	439	439	NUM
ejpam-97	474	8	-	-	SYM
ejpam-97	474	9	444	444	NUM
ejpam-97	474	10	.	.	PUNCT
ejpam-97	475	1	[	[	X
ejpam-97	475	2	5	5	NUM
ejpam-97	475	3	]	]	PUNCT
ejpam-97	475	4	ebrahimi	ebrahimi	PROPN
ejpam-97	475	5	m.m	m.m	PROPN
ejpam-97	475	6	.	.	PROPN
ejpam-97	475	7	,	,	PUNCT
ejpam-97	475	8	mahmoudi	mahmoudi	NOUN
ejpam-97	475	9	,	,	PUNCT
ejpam-97	475	10	m.	m.	NOUN
ejpam-97	475	11	,	,	PUNCT
ejpam-97	475	12	the	the	DET
ejpam-97	475	13	category	category	NOUN
ejpam-97	475	14	of	of	ADP
ejpam-97	475	15	m	m	NOUN
ejpam-97	475	16	-	-	PUNCT
ejpam-97	475	17	sets	set	NOUN
ejpam-97	475	18	,	,	PUNCT
ejpam-97	475	19	italian	italian	ADJ
ejpam-97	475	20	j.	j.	PROPN
ejpam-97	475	21	pure	pure	PROPN
ejpam-97	475	22	appl	appl	PROPN
ejpam-97	475	23	.	.	PUNCT
ejpam-97	475	24	math	math	PROPN
ejpam-97	475	25	.	.	PUNCT
ejpam-97	475	26	,	,	PUNCT
ejpam-97	475	27	9	9	NUM
ejpam-97	475	28	(	(	PUNCT
ejpam-97	475	29	2001	2001	NUM
ejpam-97	475	30	)	)	PUNCT
ejpam-97	475	31	,	,	PUNCT
ejpam-97	475	32	123	123	NUM
ejpam-97	475	33	-	-	SYM
ejpam-97	475	34	132	132	NUM
ejpam-97	475	35	.	.	PUNCT
ejpam-97	476	1	[	[	X
ejpam-97	476	2	6	6	NUM
ejpam-97	476	3	]	]	PUNCT
ejpam-97	476	4	ebrahimi	ebrahimi	PROPN
ejpam-97	476	5	m.m	m.m	PROPN
ejpam-97	476	6	.	.	PROPN
ejpam-97	476	7	,	,	PUNCT
ejpam-97	476	8	mahmoudi	mahmoudi	NOUN
ejpam-97	476	9	,	,	PUNCT
ejpam-97	476	10	m.	m.	NOUN
ejpam-97	476	11	,	,	PUNCT
ejpam-97	476	12	baer	baer	PROPN
ejpam-97	476	13	criterion	criterion	NOUN
ejpam-97	476	14	and	and	CCONJ
ejpam-97	476	15	injectivity	injectivity	NOUN
ejpam-97	476	16	of	of	ADP
ejpam-97	476	17	projection	projection	NOUN
ejpam-97	476	18	algebras	algebra	NOUN
ejpam-97	476	19	,	,	PUNCT
ejpam-97	476	20	semigroup	semigroup	PROPN
ejpam-97	476	21	forum	forum	PROPN
ejpam-97	476	22	,	,	PUNCT
ejpam-97	476	23	71(2	71(2	NUM
ejpam-97	476	24	)	)	PUNCT
ejpam-97	476	25	(	(	PUNCT
ejpam-97	476	26	2005	2005	NUM
ejpam-97	476	27	)	)	PUNCT
ejpam-97	476	28	,	,	PUNCT
ejpam-97	476	29	332	332	NUM
ejpam-97	476	30	-	-	SYM
ejpam-97	476	31	335	335	NUM
ejpam-97	476	32	.	.	PUNCT
ejpam-97	477	1	[	[	X
ejpam-97	477	2	7	7	NUM
ejpam-97	477	3	]	]	X
ejpam-97	477	4	ehrig	ehrig	NOUN
ejpam-97	477	5	,	,	PUNCT
ejpam-97	477	6	h.	h.	PROPN
ejpam-97	477	7	,	,	PUNCT
ejpam-97	477	8	parisi	parisi	PROPN
ejpam-97	477	9	-	-	PUNCT
ejpam-97	477	10	presicce	presicce	NOUN
ejpam-97	477	11	,	,	PUNCT
ejpam-97	477	12	f.	f.	PROPN
ejpam-97	477	13	,	,	PUNCT
ejpam-97	477	14	boehm	boehm	NOUN
ejpam-97	477	15	,	,	PUNCT
ejpam-97	477	16	p.	p.	NOUN
ejpam-97	477	17	,	,	PUNCT
ejpam-97	477	18	rieckhoff	rieckhoff	NOUN
ejpam-97	477	19	,	,	PUNCT
ejpam-97	477	20	c.	c.	NOUN
ejpam-97	477	21	,	,	PUNCT
ejpam-97	477	22	dimitrovici	dimitrovici	NOUN
ejpam-97	477	23	c.	c.	NOUN
ejpam-97	477	24	,	,	PUNCT
ejpam-97	477	25	grosse	grosse	NOUN
ejpam-97	477	26	-	-	PUNCT
ejpam-97	477	27	rhode	rhode	NOUN
ejpam-97	477	28	,	,	PUNCT
ejpam-97	477	29	m.	m.	NOUN
ejpam-97	477	30	,	,	PUNCT
ejpam-97	477	31	algebraic	algebraic	ADJ
ejpam-97	477	32	data	datum	NOUN
ejpam-97	477	33	type	type	NOUN
ejpam-97	477	34	and	and	CCONJ
ejpam-97	477	35	process	process	NOUN
ejpam-97	477	36	specifications	specification	NOUN
ejpam-97	477	37	based	base	VERB
ejpam-97	477	38	on	on	ADP
ejpam-97	477	39	projection	projection	NOUN
ejpam-97	477	40	spaces	space	NOUN
ejpam-97	477	41	,	,	PUNCT
ejpam-97	477	42	lncs	lncs	VERB
ejpam-97	477	43	332	332	NUM
ejpam-97	477	44	(	(	PUNCT
ejpam-97	477	45	1988	1988	NUM
ejpam-97	477	46	)	)	PUNCT
ejpam-97	477	47	,	,	PUNCT
ejpam-97	477	48	23	23	NUM
ejpam-97	477	49	-	-	SYM
ejpam-97	477	50	43	43	NUM
ejpam-97	477	51	.	.	PUNCT
ejpam-97	478	1	[	[	X
ejpam-97	478	2	8	8	NUM
ejpam-97	478	3	]	]	X
ejpam-97	478	4	ehrig	ehrig	NOUN
ejpam-97	478	5	,	,	PUNCT
ejpam-97	478	6	h.	h.	PROPN
ejpam-97	478	7	,	,	PUNCT
ejpam-97	478	8	parisi	parisi	PROPN
ejpam-97	478	9	-	-	PUNCT
ejpam-97	478	10	presicce	presicce	NOUN
ejpam-97	478	11	f.	f.	PROPN
ejpam-97	478	12	,	,	PUNCT
ejpam-97	478	13	bohem	bohem	PROPN
ejpam-97	478	14	,	,	PUNCT
ejpam-97	478	15	p.	p.	NOUN
ejpam-97	478	16	,	,	PUNCT
ejpam-97	478	17	rieckhoff	rieckhoff	NOUN
ejpam-97	478	18	,	,	PUNCT
ejpam-97	478	19	c.	c.	NOUN
ejpam-97	478	20	,	,	PUNCT
ejpam-97	478	21	dimitrovici	dimitrovici	NOUN
ejpam-97	478	22	,	,	PUNCT
ejpam-97	478	23	c.	c.	NOUN
ejpam-97	478	24	,	,	PUNCT
ejpam-97	478	25	grosse	grosse	NOUN
ejpam-97	478	26	-	-	PUNCT
ejpam-97	478	27	rhode	rhode	NOUN
ejpam-97	478	28	,	,	PUNCT
ejpam-97	478	29	m.	m.	NOUN
ejpam-97	478	30	,	,	PUNCT
ejpam-97	478	31	combining	combine	VERB
ejpam-97	478	32	data	datum	NOUN
ejpam-97	478	33	type	type	NOUN
ejpam-97	478	34	and	and	CCONJ
ejpam-97	478	35	recursive	recursive	ADJ
ejpam-97	478	36	process	process	NOUN
ejpam-97	478	37	specifications	specification	NOUN
ejpam-97	478	38	using	use	VERB
ejpam-97	478	39	projection	projection	NOUN
ejpam-97	478	40	algebras	algebra	NOUN
ejpam-97	478	41	,	,	PUNCT
ejpam-97	478	42	theoretical	theoretical	ADJ
ejpam-97	478	43	computer	computer	NOUN
ejpam-97	478	44	science	science	NOUN
ejpam-97	478	45	,	,	PUNCT
ejpam-97	478	46	71	71	NUM
ejpam-97	478	47	(	(	PUNCT
ejpam-97	478	48	1990	1990	NUM
ejpam-97	478	49	)	)	PUNCT
ejpam-97	478	50	,	,	PUNCT
ejpam-97	478	51	347	347	NUM
ejpam-97	478	52	-	-	SYM
ejpam-97	478	53	380	380	NUM
ejpam-97	478	54	.	.	PUNCT
ejpam-97	479	1	[	[	X
ejpam-97	479	2	9	9	NUM
ejpam-97	479	3	]	]	X
ejpam-97	479	4	giuli	giuli	PROPN
ejpam-97	479	5	,	,	PUNCT
ejpam-97	479	6	e.	e.	PROPN
ejpam-97	479	7	,	,	PUNCT
ejpam-97	479	8	on	on	ADP
ejpam-97	479	9	m	m	ADV
ejpam-97	479	10	-	-	PUNCT
ejpam-97	479	11	separated	separate	VERB
ejpam-97	479	12	projection	projection	NOUN
ejpam-97	479	13	spaces	space	NOUN
ejpam-97	479	14	,	,	PUNCT
ejpam-97	479	15	appl	appl	PROPN
ejpam-97	479	16	.	.	PUNCT
ejpam-97	479	17	categ	categ	PROPN
ejpam-97	479	18	.	.	PUNCT
ejpam-97	479	19	struc	struc	PROPN
ejpam-97	479	20	.	.	PUNCT
ejpam-97	479	21	,	,	PUNCT
ejpam-97	479	22	2	2	NUM
ejpam-97	479	23	(	(	PUNCT
ejpam-97	479	24	1994	1994	NUM
ejpam-97	479	25	)	)	PUNCT
ejpam-97	479	26	,	,	PUNCT
ejpam-97	479	27	91	91	NUM
ejpam-97	479	28	-	-	SYM
ejpam-97	479	29	99	99	NUM
ejpam-97	479	30	.	.	PUNCT
ejpam-97	480	1	[	[	X
ejpam-97	480	2	10	10	NUM
ejpam-97	480	3	]	]	SYM
ejpam-97	480	4	gould	gould	PROPN
ejpam-97	480	5	,	,	PUNCT
ejpam-97	480	6	v.	v.	ADV
ejpam-97	480	7	,	,	PUNCT
ejpam-97	480	8	the	the	DET
ejpam-97	480	9	characterisation	characterisation	NOUN
ejpam-97	480	10	of	of	ADP
ejpam-97	480	11	monoids	monoid	NOUN
ejpam-97	480	12	by	by	ADP
ejpam-97	480	13	properties	property	NOUN
ejpam-97	480	14	of	of	ADP
ejpam-97	480	15	their	their	PRON
ejpam-97	480	16	s	s	NOUN
ejpam-97	480	17	-	-	PUNCT
ejpam-97	480	18	systems	system	NOUN
ejpam-97	480	19	,	,	PUNCT
ejpam-97	480	20	semigroup	semigroup	PROPN
ejpam-97	480	21	forum	forum	PROPN
ejpam-97	480	22	,	,	PUNCT
ejpam-97	480	23	32(3	32(3	NUM
ejpam-97	480	24	)	)	PUNCT
ejpam-97	480	25	(	(	PUNCT
ejpam-97	480	26	1985	1985	NUM
ejpam-97	480	27	)	)	PUNCT
ejpam-97	480	28	,	,	PUNCT
ejpam-97	480	29	251	251	NUM
ejpam-97	480	30	-	-	SYM
ejpam-97	480	31	265	265	NUM
ejpam-97	480	32	.	.	PUNCT
ejpam-97	481	1	[	[	X
ejpam-97	481	2	11	11	NUM
ejpam-97	481	3	]	]	X
ejpam-97	481	4	herrlich	herrlich	PROPN
ejpam-97	481	5	h.	h.	PROPN
ejpam-97	481	6	,	,	PUNCT
ejpam-97	481	7	ehrig	ehrig	PROPN
ejpam-97	481	8	,	,	PUNCT
ejpam-97	481	9	h.	h.	PROPN
ejpam-97	481	10	,	,	PUNCT
ejpam-97	481	11	the	the	DET
ejpam-97	481	12	construct	construct	NOUN
ejpam-97	481	13	pro	pro	NOUN
ejpam-97	481	14	of	of	ADP
ejpam-97	481	15	projection	projection	NOUN
ejpam-97	481	16	spaces	space	NOUN
ejpam-97	481	17	:	:	PUNCT
ejpam-97	481	18	its	its	PRON
ejpam-97	481	19	internal	internal	ADJ
ejpam-97	481	20	structure	structure	NOUN
ejpam-97	481	21	,	,	PUNCT
ejpam-97	481	22	lncs	lncs	VERB
ejpam-97	481	23	393	393	NUM
ejpam-97	481	24	(	(	PUNCT
ejpam-97	481	25	1988	1988	NUM
ejpam-97	481	26	)	)	PUNCT
ejpam-97	481	27	,	,	PUNCT
ejpam-97	481	28	286	286	NUM
ejpam-97	481	29	-	-	SYM
ejpam-97	481	30	293	293	NUM
ejpam-97	481	31	.	.	PUNCT
ejpam-97	482	1	references	reference	NOUN
ejpam-97	482	2	55	55	NUM
ejpam-97	482	3	[	[	X
ejpam-97	482	4	12	12	NUM
ejpam-97	482	5	]	]	X
ejpam-97	482	6	howie	howie	NOUN
ejpam-97	482	7	,	,	PUNCT
ejpam-97	482	8	j.m	j.m	PROPN
ejpam-97	482	9	.	.	PROPN
ejpam-97	482	10	,	,	PUNCT
ejpam-97	482	11	fundamentals	fundamental	NOUN
ejpam-97	482	12	of	of	ADP
ejpam-97	482	13	semigroup	semigroup	PROPN
ejpam-97	482	14	theory	theory	NOUN
ejpam-97	482	15	,	,	PUNCT
ejpam-97	482	16	oxford	oxford	PROPN
ejpam-97	482	17	science	science	NOUN
ejpam-97	482	18	publications	publication	NOUN
ejpam-97	482	19	,	,	PUNCT
ejpam-97	482	20	oxford	oxford	PROPN
ejpam-97	482	21	,	,	PUNCT
ejpam-97	482	22	1995	1995	NUM
ejpam-97	482	23	.	.	PUNCT
ejpam-97	483	1	[	[	X
ejpam-97	483	2	13	13	NUM
ejpam-97	483	3	]	]	SYM
ejpam-97	483	4	kilp	kilp	PROPN
ejpam-97	483	5	,	,	PUNCT
ejpam-97	483	6	m.	m.	NOUN
ejpam-97	483	7	,	,	PUNCT
ejpam-97	483	8	knauer	knauer	NOUN
ejpam-97	483	9	,	,	PUNCT
ejpam-97	483	10	u.	u.	PROPN
ejpam-97	483	11	,	,	PUNCT
ejpam-97	483	12	mikhalev	mikhalev	PROPN
ejpam-97	483	13	,	,	PUNCT
ejpam-97	483	14	a.	a.	PROPN
ejpam-97	483	15	,	,	PUNCT
ejpam-97	483	16	monoids	monoid	NOUN
ejpam-97	483	17	,	,	PUNCT
ejpam-97	483	18	acts	act	NOUN
ejpam-97	483	19	and	and	CCONJ
ejpam-97	483	20	categories	category	NOUN
ejpam-97	483	21	,	,	PUNCT
ejpam-97	483	22	walter	walter	PROPN
ejpam-97	483	23	de	de	PROPN
ejpam-97	483	24	gruyter	gruyter	PROPN
ejpam-97	483	25	,	,	PUNCT
ejpam-97	483	26	berlin	berlin	PROPN
ejpam-97	483	27	,	,	PUNCT
ejpam-97	483	28	new	new	PROPN
ejpam-97	483	29	york	york	PROPN
ejpam-97	483	30	,	,	PUNCT
ejpam-97	483	31	2000	2000	NUM
ejpam-97	483	32	.	.	PUNCT
ejpam-97	484	1	[	[	X
ejpam-97	484	2	14	14	NUM
ejpam-97	484	3	]	]	X
ejpam-97	484	4	mahmoudi	mahmoudi	NOUN
ejpam-97	484	5	,	,	PUNCT
ejpam-97	484	6	m.	m.	NOUN
ejpam-97	484	7	,	,	PUNCT
ejpam-97	484	8	ebrahimi	ebrahimi	PROPN
ejpam-97	484	9	,	,	PUNCT
ejpam-97	484	10	m.m	m.m	PROPN
ejpam-97	484	11	.	.	PROPN
ejpam-97	484	12	,	,	PUNCT
ejpam-97	484	13	purity	purity	NOUN
ejpam-97	484	14	and	and	CCONJ
ejpam-97	484	15	equational	equational	ADJ
ejpam-97	484	16	compactness	compactness	NOUN
ejpam-97	484	17	of	of	ADP
ejpam-97	484	18	projection	projection	NOUN
ejpam-97	484	19	algebras	algebra	NOUN
ejpam-97	484	20	,	,	PUNCT
ejpam-97	484	21	appl	appl	PROPN
ejpam-97	484	22	.	.	PUNCT
ejpam-97	485	1	categ	categ	PROPN
ejpam-97	485	2	.	.	PUNCT
ejpam-97	485	3	struc	struc	PROPN
ejpam-97	485	4	.	.	PUNCT
ejpam-97	485	5	,	,	PUNCT
ejpam-97	485	6	9	9	NUM
ejpam-97	485	7	(	(	PUNCT
ejpam-97	485	8	2001	2001	NUM
ejpam-97	485	9	)	)	PUNCT
ejpam-97	485	10	,	,	PUNCT
ejpam-97	485	11	381	381	NUM
ejpam-97	485	12	-	-	SYM
ejpam-97	485	13	394	394	NUM
ejpam-97	485	14	.	.	PUNCT
ejpam-97	486	1	[	[	X
ejpam-97	486	2	15	15	NUM
ejpam-97	486	3	]	]	X
ejpam-97	486	4	mahmoudi	mahmoudi	ADJ
ejpam-97	486	5	m.	m.	NOUN
ejpam-97	486	6	,	,	PUNCT
ejpam-97	486	7	shahbaz	shahbaz	PROPN
ejpam-97	486	8	,	,	PUNCT
ejpam-97	486	9	l.	l.	PROPN
ejpam-97	486	10	,	,	PUNCT
ejpam-97	486	11	characterizing	characterize	VERB
ejpam-97	486	12	semigroups	semigroup	NOUN
ejpam-97	486	13	by	by	ADP
ejpam-97	486	14	sequentially	sequentially	ADV
ejpam-97	486	15	dense	dense	ADJ
ejpam-97	486	16	injective	injective	ADJ
ejpam-97	486	17	acts	act	NOUN
ejpam-97	486	18	,	,	PUNCT
ejpam-97	486	19	semigroup	semigroup	PROPN
ejpam-97	486	20	forum	forum	PROPN
ejpam-97	486	21	75(1	75(1	PROPN
ejpam-97	486	22	)	)	PUNCT
ejpam-97	486	23	(	(	PUNCT
ejpam-97	486	24	2007	2007	NUM
ejpam-97	486	25	)	)	PUNCT
ejpam-97	486	26	,	,	PUNCT
ejpam-97	486	27	116	116	NUM
ejpam-97	486	28	-	-	SYM
ejpam-97	486	29	128	128	NUM
ejpam-97	486	30	.	.	PUNCT
ejpam-97	487	1	[	[	X
ejpam-97	487	2	16	16	NUM
ejpam-97	487	3	]	]	X
ejpam-97	487	4	normak	normak	PROPN
ejpam-97	487	5	,	,	PUNCT
ejpam-97	487	6	p.	p.	NOUN
ejpam-97	487	7	,	,	PUNCT
ejpam-97	487	8	purity	purity	NOUN
ejpam-97	487	9	in	in	ADP
ejpam-97	487	10	the	the	DET
ejpam-97	487	11	category	category	NOUN
ejpam-97	487	12	of	of	ADP
ejpam-97	487	13	m	m	NOUN
ejpam-97	487	14	-	-	PUNCT
ejpam-97	487	15	sets	set	NOUN
ejpam-97	487	16	,	,	PUNCT
ejpam-97	487	17	semigroup	semigroup	PROPN
ejpam-97	487	18	forum	forum	PROPN
ejpam-97	487	19	,	,	PUNCT
ejpam-97	487	20	20(2	20(2	NUM
ejpam-97	487	21	)	)	PUNCT
ejpam-97	487	22	(	(	PUNCT
ejpam-97	487	23	1980	1980	NUM
ejpam-97	487	24	)	)	PUNCT
ejpam-97	487	25	,	,	PUNCT
ejpam-97	487	26	157	157	NUM
ejpam-97	487	27	-	-	SYM
ejpam-97	487	28	170	170	NUM
ejpam-97	487	29	.	.	PUNCT
ejpam-97	488	1	[	[	X
ejpam-97	488	2	17	17	NUM
ejpam-97	488	3	]	]	X
ejpam-97	488	4	tholen	tholen	VERB
ejpam-97	488	5	,	,	PUNCT
ejpam-97	488	6	w.	w.	PROPN
ejpam-97	488	7	,	,	PUNCT
ejpam-97	488	8	injective	injective	ADJ
ejpam-97	488	9	objects	object	NOUN
ejpam-97	488	10	and	and	CCONJ
ejpam-97	488	11	cogenerating	cogenerating	NOUN
ejpam-97	488	12	sets	set	NOUN
ejpam-97	488	13	,	,	PUNCT
ejpam-97	488	14	j.	j.	PROPN
ejpam-97	488	15	alg	alg	PROPN
ejpam-97	488	16	.	.	PROPN
ejpam-97	488	17	,	,	PUNCT
ejpam-97	488	18	73(1	73(1	X
ejpam-97	488	19	)	)	PUNCT
ejpam-97	488	20	(	(	PUNCT
ejpam-97	488	21	1981	1981	NUM
ejpam-97	488	22	)	)	PUNCT
ejpam-97	488	23	,	,	PUNCT
ejpam-97	488	24	139	139	NUM
ejpam-97	488	25	-	-	SYM
ejpam-97	488	26	155	155	NUM
ejpam-97	488	27	.	.	PUNCT