id	sid	tid	token	lemma	pos
ejpam-1871	1	1	european	european	PROPN
ejpam-1871	1	2	journal	journal	PROPN
ejpam-1871	1	3	of	of	ADP
ejpam-1871	1	4	pure	pure	ADJ
ejpam-1871	1	5	and	and	CCONJ
ejpam-1871	1	6	applied	apply	VERB
ejpam-1871	1	7	mathematics	mathematic	NOUN
ejpam-1871	1	8	vol	vol	NOUN
ejpam-1871	1	9	.	.	PUNCT
ejpam-1871	2	1	7	7	NUM
ejpam-1871	2	2	,	,	PUNCT
ejpam-1871	2	3	no	no	INTJ
ejpam-1871	2	4	.	.	NOUN
ejpam-1871	2	5	2	2	NUM
ejpam-1871	2	6	,	,	PUNCT
ejpam-1871	2	7	2014	2014	NUM
ejpam-1871	2	8	,	,	PUNCT
ejpam-1871	2	9	166	166	NUM
ejpam-1871	2	10	-	-	SYM
ejpam-1871	2	11	178	178	NUM
ejpam-1871	2	12	issn	issn	PROPN
ejpam-1871	2	13	1307	1307	NUM
ejpam-1871	2	14	-	-	SYM
ejpam-1871	2	15	5543	5543	NUM
ejpam-1871	2	16	–	–	PUNCT
ejpam-1871	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1871	3	1	categorical	categorical	ADJ
ejpam-1871	3	2	properties	property	NOUN
ejpam-1871	3	3	of	of	ADP
ejpam-1871	3	4	regular	regular	ADJ
ejpam-1871	3	5	monomorphisms	monomorphism	NOUN
ejpam-1871	3	6	of	of	ADP
ejpam-1871	3	7	s	s	NOUN
ejpam-1871	3	8	-	-	PUNCT
ejpam-1871	3	9	posets	poset	NOUN
ejpam-1871	3	10	hamid	hamid	PROPN
ejpam-1871	3	11	rasouli	rasouli	PROPN
ejpam-1871	3	12	department	department	PROPN
ejpam-1871	3	13	of	of	ADP
ejpam-1871	3	14	mathematics	mathematics	PROPN
ejpam-1871	3	15	,	,	PUNCT
ejpam-1871	3	16	college	college	NOUN
ejpam-1871	3	17	of	of	ADP
ejpam-1871	3	18	basic	basic	ADJ
ejpam-1871	3	19	sciences	science	NOUN
ejpam-1871	3	20	,	,	PUNCT
ejpam-1871	3	21	tehran	tehran	NOUN
ejpam-1871	3	22	science	science	NOUN
ejpam-1871	3	23	and	and	CCONJ
ejpam-1871	3	24	research	research	NOUN
ejpam-1871	3	25	branch	branch	NOUN
ejpam-1871	3	26	,	,	PUNCT
ejpam-1871	3	27	islamic	islamic	PROPN
ejpam-1871	3	28	azad	azad	PROPN
ejpam-1871	3	29	university	university	PROPN
ejpam-1871	3	30	,	,	PUNCT
ejpam-1871	3	31	tehran	tehran	PROPN
ejpam-1871	3	32	,	,	PUNCT
ejpam-1871	3	33	iran	iran	PROPN
ejpam-1871	3	34	abstract	abstract	NOUN
ejpam-1871	3	35	.	.	PUNCT
ejpam-1871	4	1	recall	recall	NOUN
ejpam-1871	4	2	that	that	PRON
ejpam-1871	4	3	monomorphisms	monomorphism	VERB
ejpam-1871	4	4	in	in	ADP
ejpam-1871	4	5	some	some	DET
ejpam-1871	4	6	categories	category	NOUN
ejpam-1871	4	7	such	such	ADJ
ejpam-1871	4	8	as	as	ADP
ejpam-1871	4	9	the	the	DET
ejpam-1871	4	10	category	category	NOUN
ejpam-1871	4	11	of	of	ADP
ejpam-1871	4	12	posets	poset	NOUN
ejpam-1871	4	13	,	,	PUNCT
ejpam-1871	4	14	and	and	CCONJ
ejpam-1871	4	15	the	the	DET
ejpam-1871	4	16	category	category	NOUN
ejpam-1871	4	17	of	of	ADP
ejpam-1871	4	18	topological	topological	ADJ
ejpam-1871	4	19	spaces	space	NOUN
ejpam-1871	4	20	,	,	PUNCT
ejpam-1871	4	21	are	be	AUX
ejpam-1871	4	22	not	not	PART
ejpam-1871	4	23	necessarily	necessarily	ADV
ejpam-1871	4	24	embeddings	embedding	NOUN
ejpam-1871	4	25	.	.	PUNCT
ejpam-1871	5	1	the	the	DET
ejpam-1871	5	2	notion	notion	NOUN
ejpam-1871	5	3	of	of	ADP
ejpam-1871	5	4	regular	regular	ADJ
ejpam-1871	5	5	monomorphism	monomorphism	NOUN
ejpam-1871	5	6	,	,	PUNCT
ejpam-1871	5	7	solves	solve	VERB
ejpam-1871	5	8	this	this	DET
ejpam-1871	5	9	problem	problem	NOUN
ejpam-1871	5	10	in	in	ADP
ejpam-1871	5	11	these	these	DET
ejpam-1871	5	12	two	two	NUM
ejpam-1871	5	13	categories	category	NOUN
ejpam-1871	5	14	.	.	PUNCT
ejpam-1871	6	1	we	we	PRON
ejpam-1871	6	2	have	have	VERB
ejpam-1871	6	3	the	the	DET
ejpam-1871	6	4	same	same	ADJ
ejpam-1871	6	5	situation	situation	NOUN
ejpam-1871	6	6	in	in	ADP
ejpam-1871	6	7	the	the	DET
ejpam-1871	6	8	category	category	NOUN
ejpam-1871	6	9	s	s	NOUN
ejpam-1871	6	10	-	-	PUNCT
ejpam-1871	6	11	pos	pos	NOUN
ejpam-1871	6	12	of	of	ADP
ejpam-1871	6	13	sposets	sposet	NOUN
ejpam-1871	6	14	;	;	PUNCT
ejpam-1871	6	15	that	that	PRON
ejpam-1871	6	16	is	be	AUX
ejpam-1871	6	17	posets	poset	NOUN
ejpam-1871	6	18	with	with	ADP
ejpam-1871	6	19	an	an	DET
ejpam-1871	6	20	action	action	NOUN
ejpam-1871	6	21	of	of	ADP
ejpam-1871	6	22	a	a	DET
ejpam-1871	6	23	pomonoid	pomonoid	NOUN
ejpam-1871	6	24	s	s	PROPN
ejpam-1871	6	25	which	which	PRON
ejpam-1871	6	26	preserves	preserve	VERB
ejpam-1871	6	27	the	the	DET
ejpam-1871	6	28	order	order	NOUN
ejpam-1871	6	29	.	.	PUNCT
ejpam-1871	7	1	in	in	ADP
ejpam-1871	7	2	this	this	DET
ejpam-1871	7	3	category	category	NOUN
ejpam-1871	7	4	,	,	PUNCT
ejpam-1871	7	5	regular	regular	ADJ
ejpam-1871	7	6	monomorphisms	monomorphism	NOUN
ejpam-1871	7	7	exactly	exactly	ADV
ejpam-1871	7	8	determine	determine	VERB
ejpam-1871	7	9	sub	sub	NOUN
ejpam-1871	7	10	s	s	NOUN
ejpam-1871	7	11	-	-	NOUN
ejpam-1871	7	12	posets	poset	NOUN
ejpam-1871	7	13	.	.	PUNCT
ejpam-1871	8	1	in	in	ADP
ejpam-1871	8	2	this	this	DET
ejpam-1871	8	3	paper	paper	NOUN
ejpam-1871	8	4	,	,	PUNCT
ejpam-1871	8	5	we	we	PRON
ejpam-1871	8	6	study	study	VERB
ejpam-1871	8	7	some	some	DET
ejpam-1871	8	8	categorical	categorical	ADJ
ejpam-1871	8	9	properties	property	NOUN
ejpam-1871	8	10	of	of	ADP
ejpam-1871	8	11	regular	regular	ADJ
ejpam-1871	8	12	monomorphisms	monomorphism	NOUN
ejpam-1871	8	13	in	in	ADP
ejpam-1871	8	14	the	the	DET
ejpam-1871	8	15	category	category	NOUN
ejpam-1871	8	16	of	of	ADP
ejpam-1871	8	17	sposets	sposet	NOUN
ejpam-1871	8	18	with	with	ADP
ejpam-1871	8	19	action	action	NOUN
ejpam-1871	8	20	-	-	PUNCT
ejpam-1871	8	21	preserving	preserve	VERB
ejpam-1871	8	22	monotone	monotone	ADJ
ejpam-1871	8	23	maps	map	NOUN
ejpam-1871	8	24	.	.	PUNCT
ejpam-1871	9	1	2010	2010	NUM
ejpam-1871	9	2	mathematics	mathematic	NOUN
ejpam-1871	9	3	subject	subject	NOUN
ejpam-1871	9	4	classifications	classification	NOUN
ejpam-1871	9	5	:	:	PUNCT
ejpam-1871	9	6	06f05	06f05	NUM
ejpam-1871	9	7	,	,	PUNCT
ejpam-1871	9	8	18a20	18a20	NUM
ejpam-1871	9	9	,	,	PUNCT
ejpam-1871	9	10	18a30	18a30	NUM
ejpam-1871	9	11	,	,	PUNCT
ejpam-1871	9	12	20m30	20m30	NUM
ejpam-1871	9	13	key	key	ADJ
ejpam-1871	9	14	words	word	NOUN
ejpam-1871	9	15	and	and	CCONJ
ejpam-1871	9	16	phrases	phrase	NOUN
ejpam-1871	9	17	:	:	PUNCT
ejpam-1871	9	18	s	s	X
ejpam-1871	9	19	-	-	PUNCT
ejpam-1871	9	20	poset	poset	ADJ
ejpam-1871	9	21	,	,	PUNCT
ejpam-1871	9	22	regular	regular	ADJ
ejpam-1871	9	23	monomorphism	monomorphism	NOUN
ejpam-1871	9	24	1	1	NUM
ejpam-1871	9	25	.	.	PUNCT
ejpam-1871	10	1	introduction	introduction	NOUN
ejpam-1871	10	2	and	and	CCONJ
ejpam-1871	10	3	preliminaries	preliminary	NOUN
ejpam-1871	10	4	one	one	NUM
ejpam-1871	10	5	of	of	ADP
ejpam-1871	10	6	the	the	DET
ejpam-1871	10	7	very	very	ADV
ejpam-1871	10	8	useful	useful	ADJ
ejpam-1871	10	9	notions	notion	NOUN
ejpam-1871	10	10	in	in	ADP
ejpam-1871	10	11	many	many	ADJ
ejpam-1871	10	12	branches	branch	NOUN
ejpam-1871	10	13	of	of	ADP
ejpam-1871	10	14	mathematics	mathematic	NOUN
ejpam-1871	10	15	as	as	ADV
ejpam-1871	10	16	well	well	ADV
ejpam-1871	10	17	as	as	ADP
ejpam-1871	10	18	in	in	ADP
ejpam-1871	10	19	computer	computer	NOUN
ejpam-1871	10	20	science	science	NOUN
ejpam-1871	10	21	is	be	AUX
ejpam-1871	10	22	the	the	DET
ejpam-1871	10	23	action	action	NOUN
ejpam-1871	10	24	of	of	ADP
ejpam-1871	10	25	a	a	DET
ejpam-1871	10	26	semigroup	semigroup	NOUN
ejpam-1871	10	27	or	or	CCONJ
ejpam-1871	10	28	a	a	DET
ejpam-1871	10	29	monoid	monoid	NOUN
ejpam-1871	10	30	on	on	ADP
ejpam-1871	10	31	a	a	DET
ejpam-1871	10	32	set	set	NOUN
ejpam-1871	10	33	.	.	PUNCT
ejpam-1871	11	1	such	such	ADJ
ejpam-1871	11	2	acts	act	NOUN
ejpam-1871	11	3	corresponds	correspond	VERB
ejpam-1871	11	4	to	to	ADP
ejpam-1871	11	5	representation	representation	NOUN
ejpam-1871	11	6	of	of	ADP
ejpam-1871	11	7	monoids	monoid	NOUN
ejpam-1871	11	8	.	.	PUNCT
ejpam-1871	12	1	also	also	ADV
ejpam-1871	12	2	the	the	DET
ejpam-1871	12	3	action	action	NOUN
ejpam-1871	12	4	of	of	ADP
ejpam-1871	12	5	a	a	DET
ejpam-1871	12	6	pomonoid	pomonoid	NOUN
ejpam-1871	12	7	s	s	VERB
ejpam-1871	12	8	on	on	ADP
ejpam-1871	12	9	partially	partially	ADV
ejpam-1871	12	10	ordered	order	VERB
ejpam-1871	12	11	sets	set	NOUN
ejpam-1871	12	12	,	,	PUNCT
ejpam-1871	12	13	namely	namely	ADV
ejpam-1871	12	14	s	s	NOUN
ejpam-1871	12	15	-	-	NOUN
ejpam-1871	12	16	posets	poset	NOUN
ejpam-1871	12	17	,	,	PUNCT
ejpam-1871	12	18	appears	appear	VERB
ejpam-1871	12	19	as	as	ADP
ejpam-1871	12	20	representations	representation	NOUN
ejpam-1871	12	21	of	of	ADP
ejpam-1871	12	22	mappings	mapping	NOUN
ejpam-1871	12	23	between	between	ADP
ejpam-1871	12	24	pomonoids	pomonoid	NOUN
ejpam-1871	12	25	(	(	PUNCT
ejpam-1871	12	26	cf	cf	NOUN
ejpam-1871	12	27	.	.	PUNCT
ejpam-1871	13	1	[	[	X
ejpam-1871	13	2	6	6	NUM
ejpam-1871	13	3	]	]	PUNCT
ejpam-1871	13	4	)	)	PUNCT
ejpam-1871	13	5	.	.	PUNCT
ejpam-1871	14	1	brazegar	brazegar	NOUN
ejpam-1871	14	2	et	et	PROPN
ejpam-1871	14	3	al	al	PROPN
ejpam-1871	14	4	.	.	PUNCT
ejpam-1871	15	1	[	[	X
ejpam-1871	15	2	5	5	NUM
ejpam-1871	15	3	]	]	PUNCT
ejpam-1871	15	4	,	,	PUNCT
ejpam-1871	15	5	inspired	inspire	VERB
ejpam-1871	15	6	by	by	ADP
ejpam-1871	15	7	the	the	DET
ejpam-1871	15	8	work	work	NOUN
ejpam-1871	15	9	of	of	ADP
ejpam-1871	15	10	banaschewski	banaschewski	NOUN
ejpam-1871	15	11	[	[	X
ejpam-1871	15	12	2	2	X
ejpam-1871	15	13	]	]	PUNCT
ejpam-1871	15	14	on	on	ADP
ejpam-1871	15	15	m	m	PROPN
ejpam-1871	15	16	-injectivity	-injectivity	NOUN
ejpam-1871	15	17	,	,	PUNCT
ejpam-1871	15	18	introduced	introduce	VERB
ejpam-1871	15	19	three	three	NUM
ejpam-1871	15	20	different	different	ADJ
ejpam-1871	15	21	kinds	kind	NOUN
ejpam-1871	15	22	of	of	ADP
ejpam-1871	15	23	essentiality	essentiality	NOUN
ejpam-1871	15	24	for	for	ADP
ejpam-1871	15	25	a	a	DET
ejpam-1871	15	26	subclass	subclass	NOUN
ejpam-1871	15	27	m	m	NOUN
ejpam-1871	15	28	of	of	ADP
ejpam-1871	15	29	monomorphisms	monomorphism	NOUN
ejpam-1871	15	30	of	of	ADP
ejpam-1871	15	31	a	a	DET
ejpam-1871	15	32	category	category	NOUN
ejpam-1871	15	33	,	,	PUNCT
ejpam-1871	15	34	and	and	CCONJ
ejpam-1871	15	35	considered	consider	VERB
ejpam-1871	15	36	some	some	DET
ejpam-1871	15	37	category	category	NOUN
ejpam-1871	15	38	-	-	PUNCT
ejpam-1871	15	39	theoretic	theoretic	NOUN
ejpam-1871	15	40	conditions	condition	NOUN
ejpam-1871	15	41	onm	onm	VERB
ejpam-1871	15	42	to	to	PART
ejpam-1871	15	43	study	study	VERB
ejpam-1871	15	44	well	well	ADJ
ejpam-1871	15	45	-	-	PUNCT
ejpam-1871	15	46	behaviour	behaviour	NOUN
ejpam-1871	15	47	ofm	ofm	PROPN
ejpam-1871	15	48	-injectivity	-injectivity	PROPN
ejpam-1871	15	49	via	via	ADP
ejpam-1871	15	50	these	these	DET
ejpam-1871	15	51	essential	essential	ADJ
ejpam-1871	15	52	monomorphisms	monomorphism	NOUN
ejpam-1871	15	53	.	.	PUNCT
ejpam-1871	16	1	in	in	ADP
ejpam-1871	16	2	the	the	DET
ejpam-1871	16	3	present	present	ADJ
ejpam-1871	16	4	paper	paper	NOUN
ejpam-1871	16	5	,	,	PUNCT
ejpam-1871	16	6	considering	consider	VERB
ejpam-1871	16	7	m	m	VERB
ejpam-1871	16	8	to	to	PART
ejpam-1871	16	9	be	be	AUX
ejpam-1871	16	10	the	the	DET
ejpam-1871	16	11	class	class	NOUN
ejpam-1871	16	12	of	of	ADP
ejpam-1871	16	13	regular	regular	ADJ
ejpam-1871	16	14	monomorphisms	monomorphism	NOUN
ejpam-1871	16	15	(	(	PUNCT
ejpam-1871	16	16	order	order	NOUN
ejpam-1871	16	17	-	-	PUNCT
ejpam-1871	16	18	embeddings	embedding	NOUN
ejpam-1871	16	19	)	)	PUNCT
ejpam-1871	16	20	in	in	ADP
ejpam-1871	16	21	the	the	DET
ejpam-1871	16	22	category	category	NOUN
ejpam-1871	16	23	s	s	NOUN
ejpam-1871	16	24	-	-	PUNCT
ejpam-1871	16	25	pos	pos	NOUN
ejpam-1871	16	26	of	of	ADP
ejpam-1871	16	27	s	s	NOUN
ejpam-1871	16	28	-	-	NOUN
ejpam-1871	16	29	posets	poset	NOUN
ejpam-1871	16	30	with	with	ADP
ejpam-1871	16	31	action	action	NOUN
ejpam-1871	16	32	-	-	PUNCT
ejpam-1871	16	33	preserving	preserve	VERB
ejpam-1871	16	34	monotone	monotone	ADJ
ejpam-1871	16	35	maps	map	NOUN
ejpam-1871	16	36	,	,	PUNCT
ejpam-1871	16	37	we	we	PRON
ejpam-1871	16	38	investigate	investigate	VERB
ejpam-1871	16	39	some	some	DET
ejpam-1871	16	40	categorical	categorical	ADJ
ejpam-1871	16	41	properties	property	NOUN
ejpam-1871	16	42	of	of	ADP
ejpam-1871	16	43	m	m	PRON
ejpam-1871	16	44	which	which	PRON
ejpam-1871	16	45	mostly	mostly	ADV
ejpam-1871	16	46	are	be	AUX
ejpam-1871	16	47	useful	useful	ADJ
ejpam-1871	16	48	in	in	ADP
ejpam-1871	16	49	the	the	DET
ejpam-1871	16	50	study	study	NOUN
ejpam-1871	16	51	of	of	ADP
ejpam-1871	16	52	well	well	NOUN
ejpam-1871	16	53	-	-	PUNCT
ejpam-1871	16	54	behaviour	behaviour	NOUN
ejpam-1871	16	55	of	of	ADP
ejpam-1871	16	56	regular	regular	ADJ
ejpam-1871	16	57	injectivity	injectivity	NOUN
ejpam-1871	16	58	of	of	ADP
ejpam-1871	16	59	s	s	NOUN
ejpam-1871	16	60	-	-	NOUN
ejpam-1871	16	61	posets	poset	NOUN
ejpam-1871	16	62	(	(	PUNCT
ejpam-1871	16	63	see	see	VERB
ejpam-1871	16	64	also	also	ADV
ejpam-1871	16	65	[	[	X
ejpam-1871	16	66	4	4	NUM
ejpam-1871	16	67	,	,	PUNCT
ejpam-1871	16	68	13	13	NUM
ejpam-1871	16	69	]	]	NUM
ejpam-1871	16	70	)	)	PUNCT
ejpam-1871	16	71	.	.	PUNCT
ejpam-1871	17	1	then	then	ADV
ejpam-1871	17	2	we	we	PRON
ejpam-1871	17	3	compare	compare	VERB
ejpam-1871	17	4	some	some	DET
ejpam-1871	17	5	categorical	categorical	ADJ
ejpam-1871	17	6	properties	property	NOUN
ejpam-1871	17	7	of	of	ADP
ejpam-1871	17	8	monomorphisms	monomorphism	NOUN
ejpam-1871	17	9	and	and	CCONJ
ejpam-1871	17	10	regular	regular	ADJ
ejpam-1871	17	11	monomorphims	monomorphim	NOUN
ejpam-1871	17	12	in	in	ADP
ejpam-1871	17	13	the	the	DET
ejpam-1871	17	14	categories	category	NOUN
ejpam-1871	17	15	of	of	ADP
ejpam-1871	17	16	posets	poset	NOUN
ejpam-1871	17	17	and	and	CCONJ
ejpam-1871	17	18	s	s	NOUN
ejpam-1871	17	19	-	-	NOUN
ejpam-1871	17	20	posets	poset	NOUN
ejpam-1871	17	21	.	.	PUNCT
ejpam-1871	18	1	a	a	DET
ejpam-1871	18	2	study	study	NOUN
ejpam-1871	18	3	of	of	ADP
ejpam-1871	18	4	s	s	NOUN
ejpam-1871	18	5	-	-	NOUN
ejpam-1871	18	6	posets	poset	NOUN
ejpam-1871	18	7	from	from	ADP
ejpam-1871	18	8	a	a	DET
ejpam-1871	18	9	category	category	NOUN
ejpam-1871	18	10	-	-	PUNCT
ejpam-1871	18	11	theoretic	theoretic	NOUN
ejpam-1871	18	12	standpoint	standpoint	NOUN
ejpam-1871	18	13	forms	form	VERB
ejpam-1871	18	14	the	the	DET
ejpam-1871	18	15	content	content	NOUN
ejpam-1871	18	16	of	of	ADP
ejpam-1871	18	17	[	[	X
ejpam-1871	18	18	11	11	NUM
ejpam-1871	18	19	]	]	PUNCT
ejpam-1871	18	20	,	,	PUNCT
ejpam-1871	18	21	and	and	CCONJ
ejpam-1871	18	22	extends	extend	VERB
ejpam-1871	18	23	the	the	DET
ejpam-1871	18	24	results	result	NOUN
ejpam-1871	18	25	found	find	VERB
ejpam-1871	18	26	in	in	ADP
ejpam-1871	18	27	[	[	X
ejpam-1871	18	28	8	8	NUM
ejpam-1871	18	29	]	]	PUNCT
ejpam-1871	18	30	.	.	PUNCT
ejpam-1871	19	1	for	for	ADP
ejpam-1871	19	2	more	more	ADJ
ejpam-1871	19	3	information	information	NOUN
ejpam-1871	19	4	on	on	ADP
ejpam-1871	19	5	various	various	ADJ
ejpam-1871	19	6	properties	property	NOUN
ejpam-1871	19	7	of	of	ADP
ejpam-1871	19	8	s	s	NOUN
ejpam-1871	19	9	-	-	NOUN
ejpam-1871	19	10	posets	poset	NOUN
ejpam-1871	19	11	,	,	PUNCT
ejpam-1871	19	12	see	see	VERB
ejpam-1871	19	13	also	also	ADV
ejpam-1871	19	14	[	[	X
ejpam-1871	19	15	7	7	NUM
ejpam-1871	19	16	,	,	PUNCT
ejpam-1871	19	17	9	9	NUM
ejpam-1871	19	18	,	,	PUNCT
ejpam-1871	19	19	10	10	NUM
ejpam-1871	19	20	,	,	PUNCT
ejpam-1871	19	21	15	15	NUM
ejpam-1871	19	22	]	]	PUNCT
ejpam-1871	19	23	.	.	PUNCT
ejpam-1871	20	1	email	email	NOUN
ejpam-1871	20	2	address	address	NOUN
ejpam-1871	20	3	:	:	PUNCT
ejpam-1871	20	4	hrasouli@srbiau.ac.ir	hrasouli@srbiau.ac.ir	ADJ
ejpam-1871	20	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1871	20	6	166	166	NUM
ejpam-1871	20	7	c	c	X
ejpam-1871	20	8	©	©	PROPN
ejpam-1871	20	9	2014	2014	NUM
ejpam-1871	20	10	ejpam	ejpam	NOUN
ejpam-1871	20	11	all	all	DET
ejpam-1871	20	12	rights	right	NOUN
ejpam-1871	20	13	reserved	reserve	VERB
ejpam-1871	20	14	.	.	PUNCT
ejpam-1871	21	1	h.	h.	PROPN
ejpam-1871	21	2	rasouli	rasouli	PROPN
ejpam-1871	21	3	/	/	SYM
ejpam-1871	21	4	eur	eur	PROPN
ejpam-1871	21	5	.	.	PUNCT
ejpam-1871	22	1	j.	j.	PROPN
ejpam-1871	22	2	pure	pure	PROPN
ejpam-1871	22	3	appl	appl	PROPN
ejpam-1871	22	4	.	.	PROPN
ejpam-1871	22	5	math	math	PROPN
ejpam-1871	22	6	,	,	PUNCT
ejpam-1871	22	7	7	7	NUM
ejpam-1871	22	8	(	(	PUNCT
ejpam-1871	22	9	2014	2014	NUM
ejpam-1871	22	10	)	)	PUNCT
ejpam-1871	22	11	,	,	PUNCT
ejpam-1871	22	12	166	166	NUM
ejpam-1871	22	13	-	-	SYM
ejpam-1871	22	14	178	178	NUM
ejpam-1871	22	15	167	167	NUM
ejpam-1871	22	16	in	in	ADP
ejpam-1871	22	17	the	the	DET
ejpam-1871	22	18	rest	rest	NOUN
ejpam-1871	22	19	of	of	ADP
ejpam-1871	22	20	this	this	DET
ejpam-1871	22	21	section	section	NOUN
ejpam-1871	22	22	we	we	PRON
ejpam-1871	22	23	give	give	VERB
ejpam-1871	22	24	some	some	DET
ejpam-1871	22	25	preliminaries	preliminary	NOUN
ejpam-1871	22	26	about	about	ADP
ejpam-1871	22	27	s	s	NOUN
ejpam-1871	22	28	-	-	PUNCT
ejpam-1871	22	29	acts	act	NOUN
ejpam-1871	22	30	,	,	PUNCT
ejpam-1871	22	31	posets	poset	NOUN
ejpam-1871	22	32	,	,	PUNCT
ejpam-1871	22	33	and	and	CCONJ
ejpam-1871	22	34	s	s	NOUN
ejpam-1871	22	35	-	-	PUNCT
ejpam-1871	22	36	posets	poset	NOUN
ejpam-1871	22	37	needed	need	VERB
ejpam-1871	22	38	in	in	ADP
ejpam-1871	22	39	the	the	DET
ejpam-1871	22	40	sequel	sequel	NOUN
ejpam-1871	22	41	.	.	PUNCT
ejpam-1871	23	1	let	let	VERB
ejpam-1871	23	2	s	s	PRON
ejpam-1871	23	3	be	be	AUX
ejpam-1871	23	4	a	a	DET
ejpam-1871	23	5	monoid	monoid	NOUN
ejpam-1871	23	6	with	with	ADP
ejpam-1871	23	7	identity	identity	NOUN
ejpam-1871	23	8	1	1	NUM
ejpam-1871	23	9	.	.	PUNCT
ejpam-1871	23	10	recall	recall	VERB
ejpam-1871	23	11	that	that	SCONJ
ejpam-1871	23	12	a	a	DET
ejpam-1871	23	13	(	(	PUNCT
ejpam-1871	23	14	left	left	ADJ
ejpam-1871	23	15	)	)	PUNCT
ejpam-1871	23	16	s	s	X
ejpam-1871	23	17	-	-	PUNCT
ejpam-1871	23	18	act	act	NOUN
ejpam-1871	23	19	a	a	PRON
ejpam-1871	23	20	is	be	AUX
ejpam-1871	23	21	a	a	DET
ejpam-1871	23	22	set	set	NOUN
ejpam-1871	23	23	equipped	equip	VERB
ejpam-1871	23	24	with	with	ADP
ejpam-1871	23	25	a	a	DET
ejpam-1871	23	26	map	map	NOUN
ejpam-1871	24	1	λ	λ	X
ejpam-1871	24	2	:	:	PUNCT
ejpam-1871	24	3	s	s	X
ejpam-1871	24	4	×	×	NOUN
ejpam-1871	24	5	a→	a→	PUNCT
ejpam-1871	24	6	a	a	PRON
ejpam-1871	24	7	,	,	PUNCT
ejpam-1871	24	8	called	call	VERB
ejpam-1871	24	9	its	its	PRON
ejpam-1871	24	10	action	action	NOUN
ejpam-1871	24	11	,	,	PUNCT
ejpam-1871	24	12	such	such	ADJ
ejpam-1871	24	13	that	that	SCONJ
ejpam-1871	24	14	,	,	PUNCT
ejpam-1871	24	15	denoting	denote	VERB
ejpam-1871	24	16	λ(s	λ(s	PROPN
ejpam-1871	24	17	,	,	PUNCT
ejpam-1871	24	18	a	a	PRON
ejpam-1871	24	19	)	)	PUNCT
ejpam-1871	24	20	by	by	ADP
ejpam-1871	24	21	sa	sa	PROPN
ejpam-1871	24	22	,	,	PUNCT
ejpam-1871	24	23	we	we	PRON
ejpam-1871	24	24	have	have	VERB
ejpam-1871	24	25	1a	1a	NOUN
ejpam-1871	24	26	=	=	PUNCT
ejpam-1871	24	27	a	a	PROPN
ejpam-1871	24	28	and	and	CCONJ
ejpam-1871	24	29	(	(	PUNCT
ejpam-1871	24	30	st)a	st)a	PROPN
ejpam-1871	24	31	=	=	SYM
ejpam-1871	24	32	s(ta	s(ta	NUM
ejpam-1871	24	33	)	)	PUNCT
ejpam-1871	24	34	,	,	PUNCT
ejpam-1871	24	35	for	for	ADP
ejpam-1871	24	36	all	all	DET
ejpam-1871	24	37	a	a	DET
ejpam-1871	24	38	∈	∈	PROPN
ejpam-1871	24	39	a	a	PRON
ejpam-1871	24	40	,	,	PUNCT
ejpam-1871	24	41	and	and	CCONJ
ejpam-1871	24	42	s	s	PROPN
ejpam-1871	24	43	,	,	PUNCT
ejpam-1871	24	44	t	t	PROPN
ejpam-1871	24	45	∈	∈	PROPN
ejpam-1871	24	46	s.	s.	PROPN
ejpam-1871	24	47	the	the	DET
ejpam-1871	24	48	category	category	NOUN
ejpam-1871	24	49	of	of	ADP
ejpam-1871	24	50	all	all	DET
ejpam-1871	24	51	s	s	NOUN
ejpam-1871	24	52	-	-	NOUN
ejpam-1871	24	53	acts	act	NOUN
ejpam-1871	24	54	,	,	PUNCT
ejpam-1871	24	55	with	with	ADP
ejpam-1871	24	56	action	action	NOUN
ejpam-1871	24	57	-	-	PUNCT
ejpam-1871	24	58	preserving	preserve	VERB
ejpam-1871	24	59	maps	map	NOUN
ejpam-1871	24	60	between	between	ADP
ejpam-1871	24	61	them	they	PRON
ejpam-1871	24	62	,	,	PUNCT
ejpam-1871	24	63	is	be	AUX
ejpam-1871	24	64	denoted	denote	VERB
ejpam-1871	24	65	by	by	ADP
ejpam-1871	24	66	s	s	NOUN
ejpam-1871	24	67	-	-	NOUN
ejpam-1871	24	68	act	act	NOUN
ejpam-1871	24	69	.	.	PUNCT
ejpam-1871	25	1	an	an	DET
ejpam-1871	25	2	s	s	NOUN
ejpam-1871	25	3	-	-	PUNCT
ejpam-1871	25	4	act	act	NOUN
ejpam-1871	25	5	congruence	congruence	NOUN
ejpam-1871	25	6	θ	θ	PROPN
ejpam-1871	25	7	on	on	ADP
ejpam-1871	25	8	a	a	PRON
ejpam-1871	25	9	is	be	AUX
ejpam-1871	25	10	an	an	DET
ejpam-1871	25	11	equivalence	equivalence	NOUN
ejpam-1871	25	12	relation	relation	NOUN
ejpam-1871	25	13	with	with	ADP
ejpam-1871	25	14	the	the	DET
ejpam-1871	25	15	property	property	NOUN
ejpam-1871	25	16	that	that	PRON
ejpam-1871	25	17	aθa′	aθa′	NOUN
ejpam-1871	25	18	,	,	PUNCT
ejpam-1871	25	19	a	a	PRON
ejpam-1871	25	20	,	,	PUNCT
ejpam-1871	25	21	a′	a′	PROPN
ejpam-1871	25	22	∈	∈	PROPN
ejpam-1871	25	23	a	a	PRON
ejpam-1871	25	24	,	,	PUNCT
ejpam-1871	25	25	implies	imply	VERB
ejpam-1871	25	26	that	that	SCONJ
ejpam-1871	25	27	saθ	saθ	NOUN
ejpam-1871	25	28	sa′	sa′	NUM
ejpam-1871	25	29	,	,	PUNCT
ejpam-1871	25	30	for	for	ADP
ejpam-1871	25	31	all	all	DET
ejpam-1871	25	32	s	s	PROPN
ejpam-1871	25	33	∈	∈	PROPN
ejpam-1871	25	34	s.	s.	PROPN
ejpam-1871	25	35	a	a	DET
ejpam-1871	25	36	quotient	quotient	NOUN
ejpam-1871	25	37	s	s	NOUN
ejpam-1871	25	38	-	-	NOUN
ejpam-1871	25	39	act	act	NOUN
ejpam-1871	25	40	is	be	AUX
ejpam-1871	25	41	the	the	DET
ejpam-1871	25	42	set	set	NOUN
ejpam-1871	25	43	a	a	PRON
ejpam-1871	25	44	/	/	SYM
ejpam-1871	25	45	θ	θ	NOUN
ejpam-1871	25	46	with	with	ADP
ejpam-1871	25	47	the	the	DET
ejpam-1871	25	48	natural	natural	ADJ
ejpam-1871	25	49	action	action	NOUN
ejpam-1871	25	50	,	,	PUNCT
ejpam-1871	25	51	s[a	s[a	PROPN
ejpam-1871	25	52	]	]	X
ejpam-1871	26	1	=	=	PUNCT
ejpam-1871	27	1	[	[	X
ejpam-1871	27	2	sa	sa	X
ejpam-1871	27	3	]	]	X
ejpam-1871	27	4	,	,	PUNCT
ejpam-1871	27	5	which	which	PRON
ejpam-1871	27	6	makes	make	VERB
ejpam-1871	27	7	the	the	DET
ejpam-1871	27	8	canonical	canonical	ADJ
ejpam-1871	27	9	map	map	NOUN
ejpam-1871	27	10	γ	γ	X
ejpam-1871	27	11	:	:	PUNCT
ejpam-1871	27	12	a→	a→	PUNCT
ejpam-1871	27	13	a	a	PRON
ejpam-1871	27	14	/	/	SYM
ejpam-1871	27	15	θ	θ	NOUN
ejpam-1871	27	16	,	,	PUNCT
ejpam-1871	27	17	a	a	DET
ejpam-1871	27	18	7→	7→	NOUN
ejpam-1871	28	1	[	[	X
ejpam-1871	28	2	a	a	X
ejpam-1871	28	3	]	]	X
ejpam-1871	28	4	,	,	PUNCT
ejpam-1871	28	5	an	an	DET
ejpam-1871	28	6	s	s	NOUN
ejpam-1871	28	7	-	-	PUNCT
ejpam-1871	28	8	act	act	NOUN
ejpam-1871	28	9	map	map	NOUN
ejpam-1871	28	10	.	.	PUNCT
ejpam-1871	29	1	for	for	ADP
ejpam-1871	29	2	more	more	ADJ
ejpam-1871	29	3	information	information	NOUN
ejpam-1871	29	4	about	about	ADP
ejpam-1871	29	5	s	s	NOUN
ejpam-1871	29	6	-	-	PUNCT
ejpam-1871	29	7	acts	act	NOUN
ejpam-1871	29	8	,	,	PUNCT
ejpam-1871	29	9	see	see	VERB
ejpam-1871	29	10	[	[	X
ejpam-1871	29	11	12	12	NUM
ejpam-1871	29	12	]	]	PUNCT
ejpam-1871	29	13	.	.	PUNCT
ejpam-1871	30	1	a	a	DET
ejpam-1871	30	2	monoid	monoid	NOUN
ejpam-1871	30	3	s	s	NOUN
ejpam-1871	30	4	is	be	AUX
ejpam-1871	30	5	said	say	VERB
ejpam-1871	30	6	to	to	PART
ejpam-1871	30	7	be	be	AUX
ejpam-1871	30	8	a	a	DET
ejpam-1871	30	9	pomonoid	pomonoid	NOUN
ejpam-1871	30	10	if	if	SCONJ
ejpam-1871	30	11	it	it	PRON
ejpam-1871	30	12	is	be	AUX
ejpam-1871	30	13	also	also	ADV
ejpam-1871	30	14	a	a	DET
ejpam-1871	30	15	poset	poset	NOUN
ejpam-1871	30	16	whose	whose	DET
ejpam-1871	30	17	partial	partial	ADJ
ejpam-1871	30	18	order	order	NOUN
ejpam-1871	30	19	is	be	AUX
ejpam-1871	30	20	compatible	compatible	ADJ
ejpam-1871	30	21	with	with	ADP
ejpam-1871	30	22	the	the	DET
ejpam-1871	30	23	binary	binary	ADJ
ejpam-1871	30	24	operation	operation	NOUN
ejpam-1871	30	25	.	.	PUNCT
ejpam-1871	31	1	for	for	ADP
ejpam-1871	31	2	a	a	DET
ejpam-1871	31	3	pomonoid	pomonoid	NOUN
ejpam-1871	31	4	s	s	PROPN
ejpam-1871	31	5	,	,	PUNCT
ejpam-1871	31	6	a	a	DET
ejpam-1871	31	7	(	(	PUNCT
ejpam-1871	31	8	left	left	ADJ
ejpam-1871	31	9	)	)	PUNCT
ejpam-1871	32	1	s	s	X
ejpam-1871	32	2	-	-	PUNCT
ejpam-1871	32	3	poset	poset	NOUN
ejpam-1871	32	4	is	be	AUX
ejpam-1871	32	5	a	a	DET
ejpam-1871	32	6	poset	poset	NOUN
ejpam-1871	32	7	a	a	DET
ejpam-1871	32	8	which	which	PRON
ejpam-1871	32	9	is	be	AUX
ejpam-1871	32	10	also	also	ADV
ejpam-1871	32	11	an	an	DET
ejpam-1871	32	12	s	s	NOUN
ejpam-1871	32	13	-	-	NOUN
ejpam-1871	32	14	act	act	NOUN
ejpam-1871	32	15	whose	whose	DET
ejpam-1871	32	16	action	action	NOUN
ejpam-1871	32	17	is	be	AUX
ejpam-1871	32	18	monotone	monotone	ADJ
ejpam-1871	32	19	in	in	ADP
ejpam-1871	32	20	both	both	DET
ejpam-1871	32	21	arguments	argument	NOUN
ejpam-1871	32	22	.	.	PUNCT
ejpam-1871	33	1	an	an	DET
ejpam-1871	33	2	s	s	X
ejpam-1871	33	3	-	-	PUNCT
ejpam-1871	33	4	poset	poset	ADJ
ejpam-1871	33	5	map	map	NOUN
ejpam-1871	33	6	(	(	PUNCT
ejpam-1871	33	7	morphism	morphism	NOUN
ejpam-1871	33	8	)	)	PUNCT
ejpam-1871	33	9	is	be	AUX
ejpam-1871	33	10	an	an	DET
ejpam-1871	33	11	action	action	NOUN
ejpam-1871	33	12	preserving	preserve	VERB
ejpam-1871	33	13	monotone	monotone	ADJ
ejpam-1871	33	14	map	map	NOUN
ejpam-1871	33	15	between	between	ADP
ejpam-1871	33	16	s	s	NOUN
ejpam-1871	33	17	-	-	NOUN
ejpam-1871	33	18	posets	poset	NOUN
ejpam-1871	33	19	.	.	PUNCT
ejpam-1871	34	1	note	note	VERB
ejpam-1871	34	2	that	that	SCONJ
ejpam-1871	34	3	each	each	DET
ejpam-1871	34	4	poset	poset	NOUN
ejpam-1871	34	5	p	p	NOUN
ejpam-1871	34	6	can	can	AUX
ejpam-1871	34	7	be	be	AUX
ejpam-1871	34	8	made	make	VERB
ejpam-1871	34	9	into	into	ADP
ejpam-1871	34	10	an	an	DET
ejpam-1871	34	11	s	s	NOUN
ejpam-1871	34	12	-	-	NOUN
ejpam-1871	34	13	poset	poset	NOUN
ejpam-1871	34	14	with	with	ADP
ejpam-1871	34	15	trivial	trivial	ADJ
ejpam-1871	34	16	action	action	NOUN
ejpam-1871	34	17	:	:	PUNCT
ejpam-1871	34	18	sp	sp	ADP
ejpam-1871	34	19	=	=	SYM
ejpam-1871	34	20	p	p	NOUN
ejpam-1871	34	21	,	,	PUNCT
ejpam-1871	34	22	for	for	ADP
ejpam-1871	34	23	every	every	DET
ejpam-1871	34	24	p	p	NOUN
ejpam-1871	34	25	∈	∈	PROPN
ejpam-1871	34	26	p	p	NOUN
ejpam-1871	34	27	,	,	PUNCT
ejpam-1871	34	28	s	s	PART
ejpam-1871	34	29	∈	∈	PROPN
ejpam-1871	34	30	s.	s.	PROPN
ejpam-1871	34	31	let	let	VERB
ejpam-1871	34	32	a	a	PRON
ejpam-1871	34	33	be	be	AUX
ejpam-1871	34	34	an	an	DET
ejpam-1871	34	35	s	s	NOUN
ejpam-1871	34	36	-	-	NOUN
ejpam-1871	34	37	poset	poset	NOUN
ejpam-1871	34	38	.	.	PUNCT
ejpam-1871	35	1	an	an	DET
ejpam-1871	35	2	s	s	NOUN
ejpam-1871	35	3	-	-	PUNCT
ejpam-1871	35	4	poset	poset	ADJ
ejpam-1871	35	5	congruence	congruence	NOUN
ejpam-1871	35	6	on	on	ADP
ejpam-1871	35	7	a	a	PRON
ejpam-1871	35	8	is	be	AUX
ejpam-1871	35	9	an	an	DET
ejpam-1871	35	10	s	s	NOUN
ejpam-1871	35	11	-	-	PUNCT
ejpam-1871	35	12	act	act	NOUN
ejpam-1871	35	13	congruence	congruence	NOUN
ejpam-1871	35	14	θ	θ	PROPN
ejpam-1871	35	15	with	with	ADP
ejpam-1871	35	16	the	the	DET
ejpam-1871	35	17	property	property	NOUN
ejpam-1871	35	18	that	that	PRON
ejpam-1871	35	19	the	the	DET
ejpam-1871	35	20	s	s	NOUN
ejpam-1871	35	21	-	-	NOUN
ejpam-1871	35	22	act	act	NOUN
ejpam-1871	35	23	a	a	PRON
ejpam-1871	35	24	/	/	SYM
ejpam-1871	35	25	θ	θ	NOUN
ejpam-1871	35	26	can	can	AUX
ejpam-1871	35	27	be	be	AUX
ejpam-1871	35	28	made	make	VERB
ejpam-1871	35	29	into	into	ADP
ejpam-1871	35	30	an	an	DET
ejpam-1871	35	31	s	s	NOUN
ejpam-1871	35	32	-	-	NOUN
ejpam-1871	35	33	poset	poset	NOUN
ejpam-1871	35	34	in	in	ADP
ejpam-1871	35	35	such	such	DET
ejpam-1871	35	36	a	a	DET
ejpam-1871	35	37	way	way	NOUN
ejpam-1871	35	38	that	that	PRON
ejpam-1871	35	39	the	the	DET
ejpam-1871	35	40	canonical	canonical	ADJ
ejpam-1871	35	41	s	s	NOUN
ejpam-1871	35	42	-	-	PUNCT
ejpam-1871	35	43	act	act	NOUN
ejpam-1871	35	44	map	map	NOUN
ejpam-1871	35	45	a→	a→	PUNCT
ejpam-1871	35	46	a	a	PRON
ejpam-1871	35	47	/	/	SYM
ejpam-1871	35	48	θ	θ	NOUN
ejpam-1871	35	49	is	be	AUX
ejpam-1871	35	50	an	an	DET
ejpam-1871	35	51	s	s	NOUN
ejpam-1871	35	52	-	-	PUNCT
ejpam-1871	35	53	poset	poset	VERB
ejpam-1871	35	54	map	map	NOUN
ejpam-1871	35	55	.	.	PUNCT
ejpam-1871	36	1	for	for	ADP
ejpam-1871	36	2	a	a	DET
ejpam-1871	36	3	binary	binary	ADJ
ejpam-1871	36	4	relation	relation	NOUN
ejpam-1871	36	5	r	r	NOUN
ejpam-1871	36	6	on	on	ADP
ejpam-1871	36	7	a	a	PRON
ejpam-1871	36	8	,	,	PUNCT
ejpam-1871	36	9	define	define	VERB
ejpam-1871	36	10	the	the	DET
ejpam-1871	36	11	relation≤r	relation≤r	NOUN
ejpam-1871	36	12	on	on	ADP
ejpam-1871	36	13	a	a	PRON
ejpam-1871	36	14	by	by	ADP
ejpam-1871	36	15	a	a	DET
ejpam-1871	36	16	≤r	≤r	NOUN
ejpam-1871	36	17	a′	a′	NOUN
ejpam-1871	36	18	if	if	SCONJ
ejpam-1871	37	1	and	and	CCONJ
ejpam-1871	37	2	only	only	ADV
ejpam-1871	37	3	if	if	SCONJ
ejpam-1871	37	4	a	a	DET
ejpam-1871	37	5	≤	≤	NUM
ejpam-1871	37	6	a1ra′1	a1ra′1	X
ejpam-1871	37	7	≤	≤	NOUN
ejpam-1871	37	8	.	.	PUNCT
ejpam-1871	37	9	.	.	PUNCT
ejpam-1871	38	1	.≤	.≤	PUNCT
ejpam-1871	39	1	anra′n	anra′n	ADV
ejpam-1871	39	2	≤	≤	ADJ
ejpam-1871	39	3	a′	a′	PROPN
ejpam-1871	39	4	,	,	PUNCT
ejpam-1871	39	5	for	for	ADP
ejpam-1871	39	6	some	some	DET
ejpam-1871	39	7	a1	a1	NOUN
ejpam-1871	39	8	,	,	PUNCT
ejpam-1871	39	9	a′1	a′1	PROPN
ejpam-1871	39	10	,	,	PUNCT
ejpam-1871	39	11	.	.	PUNCT
ejpam-1871	39	12	.	.	PUNCT
ejpam-1871	40	1	.	.	PUNCT
ejpam-1871	41	1	,	,	PUNCT
ejpam-1871	41	2	an	an	DET
ejpam-1871	41	3	,	,	PUNCT
ejpam-1871	41	4	a′n	a′n	ADP
ejpam-1871	41	5	∈	∈	PROPN
ejpam-1871	41	6	a.	a.	NOUN
ejpam-1871	41	7	then	then	ADV
ejpam-1871	41	8	an	an	DET
ejpam-1871	41	9	s	s	NOUN
ejpam-1871	41	10	-	-	PUNCT
ejpam-1871	41	11	act	act	NOUN
ejpam-1871	41	12	congruence	congruence	NOUN
ejpam-1871	41	13	θ	θ	PROPN
ejpam-1871	41	14	on	on	ADP
ejpam-1871	41	15	a	a	PRON
ejpam-1871	41	16	is	be	AUX
ejpam-1871	41	17	an	an	DET
ejpam-1871	41	18	s	s	NOUN
ejpam-1871	41	19	-	-	PUNCT
ejpam-1871	41	20	poset	poset	ADJ
ejpam-1871	41	21	congruence	congruence	NOUN
ejpam-1871	41	22	if	if	SCONJ
ejpam-1871	41	23	and	and	CCONJ
ejpam-1871	41	24	only	only	ADV
ejpam-1871	41	25	if	if	SCONJ
ejpam-1871	41	26	aθa′	aθa′	NUM
ejpam-1871	41	27	whenever	whenever	SCONJ
ejpam-1871	41	28	a	a	DET
ejpam-1871	41	29	≤θ	≤θ	PROPN
ejpam-1871	41	30	a′	a′	PROPN
ejpam-1871	41	31	≤θ	≤θ	PROPN
ejpam-1871	41	32	a.	a.	NOUN
ejpam-1871	42	1	the	the	DET
ejpam-1871	42	2	s	s	NOUN
ejpam-1871	42	3	-	-	PUNCT
ejpam-1871	42	4	poset	poset	VERB
ejpam-1871	42	5	quotient	quotient	NOUN
ejpam-1871	42	6	is	be	AUX
ejpam-1871	42	7	then	then	ADV
ejpam-1871	42	8	the	the	DET
ejpam-1871	42	9	s	s	PROPN
ejpam-1871	42	10	-	-	PUNCT
ejpam-1871	42	11	act	act	NOUN
ejpam-1871	42	12	quotient	quotient	NOUN
ejpam-1871	42	13	a	a	PRON
ejpam-1871	42	14	/	/	SYM
ejpam-1871	42	15	θ	θ	NOUN
ejpam-1871	42	16	with	with	ADP
ejpam-1871	42	17	the	the	DET
ejpam-1871	42	18	partial	partial	ADJ
ejpam-1871	42	19	order	order	NOUN
ejpam-1871	42	20	given	give	VERB
ejpam-1871	42	21	by	by	ADP
ejpam-1871	42	22	[	[	X
ejpam-1871	42	23	a	a	X
ejpam-1871	42	24	]	]	PUNCT
ejpam-1871	42	25	≤	≤	NOUN
ejpam-1871	43	1	[	[	X
ejpam-1871	43	2	b	b	X
ejpam-1871	43	3	]	]	X
ejpam-1871	43	4	if	if	SCONJ
ejpam-1871	43	5	and	and	CCONJ
ejpam-1871	43	6	only	only	ADV
ejpam-1871	43	7	if	if	SCONJ
ejpam-1871	43	8	a	a	DET
ejpam-1871	43	9	≤θ	≤θ	PROPN
ejpam-1871	43	10	b.	b.	PROPN
ejpam-1871	43	11	also	also	ADV
ejpam-1871	43	12	the	the	DET
ejpam-1871	43	13	s	s	NOUN
ejpam-1871	43	14	-	-	PUNCT
ejpam-1871	43	15	poset	poset	VERB
ejpam-1871	43	16	congruence	congruence	NOUN
ejpam-1871	43	17	θ	θ	PROPN
ejpam-1871	43	18	(	(	PUNCT
ejpam-1871	43	19	h	h	NOUN
ejpam-1871	43	20	)	)	PUNCT
ejpam-1871	43	21	on	on	ADP
ejpam-1871	43	22	a	a	DET
ejpam-1871	43	23	generated	generate	VERB
ejpam-1871	43	24	by	by	ADP
ejpam-1871	43	25	h	h	PROPN
ejpam-1871	43	26	⊆	⊆	NUM
ejpam-1871	43	27	a×a	a×a	PROPN
ejpam-1871	43	28	can	can	AUX
ejpam-1871	43	29	be	be	AUX
ejpam-1871	43	30	characterized	characterize	VERB
ejpam-1871	43	31	as	as	SCONJ
ejpam-1871	43	32	follows	follow	VERB
ejpam-1871	43	33	(	(	PUNCT
ejpam-1871	43	34	see	see	VERB
ejpam-1871	43	35	[	[	X
ejpam-1871	43	36	15	15	NUM
ejpam-1871	43	37	,	,	PUNCT
ejpam-1871	43	38	proposition	proposition	NOUN
ejpam-1871	43	39	3.3	3.3	NUM
ejpam-1871	43	40	]	]	PUNCT
ejpam-1871	43	41	):	):	PUNCT
ejpam-1871	43	42	aθ	aθ	INTJ
ejpam-1871	43	43	(	(	PUNCT
ejpam-1871	43	44	h)a′	h)a′	VERB
ejpam-1871	43	45	if	if	SCONJ
ejpam-1871	43	46	and	and	CCONJ
ejpam-1871	43	47	only	only	ADV
ejpam-1871	43	48	if	if	SCONJ
ejpam-1871	43	49	a	a	DET
ejpam-1871	43	50	=	=	PUNCT
ejpam-1871	43	51	a′	a′	PROPN
ejpam-1871	43	52	,	,	PUNCT
ejpam-1871	43	53	or	or	CCONJ
ejpam-1871	43	54	there	there	PRON
ejpam-1871	43	55	exist	exist	VERB
ejpam-1871	43	56	s1	s1	NOUN
ejpam-1871	43	57	,	,	PUNCT
ejpam-1871	43	58	s2	s2	NOUN
ejpam-1871	43	59	,	,	PUNCT
ejpam-1871	43	60	.	.	PUNCT
ejpam-1871	43	61	.	.	PUNCT
ejpam-1871	44	1	.	.	PUNCT
ejpam-1871	45	1	,	,	PUNCT
ejpam-1871	45	2	sn	sn	PROPN
ejpam-1871	45	3	,	,	PUNCT
ejpam-1871	45	4	t1	t1	NOUN
ejpam-1871	45	5	,	,	PUNCT
ejpam-1871	45	6	t2	t2	NOUN
ejpam-1871	45	7	,	,	PUNCT
ejpam-1871	45	8	.	.	PUNCT
ejpam-1871	45	9	.	.	PUNCT
ejpam-1871	45	10	.	.	PUNCT
ejpam-1871	46	1	,	,	PUNCT
ejpam-1871	46	2	tm	tm	PROPN
ejpam-1871	46	3	∈	∈	PROPN
ejpam-1871	46	4	s	s	VERB
ejpam-1871	46	5	such	such	ADJ
ejpam-1871	46	6	that	that	SCONJ
ejpam-1871	46	7	a	a	DET
ejpam-1871	46	8	≤	≤	NUM
ejpam-1871	46	9	s1c1	s1c1	NOUN
ejpam-1871	46	10	,	,	PUNCT
ejpam-1871	46	11	s1d1	s1d1	NOUN
ejpam-1871	46	12	≤	≤	NOUN
ejpam-1871	46	13	s2c2	s2c2	NOUN
ejpam-1871	46	14	,	,	PUNCT
ejpam-1871	46	15	s2d2	s2d2	NOUN
ejpam-1871	46	16	≤	≤	NUM
ejpam-1871	46	17	s3c3	s3c3	NOUN
ejpam-1871	46	18	,	,	PUNCT
ejpam-1871	46	19	.	.	PUNCT
ejpam-1871	46	20	.	.	PUNCT
ejpam-1871	46	21	.	.	PUNCT
ejpam-1871	47	1	,	,	PUNCT
ejpam-1871	47	2	sndn	sndn	ADJ
ejpam-1871	47	3	≤	≤	NOUN
ejpam-1871	47	4	a′	a′	PROPN
ejpam-1871	47	5	;	;	PUNCT
ejpam-1871	47	6	a′	a′	PROPN
ejpam-1871	47	7	≤	≤	NUM
ejpam-1871	47	8	t1p1	t1p1	PUNCT
ejpam-1871	47	9	,	,	PUNCT
ejpam-1871	47	10	t1q1	t1q1	PROPN
ejpam-1871	47	11	≤	≤	NUM
ejpam-1871	47	12	t2p2	t2p2	NOUN
ejpam-1871	47	13	,	,	PUNCT
ejpam-1871	47	14	t2q2	t2q2	ADP
ejpam-1871	47	15	≤	≤	ADV
ejpam-1871	47	16	t3p3	t3p3	ADV
ejpam-1871	47	17	,	,	PUNCT
ejpam-1871	47	18	.	.	PUNCT
ejpam-1871	47	19	.	.	PUNCT
ejpam-1871	48	1	.	.	PUNCT
ejpam-1871	49	1	,	,	PUNCT
ejpam-1871	49	2	tmqm	tmqm	NOUN
ejpam-1871	49	3	≤	≤	ADV
ejpam-1871	50	1	a	a	PRON
ejpam-1871	50	2	,	,	PUNCT
ejpam-1871	50	3	where	where	SCONJ
ejpam-1871	50	4	(	(	PUNCT
ejpam-1871	50	5	ci	ci	NOUN
ejpam-1871	50	6	,	,	PUNCT
ejpam-1871	50	7	di	di	NOUN
ejpam-1871	50	8	)	)	PUNCT
ejpam-1871	50	9	,	,	PUNCT
ejpam-1871	50	10	(	(	PUNCT
ejpam-1871	50	11	p	p	PROPN
ejpam-1871	50	12	j	j	PROPN
ejpam-1871	50	13	,	,	PUNCT
ejpam-1871	50	14	q	q	PROPN
ejpam-1871	50	15	j	j	PROPN
ejpam-1871	50	16	)	)	PUNCT
ejpam-1871	50	17	∈	∈	PROPN
ejpam-1871	50	18	h	h	NOUN
ejpam-1871	50	19	∪h−1	∪h−1	PUNCT
ejpam-1871	50	20	for	for	ADP
ejpam-1871	50	21	i	i	PRON
ejpam-1871	50	22	=	=	NOUN
ejpam-1871	50	23	1	1	NUM
ejpam-1871	50	24	,	,	PUNCT
ejpam-1871	50	25	2	2	NUM
ejpam-1871	50	26	,	,	PUNCT
ejpam-1871	50	27	.	.	PUNCT
ejpam-1871	50	28	.	.	PUNCT
ejpam-1871	51	1	.	.	PUNCT
ejpam-1871	52	1	,	,	PUNCT
ejpam-1871	52	2	n	n	PROPN
ejpam-1871	52	3	and	and	CCONJ
ejpam-1871	52	4	j	j	PROPN
ejpam-1871	52	5	=	=	SYM
ejpam-1871	52	6	1,2	1,2	NUM
ejpam-1871	52	7	,	,	PUNCT
ejpam-1871	52	8	.	.	PUNCT
ejpam-1871	53	1	.	.	PUNCT
ejpam-1871	53	2	.	.	PUNCT
ejpam-1871	54	1	,	,	PUNCT
ejpam-1871	54	2	m.	m.	NOUN
ejpam-1871	54	3	moreover	moreover	ADV
ejpam-1871	54	4	,	,	PUNCT
ejpam-1871	54	5	the	the	DET
ejpam-1871	54	6	order	order	NOUN
ejpam-1871	54	7	relation	relation	NOUN
ejpam-1871	54	8	on	on	ADP
ejpam-1871	54	9	a	a	DET
ejpam-1871	54	10	/	/	SYM
ejpam-1871	54	11	θ	θ	NOUN
ejpam-1871	54	12	(	(	PUNCT
ejpam-1871	54	13	h	h	NOUN
ejpam-1871	54	14	)	)	PUNCT
ejpam-1871	54	15	can	can	AUX
ejpam-1871	54	16	be	be	AUX
ejpam-1871	54	17	defined	define	VERB
ejpam-1871	54	18	by	by	ADP
ejpam-1871	54	19	:	:	PUNCT
ejpam-1871	55	1	[	[	X
ejpam-1871	55	2	a]≤	a]≤	NOUN
ejpam-1871	55	3	[	[	X
ejpam-1871	55	4	a′	a′	X
ejpam-1871	55	5	]	]	X
ejpam-1871	55	6	if	if	SCONJ
ejpam-1871	55	7	and	and	CCONJ
ejpam-1871	55	8	only	only	ADV
ejpam-1871	55	9	if	if	SCONJ
ejpam-1871	55	10	a	a	DET
ejpam-1871	55	11	≤	≤	NUM
ejpam-1871	55	12	a′	a′	PROPN
ejpam-1871	55	13	,	,	PUNCT
ejpam-1871	55	14	or	or	CCONJ
ejpam-1871	55	15	there	there	PRON
ejpam-1871	55	16	exist	exist	VERB
ejpam-1871	55	17	s1	s1	NOUN
ejpam-1871	55	18	,	,	PUNCT
ejpam-1871	55	19	s2	s2	NOUN
ejpam-1871	55	20	,	,	PUNCT
ejpam-1871	55	21	.	.	PUNCT
ejpam-1871	55	22	.	.	PUNCT
ejpam-1871	55	23	.	.	PUNCT
ejpam-1871	56	1	,	,	PUNCT
ejpam-1871	56	2	sn	sn	PROPN
ejpam-1871	56	3	∈	∈	PROPN
ejpam-1871	56	4	s	s	VERB
ejpam-1871	56	5	such	such	ADJ
ejpam-1871	56	6	that	that	SCONJ
ejpam-1871	56	7	a	a	DET
ejpam-1871	56	8	≤	≤	NUM
ejpam-1871	56	9	s1c1	s1c1	NOUN
ejpam-1871	56	10	,	,	PUNCT
ejpam-1871	56	11	s1d1	s1d1	NOUN
ejpam-1871	56	12	≤	≤	NOUN
ejpam-1871	56	13	s2c2	s2c2	NOUN
ejpam-1871	56	14	,	,	PUNCT
ejpam-1871	56	15	s2d2	s2d2	NOUN
ejpam-1871	56	16	≤	≤	NUM
ejpam-1871	56	17	s3c3	s3c3	NOUN
ejpam-1871	56	18	,	,	PUNCT
ejpam-1871	56	19	.	.	PUNCT
ejpam-1871	56	20	.	.	PUNCT
ejpam-1871	56	21	.	.	PUNCT
ejpam-1871	57	1	,	,	PUNCT
ejpam-1871	57	2	sndn	sndn	ADJ
ejpam-1871	57	3	≤	≤	NOUN
ejpam-1871	57	4	a′	a′	PROPN
ejpam-1871	57	5	,	,	PUNCT
ejpam-1871	57	6	where	where	SCONJ
ejpam-1871	57	7	(	(	PUNCT
ejpam-1871	57	8	ci	ci	NOUN
ejpam-1871	57	9	,	,	PUNCT
ejpam-1871	57	10	di	di	NOUN
ejpam-1871	57	11	)	)	PUNCT
ejpam-1871	57	12	∈	∈	PROPN
ejpam-1871	57	13	h	h	NOUN
ejpam-1871	57	14	∪h−1	∪h−1	PUNCT
ejpam-1871	57	15	for	for	ADP
ejpam-1871	57	16	i	i	X
ejpam-1871	57	17	=	=	SYM
ejpam-1871	57	18	1,2	1,2	NUM
ejpam-1871	57	19	,	,	PUNCT
ejpam-1871	57	20	.	.	PUNCT
ejpam-1871	57	21	.	.	PUNCT
ejpam-1871	58	1	.	.	PUNCT
ejpam-1871	59	1	,	,	PUNCT
ejpam-1871	59	2	n.	n.	PROPN
ejpam-1871	59	3	recall	recall	VERB
ejpam-1871	59	4	that	that	SCONJ
ejpam-1871	59	5	the	the	DET
ejpam-1871	59	6	product	product	NOUN
ejpam-1871	59	7	of	of	ADP
ejpam-1871	59	8	a	a	DET
ejpam-1871	59	9	family	family	NOUN
ejpam-1871	59	10	of	of	ADP
ejpam-1871	59	11	s	s	NOUN
ejpam-1871	59	12	-	-	PUNCT
ejpam-1871	59	13	posets	poset	NOUN
ejpam-1871	59	14	is	be	AUX
ejpam-1871	59	15	their	their	PRON
ejpam-1871	59	16	cartesian	cartesian	ADJ
ejpam-1871	59	17	product	product	NOUN
ejpam-1871	59	18	,	,	PUNCT
ejpam-1871	59	19	with	with	ADP
ejpam-1871	59	20	componentwise	componentwise	NOUN
ejpam-1871	59	21	action	action	NOUN
ejpam-1871	59	22	and	and	CCONJ
ejpam-1871	59	23	order	order	NOUN
ejpam-1871	59	24	.	.	PUNCT
ejpam-1871	60	1	the	the	DET
ejpam-1871	60	2	coproduct	coproduct	NOUN
ejpam-1871	60	3	is	be	AUX
ejpam-1871	60	4	their	their	PRON
ejpam-1871	60	5	disjoint	disjoint	NOUN
ejpam-1871	60	6	union	union	NOUN
ejpam-1871	60	7	,	,	PUNCT
ejpam-1871	60	8	with	with	ADP
ejpam-1871	60	9	natural	natural	ADJ
ejpam-1871	60	10	action	action	NOUN
ejpam-1871	60	11	and	and	CCONJ
ejpam-1871	60	12	componentwise	componentwise	NOUN
ejpam-1871	60	13	order	order	NOUN
ejpam-1871	60	14	.	.	PUNCT
ejpam-1871	61	1	as	as	ADP
ejpam-1871	61	2	usual	usual	ADJ
ejpam-1871	61	3	,	,	PUNCT
ejpam-1871	61	4	we	we	PRON
ejpam-1871	61	5	use	use	VERB
ejpam-1871	61	6	the	the	DET
ejpam-1871	61	7	symbols	symbol	NOUN
ejpam-1871	61	8	∏	∏	PROPN
ejpam-1871	61	9	and	and	CCONJ
ejpam-1871	61	10	∐	∐	PROPN
ejpam-1871	61	11	for	for	ADP
ejpam-1871	61	12	product	product	NOUN
ejpam-1871	61	13	and	and	CCONJ
ejpam-1871	61	14	coproduct	coproduct	NOUN
ejpam-1871	61	15	,	,	PUNCT
ejpam-1871	61	16	respectively	respectively	ADV
ejpam-1871	61	17	.	.	PUNCT
ejpam-1871	62	1	also	also	ADV
ejpam-1871	62	2	for	for	ADP
ejpam-1871	62	3	a	a	DET
ejpam-1871	62	4	family	family	NOUN
ejpam-1871	62	5	(	(	PUNCT
ejpam-1871	62	6	aα)α∈i	aα)α∈i	NUM
ejpam-1871	62	7	of	of	ADP
ejpam-1871	62	8	s	s	NOUN
ejpam-1871	62	9	-	-	NOUN
ejpam-1871	62	10	posets	poset	NOUN
ejpam-1871	62	11	each	each	PRON
ejpam-1871	62	12	with	with	ADP
ejpam-1871	62	13	a	a	DET
ejpam-1871	62	14	unique	unique	ADJ
ejpam-1871	62	15	fixed	fix	VERB
ejpam-1871	62	16	element	element	NOUN
ejpam-1871	62	17	0	0	NUM
ejpam-1871	62	18	,	,	PUNCT
ejpam-1871	62	19	the	the	DET
ejpam-1871	62	20	direct	direct	ADJ
ejpam-1871	62	21	sum	sum	NOUN
ejpam-1871	62	22	⊕	⊕	PROPN
ejpam-1871	62	23	aα	aα	NOUN
ejpam-1871	62	24	is	be	AUX
ejpam-1871	62	25	defined	define	VERB
ejpam-1871	62	26	to	to	PART
ejpam-1871	62	27	be	be	AUX
ejpam-1871	62	28	the	the	DET
ejpam-1871	62	29	sub	sub	NOUN
ejpam-1871	62	30	s	s	NOUN
ejpam-1871	62	31	-	-	NOUN
ejpam-1871	62	32	poset	poset	NOUN
ejpam-1871	62	33	of	of	ADP
ejpam-1871	62	34	the	the	DET
ejpam-1871	62	35	product	product	NOUN
ejpam-1871	62	36	∏	∏	NUM
ejpam-1871	62	37	aα	aα	NOUN
ejpam-1871	62	38	consisting	consist	VERB
ejpam-1871	62	39	of	of	ADP
ejpam-1871	62	40	all	all	PRON
ejpam-1871	62	41	(	(	PUNCT
ejpam-1871	62	42	aα)α∈i	aα)α∈i	NUM
ejpam-1871	62	43	such	such	ADJ
ejpam-1871	62	44	that	that	DET
ejpam-1871	62	45	aα	aα	NOUN
ejpam-1871	63	1	=	=	NOUN
ejpam-1871	63	2	0	0	NUM
ejpam-1871	63	3	for	for	ADP
ejpam-1871	63	4	all	all	DET
ejpam-1871	63	5	α	α	NOUN
ejpam-1871	63	6	∈	∈	NOUN
ejpam-1871	64	1	i	i	PRON
ejpam-1871	64	2	except	except	SCONJ
ejpam-1871	64	3	a	a	DET
ejpam-1871	64	4	finite	finite	ADJ
ejpam-1871	64	5	number	number	NOUN
ejpam-1871	64	6	of	of	ADP
ejpam-1871	64	7	indices	index	NOUN
ejpam-1871	64	8	.	.	PUNCT
ejpam-1871	65	1	throughout	throughout	ADP
ejpam-1871	65	2	s	s	PART
ejpam-1871	65	3	denotes	denote	NOUN
ejpam-1871	65	4	a	a	DET
ejpam-1871	65	5	pomonoid	pomonoid	NOUN
ejpam-1871	65	6	unless	unless	SCONJ
ejpam-1871	65	7	otherwise	otherwise	ADV
ejpam-1871	65	8	stated	state	VERB
ejpam-1871	65	9	,	,	PUNCT
ejpam-1871	65	10	andm	andm	PROPN
ejpam-1871	65	11	stands	stand	VERB
ejpam-1871	65	12	for	for	ADP
ejpam-1871	65	13	the	the	DET
ejpam-1871	65	14	class	class	NOUN
ejpam-1871	65	15	of	of	ADP
ejpam-1871	65	16	regular	regular	ADJ
ejpam-1871	65	17	monomorphisms	monomorphism	NOUN
ejpam-1871	65	18	of	of	ADP
ejpam-1871	65	19	s	s	NOUN
ejpam-1871	65	20	-	-	NOUN
ejpam-1871	65	21	posets	poset	NOUN
ejpam-1871	65	22	.	.	PUNCT
ejpam-1871	66	1	h.	h.	PROPN
ejpam-1871	66	2	rasouli	rasouli	PROPN
ejpam-1871	66	3	/	/	SYM
ejpam-1871	66	4	eur	eur	PROPN
ejpam-1871	66	5	.	.	PUNCT
ejpam-1871	67	1	j.	j.	PROPN
ejpam-1871	67	2	pure	pure	PROPN
ejpam-1871	67	3	appl	appl	PROPN
ejpam-1871	67	4	.	.	PROPN
ejpam-1871	67	5	math	math	PROPN
ejpam-1871	67	6	,	,	PUNCT
ejpam-1871	67	7	7	7	NUM
ejpam-1871	67	8	(	(	PUNCT
ejpam-1871	67	9	2014	2014	NUM
ejpam-1871	67	10	)	)	PUNCT
ejpam-1871	67	11	,	,	PUNCT
ejpam-1871	67	12	166	166	NUM
ejpam-1871	67	13	-	-	SYM
ejpam-1871	67	14	178	178	NUM
ejpam-1871	67	15	168	168	NUM
ejpam-1871	67	16	2	2	NUM
ejpam-1871	67	17	.	.	PUNCT
ejpam-1871	68	1	categorical	categorical	ADJ
ejpam-1871	68	2	properties	property	NOUN
ejpam-1871	68	3	of	of	ADP
ejpam-1871	68	4	regular	regular	ADJ
ejpam-1871	68	5	monomorphisms	monomorphism	NOUN
ejpam-1871	68	6	in	in	ADP
ejpam-1871	68	7	s	s	NOUN
ejpam-1871	68	8	-	-	PUNCT
ejpam-1871	68	9	pos	pos	NOUN
ejpam-1871	68	10	in	in	ADP
ejpam-1871	68	11	this	this	DET
ejpam-1871	68	12	section	section	NOUN
ejpam-1871	68	13	we	we	PRON
ejpam-1871	68	14	investigate	investigate	VERB
ejpam-1871	68	15	the	the	DET
ejpam-1871	68	16	categorical	categorical	ADJ
ejpam-1871	68	17	and	and	CCONJ
ejpam-1871	68	18	algebraic	algebraic	ADJ
ejpam-1871	68	19	properties	property	NOUN
ejpam-1871	68	20	,	,	PUNCT
ejpam-1871	68	21	regarding	regard	VERB
ejpam-1871	68	22	composition	composition	NOUN
ejpam-1871	68	23	,	,	PUNCT
ejpam-1871	68	24	limits	limit	NOUN
ejpam-1871	68	25	and	and	CCONJ
ejpam-1871	68	26	colimits	colimit	NOUN
ejpam-1871	68	27	of	of	ADP
ejpam-1871	68	28	the	the	DET
ejpam-1871	68	29	category	category	NOUN
ejpam-1871	68	30	s	s	NOUN
ejpam-1871	68	31	-	-	PUNCT
ejpam-1871	68	32	pos	pos	NOUN
ejpam-1871	68	33	with	with	ADP
ejpam-1871	68	34	respect	respect	NOUN
ejpam-1871	68	35	to	to	ADP
ejpam-1871	68	36	the	the	DET
ejpam-1871	68	37	classm	classm	NOUN
ejpam-1871	68	38	of	of	ADP
ejpam-1871	68	39	regular	regular	ADJ
ejpam-1871	68	40	monomorphisms	monomorphism	NOUN
ejpam-1871	68	41	which	which	PRON
ejpam-1871	68	42	are	be	AUX
ejpam-1871	68	43	exactly	exactly	ADV
ejpam-1871	68	44	order	order	NOUN
ejpam-1871	68	45	-	-	PUNCT
ejpam-1871	68	46	embeddings	embedding	NOUN
ejpam-1871	68	47	.	.	PUNCT
ejpam-1871	69	1	we	we	PRON
ejpam-1871	69	2	have	have	AUX
ejpam-1871	69	3	divided	divide	VERB
ejpam-1871	69	4	the	the	DET
ejpam-1871	69	5	section	section	NOUN
ejpam-1871	69	6	into	into	ADP
ejpam-1871	69	7	three	three	NUM
ejpam-1871	69	8	subsections	subsection	NOUN
ejpam-1871	69	9	as	as	SCONJ
ejpam-1871	69	10	follows	follow	VERB
ejpam-1871	69	11	:	:	PUNCT
ejpam-1871	69	12	2.1	2.1	NUM
ejpam-1871	69	13	.	.	PUNCT
ejpam-1871	70	1	composition	composition	NOUN
ejpam-1871	70	2	properties	property	NOUN
ejpam-1871	70	3	of	of	ADP
ejpam-1871	70	4	regular	regular	ADJ
ejpam-1871	70	5	monomorphisms	monomorphism	NOUN
ejpam-1871	70	6	in	in	ADP
ejpam-1871	70	7	this	this	DET
ejpam-1871	70	8	subsection	subsection	NOUN
ejpam-1871	70	9	we	we	PRON
ejpam-1871	70	10	study	study	VERB
ejpam-1871	70	11	the	the	DET
ejpam-1871	70	12	composition	composition	NOUN
ejpam-1871	70	13	properties	property	NOUN
ejpam-1871	70	14	of	of	ADP
ejpam-1871	70	15	regular	regular	ADJ
ejpam-1871	70	16	monomorphisms	monomorphism	NOUN
ejpam-1871	70	17	of	of	ADP
ejpam-1871	70	18	sposets	sposet	NOUN
ejpam-1871	70	19	.	.	PUNCT
ejpam-1871	71	1	to	to	PART
ejpam-1871	71	2	find	find	VERB
ejpam-1871	71	3	the	the	DET
ejpam-1871	71	4	importance	importance	NOUN
ejpam-1871	71	5	of	of	ADP
ejpam-1871	71	6	these	these	DET
ejpam-1871	71	7	properties	property	NOUN
ejpam-1871	71	8	,	,	PUNCT
ejpam-1871	71	9	the	the	DET
ejpam-1871	71	10	reader	reader	NOUN
ejpam-1871	71	11	is	be	AUX
ejpam-1871	71	12	referred	refer	VERB
ejpam-1871	71	13	to	to	ADP
ejpam-1871	71	14	[	[	X
ejpam-1871	71	15	1	1	NUM
ejpam-1871	71	16	,	,	PUNCT
ejpam-1871	71	17	2	2	NUM
ejpam-1871	71	18	]	]	PUNCT
ejpam-1871	71	19	.	.	PUNCT
ejpam-1871	72	1	lemma	lemma	PROPN
ejpam-1871	72	2	1	1	NUM
ejpam-1871	72	3	.	.	PUNCT
ejpam-1871	73	1	the	the	DET
ejpam-1871	73	2	classm	classm	PROPN
ejpam-1871	73	3	is	be	AUX
ejpam-1871	73	4	:	:	PUNCT
ejpam-1871	73	5	i	i	X
ejpam-1871	73	6	)	)	PUNCT
ejpam-1871	73	7	composition	composition	NOUN
ejpam-1871	73	8	closed	close	VERB
ejpam-1871	73	9	;	;	PUNCT
ejpam-1871	73	10	that	that	PRON
ejpam-1871	73	11	is	is	ADV
ejpam-1871	73	12	,	,	PUNCT
ejpam-1871	73	13	if	if	SCONJ
ejpam-1871	73	14	f	f	X
ejpam-1871	73	15	:	:	PUNCT
ejpam-1871	73	16	a→	a→	PROPN
ejpam-1871	73	17	b	b	NOUN
ejpam-1871	73	18	and	and	CCONJ
ejpam-1871	73	19	g	g	NOUN
ejpam-1871	73	20	:	:	PUNCT
ejpam-1871	73	21	b→	b→	PROPN
ejpam-1871	73	22	c	c	PROPN
ejpam-1871	73	23	belong	belong	VERB
ejpam-1871	73	24	tom	tom	PROPN
ejpam-1871	73	25	,	,	PUNCT
ejpam-1871	73	26	then	then	ADV
ejpam-1871	73	27	g	g	PROPN
ejpam-1871	73	28	f	f	PROPN
ejpam-1871	73	29	also	also	ADV
ejpam-1871	73	30	belongs	belong	VERB
ejpam-1871	73	31	tom	tom	PROPN
ejpam-1871	73	32	.	.	PUNCT
ejpam-1871	74	1	ii	ii	PROPN
ejpam-1871	74	2	)	)	PUNCT
ejpam-1871	74	3	isomorphism	isomorphism	NOUN
ejpam-1871	74	4	closed	close	VERB
ejpam-1871	74	5	;	;	PUNCT
ejpam-1871	74	6	that	that	PRON
ejpam-1871	74	7	is	is	ADV
ejpam-1871	74	8	,	,	PUNCT
ejpam-1871	74	9	it	it	PRON
ejpam-1871	74	10	contains	contain	VERB
ejpam-1871	74	11	all	all	DET
ejpam-1871	74	12	isomorphisms	isomorphism	NOUN
ejpam-1871	74	13	and	and	CCONJ
ejpam-1871	74	14	is	be	AUX
ejpam-1871	74	15	closed	close	VERB
ejpam-1871	74	16	under	under	ADP
ejpam-1871	74	17	composition	composition	NOUN
ejpam-1871	74	18	with	with	ADP
ejpam-1871	74	19	isomorphisms	isomorphism	NOUN
ejpam-1871	74	20	.	.	PUNCT
ejpam-1871	75	1	iii	iii	X
ejpam-1871	75	2	)	)	PUNCT
ejpam-1871	75	3	left	leave	VERB
ejpam-1871	75	4	cancellable	cancellable	ADJ
ejpam-1871	75	5	;	;	PUNCT
ejpam-1871	75	6	that	that	PRON
ejpam-1871	75	7	is	is	ADV
ejpam-1871	75	8	,	,	PUNCT
ejpam-1871	75	9	if	if	SCONJ
ejpam-1871	75	10	g	g	PROPN
ejpam-1871	75	11	f	f	PROPN
ejpam-1871	75	12	∈m	∈m	NOUN
ejpam-1871	75	13	,	,	PUNCT
ejpam-1871	75	14	then	then	ADV
ejpam-1871	75	15	f	f	PROPN
ejpam-1871	75	16	∈m	∈m	NOUN
ejpam-1871	75	17	.	.	PUNCT
ejpam-1871	76	1	proof	proof	NOUN
ejpam-1871	76	2	.	.	PUNCT
ejpam-1871	77	1	sincem	sincem	NOUN
ejpam-1871	77	2	is	be	AUX
ejpam-1871	77	3	in	in	ADP
ejpam-1871	77	4	fact	fact	NOUN
ejpam-1871	77	5	the	the	DET
ejpam-1871	77	6	class	class	NOUN
ejpam-1871	77	7	of	of	ADP
ejpam-1871	77	8	all	all	DET
ejpam-1871	77	9	order	order	NOUN
ejpam-1871	77	10	-	-	PUNCT
ejpam-1871	77	11	embeddings	embedding	NOUN
ejpam-1871	77	12	,	,	PUNCT
ejpam-1871	77	13	the	the	DET
ejpam-1871	77	14	proof	proof	NOUN
ejpam-1871	77	15	is	be	AUX
ejpam-1871	77	16	obvious	obvious	ADJ
ejpam-1871	77	17	.	.	PUNCT
ejpam-1871	78	1	remark	remark	NOUN
ejpam-1871	78	2	1	1	NUM
ejpam-1871	78	3	.	.	PUNCT
ejpam-1871	79	1	for	for	ADP
ejpam-1871	79	2	every	every	DET
ejpam-1871	79	3	pomonoid	pomonoid	NOUN
ejpam-1871	79	4	s	s	PROPN
ejpam-1871	79	5	,	,	PUNCT
ejpam-1871	79	6	the	the	DET
ejpam-1871	79	7	classm	classm	NOUN
ejpam-1871	79	8	is	be	AUX
ejpam-1871	79	9	not	not	PART
ejpam-1871	79	10	right	right	ADV
ejpam-1871	79	11	cancellable	cancellable	ADJ
ejpam-1871	79	12	.	.	PUNCT
ejpam-1871	80	1	for	for	ADP
ejpam-1871	80	2	example	example	NOUN
ejpam-1871	80	3	,	,	PUNCT
ejpam-1871	80	4	consider	consider	VERB
ejpam-1871	80	5	the	the	DET
ejpam-1871	80	6	inclusions	inclusion	NOUN
ejpam-1871	80	7	2	2	NUM
ejpam-1871	80	8	f	f	NOUN
ejpam-1871	80	9	,	,	PUNCT
ejpam-1871	80	10	→	→	SYM
ejpam-1871	80	11	2∪̇1	2∪̇1	NUM
ejpam-1871	80	12	g	g	NOUN
ejpam-1871	80	13	,	,	PUNCT
ejpam-1871	80	14	→	→	SYM
ejpam-1871	80	15	3	3	NUM
ejpam-1871	80	16	with	with	ADP
ejpam-1871	80	17	trivial	trivial	ADJ
ejpam-1871	80	18	actions	action	NOUN
ejpam-1871	80	19	of	of	ADP
ejpam-1871	80	20	a	a	DET
ejpam-1871	80	21	pomonoid	pomonoid	NOUN
ejpam-1871	80	22	s	s	VERB
ejpam-1871	80	23	on	on	ADP
ejpam-1871	80	24	2	2	NUM
ejpam-1871	80	25	,	,	PUNCT
ejpam-1871	80	26	2∪̇1	2∪̇1	NUM
ejpam-1871	80	27	and	and	CCONJ
ejpam-1871	80	28	3	3	NUM
ejpam-1871	80	29	.	.	PUNCT
ejpam-1871	81	1	then	then	ADV
ejpam-1871	81	2	g	g	PROPN
ejpam-1871	81	3	f	f	X
ejpam-1871	81	4	∈m	∈m	NOUN
ejpam-1871	81	5	but	but	CCONJ
ejpam-1871	81	6	g	g	NOUN
ejpam-1871	81	7	is	be	AUX
ejpam-1871	81	8	not	not	PART
ejpam-1871	81	9	inm	inm	PROPN
ejpam-1871	81	10	.	.	PUNCT
ejpam-1871	82	1	also	also	ADV
ejpam-1871	82	2	,	,	PUNCT
ejpam-1871	82	3	for	for	ADP
ejpam-1871	82	4	every	every	DET
ejpam-1871	82	5	pomonoid	pomonoid	NOUN
ejpam-1871	82	6	s	s	PROPN
ejpam-1871	82	7	,	,	PUNCT
ejpam-1871	82	8	there	there	PRON
ejpam-1871	82	9	always	always	ADV
ejpam-1871	82	10	exists	exist	VERB
ejpam-1871	82	11	a	a	DET
ejpam-1871	82	12	monomorphism	monomorphism	NOUN
ejpam-1871	82	13	that	that	PRON
ejpam-1871	82	14	is	be	AUX
ejpam-1871	82	15	not	not	PART
ejpam-1871	82	16	regular	regular	ADJ
ejpam-1871	82	17	.	.	PUNCT
ejpam-1871	83	1	to	to	PART
ejpam-1871	83	2	see	see	VERB
ejpam-1871	83	3	this	this	PRON
ejpam-1871	83	4	,	,	PUNCT
ejpam-1871	83	5	it	it	PRON
ejpam-1871	83	6	suffices	suffice	VERB
ejpam-1871	83	7	to	to	PART
ejpam-1871	83	8	take	take	VERB
ejpam-1871	83	9	the	the	DET
ejpam-1871	83	10	inclusion	inclusion	NOUN
ejpam-1871	84	1	i	i	PRON
ejpam-1871	84	2	:	:	PUNCT
ejpam-1871	84	3	1∪̇1	1∪̇1	NUM
ejpam-1871	84	4	,	,	PUNCT
ejpam-1871	84	5	→	→	SYM
ejpam-1871	84	6	2	2	NUM
ejpam-1871	84	7	with	with	ADP
ejpam-1871	84	8	trivial	trivial	ADJ
ejpam-1871	84	9	actions	action	NOUN
ejpam-1871	84	10	of	of	ADP
ejpam-1871	84	11	a	a	DET
ejpam-1871	84	12	pomonoid	pomonoid	NOUN
ejpam-1871	84	13	s	s	VERB
ejpam-1871	84	14	on	on	ADP
ejpam-1871	84	15	1∪̇1	1∪̇1	NUM
ejpam-1871	84	16	and	and	CCONJ
ejpam-1871	84	17	2	2	NUM
ejpam-1871	84	18	.	.	PUNCT
ejpam-1871	85	1	here	here	ADV
ejpam-1871	85	2	we	we	PRON
ejpam-1871	85	3	investigate	investigate	VERB
ejpam-1871	85	4	the	the	DET
ejpam-1871	85	5	factorization	factorization	NOUN
ejpam-1871	85	6	property	property	NOUN
ejpam-1871	85	7	in	in	ADP
ejpam-1871	85	8	s	s	NOUN
ejpam-1871	85	9	-	-	PUNCT
ejpam-1871	85	10	pos	pos	NOUN
ejpam-1871	85	11	.	.	PUNCT
ejpam-1871	86	1	recall	recall	VERB
ejpam-1871	86	2	that	that	PRON
ejpam-1871	86	3	for	for	ADP
ejpam-1871	86	4	two	two	NUM
ejpam-1871	86	5	morphisms	morphism	NOUN
ejpam-1871	86	6	f	f	NOUN
ejpam-1871	86	7	:	:	PUNCT
ejpam-1871	86	8	a→	a→	PROPN
ejpam-1871	86	9	b	b	NOUN
ejpam-1871	86	10	and	and	CCONJ
ejpam-1871	86	11	g	g	NOUN
ejpam-1871	86	12	:	:	PUNCT
ejpam-1871	86	13	c	c	X
ejpam-1871	86	14	→	→	SYM
ejpam-1871	86	15	d	d	NOUN
ejpam-1871	86	16	in	in	ADP
ejpam-1871	86	17	a	a	DET
ejpam-1871	86	18	category	category	NOUN
ejpam-1871	86	19	c	c	NOUN
ejpam-1871	86	20	,	,	PUNCT
ejpam-1871	86	21	f	f	PROPN
ejpam-1871	86	22	is	be	AUX
ejpam-1871	86	23	called	call	VERB
ejpam-1871	86	24	vertical	vertical	ADJ
ejpam-1871	86	25	on	on	ADP
ejpam-1871	86	26	g	g	PROPN
ejpam-1871	86	27	if	if	SCONJ
ejpam-1871	86	28	for	for	ADP
ejpam-1871	86	29	morphisms	morphisms	ADJ
ejpam-1871	86	30	u	u	NOUN
ejpam-1871	86	31	:	:	PUNCT
ejpam-1871	86	32	a→	a→	PUNCT
ejpam-1871	86	33	c	c	NOUN
ejpam-1871	86	34	and	and	CCONJ
ejpam-1871	86	35	v	v	ADP
ejpam-1871	86	36	:	:	PUNCT
ejpam-1871	86	37	b	b	X
ejpam-1871	86	38	→	→	SYM
ejpam-1871	86	39	d	d	X
ejpam-1871	86	40	which	which	PRON
ejpam-1871	86	41	v	v	NUM
ejpam-1871	86	42	◦	◦	NOUN
ejpam-1871	86	43	f	f	X
ejpam-1871	87	1	=	=	SYM
ejpam-1871	87	2	g	g	PROPN
ejpam-1871	87	3	◦	◦	NOUN
ejpam-1871	87	4	u	u	NOUN
ejpam-1871	87	5	,	,	PUNCT
ejpam-1871	87	6	there	there	PRON
ejpam-1871	87	7	exists	exist	VERB
ejpam-1871	87	8	a	a	DET
ejpam-1871	87	9	unique	unique	ADJ
ejpam-1871	87	10	morphism	morphism	NOUN
ejpam-1871	87	11	w	w	PROPN
ejpam-1871	87	12	:	:	PUNCT
ejpam-1871	87	13	b	b	X
ejpam-1871	87	14	→	→	SYM
ejpam-1871	87	15	c	c	NOUN
ejpam-1871	87	16	such	such	ADJ
ejpam-1871	87	17	that	that	DET
ejpam-1871	87	18	w	w	PROPN
ejpam-1871	87	19	◦	◦	NOUN
ejpam-1871	87	20	f	f	X
ejpam-1871	87	21	=	=	SYM
ejpam-1871	87	22	u	u	PROPN
ejpam-1871	87	23	and	and	CCONJ
ejpam-1871	87	24	g	g	ADP
ejpam-1871	87	25	◦	◦	NOUN
ejpam-1871	87	26	w	w	PROPN
ejpam-1871	87	27	=	=	VERB
ejpam-1871	88	1	v.	v.	ADP
ejpam-1871	88	2	also	also	ADV
ejpam-1871	88	3	a	a	DET
ejpam-1871	88	4	factorization	factorization	NOUN
ejpam-1871	88	5	diagonalization	diagonalization	NOUN
ejpam-1871	88	6	system	system	NOUN
ejpam-1871	88	7	for	for	ADP
ejpam-1871	88	8	c	c	PROPN
ejpam-1871	88	9	,	,	PUNCT
ejpam-1871	88	10	is	be	AUX
ejpam-1871	88	11	a	a	DET
ejpam-1871	88	12	pair	pair	NOUN
ejpam-1871	88	13	(	(	PUNCT
ejpam-1871	88	14	e	e	NOUN
ejpam-1871	88	15	,	,	PUNCT
ejpam-1871	88	16	m	m	PROPN
ejpam-1871	88	17	)	)	PUNCT
ejpam-1871	88	18	where	where	SCONJ
ejpam-1871	88	19	e	e	X
ejpam-1871	88	20	andm	andm	NOUN
ejpam-1871	88	21	are	be	AUX
ejpam-1871	88	22	some	some	DET
ejpam-1871	88	23	classes	class	NOUN
ejpam-1871	88	24	of	of	ADP
ejpam-1871	88	25	morphisms	morphism	NOUN
ejpam-1871	88	26	,	,	PUNCT
ejpam-1871	88	27	with	with	ADP
ejpam-1871	88	28	the	the	DET
ejpam-1871	88	29	following	follow	VERB
ejpam-1871	88	30	properties	property	NOUN
ejpam-1871	88	31	:	:	PUNCT
ejpam-1871	88	32	•	•	NUM
ejpam-1871	88	33	e	e	X
ejpam-1871	88	34	andm	andm	NOUN
ejpam-1871	88	35	are	be	AUX
ejpam-1871	88	36	composition	composition	NOUN
ejpam-1871	88	37	and	and	CCONJ
ejpam-1871	88	38	isomorphism	isomorphism	NOUN
ejpam-1871	88	39	closed	close	VERB
ejpam-1871	88	40	.	.	PUNCT
ejpam-1871	89	1	•	•	NOUN
ejpam-1871	89	2	for	for	ADP
ejpam-1871	89	3	every	every	DET
ejpam-1871	89	4	e	e	NOUN
ejpam-1871	89	5	∈	∈	PROPN
ejpam-1871	89	6	e	e	X
ejpam-1871	89	7	and	and	CCONJ
ejpam-1871	89	8	m	m	PROPN
ejpam-1871	89	9	∈m	∈m	NOUN
ejpam-1871	89	10	,	,	PUNCT
ejpam-1871	89	11	e	e	NOUN
ejpam-1871	89	12	is	be	AUX
ejpam-1871	89	13	vertical	vertical	ADJ
ejpam-1871	89	14	on	on	ADP
ejpam-1871	89	15	m.	m.	NOUN
ejpam-1871	89	16	•	•	NOUN
ejpam-1871	90	1	every	every	DET
ejpam-1871	90	2	morphism	morphism	NOUN
ejpam-1871	90	3	f	f	PROPN
ejpam-1871	90	4	∈	∈	PROPN
ejpam-1871	90	5	c	c	PROPN
ejpam-1871	90	6	has	have	VERB
ejpam-1871	90	7	a	a	DET
ejpam-1871	90	8	factorization	factorization	NOUN
ejpam-1871	90	9	of	of	ADP
ejpam-1871	90	10	the	the	DET
ejpam-1871	90	11	form	form	NOUN
ejpam-1871	90	12	f	f	X
ejpam-1871	90	13	=	=	NOUN
ejpam-1871	91	1	m	m	VERB
ejpam-1871	91	2	◦	◦	NOUN
ejpam-1871	91	3	e	e	NOUN
ejpam-1871	91	4	in	in	ADP
ejpam-1871	91	5	which	which	PRON
ejpam-1871	91	6	m	m	VERB
ejpam-1871	91	7	∈m	∈m	NOUN
ejpam-1871	91	8	and	and	CCONJ
ejpam-1871	91	9	e	e	NOUN
ejpam-1871	91	10	∈	∈	PROPN
ejpam-1871	91	11	e	e	X
ejpam-1871	91	12	.	.	PUNCT
ejpam-1871	92	1	in	in	ADP
ejpam-1871	92	2	this	this	DET
ejpam-1871	92	3	case	case	NOUN
ejpam-1871	92	4	,	,	PUNCT
ejpam-1871	92	5	we	we	PRON
ejpam-1871	92	6	say	say	VERB
ejpam-1871	92	7	that	that	SCONJ
ejpam-1871	92	8	c	c	PROPN
ejpam-1871	92	9	has	have	VERB
ejpam-1871	92	10	(	(	PUNCT
ejpam-1871	92	11	e	e	NOUN
ejpam-1871	92	12	,	,	PUNCT
ejpam-1871	92	13	m	m	NOUN
ejpam-1871	92	14	)	)	PUNCT
ejpam-1871	92	15	-factorization	-factorization	NOUN
ejpam-1871	92	16	diagonalization	diagonalization	NOUN
ejpam-1871	92	17	property	property	NOUN
ejpam-1871	92	18	.	.	PUNCT
ejpam-1871	93	1	to	to	PART
ejpam-1871	93	2	find	find	VERB
ejpam-1871	93	3	a	a	DET
ejpam-1871	93	4	factorization	factorization	NOUN
ejpam-1871	93	5	diagonalization	diagonalization	NOUN
ejpam-1871	93	6	system	system	NOUN
ejpam-1871	93	7	for	for	ADP
ejpam-1871	93	8	s	s	NOUN
ejpam-1871	93	9	-	-	NOUN
ejpam-1871	93	10	posets	poset	NOUN
ejpam-1871	93	11	,	,	PUNCT
ejpam-1871	93	12	we	we	PRON
ejpam-1871	93	13	use	use	VERB
ejpam-1871	93	14	the	the	DET
ejpam-1871	93	15	decomposition	decomposition	NOUN
ejpam-1871	93	16	and	and	CCONJ
ejpam-1871	93	17	first	first	ADJ
ejpam-1871	93	18	isomorphism	isomorphism	NOUN
ejpam-1871	93	19	theorems	theorem	NOUN
ejpam-1871	93	20	(	(	PUNCT
ejpam-1871	93	21	see	see	VERB
ejpam-1871	93	22	[	[	X
ejpam-1871	93	23	7	7	NUM
ejpam-1871	93	24	,	,	PUNCT
ejpam-1871	93	25	proposition	proposition	NOUN
ejpam-1871	93	26	2.3	2.3	NUM
ejpam-1871	93	27	]	]	PUNCT
ejpam-1871	93	28	,	,	PUNCT
ejpam-1871	94	1	[	[	X
ejpam-1871	94	2	8	8	NUM
ejpam-1871	94	3	,	,	PUNCT
ejpam-1871	94	4	theorem	theorem	VERB
ejpam-1871	94	5	1	1	NUM
ejpam-1871	94	6	]	]	PUNCT
ejpam-1871	94	7	)	)	PUNCT
ejpam-1871	94	8	.	.	PUNCT
ejpam-1871	95	1	first	first	ADV
ejpam-1871	95	2	recall	recall	VERB
ejpam-1871	95	3	that	that	SCONJ
ejpam-1871	95	4	for	for	ADP
ejpam-1871	95	5	every	every	DET
ejpam-1871	95	6	s	s	NOUN
ejpam-1871	95	7	-	-	PUNCT
ejpam-1871	95	8	poset	poset	VERB
ejpam-1871	95	9	homomorphism	homomorphism	PROPN
ejpam-1871	95	10	f	f	X
ejpam-1871	95	11	:	:	PUNCT
ejpam-1871	95	12	a→	a→	PROPN
ejpam-1871	95	13	b	b	X
ejpam-1871	95	14	,	,	PUNCT
ejpam-1871	95	15	the	the	DET
ejpam-1871	95	16	subkernel	subkernel	NOUN
ejpam-1871	95	17	of	of	ADP
ejpam-1871	95	18	f	f	PROPN
ejpam-1871	95	19	is	be	AUX
ejpam-1871	95	20	defined	define	VERB
ejpam-1871	95	21	by	by	ADP
ejpam-1871	95	22	k	k	PROPN
ejpam-1871	95	23	f	f	PROPN
ejpam-1871	95	24	=	=	PRON
ejpam-1871	95	25	{	{	PUNCT
ejpam-1871	95	26	(	(	PUNCT
ejpam-1871	95	27	a	a	PRON
ejpam-1871	95	28	,	,	PUNCT
ejpam-1871	95	29	a′	a′	ADJ
ejpam-1871	95	30	)	)	PUNCT
ejpam-1871	95	31	∈	∈	PROPN
ejpam-1871	96	1	a×	a×	PROPN
ejpam-1871	96	2	a|	a|	PROPN
ejpam-1871	96	3	f	f	PROPN
ejpam-1871	96	4	(	(	PUNCT
ejpam-1871	96	5	a)≤	a)≤	PROPN
ejpam-1871	96	6	f	f	X
ejpam-1871	96	7	(	(	PUNCT
ejpam-1871	96	8	a′	a′	PROPN
ejpam-1871	96	9	)	)	PUNCT
ejpam-1871	96	10	}	}	PUNCT
ejpam-1871	96	11	.	.	PUNCT
ejpam-1871	97	1	h.	h.	PROPN
ejpam-1871	97	2	rasouli	rasouli	PROPN
ejpam-1871	97	3	/	/	SYM
ejpam-1871	97	4	eur	eur	PROPN
ejpam-1871	97	5	.	.	PUNCT
ejpam-1871	98	1	j.	j.	PROPN
ejpam-1871	98	2	pure	pure	PROPN
ejpam-1871	98	3	appl	appl	PROPN
ejpam-1871	98	4	.	.	PROPN
ejpam-1871	98	5	math	math	PROPN
ejpam-1871	98	6	,	,	PUNCT
ejpam-1871	98	7	7	7	NUM
ejpam-1871	98	8	(	(	PUNCT
ejpam-1871	98	9	2014	2014	NUM
ejpam-1871	98	10	)	)	PUNCT
ejpam-1871	98	11	,	,	PUNCT
ejpam-1871	98	12	166	166	NUM
ejpam-1871	98	13	-	-	SYM
ejpam-1871	98	14	178	178	NUM
ejpam-1871	98	15	169	169	NUM
ejpam-1871	98	16	proposition	proposition	NOUN
ejpam-1871	98	17	1	1	NUM
ejpam-1871	98	18	.	.	PUNCT
ejpam-1871	99	1	let	let	VERB
ejpam-1871	99	2	e	e	PRON
ejpam-1871	99	3	be	be	AUX
ejpam-1871	99	4	the	the	DET
ejpam-1871	99	5	class	class	NOUN
ejpam-1871	99	6	of	of	ADP
ejpam-1871	99	7	all	all	DET
ejpam-1871	99	8	s	s	NOUN
ejpam-1871	99	9	-	-	PUNCT
ejpam-1871	99	10	poset	poset	VERB
ejpam-1871	99	11	epimorphisms	epimorphism	NOUN
ejpam-1871	99	12	.	.	PUNCT
ejpam-1871	100	1	then	then	ADV
ejpam-1871	100	2	s	s	X
ejpam-1871	100	3	-	-	PUNCT
ejpam-1871	100	4	pos	pos	NOUN
ejpam-1871	100	5	has	have	VERB
ejpam-1871	100	6	(	(	PUNCT
ejpam-1871	100	7	e	e	NOUN
ejpam-1871	100	8	,	,	PUNCT
ejpam-1871	100	9	m	m	NOUN
ejpam-1871	100	10	)	)	PUNCT
ejpam-1871	100	11	-factorization	-factorization	NOUN
ejpam-1871	100	12	diagonalization	diagonalization	NOUN
ejpam-1871	100	13	property	property	NOUN
ejpam-1871	100	14	.	.	PUNCT
ejpam-1871	101	1	proof	proof	NOUN
ejpam-1871	101	2	.	.	PUNCT
ejpam-1871	102	1	first	first	ADV
ejpam-1871	102	2	,	,	PUNCT
ejpam-1871	102	3	notice	notice	VERB
ejpam-1871	102	4	that	that	SCONJ
ejpam-1871	102	5	in	in	ADP
ejpam-1871	102	6	view	view	NOUN
ejpam-1871	102	7	of	of	ADP
ejpam-1871	102	8	lemma	lemma	PROPN
ejpam-1871	102	9	1	1	NUM
ejpam-1871	102	10	,	,	PUNCT
ejpam-1871	102	11	e	e	X
ejpam-1871	102	12	andm	andm	NOUN
ejpam-1871	102	13	are	be	AUX
ejpam-1871	102	14	composition	composition	NOUN
ejpam-1871	102	15	and	and	CCONJ
ejpam-1871	102	16	isomorphism	isomorphism	NOUN
ejpam-1871	102	17	closed	close	VERB
ejpam-1871	102	18	.	.	PUNCT
ejpam-1871	103	1	also	also	ADV
ejpam-1871	103	2	[	[	X
ejpam-1871	103	3	7	7	NUM
ejpam-1871	103	4	,	,	PUNCT
ejpam-1871	103	5	proposition	proposition	NOUN
ejpam-1871	103	6	2.3	2.3	NUM
ejpam-1871	103	7	]	]	PUNCT
ejpam-1871	103	8	implies	imply	VERB
ejpam-1871	103	9	that	that	SCONJ
ejpam-1871	103	10	each	each	DET
ejpam-1871	103	11	s	s	NOUN
ejpam-1871	103	12	-	-	PUNCT
ejpam-1871	103	13	poset	poset	VERB
ejpam-1871	103	14	homomorphism	homomorphism	PROPN
ejpam-1871	103	15	f	f	X
ejpam-1871	103	16	:	:	PUNCT
ejpam-1871	103	17	a→	a→	PROPN
ejpam-1871	103	18	b	b	X
ejpam-1871	103	19	can	can	AUX
ejpam-1871	103	20	be	be	AUX
ejpam-1871	103	21	decomposed	decompose	VERB
ejpam-1871	103	22	as	as	ADP
ejpam-1871	103	23	f	f	PROPN
ejpam-1871	103	24	=	=	SYM
ejpam-1871	103	25	me	me	PROPN
ejpam-1871	103	26	,	,	PUNCT
ejpam-1871	103	27	where	where	SCONJ
ejpam-1871	103	28	e	e	NOUN
ejpam-1871	103	29	=	=	SYM
ejpam-1871	103	30	f	f	PROPN
ejpam-1871	103	31	π	π	X
ejpam-1871	103	32	:	:	PUNCT
ejpam-1871	103	33	a	a	DET
ejpam-1871	103	34	π	π	PROPN
ejpam-1871	103	35	→	→	SYM
ejpam-1871	103	36	a	a	X
ejpam-1871	103	37	/	/	SYM
ejpam-1871	103	38	ker	ker	NOUN
ejpam-1871	103	39	f	f	PROPN
ejpam-1871	103	40	f	f	PROPN
ejpam-1871	103	41	'	'	PUNCT
ejpam-1871	103	42	f	f	X
ejpam-1871	103	43	(	(	PUNCT
ejpam-1871	103	44	a	a	NOUN
ejpam-1871	103	45	)	)	PUNCT
ejpam-1871	103	46	,	,	PUNCT
ejpam-1871	103	47	and	and	CCONJ
ejpam-1871	103	48	m	m	PROPN
ejpam-1871	103	49	=	=	ADJ
ejpam-1871	104	1	i	i	PRON
ejpam-1871	104	2	:	:	PUNCT
ejpam-1871	104	3	f	f	X
ejpam-1871	104	4	(	(	PUNCT
ejpam-1871	104	5	a	a	NOUN
ejpam-1871	104	6	)	)	PUNCT
ejpam-1871	104	7	,	,	PUNCT
ejpam-1871	104	8	→	→	SYM
ejpam-1871	104	9	b.	b.	PROPN
ejpam-1871	104	10	clearly	clearly	ADV
ejpam-1871	104	11	,	,	PUNCT
ejpam-1871	104	12	m	m	VERB
ejpam-1871	104	13	∈m	∈m	NOUN
ejpam-1871	104	14	and	and	CCONJ
ejpam-1871	104	15	e	e	NOUN
ejpam-1871	104	16	∈	∈	PROPN
ejpam-1871	104	17	e	e	X
ejpam-1871	104	18	.	.	PUNCT
ejpam-1871	105	1	now	now	ADV
ejpam-1871	105	2	,	,	PUNCT
ejpam-1871	105	3	we	we	PRON
ejpam-1871	105	4	show	show	VERB
ejpam-1871	105	5	that	that	SCONJ
ejpam-1871	105	6	every	every	DET
ejpam-1871	105	7	e	e	NOUN
ejpam-1871	105	8	∈	∈	PROPN
ejpam-1871	105	9	e	e	NOUN
ejpam-1871	105	10	is	be	AUX
ejpam-1871	105	11	vertical	vertical	ADJ
ejpam-1871	105	12	on	on	ADP
ejpam-1871	105	13	every	every	DET
ejpam-1871	105	14	m	m	NOUN
ejpam-1871	105	15	∈m	∈m	NOUN
ejpam-1871	105	16	.	.	PUNCT
ejpam-1871	106	1	let	let	VERB
ejpam-1871	106	2	u	u	PRON
ejpam-1871	106	3	:	:	PUNCT
ejpam-1871	106	4	a→	a→	PROPN
ejpam-1871	106	5	c	c	NOUN
ejpam-1871	106	6	and	and	CCONJ
ejpam-1871	106	7	v	v	NOUN
ejpam-1871	106	8	:	:	PUNCT
ejpam-1871	106	9	b→	b→	PROPN
ejpam-1871	107	1	d	d	PART
ejpam-1871	107	2	be	be	AUX
ejpam-1871	107	3	some	some	DET
ejpam-1871	107	4	s	s	NOUN
ejpam-1871	107	5	-	-	PUNCT
ejpam-1871	107	6	poset	poset	ADJ
ejpam-1871	107	7	homomorphisms	homomorphism	NOUN
ejpam-1871	107	8	such	such	ADJ
ejpam-1871	107	9	that	that	SCONJ
ejpam-1871	107	10	the	the	DET
ejpam-1871	107	11	following	follow	VERB
ejpam-1871	107	12	diagram	diagram	NOUN
ejpam-1871	107	13	is	be	AUX
ejpam-1871	107	14	commutative	commutative	ADJ
ejpam-1871	107	15	:	:	PUNCT
ejpam-1871	107	16	a	a	DET
ejpam-1871	107	17	u	u	PROPN
ejpam-1871	107	18	�	�	PROPN
ejpam-1871	107	19	�	�	PROPN
ejpam-1871	107	20	e	e	PROPN
ejpam-1871	107	21	//	//	PROPN
ejpam-1871	107	22	b	b	PROPN
ejpam-1871	107	23	v	v	NUM
ejpam-1871	107	24	�	�	PROPN
ejpam-1871	107	25	�	�	PROPN
ejpam-1871	107	26	c	c	PROPN
ejpam-1871	107	27	m	m	PROPN
ejpam-1871	107	28	//	//	NOUN
ejpam-1871	108	1	d	d	NOUN
ejpam-1871	108	2	we	we	PRON
ejpam-1871	108	3	claim	claim	VERB
ejpam-1871	108	4	that	that	SCONJ
ejpam-1871	108	5	ke	ke	PROPN
ejpam-1871	108	6	⊆	⊆	NUM
ejpam-1871	108	7	ku	ku	PROPN
ejpam-1871	108	8	.	.	PROPN
ejpam-1871	108	9	suppose	suppose	VERB
ejpam-1871	108	10	e(a)≤	e(a)≤	PROPN
ejpam-1871	108	11	e(a′	e(a′	PROPN
ejpam-1871	108	12	)	)	PUNCT
ejpam-1871	108	13	,	,	PUNCT
ejpam-1871	108	14	for	for	ADP
ejpam-1871	108	15	a	a	PRON
ejpam-1871	108	16	,	,	PUNCT
ejpam-1871	108	17	a′	a′	PROPN
ejpam-1871	108	18	∈	∈	PROPN
ejpam-1871	108	19	a.	a.	NOUN
ejpam-1871	108	20	then	then	ADV
ejpam-1871	108	21	mu(a	mu(a	NOUN
ejpam-1871	108	22	)	)	PUNCT
ejpam-1871	108	23	=	=	SYM
ejpam-1871	108	24	ve(a)≤	ve(a)≤	NUM
ejpam-1871	108	25	ve(a′	ve(a′	NOUN
ejpam-1871	108	26	)	)	PUNCT
ejpam-1871	108	27	=	=	SYM
ejpam-1871	109	1	mu(a′	mu(a′	NOUN
ejpam-1871	109	2	)	)	PUNCT
ejpam-1871	109	3	.	.	PUNCT
ejpam-1871	110	1	since	since	SCONJ
ejpam-1871	110	2	m	m	PROPN
ejpam-1871	110	3	is	be	AUX
ejpam-1871	110	4	a	a	DET
ejpam-1871	110	5	regular	regular	ADJ
ejpam-1871	110	6	monomorphism	monomorphism	NOUN
ejpam-1871	110	7	,	,	PUNCT
ejpam-1871	110	8	we	we	PRON
ejpam-1871	110	9	get	get	VERB
ejpam-1871	110	10	u(a	u(a	NOUN
ejpam-1871	110	11	)	)	PUNCT
ejpam-1871	110	12	≤	≤	NOUN
ejpam-1871	110	13	u(a′	u(a′	NUM
ejpam-1871	110	14	)	)	PUNCT
ejpam-1871	110	15	,	,	PUNCT
ejpam-1871	110	16	as	as	SCONJ
ejpam-1871	110	17	claimed	claim	VERB
ejpam-1871	110	18	.	.	PUNCT
ejpam-1871	111	1	using	use	VERB
ejpam-1871	111	2	[	[	PUNCT
ejpam-1871	111	3	8	8	NUM
ejpam-1871	111	4	,	,	PUNCT
ejpam-1871	111	5	theorem	theorem	VERB
ejpam-1871	111	6	1	1	NUM
ejpam-1871	111	7	]	]	PUNCT
ejpam-1871	111	8	,	,	PUNCT
ejpam-1871	111	9	there	there	PRON
ejpam-1871	111	10	exists	exist	VERB
ejpam-1871	111	11	a	a	DET
ejpam-1871	111	12	unique	unique	ADJ
ejpam-1871	111	13	d	d	X
ejpam-1871	111	14	:	:	PUNCT
ejpam-1871	111	15	b	b	X
ejpam-1871	111	16	→	→	SYM
ejpam-1871	111	17	c	c	NOUN
ejpam-1871	111	18	such	such	ADJ
ejpam-1871	111	19	that	that	PRON
ejpam-1871	111	20	de	de	PROPN
ejpam-1871	111	21	=	=	SYM
ejpam-1871	111	22	u.	u.	PROPN
ejpam-1871	111	23	also	also	ADV
ejpam-1871	111	24	we	we	PRON
ejpam-1871	111	25	have	have	VERB
ejpam-1871	111	26	mde	mde	PROPN
ejpam-1871	111	27	=	=	SYM
ejpam-1871	111	28	mu	mu	PROPN
ejpam-1871	111	29	=	=	PUNCT
ejpam-1871	111	30	ve	ve	VERB
ejpam-1871	111	31	and	and	CCONJ
ejpam-1871	111	32	hence	hence	ADV
ejpam-1871	111	33	md	md	PROPN
ejpam-1871	111	34	=	=	SYM
ejpam-1871	111	35	v	v	PROPN
ejpam-1871	111	36	because	because	SCONJ
ejpam-1871	111	37	e	e	NOUN
ejpam-1871	111	38	is	be	AUX
ejpam-1871	111	39	an	an	DET
ejpam-1871	111	40	epimorphism	epimorphism	NOUN
ejpam-1871	111	41	.	.	PUNCT
ejpam-1871	112	1	this	this	PRON
ejpam-1871	112	2	completes	complete	VERB
ejpam-1871	112	3	the	the	DET
ejpam-1871	112	4	proof	proof	NOUN
ejpam-1871	112	5	.	.	PUNCT
ejpam-1871	113	1	2.2	2.2	NUM
ejpam-1871	113	2	.	.	PUNCT
ejpam-1871	113	3	limits	limit	NOUN
ejpam-1871	113	4	of	of	ADP
ejpam-1871	113	5	regular	regular	ADJ
ejpam-1871	113	6	monomorphisms	monomorphism	NOUN
ejpam-1871	113	7	in	in	ADP
ejpam-1871	113	8	this	this	DET
ejpam-1871	113	9	subsection	subsection	NOUN
ejpam-1871	113	10	some	some	PRON
ejpam-1871	113	11	of	of	ADP
ejpam-1871	113	12	the	the	DET
ejpam-1871	113	13	categorical	categorical	ADJ
ejpam-1871	113	14	properties	property	NOUN
ejpam-1871	113	15	of	of	ADP
ejpam-1871	113	16	regular	regular	ADJ
ejpam-1871	113	17	monomorphisms	monomorphism	NOUN
ejpam-1871	113	18	related	relate	VERB
ejpam-1871	113	19	to	to	ADP
ejpam-1871	113	20	limits	limit	NOUN
ejpam-1871	113	21	such	such	ADJ
ejpam-1871	113	22	as	as	ADP
ejpam-1871	113	23	products	product	NOUN
ejpam-1871	113	24	and	and	CCONJ
ejpam-1871	113	25	pullbacks	pullback	NOUN
ejpam-1871	113	26	are	be	AUX
ejpam-1871	113	27	studied	study	VERB
ejpam-1871	113	28	.	.	PUNCT
ejpam-1871	114	1	proposition	proposition	NOUN
ejpam-1871	114	2	2	2	NUM
ejpam-1871	114	3	.	.	PUNCT
ejpam-1871	115	1	i	i	PRON
ejpam-1871	115	2	)	)	PUNCT
ejpam-1871	116	1	the	the	DET
ejpam-1871	116	2	classm	classm	PROPN
ejpam-1871	116	3	is	be	AUX
ejpam-1871	116	4	closed	close	VERB
ejpam-1871	116	5	under	under	ADP
ejpam-1871	116	6	products	product	NOUN
ejpam-1871	116	7	.	.	PUNCT
ejpam-1871	117	1	ii	ii	X
ejpam-1871	117	2	)	)	PUNCT
ejpam-1871	117	3	let	let	VERB
ejpam-1871	117	4	{	{	PUNCT
ejpam-1871	117	5	fα	fα	ADP
ejpam-1871	117	6	:	:	PUNCT
ejpam-1871	117	7	a	a	PRON
ejpam-1871	117	8	→	→	X
ejpam-1871	117	9	bα|α	bα|α	PRON
ejpam-1871	117	10	∈	∈	PROPN
ejpam-1871	118	1	i	i	PRON
ejpam-1871	118	2	}	}	PUNCT
ejpam-1871	118	3	be	be	VERB
ejpam-1871	118	4	a	a	DET
ejpam-1871	118	5	family	family	NOUN
ejpam-1871	118	6	of	of	ADP
ejpam-1871	118	7	regular	regular	ADJ
ejpam-1871	118	8	monomorphisms	monomorphism	NOUN
ejpam-1871	118	9	.	.	PUNCT
ejpam-1871	119	1	then	then	ADV
ejpam-1871	119	2	their	their	PRON
ejpam-1871	119	3	product	product	NOUN
ejpam-1871	119	4	homomorphism	homomorphism	NOUN
ejpam-1871	119	5	f	f	X
ejpam-1871	119	6	:	:	PUNCT
ejpam-1871	119	7	a→	a→	PUNCT
ejpam-1871	119	8	∏	∏	NUM
ejpam-1871	119	9	bα	bα	NOUN
ejpam-1871	119	10	is	be	AUX
ejpam-1871	119	11	also	also	ADV
ejpam-1871	119	12	a	a	DET
ejpam-1871	119	13	regular	regular	ADJ
ejpam-1871	119	14	monomorphism	monomorphism	NOUN
ejpam-1871	119	15	.	.	PUNCT
ejpam-1871	120	1	proof	proof	NOUN
ejpam-1871	120	2	.	.	PUNCT
ejpam-1871	121	1	it	it	PRON
ejpam-1871	121	2	is	be	AUX
ejpam-1871	121	3	straightforward	straightforward	ADJ
ejpam-1871	121	4	.	.	PUNCT
ejpam-1871	122	1	proposition	proposition	NOUN
ejpam-1871	122	2	3	3	X
ejpam-1871	122	3	.	.	PUNCT
ejpam-1871	123	1	let	let	VERB
ejpam-1871	123	2	{	{	PUNCT
ejpam-1871	123	3	fα	fα	ADP
ejpam-1871	123	4	:	:	PUNCT
ejpam-1871	123	5	a	a	PRON
ejpam-1871	123	6	→	→	X
ejpam-1871	123	7	bα|α	bα|α	PRON
ejpam-1871	123	8	∈	∈	PROPN
ejpam-1871	124	1	i	i	PRON
ejpam-1871	124	2	}	}	PUNCT
ejpam-1871	124	3	be	be	VERB
ejpam-1871	124	4	a	a	DET
ejpam-1871	124	5	source	source	NOUN
ejpam-1871	124	6	of	of	ADP
ejpam-1871	124	7	regular	regular	ADJ
ejpam-1871	124	8	monomorphisms	monomorphism	NOUN
ejpam-1871	124	9	.	.	PUNCT
ejpam-1871	125	1	then	then	ADV
ejpam-1871	125	2	the	the	DET
ejpam-1871	125	3	homomorphism	homomorphism	PROPN
ejpam-1871	125	4	f	f	X
ejpam-1871	125	5	:	:	PUNCT
ejpam-1871	125	6	a	a	DET
ejpam-1871	125	7	→	→	SYM
ejpam-1871	125	8	l	l	NOUN
ejpam-1871	125	9	im←−bα	im←−bα	PROPN
ejpam-1871	125	10	(	(	PUNCT
ejpam-1871	125	11	existing	exist	VERB
ejpam-1871	125	12	by	by	ADP
ejpam-1871	125	13	the	the	DET
ejpam-1871	125	14	universal	universal	ADJ
ejpam-1871	125	15	property	property	NOUN
ejpam-1871	125	16	of	of	ADP
ejpam-1871	125	17	limits	limit	NOUN
ejpam-1871	125	18	)	)	PUNCT
ejpam-1871	125	19	is	be	AUX
ejpam-1871	125	20	also	also	ADV
ejpam-1871	125	21	a	a	DET
ejpam-1871	125	22	regular	regular	ADJ
ejpam-1871	125	23	monomorphism	monomorphism	NOUN
ejpam-1871	125	24	.	.	PUNCT
ejpam-1871	126	1	proof	proof	NOUN
ejpam-1871	126	2	.	.	PUNCT
ejpam-1871	127	1	let	let	VERB
ejpam-1871	127	2	f	f	PROPN
ejpam-1871	127	3	(	(	PUNCT
ejpam-1871	127	4	a)≤	a)≤	PROPN
ejpam-1871	127	5	f	f	X
ejpam-1871	127	6	(	(	PUNCT
ejpam-1871	127	7	a′	a′	PROPN
ejpam-1871	127	8	)	)	PUNCT
ejpam-1871	127	9	for	for	ADP
ejpam-1871	127	10	some	some	DET
ejpam-1871	127	11	a	a	PRON
ejpam-1871	127	12	,	,	PUNCT
ejpam-1871	127	13	a′	a′	PROPN
ejpam-1871	127	14	∈	∈	PROPN
ejpam-1871	127	15	a.	a.	NOUN
ejpam-1871	127	16	for	for	ADP
ejpam-1871	127	17	every	every	DET
ejpam-1871	127	18	α	α	NOUN
ejpam-1871	127	19	∈	∈	NOUN
ejpam-1871	128	1	i	i	PRON
ejpam-1871	128	2	,	,	PUNCT
ejpam-1871	128	3	we	we	PRON
ejpam-1871	128	4	have	have	VERB
ejpam-1871	128	5	fα(a	fα(a	NOUN
ejpam-1871	128	6	)	)	PUNCT
ejpam-1871	129	1	=	=	PUNCT
ejpam-1871	129	2	πα	πα	PROPN
ejpam-1871	129	3	f	f	PROPN
ejpam-1871	129	4	(	(	PUNCT
ejpam-1871	129	5	a)≤	a)≤	PROPN
ejpam-1871	129	6	πα	πα	PROPN
ejpam-1871	129	7	f	f	PROPN
ejpam-1871	129	8	(	(	PUNCT
ejpam-1871	129	9	a′	a′	PROPN
ejpam-1871	129	10	)	)	PUNCT
ejpam-1871	129	11	=	=	SYM
ejpam-1871	129	12	fα(a	fα(a	NOUN
ejpam-1871	129	13	′	′	NOUN
ejpam-1871	129	14	)	)	PUNCT
ejpam-1871	129	15	,	,	PUNCT
ejpam-1871	129	16	where	where	SCONJ
ejpam-1871	129	17	πα	πα	ADJ
ejpam-1871	129	18	:	:	PUNCT
ejpam-1871	129	19	l	l	PROPN
ejpam-1871	129	20	im←−bα	im←−bα	PROPN
ejpam-1871	129	21	→	→	PUNCT
ejpam-1871	129	22	bα	bα	PROPN
ejpam-1871	129	23	is	be	AUX
ejpam-1871	129	24	a	a	DET
ejpam-1871	129	25	limit	limit	NOUN
ejpam-1871	129	26	morphism	morphism	NOUN
ejpam-1871	129	27	.	.	PUNCT
ejpam-1871	130	1	since	since	SCONJ
ejpam-1871	130	2	fα	fα	ADV
ejpam-1871	130	3	is	be	AUX
ejpam-1871	130	4	a	a	DET
ejpam-1871	130	5	regular	regular	ADJ
ejpam-1871	130	6	monomorphism	monomorphism	NOUN
ejpam-1871	130	7	by	by	ADP
ejpam-1871	130	8	the	the	DET
ejpam-1871	130	9	assumption	assumption	NOUN
ejpam-1871	130	10	,	,	PUNCT
ejpam-1871	130	11	a	a	DET
ejpam-1871	130	12	≤	≤	NOUN
ejpam-1871	130	13	a′.	a′.	NOUN
ejpam-1871	130	14	thus	thus	ADV
ejpam-1871	130	15	f	f	PROPN
ejpam-1871	130	16	is	be	AUX
ejpam-1871	130	17	a	a	DET
ejpam-1871	130	18	regular	regular	ADJ
ejpam-1871	130	19	monomorphism	monomorphism	NOUN
ejpam-1871	130	20	.	.	PUNCT
ejpam-1871	131	1	h.	h.	PROPN
ejpam-1871	131	2	rasouli	rasouli	PROPN
ejpam-1871	131	3	/	/	SYM
ejpam-1871	131	4	eur	eur	PROPN
ejpam-1871	131	5	.	.	PUNCT
ejpam-1871	132	1	j.	j.	PROPN
ejpam-1871	132	2	pure	pure	PROPN
ejpam-1871	132	3	appl	appl	PROPN
ejpam-1871	132	4	.	.	PROPN
ejpam-1871	132	5	math	math	PROPN
ejpam-1871	132	6	,	,	PUNCT
ejpam-1871	132	7	7	7	NUM
ejpam-1871	132	8	(	(	PUNCT
ejpam-1871	132	9	2014	2014	NUM
ejpam-1871	132	10	)	)	PUNCT
ejpam-1871	132	11	,	,	PUNCT
ejpam-1871	132	12	166	166	NUM
ejpam-1871	132	13	-	-	SYM
ejpam-1871	132	14	178	178	NUM
ejpam-1871	132	15	170	170	NUM
ejpam-1871	132	16	the	the	DET
ejpam-1871	132	17	above	above	ADJ
ejpam-1871	132	18	result	result	NOUN
ejpam-1871	132	19	as	as	ADV
ejpam-1871	132	20	well	well	ADV
ejpam-1871	132	21	as	as	ADP
ejpam-1871	132	22	proposition	proposition	NOUN
ejpam-1871	132	23	2	2	NUM
ejpam-1871	132	24	(	(	PUNCT
ejpam-1871	132	25	ii	ii	NOUN
ejpam-1871	132	26	)	)	PUNCT
ejpam-1871	132	27	are	be	AUX
ejpam-1871	132	28	also	also	ADV
ejpam-1871	132	29	true	true	ADJ
ejpam-1871	132	30	whenever	whenever	SCONJ
ejpam-1871	132	31	for	for	ADP
ejpam-1871	132	32	some	some	PRON
ejpam-1871	132	33	(	(	PUNCT
ejpam-1871	132	34	not	not	PART
ejpam-1871	132	35	necessarily	necessarily	ADV
ejpam-1871	132	36	all	all	PRON
ejpam-1871	132	37	)	)	PUNCT
ejpam-1871	133	1	α	α	PRON
ejpam-1871	133	2	∈	∈	PROPN
ejpam-1871	134	1	i	i	PRON
ejpam-1871	134	2	,	,	PUNCT
ejpam-1871	134	3	fα	fα	ADV
ejpam-1871	134	4	is	be	AUX
ejpam-1871	134	5	a	a	DET
ejpam-1871	134	6	regular	regular	ADJ
ejpam-1871	134	7	monomorphism	monomorphism	NOUN
ejpam-1871	134	8	.	.	PUNCT
ejpam-1871	135	1	recall	recall	VERB
ejpam-1871	135	2	that	that	SCONJ
ejpam-1871	135	3	a	a	DET
ejpam-1871	135	4	class	class	NOUN
ejpam-1871	135	5	of	of	ADP
ejpam-1871	135	6	morphisms	morphism	NOUN
ejpam-1871	135	7	of	of	ADP
ejpam-1871	135	8	a	a	DET
ejpam-1871	135	9	category	category	NOUN
ejpam-1871	135	10	is	be	AUX
ejpam-1871	135	11	called	call	VERB
ejpam-1871	135	12	pullback	pullback	NOUN
ejpam-1871	135	13	stable	stable	ADJ
ejpam-1871	135	14	if	if	SCONJ
ejpam-1871	135	15	pullbacks	pullback	NOUN
ejpam-1871	135	16	transfer	transfer	VERB
ejpam-1871	135	17	those	those	DET
ejpam-1871	135	18	morphisms	morphism	NOUN
ejpam-1871	135	19	.	.	PUNCT
ejpam-1871	136	1	in	in	ADP
ejpam-1871	136	2	the	the	DET
ejpam-1871	136	3	next	next	ADJ
ejpam-1871	136	4	result	result	NOUN
ejpam-1871	136	5	,	,	PUNCT
ejpam-1871	136	6	we	we	PRON
ejpam-1871	136	7	study	study	VERB
ejpam-1871	136	8	this	this	DET
ejpam-1871	136	9	property	property	NOUN
ejpam-1871	136	10	for	for	ADP
ejpam-1871	136	11	regular	regular	ADJ
ejpam-1871	136	12	monomorphisms	monomorphism	NOUN
ejpam-1871	136	13	of	of	ADP
ejpam-1871	136	14	s	s	NOUN
ejpam-1871	136	15	-	-	NOUN
ejpam-1871	136	16	posets	poset	NOUN
ejpam-1871	136	17	.	.	PUNCT
ejpam-1871	137	1	proposition	proposition	NOUN
ejpam-1871	137	2	4	4	NUM
ejpam-1871	137	3	.	.	PUNCT
ejpam-1871	138	1	the	the	DET
ejpam-1871	138	2	classm	classm	PROPN
ejpam-1871	138	3	is	be	AUX
ejpam-1871	138	4	pullback	pullback	ADV
ejpam-1871	138	5	stable	stable	ADJ
ejpam-1871	138	6	.	.	PUNCT
ejpam-1871	139	1	proof	proof	NOUN
ejpam-1871	139	2	.	.	PUNCT
ejpam-1871	140	1	consider	consider	VERB
ejpam-1871	140	2	the	the	DET
ejpam-1871	140	3	pullback	pullback	NOUN
ejpam-1871	140	4	diagram	diagram	NOUN
ejpam-1871	140	5	p	p	PROPN
ejpam-1871	140	6	pa	pa	PROPN
ejpam-1871	140	7	�	�	PROPN
ejpam-1871	140	8	�	�	PROPN
ejpam-1871	140	9	pb	pb	ADP
ejpam-1871	140	10	//	//	PROPN
ejpam-1871	140	11	b	b	PROPN
ejpam-1871	140	12	g	g	PROPN
ejpam-1871	140	13	�	�	PROPN
ejpam-1871	140	14	�	�	PROPN
ejpam-1871	140	15	a	a	DET
ejpam-1871	140	16	f	f	PROPN
ejpam-1871	141	1	//	//	X
ejpam-1871	141	2	c	c	PROPN
ejpam-1871	141	3	where	where	SCONJ
ejpam-1871	141	4	p	p	NOUN
ejpam-1871	141	5	is	be	AUX
ejpam-1871	141	6	the	the	DET
ejpam-1871	141	7	sub	sub	NOUN
ejpam-1871	141	8	s	s	NOUN
ejpam-1871	141	9	-	-	PUNCT
ejpam-1871	141	10	poset	poset	ADJ
ejpam-1871	141	11	{	{	PUNCT
ejpam-1871	141	12	(	(	PUNCT
ejpam-1871	141	13	a	a	DET
ejpam-1871	141	14	,	,	PUNCT
ejpam-1871	141	15	b	b	NOUN
ejpam-1871	141	16	)	)	PUNCT
ejpam-1871	141	17	:	:	PUNCT
ejpam-1871	142	1	f	f	X
ejpam-1871	142	2	(	(	PUNCT
ejpam-1871	142	3	a	a	X
ejpam-1871	142	4	)	)	PUNCT
ejpam-1871	142	5	=	=	SYM
ejpam-1871	143	1	g(b	g(b	NOUN
ejpam-1871	143	2	)	)	PUNCT
ejpam-1871	143	3	}	}	PUNCT
ejpam-1871	143	4	of	of	ADP
ejpam-1871	143	5	a×	a×	PROPN
ejpam-1871	143	6	b	b	NOUN
ejpam-1871	143	7	,	,	PUNCT
ejpam-1871	143	8	and	and	CCONJ
ejpam-1871	143	9	pullback	pullback	NOUN
ejpam-1871	143	10	maps	map	NOUN
ejpam-1871	143	11	pa	pa	NOUN
ejpam-1871	143	12	:	:	PUNCT
ejpam-1871	143	13	p	p	X
ejpam-1871	143	14	→	→	SYM
ejpam-1871	143	15	a	a	X
ejpam-1871	143	16	,	,	PUNCT
ejpam-1871	143	17	pb	pb	X
ejpam-1871	143	18	:	:	PUNCT
ejpam-1871	143	19	p	p	X
ejpam-1871	143	20	→	→	SYM
ejpam-1871	143	21	b	b	PROPN
ejpam-1871	143	22	are	be	AUX
ejpam-1871	143	23	restrictions	restriction	NOUN
ejpam-1871	143	24	of	of	ADP
ejpam-1871	143	25	the	the	DET
ejpam-1871	143	26	projection	projection	NOUN
ejpam-1871	143	27	maps	map	NOUN
ejpam-1871	143	28	.	.	PUNCT
ejpam-1871	144	1	assume	assume	VERB
ejpam-1871	144	2	that	that	SCONJ
ejpam-1871	144	3	f	f	PROPN
ejpam-1871	144	4	∈m	∈m	NOUN
ejpam-1871	144	5	.	.	PUNCT
ejpam-1871	145	1	we	we	PRON
ejpam-1871	145	2	show	show	VERB
ejpam-1871	145	3	that	that	SCONJ
ejpam-1871	145	4	pb	pb	ADP
ejpam-1871	145	5	∈m	∈m	NOUN
ejpam-1871	145	6	.	.	PUNCT
ejpam-1871	146	1	let	let	VERB
ejpam-1871	146	2	pb(a	pb(a	NOUN
ejpam-1871	146	3	,	,	PUNCT
ejpam-1871	146	4	b)≤	b)≤	PROPN
ejpam-1871	146	5	pb(a′	pb(a′	NOUN
ejpam-1871	146	6	,	,	PUNCT
ejpam-1871	146	7	b′	b′	NUM
ejpam-1871	146	8	)	)	PUNCT
ejpam-1871	146	9	,	,	PUNCT
ejpam-1871	146	10	for	for	ADP
ejpam-1871	146	11	a	a	PRON
ejpam-1871	146	12	,	,	PUNCT
ejpam-1871	146	13	a′	a′	PROPN
ejpam-1871	146	14	∈	∈	PROPN
ejpam-1871	146	15	a	a	DET
ejpam-1871	146	16	,	,	PUNCT
ejpam-1871	146	17	b	b	NOUN
ejpam-1871	146	18	,	,	PUNCT
ejpam-1871	146	19	b′	b′	NUM
ejpam-1871	146	20	∈	∈	PROPN
ejpam-1871	146	21	b.	b.	NOUN
ejpam-1871	147	1	then	then	ADV
ejpam-1871	147	2	b	b	PROPN
ejpam-1871	147	3	≤	≤	NUM
ejpam-1871	147	4	b′	b′	NUM
ejpam-1871	147	5	and	and	CCONJ
ejpam-1871	147	6	hence	hence	ADV
ejpam-1871	147	7	f	f	X
ejpam-1871	147	8	(	(	PUNCT
ejpam-1871	147	9	a	a	NOUN
ejpam-1871	147	10	)	)	PUNCT
ejpam-1871	147	11	=	=	SYM
ejpam-1871	147	12	g(b)≤	g(b)≤	PROPN
ejpam-1871	147	13	g(b′	g(b′	PROPN
ejpam-1871	147	14	)	)	PUNCT
ejpam-1871	147	15	=	=	SYM
ejpam-1871	147	16	f	f	PROPN
ejpam-1871	147	17	(	(	PUNCT
ejpam-1871	147	18	a′	a′	PROPN
ejpam-1871	147	19	)	)	PUNCT
ejpam-1871	147	20	.	.	PUNCT
ejpam-1871	148	1	this	this	PRON
ejpam-1871	148	2	implies	imply	VERB
ejpam-1871	148	3	a	a	DET
ejpam-1871	148	4	≤	≤	NUM
ejpam-1871	148	5	a′	a′	PROPN
ejpam-1871	148	6	,	,	PUNCT
ejpam-1871	148	7	because	because	SCONJ
ejpam-1871	148	8	f	f	PROPN
ejpam-1871	148	9	is	be	AUX
ejpam-1871	148	10	a	a	DET
ejpam-1871	148	11	regular	regular	ADJ
ejpam-1871	148	12	monomorphism	monomorphism	NOUN
ejpam-1871	148	13	.	.	PUNCT
ejpam-1871	149	1	therefore	therefore	ADV
ejpam-1871	149	2	,	,	PUNCT
ejpam-1871	149	3	(	(	PUNCT
ejpam-1871	149	4	a	a	PRON
ejpam-1871	149	5	,	,	PUNCT
ejpam-1871	149	6	b	b	NOUN
ejpam-1871	149	7	)	)	PUNCT
ejpam-1871	149	8	≤	≤	NOUN
ejpam-1871	149	9	(	(	PUNCT
ejpam-1871	149	10	a′	a′	PROPN
ejpam-1871	149	11	,	,	PUNCT
ejpam-1871	149	12	b′	b′	NUM
ejpam-1871	149	13	)	)	PUNCT
ejpam-1871	149	14	,	,	PUNCT
ejpam-1871	149	15	as	as	SCONJ
ejpam-1871	149	16	required	require	VERB
ejpam-1871	149	17	.	.	PUNCT
ejpam-1871	150	1	2.3	2.3	NUM
ejpam-1871	150	2	.	.	PUNCT
ejpam-1871	150	3	colimits	colimit	NOUN
ejpam-1871	150	4	of	of	ADP
ejpam-1871	150	5	regular	regular	ADJ
ejpam-1871	150	6	monomorphisms	monomorphism	NOUN
ejpam-1871	150	7	in	in	ADP
ejpam-1871	150	8	this	this	DET
ejpam-1871	150	9	subsection	subsection	NOUN
ejpam-1871	150	10	we	we	PRON
ejpam-1871	150	11	investigate	investigate	VERB
ejpam-1871	150	12	the	the	DET
ejpam-1871	150	13	colimit	colimit	NOUN
ejpam-1871	150	14	properties	property	NOUN
ejpam-1871	150	15	,	,	PUNCT
ejpam-1871	150	16	such	such	ADJ
ejpam-1871	150	17	as	as	ADP
ejpam-1871	150	18	coproducts	coproduct	NOUN
ejpam-1871	150	19	,	,	PUNCT
ejpam-1871	150	20	direct	direct	ADJ
ejpam-1871	150	21	sums	sum	NOUN
ejpam-1871	150	22	,	,	PUNCT
ejpam-1871	150	23	pushouts	pushout	NOUN
ejpam-1871	150	24	and	and	CCONJ
ejpam-1871	150	25	directed	direct	VERB
ejpam-1871	150	26	colimits	colimit	NOUN
ejpam-1871	150	27	(	(	PUNCT
ejpam-1871	150	28	direct	direct	ADJ
ejpam-1871	150	29	limits	limit	NOUN
ejpam-1871	150	30	)	)	PUNCT
ejpam-1871	150	31	of	of	ADP
ejpam-1871	150	32	regular	regular	ADJ
ejpam-1871	150	33	monomorphisms	monomorphism	NOUN
ejpam-1871	150	34	.	.	PUNCT
ejpam-1871	151	1	proposition	proposition	NOUN
ejpam-1871	151	2	5	5	NUM
ejpam-1871	151	3	.	.	PUNCT
ejpam-1871	152	1	the	the	DET
ejpam-1871	152	2	classm	classm	PROPN
ejpam-1871	152	3	is	be	AUX
ejpam-1871	152	4	closed	close	VERB
ejpam-1871	152	5	under	under	ADP
ejpam-1871	152	6	coproducts	coproduct	NOUN
ejpam-1871	152	7	and	and	CCONJ
ejpam-1871	152	8	direct	direct	ADJ
ejpam-1871	152	9	sums	sum	NOUN
ejpam-1871	152	10	.	.	PUNCT
ejpam-1871	153	1	proof	proof	NOUN
ejpam-1871	153	2	.	.	PUNCT
ejpam-1871	154	1	assume	assume	VERB
ejpam-1871	154	2	that	that	SCONJ
ejpam-1871	154	3	{	{	PUNCT
ejpam-1871	154	4	fα	fα	NOUN
ejpam-1871	154	5	:	:	PUNCT
ejpam-1871	154	6	aα	aα	NOUN
ejpam-1871	154	7	→	→	SYM
ejpam-1871	154	8	bα|α	bα|α	PRON
ejpam-1871	154	9	∈	∈	PROPN
ejpam-1871	155	1	i	i	PRON
ejpam-1871	155	2	}	}	PUNCT
ejpam-1871	155	3	is	be	AUX
ejpam-1871	155	4	a	a	DET
ejpam-1871	155	5	family	family	NOUN
ejpam-1871	155	6	of	of	ADP
ejpam-1871	155	7	regular	regular	ADJ
ejpam-1871	155	8	monomorphisms	monomorphism	NOUN
ejpam-1871	155	9	and	and	CCONJ
ejpam-1871	155	10	∐	∐	ADV
ejpam-1871	155	11	fα	fα	ADP
ejpam-1871	155	12	:	:	PUNCT
ejpam-1871	155	13	∐	∐	PROPN
ejpam-1871	155	14	aα	aα	NOUN
ejpam-1871	155	15	→	→	SYM
ejpam-1871	155	16	∐	∐	ADJ
ejpam-1871	155	17	bα	bα	PROPN
ejpam-1871	155	18	is	be	AUX
ejpam-1871	155	19	the	the	DET
ejpam-1871	155	20	coproduct	coproduct	NOUN
ejpam-1871	155	21	morphism	morphism	NOUN
ejpam-1871	155	22	(	(	PUNCT
ejpam-1871	155	23	which	which	PRON
ejpam-1871	155	24	uniquely	uniquely	ADV
ejpam-1871	155	25	exists	exist	VERB
ejpam-1871	155	26	by	by	ADP
ejpam-1871	155	27	the	the	DET
ejpam-1871	155	28	universal	universal	ADJ
ejpam-1871	155	29	property	property	NOUN
ejpam-1871	155	30	of	of	ADP
ejpam-1871	155	31	coproducts	coproduct	NOUN
ejpam-1871	155	32	):	):	PUNCT
ejpam-1871	155	33	aα	aα	NOUN
ejpam-1871	155	34	ια	ια	NOUN
ejpam-1871	155	35	�	�	PROPN
ejpam-1871	155	36	�	�	PROPN
ejpam-1871	155	37	fα	fα	ADP
ejpam-1871	155	38	//	//	NUM
ejpam-1871	155	39	bα	bα	PROPN
ejpam-1871	155	40	ι′α	ι′α	PROPN
ejpam-1871	155	41	�	�	PROPN
ejpam-1871	155	42	�	�	PROPN
ejpam-1871	155	43	∐	∐	PROPN
ejpam-1871	155	44	aα	aα	NOUN
ejpam-1871	155	45	∐	∐	ADV
ejpam-1871	155	46	fα	fα	ADP
ejpam-1871	155	47	//	//	NUM
ejpam-1871	155	48	∐	∐	PROPN
ejpam-1871	156	1	bα	bα	VERB
ejpam-1871	157	1	we	we	PRON
ejpam-1871	157	2	show	show	VERB
ejpam-1871	157	3	that	that	SCONJ
ejpam-1871	157	4	∐	∐	ADV
ejpam-1871	157	5	fα	fα	NOUN
ejpam-1871	157	6	is	be	AUX
ejpam-1871	157	7	a	a	DET
ejpam-1871	157	8	regular	regular	ADJ
ejpam-1871	157	9	monomorphism	monomorphism	NOUN
ejpam-1871	157	10	.	.	PUNCT
ejpam-1871	158	1	let	let	VERB
ejpam-1871	158	2	(	(	PUNCT
ejpam-1871	158	3	∐	∐	ADV
ejpam-1871	158	4	fα)(a	fα)(a	PROPN
ejpam-1871	158	5	,	,	PUNCT
ejpam-1871	158	6	α	α	NOUN
ejpam-1871	158	7	)	)	PUNCT
ejpam-1871	158	8	≤	≤	NOUN
ejpam-1871	158	9	(	(	PUNCT
ejpam-1871	158	10	∐	∐	ADV
ejpam-1871	158	11	fα)(a′,α′	fα)(a′,α′	ADJ
ejpam-1871	158	12	)	)	PUNCT
ejpam-1871	158	13	,	,	PUNCT
ejpam-1871	158	14	where	where	SCONJ
ejpam-1871	158	15	a	a	DET
ejpam-1871	158	16	∈	∈	PROPN
ejpam-1871	158	17	aα	aα	NOUN
ejpam-1871	158	18	,	,	PUNCT
ejpam-1871	158	19	a′	a′	PROPN
ejpam-1871	158	20	∈	∈	PROPN
ejpam-1871	158	21	aα′	aα′	NOUN
ejpam-1871	158	22	,	,	PUNCT
ejpam-1871	158	23	α	α	X
ejpam-1871	158	24	,	,	PUNCT
ejpam-1871	158	25	α′	α′	NOUN
ejpam-1871	159	1	∈	∈	NOUN
ejpam-1871	160	1	i	i	PRON
ejpam-1871	160	2	.	.	PUNCT
ejpam-1871	161	1	it	it	PRON
ejpam-1871	161	2	can	can	AUX
ejpam-1871	161	3	be	be	AUX
ejpam-1871	161	4	written	write	VERB
ejpam-1871	161	5	as	as	ADP
ejpam-1871	161	6	(	(	PUNCT
ejpam-1871	161	7	∐	∐	X
ejpam-1871	161	8	fα)ια(a)≤	fα)ια(a)≤	PROPN
ejpam-1871	161	9	(	(	PUNCT
ejpam-1871	161	10	∐	∐	ADJ
ejpam-1871	161	11	fα)ια′(a′	fα)ια′(a′	NOUN
ejpam-1871	161	12	)	)	PUNCT
ejpam-1871	161	13	and	and	CCONJ
ejpam-1871	161	14	by	by	ADP
ejpam-1871	161	15	the	the	DET
ejpam-1871	161	16	commutativity	commutativity	NOUN
ejpam-1871	161	17	of	of	ADP
ejpam-1871	161	18	the	the	DET
ejpam-1871	161	19	diagram	diagram	NOUN
ejpam-1871	161	20	,	,	PUNCT
ejpam-1871	161	21	we	we	PRON
ejpam-1871	161	22	get	get	VERB
ejpam-1871	161	23	(	(	PUNCT
ejpam-1871	161	24	fα(a),α	fα(a),α	PROPN
ejpam-1871	161	25	)	)	PUNCT
ejpam-1871	162	1	=	=	SYM
ejpam-1871	162	2	ι	ι	PROPN
ejpam-1871	162	3	′	′	NUM
ejpam-1871	162	4	α	α	NOUN
ejpam-1871	162	5	fα(a	fα(a	NOUN
ejpam-1871	162	6	)	)	PUNCT
ejpam-1871	162	7	=	=	SYM
ejpam-1871	163	1	(	(	PUNCT
ejpam-1871	163	2	∐	∐	X
ejpam-1871	163	3	fα)ια(a)≤	fα)ια(a)≤	X
ejpam-1871	163	4	(	(	PUNCT
ejpam-1871	163	5	∐	∐	ADV
ejpam-1871	163	6	fα)ια′(a	fα)ια′(a	NOUN
ejpam-1871	163	7	′	′	NUM
ejpam-1871	163	8	)	)	PUNCT
ejpam-1871	163	9	=	=	PRON
ejpam-1871	164	1	ι′α′	ι′α′	VERB
ejpam-1871	164	2	fα′(a	fα′(a	PROPN
ejpam-1871	164	3	′	′	NUM
ejpam-1871	164	4	)	)	PUNCT
ejpam-1871	165	1	=	=	PRON
ejpam-1871	165	2	(	(	PUNCT
ejpam-1871	165	3	fα′(a	fα′(a	PROPN
ejpam-1871	165	4	′),α′	′),α′	PROPN
ejpam-1871	165	5	)	)	PUNCT
ejpam-1871	165	6	;	;	PUNCT
ejpam-1871	165	7	h.	h.	PROPN
ejpam-1871	165	8	rasouli	rasouli	PROPN
ejpam-1871	165	9	/	/	SYM
ejpam-1871	165	10	eur	eur	PROPN
ejpam-1871	165	11	.	.	PUNCT
ejpam-1871	166	1	j.	j.	PROPN
ejpam-1871	166	2	pure	pure	PROPN
ejpam-1871	166	3	appl	appl	PROPN
ejpam-1871	166	4	.	.	PROPN
ejpam-1871	166	5	math	math	PROPN
ejpam-1871	166	6	,	,	PUNCT
ejpam-1871	166	7	7	7	NUM
ejpam-1871	166	8	(	(	PUNCT
ejpam-1871	166	9	2014	2014	NUM
ejpam-1871	166	10	)	)	PUNCT
ejpam-1871	166	11	,	,	PUNCT
ejpam-1871	166	12	166	166	NUM
ejpam-1871	166	13	-	-	SYM
ejpam-1871	166	14	178	178	NUM
ejpam-1871	166	15	171	171	NUM
ejpam-1871	166	16	but	but	CCONJ
ejpam-1871	166	17	this	this	PRON
ejpam-1871	166	18	is	be	AUX
ejpam-1871	166	19	impossible	impossible	ADJ
ejpam-1871	166	20	except	except	SCONJ
ejpam-1871	166	21	α	α	NOUN
ejpam-1871	166	22	=	=	PUNCT
ejpam-1871	166	23	α′	α′	PROPN
ejpam-1871	166	24	and	and	CCONJ
ejpam-1871	166	25	then	then	ADV
ejpam-1871	166	26	fα(a	fα(a	NOUN
ejpam-1871	166	27	)	)	PUNCT
ejpam-1871	166	28	≤	≤	NOUN
ejpam-1871	167	1	fα(a′	fα(a′	NOUN
ejpam-1871	167	2	)	)	PUNCT
ejpam-1871	167	3	.	.	PUNCT
ejpam-1871	168	1	since	since	SCONJ
ejpam-1871	168	2	fα	fα	NOUN
ejpam-1871	168	3	is	be	AUX
ejpam-1871	168	4	order	order	NOUN
ejpam-1871	168	5	-	-	PUNCT
ejpam-1871	168	6	embedding	embed	VERB
ejpam-1871	168	7	,	,	PUNCT
ejpam-1871	168	8	a	a	DET
ejpam-1871	168	9	≤	≤	NUM
ejpam-1871	168	10	a′.	a′.	NOUN
ejpam-1871	168	11	consequently	consequently	ADV
ejpam-1871	168	12	,	,	PUNCT
ejpam-1871	168	13	(	(	PUNCT
ejpam-1871	168	14	a	a	DET
ejpam-1871	168	15	,	,	PUNCT
ejpam-1871	168	16	α	α	NOUN
ejpam-1871	168	17	)	)	PUNCT
ejpam-1871	168	18	=	=	SYM
ejpam-1871	168	19	(	(	PUNCT
ejpam-1871	168	20	a	a	X
ejpam-1871	168	21	,	,	PUNCT
ejpam-1871	168	22	α′)≤	α′)≤	NOUN
ejpam-1871	168	23	(	(	PUNCT
ejpam-1871	168	24	a′,α′	a′,α′	PROPN
ejpam-1871	168	25	)	)	PUNCT
ejpam-1871	168	26	,	,	PUNCT
ejpam-1871	168	27	as	as	SCONJ
ejpam-1871	168	28	claimed	claim	VERB
ejpam-1871	168	29	.	.	PUNCT
ejpam-1871	169	1	for	for	ADP
ejpam-1871	169	2	the	the	DET
ejpam-1871	169	3	second	second	ADJ
ejpam-1871	169	4	part	part	NOUN
ejpam-1871	169	5	,	,	PUNCT
ejpam-1871	169	6	let	let	VERB
ejpam-1871	169	7	{	{	PUNCT
ejpam-1871	169	8	fα	fα	PART
ejpam-1871	169	9	:	:	PUNCT
ejpam-1871	170	1	aα→	aα→	X
ejpam-1871	170	2	bα|α	bα|α	X
ejpam-1871	171	1	∈	∈	PROPN
ejpam-1871	172	1	i	i	PRON
ejpam-1871	172	2	}	}	PUNCT
ejpam-1871	172	3	be	be	VERB
ejpam-1871	172	4	a	a	DET
ejpam-1871	172	5	family	family	NOUN
ejpam-1871	172	6	of	of	ADP
ejpam-1871	172	7	regular	regular	ADJ
ejpam-1871	172	8	monomorphisms	monomorphism	NOUN
ejpam-1871	172	9	such	such	ADJ
ejpam-1871	172	10	that	that	DET
ejpam-1871	172	11	aα	aα	NOUN
ejpam-1871	173	1	and	and	CCONJ
ejpam-1871	173	2	bα	bα	PROPN
ejpam-1871	173	3	have	have	VERB
ejpam-1871	173	4	a	a	DET
ejpam-1871	173	5	unique	unique	ADJ
ejpam-1871	173	6	zero	zero	NUM
ejpam-1871	173	7	element	element	NOUN
ejpam-1871	173	8	,	,	PUNCT
ejpam-1871	173	9	and	and	CCONJ
ejpam-1871	173	10	f	f	X
ejpam-1871	173	11	:	:	PUNCT
ejpam-1871	174	1	⊕	⊕	PROPN
ejpam-1871	174	2	aα	aα	NOUN
ejpam-1871	175	1	→	→	SYM
ejpam-1871	175	2	⊕	⊕	PROPN
ejpam-1871	175	3	bα	bα	PROPN
ejpam-1871	175	4	be	be	AUX
ejpam-1871	175	5	the	the	DET
ejpam-1871	175	6	homomorphism	homomorphism	NOUN
ejpam-1871	175	7	induced	induce	VERB
ejpam-1871	175	8	by	by	ADP
ejpam-1871	175	9	the	the	DET
ejpam-1871	175	10	product	product	NOUN
ejpam-1871	175	11	of	of	ADP
ejpam-1871	175	12	fα	fα	NOUN
ejpam-1871	175	13	’s	’s	NOUN
ejpam-1871	175	14	.	.	PUNCT
ejpam-1871	176	1	in	in	ADP
ejpam-1871	176	2	fact	fact	NOUN
ejpam-1871	176	3	,	,	PUNCT
ejpam-1871	176	4	f	f	PROPN
ejpam-1871	176	5	=	=	SYM
ejpam-1871	176	6	∏	∏	PROPN
ejpam-1871	176	7	fα	fα	ADP
ejpam-1871	176	8	�	�	PROPN
ejpam-1871	176	9	�	�	PROPN
ejpam-1871	176	10	�	�	PROPN
ejpam-1871	176	11	⊕	⊕	PROPN
ejpam-1871	176	12	aα	aα	PROPN
ejpam-1871	176	13	.	.	PUNCT
ejpam-1871	177	1	since	since	SCONJ
ejpam-1871	177	2	∏	∏	NUM
ejpam-1871	177	3	fα	fα	NOUN
ejpam-1871	177	4	is	be	AUX
ejpam-1871	177	5	a	a	DET
ejpam-1871	177	6	regular	regular	ADJ
ejpam-1871	177	7	monomorphism	monomorphism	NOUN
ejpam-1871	177	8	by	by	ADP
ejpam-1871	177	9	propoition	propoition	NOUN
ejpam-1871	177	10	2	2	NUM
ejpam-1871	177	11	,	,	PUNCT
ejpam-1871	177	12	this	this	PRON
ejpam-1871	177	13	clearly	clearly	ADV
ejpam-1871	177	14	implies	imply	VERB
ejpam-1871	177	15	that	that	SCONJ
ejpam-1871	177	16	so	so	ADV
ejpam-1871	177	17	is	be	AUX
ejpam-1871	177	18	f	f	PROPN
ejpam-1871	177	19	.	.	PUNCT
ejpam-1871	178	1	here	here	ADV
ejpam-1871	178	2	we	we	PRON
ejpam-1871	178	3	show	show	VERB
ejpam-1871	178	4	that	that	SCONJ
ejpam-1871	178	5	pushouts	pushout	NOUN
ejpam-1871	178	6	transfer	transfer	VERB
ejpam-1871	178	7	regular	regular	ADJ
ejpam-1871	178	8	monomorphisms	monomorphism	NOUN
ejpam-1871	178	9	in	in	ADP
ejpam-1871	178	10	s	s	NOUN
ejpam-1871	178	11	-	-	PUNCT
ejpam-1871	178	12	pos	pos	NOUN
ejpam-1871	178	13	.	.	PUNCT
ejpam-1871	179	1	theorem	theorem	NOUN
ejpam-1871	179	2	1	1	NUM
ejpam-1871	179	3	.	.	PUNCT
ejpam-1871	179	4	s	s	X
ejpam-1871	179	5	-	-	PUNCT
ejpam-1871	179	6	pos	pos	NOUN
ejpam-1871	179	7	hasm	hasm	NOUN
ejpam-1871	179	8	-transferring	-transferring	NOUN
ejpam-1871	179	9	pushouts	pushout	NOUN
ejpam-1871	179	10	.	.	PUNCT
ejpam-1871	180	1	proof	proof	NOUN
ejpam-1871	180	2	.	.	PUNCT
ejpam-1871	181	1	consider	consider	VERB
ejpam-1871	181	2	the	the	DET
ejpam-1871	181	3	pushout	pushout	NOUN
ejpam-1871	181	4	diagram	diagram	VERB
ejpam-1871	181	5	a	a	DET
ejpam-1871	181	6	g	g	PROPN
ejpam-1871	181	7	�	�	PROPN
ejpam-1871	181	8	�	�	PROPN
ejpam-1871	181	9	f	f	PROPN
ejpam-1871	181	10	//	//	PROPN
ejpam-1871	181	11	b	b	PROPN
ejpam-1871	181	12	qb	qb	PROPN
ejpam-1871	181	13	�	�	PROPN
ejpam-1871	181	14	�	�	PROPN
ejpam-1871	181	15	c	c	PROPN
ejpam-1871	181	16	qc	qc	PROPN
ejpam-1871	181	17	//	//	PROPN
ejpam-1871	181	18	q	q	PROPN
ejpam-1871	181	19	recall	recall	VERB
ejpam-1871	181	20	that	that	PRON
ejpam-1871	181	21	q	q	NOUN
ejpam-1871	182	1	=	=	SYM
ejpam-1871	182	2	(	(	PUNCT
ejpam-1871	182	3	b	b	PROPN
ejpam-1871	182	4	t	t	PROPN
ejpam-1871	182	5	c)/θ	c)/θ	NOUN
ejpam-1871	182	6	(	(	PUNCT
ejpam-1871	182	7	h	h	NOUN
ejpam-1871	182	8	)	)	PUNCT
ejpam-1871	182	9	and	and	CCONJ
ejpam-1871	182	10	θ	θ	PROPN
ejpam-1871	182	11	(	(	PUNCT
ejpam-1871	182	12	h	h	NOUN
ejpam-1871	182	13	)	)	PUNCT
ejpam-1871	182	14	is	be	AUX
ejpam-1871	182	15	the	the	DET
ejpam-1871	182	16	s	s	NOUN
ejpam-1871	182	17	-	-	PUNCT
ejpam-1871	182	18	poset	poset	ADJ
ejpam-1871	182	19	congruence	congruence	NOUN
ejpam-1871	182	20	on	on	ADP
ejpam-1871	182	21	b	b	PROPN
ejpam-1871	182	22	t	t	PROPN
ejpam-1871	182	23	c	c	AUX
ejpam-1871	182	24	generated	generate	VERB
ejpam-1871	182	25	by	by	ADP
ejpam-1871	182	26	h	h	PROPN
ejpam-1871	182	27	=	=	PRON
ejpam-1871	182	28	{	{	PUNCT
ejpam-1871	182	29	(	(	PUNCT
ejpam-1871	182	30	(	(	PUNCT
ejpam-1871	182	31	1	1	NUM
ejpam-1871	182	32	,	,	PUNCT
ejpam-1871	182	33	f	f	PROPN
ejpam-1871	182	34	(	(	PUNCT
ejpam-1871	182	35	a	a	NOUN
ejpam-1871	182	36	)	)	PUNCT
ejpam-1871	182	37	)	)	PUNCT
ejpam-1871	182	38	,	,	PUNCT
ejpam-1871	182	39	(	(	PUNCT
ejpam-1871	182	40	2	2	NUM
ejpam-1871	182	41	,	,	PUNCT
ejpam-1871	182	42	g(a	g(a	PROPN
ejpam-1871	182	43	)	)	PUNCT
ejpam-1871	182	44	)	)	PUNCT
ejpam-1871	182	45	)	)	PUNCT
ejpam-1871	182	46	:	:	PUNCT
ejpam-1871	182	47	a	a	DET
ejpam-1871	182	48	∈	∈	PROPN
ejpam-1871	182	49	a	a	PRON
ejpam-1871	182	50	}	}	PUNCT
ejpam-1871	182	51	,	,	PUNCT
ejpam-1871	182	52	where	where	SCONJ
ejpam-1871	182	53	ib	ib	NOUN
ejpam-1871	182	54	:	:	PUNCT
ejpam-1871	182	55	b	b	X
ejpam-1871	182	56	→	→	SYM
ejpam-1871	182	57	b	b	PROPN
ejpam-1871	182	58	t	t	PROPN
ejpam-1871	182	59	c	c	NOUN
ejpam-1871	182	60	,	,	PUNCT
ejpam-1871	182	61	ic	ic	PROPN
ejpam-1871	182	62	:	:	PUNCT
ejpam-1871	182	63	c	c	X
ejpam-1871	182	64	→	→	SYM
ejpam-1871	182	65	b	b	PROPN
ejpam-1871	182	66	t	t	PROPN
ejpam-1871	182	67	c	c	NOUN
ejpam-1871	182	68	are	be	AUX
ejpam-1871	182	69	the	the	DET
ejpam-1871	182	70	coproduct	coproduct	NOUN
ejpam-1871	182	71	injections	injection	NOUN
ejpam-1871	182	72	given	give	VERB
ejpam-1871	182	73	by	by	ADP
ejpam-1871	182	74	ib(b	ib(b	NOUN
ejpam-1871	182	75	)	)	PUNCT
ejpam-1871	182	76	=	=	SYM
ejpam-1871	182	77	(	(	PUNCT
ejpam-1871	182	78	1	1	NUM
ejpam-1871	182	79	,	,	PUNCT
ejpam-1871	182	80	b	b	NOUN
ejpam-1871	182	81	)	)	PUNCT
ejpam-1871	182	82	and	and	CCONJ
ejpam-1871	182	83	ic(c	ic(c	NUM
ejpam-1871	182	84	)	)	PUNCT
ejpam-1871	183	1	=	=	SYM
ejpam-1871	183	2	(	(	PUNCT
ejpam-1871	183	3	2	2	NUM
ejpam-1871	183	4	,	,	PUNCT
ejpam-1871	183	5	c	c	NOUN
ejpam-1871	183	6	)	)	PUNCT
ejpam-1871	183	7	,	,	PUNCT
ejpam-1871	183	8	for	for	ADP
ejpam-1871	183	9	every	every	DET
ejpam-1871	183	10	b	b	PROPN
ejpam-1871	183	11	∈	∈	PROPN
ejpam-1871	183	12	b	b	PROPN
ejpam-1871	183	13	,	,	PUNCT
ejpam-1871	183	14	c	c	PROPN
ejpam-1871	183	15	∈	∈	PROPN
ejpam-1871	183	16	c	c	X
ejpam-1871	183	17	.	.	PUNCT
ejpam-1871	184	1	also	also	ADV
ejpam-1871	184	2	the	the	DET
ejpam-1871	184	3	pushout	pushout	NOUN
ejpam-1871	184	4	maps	map	NOUN
ejpam-1871	184	5	are	be	AUX
ejpam-1871	184	6	given	give	VERB
ejpam-1871	184	7	as	as	ADP
ejpam-1871	184	8	qc	qc	PROPN
ejpam-1871	184	9	=	=	PUNCT
ejpam-1871	184	10	πic	πic	NOUN
ejpam-1871	184	11	:	:	PUNCT
ejpam-1871	184	12	c	c	X
ejpam-1871	184	13	→	→	SYM
ejpam-1871	184	14	q	q	ADJ
ejpam-1871	184	15	,	,	PUNCT
ejpam-1871	184	16	qb	qb	PROPN
ejpam-1871	184	17	=	=	PUNCT
ejpam-1871	184	18	πib	πib	INTJ
ejpam-1871	184	19	:	:	PUNCT
ejpam-1871	184	20	b	b	X
ejpam-1871	184	21	→	→	SYM
ejpam-1871	184	22	q	q	NOUN
ejpam-1871	184	23	,	,	PUNCT
ejpam-1871	184	24	where	where	SCONJ
ejpam-1871	184	25	π	π	NOUN
ejpam-1871	184	26	:	:	PUNCT
ejpam-1871	184	27	b	b	X
ejpam-1871	184	28	t	t	NOUN
ejpam-1871	184	29	c	c	PROPN
ejpam-1871	184	30	→	→	X
ejpam-1871	184	31	q	q	X
ejpam-1871	184	32	is	be	AUX
ejpam-1871	184	33	the	the	DET
ejpam-1871	184	34	canonical	canonical	ADJ
ejpam-1871	184	35	epimorphism	epimorphism	NOUN
ejpam-1871	184	36	.	.	PUNCT
ejpam-1871	185	1	suppose	suppose	VERB
ejpam-1871	185	2	f	f	PROPN
ejpam-1871	185	3	is	be	AUX
ejpam-1871	185	4	a	a	DET
ejpam-1871	185	5	regular	regular	ADJ
ejpam-1871	185	6	monomorphism	monomorphism	NOUN
ejpam-1871	185	7	.	.	PUNCT
ejpam-1871	186	1	to	to	PART
ejpam-1871	186	2	show	show	VERB
ejpam-1871	186	3	that	that	SCONJ
ejpam-1871	186	4	qc	qc	PROPN
ejpam-1871	186	5	is	be	AUX
ejpam-1871	186	6	a	a	DET
ejpam-1871	186	7	regular	regular	ADJ
ejpam-1871	186	8	monomorphism	monomorphism	NOUN
ejpam-1871	186	9	,	,	PUNCT
ejpam-1871	186	10	let	let	VERB
ejpam-1871	186	11	qc(c)≤	qc(c)≤	VERB
ejpam-1871	186	12	qc(c′	qc(c′	NUM
ejpam-1871	186	13	)	)	PUNCT
ejpam-1871	186	14	,	,	PUNCT
ejpam-1871	186	15	for	for	ADP
ejpam-1871	186	16	c	c	NOUN
ejpam-1871	186	17	,	,	PUNCT
ejpam-1871	186	18	c′	c′	NOUN
ejpam-1871	186	19	∈	∈	PROPN
ejpam-1871	186	20	c	c	NOUN
ejpam-1871	186	21	.	.	PUNCT
ejpam-1871	187	1	thus	thus	ADV
ejpam-1871	187	2	we	we	PRON
ejpam-1871	187	3	have	have	VERB
ejpam-1871	187	4	[	[	X
ejpam-1871	187	5	(	(	PUNCT
ejpam-1871	187	6	2	2	NUM
ejpam-1871	187	7	,	,	PUNCT
ejpam-1871	187	8	c	c	NOUN
ejpam-1871	187	9	)	)	PUNCT
ejpam-1871	187	10	]	]	PUNCT
ejpam-1871	188	1	=	=	SYM
ejpam-1871	188	2	πic(c	πic(c	NOUN
ejpam-1871	188	3	)	)	PUNCT
ejpam-1871	188	4	=	=	SYM
ejpam-1871	188	5	qc(c)≤	qc(c)≤	NOUN
ejpam-1871	188	6	qc(c	qc(c	NOUN
ejpam-1871	188	7	′	′	NOUN
ejpam-1871	188	8	)	)	PUNCT
ejpam-1871	189	1	=	=	SYM
ejpam-1871	189	2	πic(c	πic(c	PROPN
ejpam-1871	189	3	′	′	NOUN
ejpam-1871	189	4	)	)	PUNCT
ejpam-1871	189	5	=	=	PUNCT
ejpam-1871	190	1	[	[	X
ejpam-1871	190	2	(	(	PUNCT
ejpam-1871	190	3	2	2	NUM
ejpam-1871	190	4	,	,	PUNCT
ejpam-1871	190	5	c′	c′	NUM
ejpam-1871	190	6	)	)	PUNCT
ejpam-1871	190	7	]	]	PUNCT
ejpam-1871	190	8	.	.	PUNCT
ejpam-1871	191	1	then	then	ADV
ejpam-1871	191	2	,	,	PUNCT
ejpam-1871	191	3	by	by	ADP
ejpam-1871	191	4	[	[	X
ejpam-1871	191	5	15	15	NUM
ejpam-1871	191	6	,	,	PUNCT
ejpam-1871	191	7	proposition	proposition	NOUN
ejpam-1871	191	8	3.3	3.3	NUM
ejpam-1871	191	9	]	]	PUNCT
ejpam-1871	191	10	,	,	PUNCT
ejpam-1871	191	11	we	we	PRON
ejpam-1871	191	12	get	get	VERB
ejpam-1871	191	13	(	(	PUNCT
ejpam-1871	191	14	2	2	NUM
ejpam-1871	191	15	,	,	PUNCT
ejpam-1871	191	16	c	c	NOUN
ejpam-1871	191	17	)	)	PUNCT
ejpam-1871	191	18	≤	≤	NOUN
ejpam-1871	191	19	(	(	PUNCT
ejpam-1871	191	20	2	2	NUM
ejpam-1871	191	21	,	,	PUNCT
ejpam-1871	191	22	c′	c′	NUM
ejpam-1871	191	23	)	)	PUNCT
ejpam-1871	191	24	(	(	PUNCT
ejpam-1871	191	25	and	and	CCONJ
ejpam-1871	191	26	hence	hence	ADV
ejpam-1871	191	27	c	c	X
ejpam-1871	191	28	≤	≤	NUM
ejpam-1871	191	29	c′	c′	NOUN
ejpam-1871	191	30	)	)	PUNCT
ejpam-1871	191	31	or	or	CCONJ
ejpam-1871	191	32	there	there	PRON
ejpam-1871	191	33	exist	exist	VERB
ejpam-1871	191	34	s1	s1	NOUN
ejpam-1871	191	35	,	,	PUNCT
ejpam-1871	191	36	s2	s2	NOUN
ejpam-1871	191	37	,	,	PUNCT
ejpam-1871	191	38	.	.	PUNCT
ejpam-1871	191	39	.	.	PUNCT
ejpam-1871	191	40	.	.	PUNCT
ejpam-1871	192	1	,	,	PUNCT
ejpam-1871	192	2	sn	sn	PROPN
ejpam-1871	192	3	∈	∈	PROPN
ejpam-1871	192	4	s	s	VERB
ejpam-1871	192	5	such	such	ADJ
ejpam-1871	192	6	that	that	SCONJ
ejpam-1871	192	7	(	(	PUNCT
ejpam-1871	192	8	2	2	NUM
ejpam-1871	192	9	,	,	PUNCT
ejpam-1871	192	10	c)≤	c)≤	NOUN
ejpam-1871	192	11	s1c1	s1c1	NOUN
ejpam-1871	192	12	,	,	PUNCT
ejpam-1871	192	13	s1d1	s1d1	NOUN
ejpam-1871	192	14	≤	≤	NOUN
ejpam-1871	192	15	s2c2	s2c2	NOUN
ejpam-1871	192	16	,	,	PUNCT
ejpam-1871	192	17	s2d2	s2d2	NOUN
ejpam-1871	192	18	≤	≤	NUM
ejpam-1871	192	19	s3c3	s3c3	NOUN
ejpam-1871	192	20	,	,	PUNCT
ejpam-1871	192	21	.	.	PUNCT
ejpam-1871	192	22	.	.	PUNCT
ejpam-1871	192	23	.	.	PUNCT
ejpam-1871	193	1	,	,	PUNCT
ejpam-1871	193	2	sndn	sndn	ADJ
ejpam-1871	193	3	≤	≤	NOUN
ejpam-1871	193	4	(	(	PUNCT
ejpam-1871	193	5	2	2	NUM
ejpam-1871	193	6	,	,	PUNCT
ejpam-1871	193	7	c′	c′	NUM
ejpam-1871	193	8	)	)	PUNCT
ejpam-1871	193	9	,	,	PUNCT
ejpam-1871	193	10	where	where	SCONJ
ejpam-1871	193	11	(	(	PUNCT
ejpam-1871	193	12	ci	ci	NOUN
ejpam-1871	193	13	,	,	PUNCT
ejpam-1871	193	14	di	di	NOUN
ejpam-1871	193	15	)	)	PUNCT
ejpam-1871	193	16	∈	∈	PROPN
ejpam-1871	193	17	h	h	NOUN
ejpam-1871	193	18	∪h−1	∪h−1	PUNCT
ejpam-1871	193	19	for	for	ADP
ejpam-1871	193	20	i	i	X
ejpam-1871	193	21	=	=	SYM
ejpam-1871	193	22	1,2	1,2	NUM
ejpam-1871	193	23	,	,	PUNCT
ejpam-1871	193	24	.	.	PUNCT
ejpam-1871	193	25	.	.	PUNCT
ejpam-1871	194	1	.	.	PUNCT
ejpam-1871	195	1	,	,	PUNCT
ejpam-1871	195	2	n.	n.	PROPN
ejpam-1871	195	3	it	it	PRON
ejpam-1871	195	4	follows	follow	VERB
ejpam-1871	195	5	that	that	SCONJ
ejpam-1871	195	6	there	there	PRON
ejpam-1871	195	7	exist	exist	VERB
ejpam-1871	195	8	a1	a1	NOUN
ejpam-1871	195	9	,	,	PUNCT
ejpam-1871	195	10	.	.	PUNCT
ejpam-1871	195	11	.	.	PUNCT
ejpam-1871	196	1	.	.	PUNCT
ejpam-1871	197	1	,	,	PUNCT
ejpam-1871	197	2	an	an	DET
ejpam-1871	197	3	∈	∈	PROPN
ejpam-1871	197	4	a	a	DET
ejpam-1871	197	5	such	such	ADJ
ejpam-1871	197	6	that	that	SCONJ
ejpam-1871	197	7	(	(	PUNCT
ejpam-1871	197	8	2	2	NUM
ejpam-1871	197	9	,	,	PUNCT
ejpam-1871	197	10	c)≤	c)≤	PROPN
ejpam-1871	197	11	s1(2	s1(2	PROPN
ejpam-1871	197	12	,	,	PUNCT
ejpam-1871	197	13	g(a1	g(a1	NOUN
ejpam-1871	197	14	)	)	PUNCT
ejpam-1871	197	15	)	)	PUNCT
ejpam-1871	197	16	,	,	PUNCT
ejpam-1871	197	17	s1(1	s1(1	PROPN
ejpam-1871	197	18	,	,	PUNCT
ejpam-1871	197	19	f	f	X
ejpam-1871	197	20	(	(	PUNCT
ejpam-1871	197	21	a1))≤	a1))≤	X
ejpam-1871	197	22	s2(1	s2(1	NOUN
ejpam-1871	197	23	,	,	PUNCT
ejpam-1871	197	24	f	f	PROPN
ejpam-1871	197	25	(	(	PUNCT
ejpam-1871	197	26	a2	a2	PROPN
ejpam-1871	197	27	)	)	PUNCT
ejpam-1871	197	28	)	)	PUNCT
ejpam-1871	197	29	,	,	PUNCT
ejpam-1871	197	30	s2(2	s2(2	NOUN
ejpam-1871	197	31	,	,	PUNCT
ejpam-1871	197	32	g(a2))≤	g(a2))≤	ADJ
ejpam-1871	197	33	s3(2	s3(2	NOUN
ejpam-1871	197	34	,	,	PUNCT
ejpam-1871	197	35	g(a3	g(a3	NOUN
ejpam-1871	197	36	)	)	PUNCT
ejpam-1871	197	37	)	)	PUNCT
ejpam-1871	197	38	,	,	PUNCT
ejpam-1871	197	39	.	.	PUNCT
ejpam-1871	197	40	.	.	PUNCT
ejpam-1871	198	1	.	.	PUNCT
ejpam-1871	199	1	,	,	PUNCT
ejpam-1871	199	2	sn−1(1	sn−1(1	X
ejpam-1871	199	3	,	,	PUNCT
ejpam-1871	199	4	f	f	X
ejpam-1871	199	5	(	(	PUNCT
ejpam-1871	199	6	an−1))≤	an−1))≤	ADV
ejpam-1871	199	7	sn(1	sn(1	NOUN
ejpam-1871	199	8	,	,	PUNCT
ejpam-1871	199	9	f	f	PROPN
ejpam-1871	199	10	(	(	PUNCT
ejpam-1871	199	11	an	an	PROPN
ejpam-1871	199	12	)	)	PUNCT
ejpam-1871	199	13	)	)	PUNCT
ejpam-1871	199	14	,	,	PUNCT
ejpam-1871	199	15	sn(2	sn(2	NOUN
ejpam-1871	199	16	,	,	PUNCT
ejpam-1871	199	17	g(an))≤	g(an))≤	PROPN
ejpam-1871	199	18	(	(	PUNCT
ejpam-1871	199	19	2	2	NUM
ejpam-1871	199	20	,	,	PUNCT
ejpam-1871	199	21	c′	c′	NUM
ejpam-1871	199	22	)	)	PUNCT
ejpam-1871	199	23	.	.	PUNCT
ejpam-1871	200	1	this	this	PRON
ejpam-1871	200	2	gives	give	VERB
ejpam-1871	200	3	the	the	DET
ejpam-1871	200	4	following	following	NOUN
ejpam-1871	200	5	:	:	PUNCT
ejpam-1871	200	6	c	c	PROPN
ejpam-1871	200	7	≤	≤	PROPN
ejpam-1871	200	8	g(s1a1	g(s1a1	PROPN
ejpam-1871	200	9	)	)	PUNCT
ejpam-1871	200	10	,	,	PUNCT
ejpam-1871	200	11	f	f	PROPN
ejpam-1871	201	1	(	(	PUNCT
ejpam-1871	201	2	s1a1)≤	s1a1)≤	PROPN
ejpam-1871	201	3	f	f	X
ejpam-1871	201	4	(	(	PUNCT
ejpam-1871	201	5	s2a2	s2a2	NOUN
ejpam-1871	201	6	)	)	PUNCT
ejpam-1871	201	7	,	,	PUNCT
ejpam-1871	201	8	g(s2a2)≤	g(s2a2)≤	PROPN
ejpam-1871	201	9	g(s3a3	g(s3a3	PROPN
ejpam-1871	201	10	)	)	PUNCT
ejpam-1871	201	11	,	,	PUNCT
ejpam-1871	201	12	.	.	PUNCT
ejpam-1871	201	13	.	.	PUNCT
ejpam-1871	201	14	.	.	PUNCT
ejpam-1871	202	1	,	,	PUNCT
ejpam-1871	202	2	f	f	PROPN
ejpam-1871	202	3	(	(	PUNCT
ejpam-1871	202	4	sn−1an−1)≤	sn−1an−1)≤	PROPN
ejpam-1871	202	5	f	f	X
ejpam-1871	202	6	(	(	PUNCT
ejpam-1871	202	7	snan	snan	PROPN
ejpam-1871	202	8	)	)	PUNCT
ejpam-1871	202	9	,	,	PUNCT
ejpam-1871	202	10	g(snan)≤	g(snan)≤	NOUN
ejpam-1871	202	11	c′.	c′.	VERB
ejpam-1871	202	12	since	since	SCONJ
ejpam-1871	202	13	f	f	PROPN
ejpam-1871	202	14	is	be	AUX
ejpam-1871	202	15	a	a	DET
ejpam-1871	202	16	regular	regular	ADJ
ejpam-1871	202	17	monomorphism	monomorphism	NOUN
ejpam-1871	202	18	,	,	PUNCT
ejpam-1871	202	19	s1a1	s1a1	PROPN
ejpam-1871	202	20	≤	≤	PROPN
ejpam-1871	202	21	s2a2	s2a2	NOUN
ejpam-1871	202	22	,	,	PUNCT
ejpam-1871	202	23	s3a3	s3a3	VERB
ejpam-1871	202	24	≤	≤	NOUN
ejpam-1871	202	25	s4a4	s4a4	NOUN
ejpam-1871	202	26	,	,	PUNCT
ejpam-1871	202	27	.	.	PUNCT
ejpam-1871	202	28	.	.	PUNCT
ejpam-1871	203	1	.	.	PUNCT
ejpam-1871	204	1	,	,	PUNCT
ejpam-1871	204	2	sn−1an−1	sn−1an−1	PROPN
ejpam-1871	204	3	≤	≤	NUM
ejpam-1871	204	4	snan	snan	NOUN
ejpam-1871	204	5	.	.	PUNCT
ejpam-1871	205	1	h.	h.	PROPN
ejpam-1871	205	2	rasouli	rasouli	PROPN
ejpam-1871	205	3	/	/	SYM
ejpam-1871	205	4	eur	eur	PROPN
ejpam-1871	205	5	.	.	PUNCT
ejpam-1871	206	1	j.	j.	PROPN
ejpam-1871	206	2	pure	pure	PROPN
ejpam-1871	206	3	appl	appl	PROPN
ejpam-1871	206	4	.	.	PROPN
ejpam-1871	206	5	math	math	PROPN
ejpam-1871	206	6	,	,	PUNCT
ejpam-1871	206	7	7	7	NUM
ejpam-1871	206	8	(	(	PUNCT
ejpam-1871	206	9	2014	2014	NUM
ejpam-1871	206	10	)	)	PUNCT
ejpam-1871	206	11	,	,	PUNCT
ejpam-1871	206	12	166	166	NUM
ejpam-1871	206	13	-	-	SYM
ejpam-1871	206	14	178	178	NUM
ejpam-1871	206	15	172	172	NUM
ejpam-1871	206	16	hence	hence	ADV
ejpam-1871	206	17	,	,	PUNCT
ejpam-1871	206	18	we	we	PRON
ejpam-1871	206	19	get	get	VERB
ejpam-1871	206	20	c	c	NOUN
ejpam-1871	206	21	≤	≤	NUM
ejpam-1871	207	1	g(s1a1)≤	g(s1a1)≤	INTJ
ejpam-1871	207	2	g(s2a2)≤	g(s2a2)≤	NOUN
ejpam-1871	207	3	g(s3a3)≤	g(s3a3)≤	VERB
ejpam-1871	207	4	.	.	PUNCT
ejpam-1871	207	5	.	.	PUNCT
ejpam-1871	208	1	.≤	.≤	PUNCT
ejpam-1871	209	1	g(sn−1an−1)≤	g(sn−1an−1)≤	PROPN
ejpam-1871	209	2	g(snan)≤	g(snan)≤	NOUN
ejpam-1871	209	3	c′.	c′.	NOUN
ejpam-1871	209	4	for	for	ADP
ejpam-1871	209	5	a	a	DET
ejpam-1871	209	6	class	class	NOUN
ejpam-1871	209	7	e	e	NOUN
ejpam-1871	209	8	of	of	ADP
ejpam-1871	209	9	morphisms	morphism	NOUN
ejpam-1871	209	10	of	of	ADP
ejpam-1871	209	11	a	a	DET
ejpam-1871	209	12	category	category	NOUN
ejpam-1871	209	13	,	,	PUNCT
ejpam-1871	209	14	we	we	PRON
ejpam-1871	209	15	say	say	VERB
ejpam-1871	209	16	that	that	SCONJ
ejpam-1871	209	17	multiple	multiple	ADJ
ejpam-1871	209	18	pushouts	pushout	NOUN
ejpam-1871	209	19	transfer	transfer	NOUN
ejpam-1871	209	20	e	e	NOUN
ejpam-1871	209	21	-morphisms	-morphism	NOUN
ejpam-1871	209	22	if	if	SCONJ
ejpam-1871	209	23	in	in	ADP
ejpam-1871	209	24	the	the	DET
ejpam-1871	209	25	multiple	multiple	ADJ
ejpam-1871	209	26	pushout	pushout	NOUN
ejpam-1871	209	27	(	(	PUNCT
ejpam-1871	209	28	q	q	NOUN
ejpam-1871	209	29	,	,	PUNCT
ejpam-1871	209	30	(	(	PUNCT
ejpam-1871	209	31	aα	aα	NOUN
ejpam-1871	209	32	qα→	qα→	PROPN
ejpam-1871	209	33	q)α∈i	q)α∈i	PROPN
ejpam-1871	209	34	)	)	PUNCT
ejpam-1871	209	35	of	of	ADP
ejpam-1871	209	36	a	a	DET
ejpam-1871	209	37	family	family	NOUN
ejpam-1871	209	38	{	{	PUNCT
ejpam-1871	209	39	fα	fα	ADP
ejpam-1871	209	40	:	:	PUNCT
ejpam-1871	209	41	a→	a→	X
ejpam-1871	210	1	aα|α	aα|α	ADV
ejpam-1871	210	2	∈	∈	PROPN
ejpam-1871	210	3	i	i	PRON
ejpam-1871	210	4	}	}	PUNCT
ejpam-1871	210	5	of	of	ADP
ejpam-1871	210	6	e	e	PROPN
ejpam-1871	210	7	-morphisms	-morphism	NOUN
ejpam-1871	210	8	,	,	PUNCT
ejpam-1871	210	9	qα	qα	PROPN
ejpam-1871	210	10	∈	∈	PROPN
ejpam-1871	210	11	e	e	PROPN
ejpam-1871	210	12	,	,	PUNCT
ejpam-1871	210	13	for	for	ADP
ejpam-1871	210	14	every	every	DET
ejpam-1871	210	15	α	α	NOUN
ejpam-1871	210	16	∈	∈	NOUN
ejpam-1871	211	1	i	i	PRON
ejpam-1871	211	2	.	.	PUNCT
ejpam-1871	212	1	analogously	analogously	ADV
ejpam-1871	212	2	to	to	ADP
ejpam-1871	212	3	the	the	DET
ejpam-1871	212	4	pushouts	pushout	NOUN
ejpam-1871	212	5	,	,	PUNCT
ejpam-1871	212	6	the	the	DET
ejpam-1871	212	7	following	following	ADJ
ejpam-1871	212	8	result	result	NOUN
ejpam-1871	212	9	is	be	AUX
ejpam-1871	212	10	obtained	obtain	VERB
ejpam-1871	212	11	.	.	PUNCT
ejpam-1871	213	1	theorem	theorem	VERB
ejpam-1871	213	2	2	2	NUM
ejpam-1871	213	3	.	.	PUNCT
ejpam-1871	213	4	multiple	multiple	ADJ
ejpam-1871	213	5	pushouts	pushout	NOUN
ejpam-1871	213	6	transfer	transfer	VERB
ejpam-1871	213	7	regular	regular	ADJ
ejpam-1871	213	8	monomorphisms	monomorphism	NOUN
ejpam-1871	213	9	.	.	PUNCT
ejpam-1871	214	1	proof	proof	NOUN
ejpam-1871	214	2	.	.	PUNCT
ejpam-1871	215	1	assume	assume	VERB
ejpam-1871	215	2	that	that	SCONJ
ejpam-1871	215	3	(	(	PUNCT
ejpam-1871	215	4	q	q	X
ejpam-1871	215	5	,	,	PUNCT
ejpam-1871	215	6	(	(	PUNCT
ejpam-1871	215	7	aα	aα	NOUN
ejpam-1871	215	8	qα→q)α∈i	qα→q)α∈i	NOUN
ejpam-1871	215	9	)	)	PUNCT
ejpam-1871	215	10	is	be	AUX
ejpam-1871	215	11	the	the	DET
ejpam-1871	215	12	multiple	multiple	ADJ
ejpam-1871	215	13	pushout	pushout	NOUN
ejpam-1871	215	14	of	of	ADP
ejpam-1871	215	15	a	a	DET
ejpam-1871	215	16	family	family	NOUN
ejpam-1871	215	17	{	{	PUNCT
ejpam-1871	215	18	fα	fα	ADP
ejpam-1871	215	19	:	:	PUNCT
ejpam-1871	215	20	a→	a→	X
ejpam-1871	216	1	aα|α	aα|α	ADV
ejpam-1871	216	2	∈	∈	PROPN
ejpam-1871	216	3	i	i	X
ejpam-1871	216	4	}	}	PUNCT
ejpam-1871	216	5	of	of	ADP
ejpam-1871	216	6	regular	regular	ADJ
ejpam-1871	216	7	monomorphisms	monomorphism	NOUN
ejpam-1871	216	8	.	.	PUNCT
ejpam-1871	217	1	recall	recall	VERB
ejpam-1871	217	2	that	that	PRON
ejpam-1871	217	3	q	q	NOUN
ejpam-1871	218	1	=	=	PRON
ejpam-1871	218	2	(	(	PUNCT
ejpam-1871	218	3	∐	∐	ADV
ejpam-1871	218	4	aα)/θ	aα)/θ	PROPN
ejpam-1871	218	5	(	(	PUNCT
ejpam-1871	218	6	h	h	NOUN
ejpam-1871	218	7	)	)	PUNCT
ejpam-1871	218	8	,	,	PUNCT
ejpam-1871	218	9	where	where	SCONJ
ejpam-1871	218	10	θ	θ	PROPN
ejpam-1871	218	11	(	(	PUNCT
ejpam-1871	218	12	h	h	NOUN
ejpam-1871	218	13	)	)	PUNCT
ejpam-1871	218	14	is	be	AUX
ejpam-1871	218	15	the	the	DET
ejpam-1871	218	16	s	s	NOUN
ejpam-1871	218	17	-	-	PUNCT
ejpam-1871	218	18	poset	poset	ADJ
ejpam-1871	218	19	congruence	congruence	NOUN
ejpam-1871	218	20	on	on	ADP
ejpam-1871	218	21	∐	∐	PROPN
ejpam-1871	218	22	aα	aα	PROPN
ejpam-1871	218	23	generated	generate	VERB
ejpam-1871	218	24	by	by	ADP
ejpam-1871	218	25	h	h	PROPN
ejpam-1871	218	26	=	=	SYM
ejpam-1871	218	27	{	{	PUNCT
ejpam-1871	218	28	(	(	PUNCT
ejpam-1871	218	29	iα	iα	NOUN
ejpam-1871	218	30	(	(	PUNCT
ejpam-1871	218	31	fα(a	fα(a	NOUN
ejpam-1871	218	32	)	)	PUNCT
ejpam-1871	218	33	)	)	PUNCT
ejpam-1871	218	34	,	,	PUNCT
ejpam-1871	218	35	iβ	iβ	ADP
ejpam-1871	218	36	(	(	PUNCT
ejpam-1871	218	37	fβ(a)))|a	fβ(a)))|a	PROPN
ejpam-1871	218	38	∈	∈	PROPN
ejpam-1871	218	39	a	a	DET
ejpam-1871	218	40	,	,	PUNCT
ejpam-1871	218	41	α	α	X
ejpam-1871	218	42	,	,	PUNCT
ejpam-1871	218	43	β	β	X
ejpam-1871	218	44	∈	∈	PROPN
ejpam-1871	218	45	i	i	X
ejpam-1871	218	46	}	}	PUNCT
ejpam-1871	218	47	,	,	PUNCT
ejpam-1871	218	48	and	and	CCONJ
ejpam-1871	218	49	qα	qα	PROPN
ejpam-1871	218	50	=	=	SYM
ejpam-1871	218	51	πiα	πiα	PROPN
ejpam-1871	218	52	,	,	PUNCT
ejpam-1871	218	53	where	where	SCONJ
ejpam-1871	218	54	π	π	X
ejpam-1871	218	55	:	:	PUNCT
ejpam-1871	218	56	∐	∐	PROPN
ejpam-1871	218	57	aα	aα	NOUN
ejpam-1871	218	58	→	→	SYM
ejpam-1871	218	59	q	q	X
ejpam-1871	218	60	and	and	CCONJ
ejpam-1871	218	61	iα	iα	INTJ
ejpam-1871	218	62	:	:	PUNCT
ejpam-1871	218	63	aα	aα	NOUN
ejpam-1871	218	64	→	→	SYM
ejpam-1871	218	65	∐	∐	ADJ
ejpam-1871	218	66	aα	aα	NOUN
ejpam-1871	218	67	are	be	AUX
ejpam-1871	218	68	the	the	DET
ejpam-1871	218	69	natural	natural	ADJ
ejpam-1871	218	70	map	map	NOUN
ejpam-1871	218	71	and	and	CCONJ
ejpam-1871	218	72	coproduct	coproduct	NOUN
ejpam-1871	218	73	injection	injection	NOUN
ejpam-1871	218	74	,	,	PUNCT
ejpam-1871	218	75	respectively	respectively	ADV
ejpam-1871	218	76	.	.	PUNCT
ejpam-1871	219	1	we	we	PRON
ejpam-1871	219	2	take	take	VERB
ejpam-1871	219	3	α	α	DET
ejpam-1871	219	4	∈	∈	NOUN
ejpam-1871	219	5	i	i	PRON
ejpam-1871	219	6	and	and	CCONJ
ejpam-1871	219	7	prove	prove	VERB
ejpam-1871	219	8	that	that	SCONJ
ejpam-1871	219	9	qα	qα	PROPN
ejpam-1871	219	10	is	be	AUX
ejpam-1871	219	11	a	a	DET
ejpam-1871	219	12	regular	regular	ADJ
ejpam-1871	219	13	monomorphism	monomorphism	NOUN
ejpam-1871	219	14	.	.	PUNCT
ejpam-1871	220	1	let	let	VERB
ejpam-1871	220	2	qα(aα)≤	qα(aα)≤	PROPN
ejpam-1871	220	3	qα(a′α	qα(a′α	PROPN
ejpam-1871	220	4	)	)	PUNCT
ejpam-1871	220	5	,	,	PUNCT
ejpam-1871	220	6	for	for	ADP
ejpam-1871	220	7	aα	aα	NOUN
ejpam-1871	220	8	,	,	PUNCT
ejpam-1871	220	9	a′α	a′α	PROPN
ejpam-1871	220	10	∈	∈	PROPN
ejpam-1871	220	11	aα	aα	NOUN
ejpam-1871	220	12	.	.	PUNCT
ejpam-1871	221	1	then	then	ADV
ejpam-1871	221	2	we	we	PRON
ejpam-1871	221	3	have	have	VERB
ejpam-1871	221	4	[	[	X
ejpam-1871	221	5	(	(	PUNCT
ejpam-1871	221	6	α	α	NOUN
ejpam-1871	221	7	,	,	PUNCT
ejpam-1871	221	8	aα	aα	NOUN
ejpam-1871	221	9	)	)	PUNCT
ejpam-1871	221	10	]	]	PUNCT
ejpam-1871	222	1	=	=	SYM
ejpam-1871	222	2	πiα(aα	πiα(aα	X
ejpam-1871	222	3	)	)	PUNCT
ejpam-1871	222	4	=	=	SYM
ejpam-1871	222	5	qα(aα)≤	qα(aα)≤	NOUN
ejpam-1871	222	6	qα(a	qα(a	NOUN
ejpam-1871	223	1	′	′	NUM
ejpam-1871	223	2	α	α	NOUN
ejpam-1871	223	3	)	)	PUNCT
ejpam-1871	224	1	=	=	SYM
ejpam-1871	224	2	πiα(a	πiα(a	NOUN
ejpam-1871	224	3	′	′	NUM
ejpam-1871	225	1	α	α	X
ejpam-1871	225	2	)	)	PUNCT
ejpam-1871	225	3	=	=	SYM
ejpam-1871	226	1	[	[	X
ejpam-1871	226	2	(	(	PUNCT
ejpam-1871	226	3	α	α	NOUN
ejpam-1871	226	4	,	,	PUNCT
ejpam-1871	226	5	a′α	a′α	ADJ
ejpam-1871	226	6	)	)	PUNCT
ejpam-1871	226	7	]	]	PUNCT
ejpam-1871	226	8	.	.	PUNCT
ejpam-1871	227	1	using	use	VERB
ejpam-1871	227	2	[	[	X
ejpam-1871	227	3	15	15	NUM
ejpam-1871	227	4	,	,	PUNCT
ejpam-1871	227	5	proposition	proposition	NOUN
ejpam-1871	227	6	3.3	3.3	NUM
ejpam-1871	227	7	]	]	PUNCT
ejpam-1871	227	8	,	,	PUNCT
ejpam-1871	227	9	this	this	PRON
ejpam-1871	227	10	implies	imply	VERB
ejpam-1871	227	11	that	that	SCONJ
ejpam-1871	227	12	(	(	PUNCT
ejpam-1871	227	13	α	α	NOUN
ejpam-1871	227	14	,	,	PUNCT
ejpam-1871	227	15	aα	aα	NOUN
ejpam-1871	227	16	)	)	PUNCT
ejpam-1871	227	17	≤	≤	NOUN
ejpam-1871	227	18	(	(	PUNCT
ejpam-1871	227	19	α	α	NOUN
ejpam-1871	227	20	,	,	PUNCT
ejpam-1871	227	21	a′α	a′α	ADJ
ejpam-1871	227	22	)	)	PUNCT
ejpam-1871	227	23	(	(	PUNCT
ejpam-1871	227	24	and	and	CCONJ
ejpam-1871	227	25	then	then	ADV
ejpam-1871	227	26	aα	aα	NOUN
ejpam-1871	227	27	≤	≤	NOUN
ejpam-1871	227	28	a′α	a′α	CCONJ
ejpam-1871	227	29	)	)	PUNCT
ejpam-1871	227	30	or	or	CCONJ
ejpam-1871	227	31	there	there	PRON
ejpam-1871	227	32	exist	exist	VERB
ejpam-1871	227	33	s1	s1	NOUN
ejpam-1871	227	34	,	,	PUNCT
ejpam-1871	227	35	s2	s2	NOUN
ejpam-1871	227	36	,	,	PUNCT
ejpam-1871	227	37	.	.	PUNCT
ejpam-1871	227	38	.	.	PUNCT
ejpam-1871	228	1	.	.	PUNCT
ejpam-1871	229	1	,	,	PUNCT
ejpam-1871	229	2	sn	sn	PROPN
ejpam-1871	229	3	∈	∈	PROPN
ejpam-1871	229	4	s	s	VERB
ejpam-1871	229	5	such	such	ADJ
ejpam-1871	229	6	that	that	SCONJ
ejpam-1871	229	7	(	(	PUNCT
ejpam-1871	229	8	α	α	NOUN
ejpam-1871	229	9	,	,	PUNCT
ejpam-1871	229	10	aα)≤	aα)≤	X
ejpam-1871	229	11	s1c1	s1c1	NOUN
ejpam-1871	229	12	,	,	PUNCT
ejpam-1871	229	13	s1d1	s1d1	NOUN
ejpam-1871	229	14	≤	≤	NOUN
ejpam-1871	229	15	s2c2	s2c2	NOUN
ejpam-1871	229	16	,	,	PUNCT
ejpam-1871	229	17	s2d2	s2d2	NOUN
ejpam-1871	229	18	≤	≤	NUM
ejpam-1871	229	19	s3c3	s3c3	NOUN
ejpam-1871	229	20	,	,	PUNCT
ejpam-1871	229	21	.	.	PUNCT
ejpam-1871	229	22	.	.	PUNCT
ejpam-1871	229	23	.	.	PUNCT
ejpam-1871	230	1	,	,	PUNCT
ejpam-1871	230	2	sndn	sndn	ADJ
ejpam-1871	230	3	≤	≤	NOUN
ejpam-1871	230	4	(	(	PUNCT
ejpam-1871	230	5	α	α	NOUN
ejpam-1871	230	6	,	,	PUNCT
ejpam-1871	230	7	a′α	a′α	ADJ
ejpam-1871	230	8	)	)	PUNCT
ejpam-1871	230	9	,	,	PUNCT
ejpam-1871	231	1	where	where	SCONJ
ejpam-1871	231	2	(	(	PUNCT
ejpam-1871	231	3	ci	ci	NOUN
ejpam-1871	231	4	,	,	PUNCT
ejpam-1871	231	5	di	di	NOUN
ejpam-1871	231	6	)	)	PUNCT
ejpam-1871	231	7	∈	∈	PROPN
ejpam-1871	231	8	h	h	NOUN
ejpam-1871	231	9	∪h−1	∪h−1	PUNCT
ejpam-1871	231	10	for	for	ADP
ejpam-1871	231	11	i	i	X
ejpam-1871	231	12	=	=	SYM
ejpam-1871	231	13	1,2	1,2	NUM
ejpam-1871	231	14	,	,	PUNCT
ejpam-1871	231	15	.	.	PUNCT
ejpam-1871	231	16	.	.	PUNCT
ejpam-1871	231	17	.	.	PUNCT
ejpam-1871	232	1	,	,	PUNCT
ejpam-1871	232	2	n.	n.	PROPN
ejpam-1871	232	3	thus	thus	ADV
ejpam-1871	232	4	there	there	ADV
ejpam-1871	232	5	exist	exist	VERB
ejpam-1871	232	6	a1	a1	NOUN
ejpam-1871	232	7	,	,	PUNCT
ejpam-1871	232	8	.	.	PUNCT
ejpam-1871	232	9	.	.	PUNCT
ejpam-1871	233	1	.	.	PUNCT
ejpam-1871	234	1	,	,	PUNCT
ejpam-1871	234	2	an	an	DET
ejpam-1871	234	3	∈	∈	PROPN
ejpam-1871	234	4	a	a	DET
ejpam-1871	234	5	such	such	ADJ
ejpam-1871	234	6	that	that	SCONJ
ejpam-1871	234	7	(	(	PUNCT
ejpam-1871	234	8	α	α	NOUN
ejpam-1871	234	9	,	,	PUNCT
ejpam-1871	234	10	aα)≤	aα)≤	X
ejpam-1871	234	11	s1(α	s1(α	X
ejpam-1871	234	12	,	,	PUNCT
ejpam-1871	234	13	fα(a1	fα(a1	NOUN
ejpam-1871	234	14	)	)	PUNCT
ejpam-1871	234	15	)	)	PUNCT
ejpam-1871	234	16	,	,	PUNCT
ejpam-1871	234	17	s1(α1	s1(α1	NOUN
ejpam-1871	234	18	,	,	PUNCT
ejpam-1871	234	19	fα1	fα1	NOUN
ejpam-1871	234	20	(	(	PUNCT
ejpam-1871	234	21	a1))≤	a1))≤	NUM
ejpam-1871	234	22	s2(α1	s2(α1	NOUN
ejpam-1871	234	23	,	,	PUNCT
ejpam-1871	234	24	fα1	fα1	NOUN
ejpam-1871	234	25	(	(	PUNCT
ejpam-1871	234	26	a2	a2	PROPN
ejpam-1871	234	27	)	)	PUNCT
ejpam-1871	234	28	)	)	PUNCT
ejpam-1871	234	29	,	,	PUNCT
ejpam-1871	234	30	s2(α2	s2(α2	NOUN
ejpam-1871	234	31	,	,	PUNCT
ejpam-1871	234	32	fα2	fα2	PROPN
ejpam-1871	234	33	(	(	PUNCT
ejpam-1871	234	34	a2))≤	a2))≤	ADJ
ejpam-1871	234	35	s3(α2	s3(α2	NOUN
ejpam-1871	234	36	,	,	PUNCT
ejpam-1871	234	37	fα2	fα2	PROPN
ejpam-1871	234	38	(	(	PUNCT
ejpam-1871	234	39	a3	a3	NOUN
ejpam-1871	234	40	)	)	PUNCT
ejpam-1871	234	41	)	)	PUNCT
ejpam-1871	234	42	,	,	PUNCT
ejpam-1871	234	43	.	.	PUNCT
ejpam-1871	234	44	.	.	PUNCT
ejpam-1871	235	1	.	.	PUNCT
ejpam-1871	236	1	,	,	PUNCT
ejpam-1871	236	2	sn−1(αn−1	sn−1(αn−1	PROPN
ejpam-1871	236	3	,	,	PUNCT
ejpam-1871	236	4	fαn−1	fαn−1	PROPN
ejpam-1871	236	5	(	(	PUNCT
ejpam-1871	236	6	an−1	an−1	PROPN
ejpam-1871	236	7	)	)	PUNCT
ejpam-1871	236	8	)	)	PUNCT
ejpam-1871	236	9	≤	≤	ADV
ejpam-1871	236	10	sn(αn−1	sn(αn−1	PROPN
ejpam-1871	236	11	,	,	PUNCT
ejpam-1871	236	12	fαn−1	fαn−1	PROPN
ejpam-1871	236	13	(	(	PUNCT
ejpam-1871	236	14	an	an	NOUN
ejpam-1871	236	15	)	)	PUNCT
ejpam-1871	236	16	)	)	PUNCT
ejpam-1871	236	17	,	,	PUNCT
ejpam-1871	236	18	sn(α	sn(α	PROPN
ejpam-1871	236	19	,	,	PUNCT
ejpam-1871	236	20	fα(an))≤	fα(an))≤	PROPN
ejpam-1871	236	21	(	(	PUNCT
ejpam-1871	236	22	α	α	NOUN
ejpam-1871	236	23	,	,	PUNCT
ejpam-1871	236	24	a′α	a′α	ADJ
ejpam-1871	236	25	)	)	PUNCT
ejpam-1871	236	26	.	.	PUNCT
ejpam-1871	237	1	then	then	ADV
ejpam-1871	237	2	we	we	PRON
ejpam-1871	237	3	get	get	VERB
ejpam-1871	237	4	aα	aα	NOUN
ejpam-1871	237	5	≤	≤	NOUN
ejpam-1871	237	6	fα(s1a1	fα(s1a1	PROPN
ejpam-1871	237	7	)	)	PUNCT
ejpam-1871	237	8	,	,	PUNCT
ejpam-1871	237	9	fα1	fα1	NOUN
ejpam-1871	237	10	(	(	PUNCT
ejpam-1871	237	11	s1a1)≤	s1a1)≤	NOUN
ejpam-1871	237	12	fα1	fα1	NOUN
ejpam-1871	237	13	(	(	PUNCT
ejpam-1871	237	14	s2a2	s2a2	NOUN
ejpam-1871	237	15	)	)	PUNCT
ejpam-1871	237	16	,	,	PUNCT
ejpam-1871	237	17	fα2	fα2	PROPN
ejpam-1871	237	18	(	(	PUNCT
ejpam-1871	237	19	s2a2)≤	s2a2)≤	NOUN
ejpam-1871	237	20	fα2	fα2	PROPN
ejpam-1871	237	21	(	(	PUNCT
ejpam-1871	237	22	s3a3	s3a3	NOUN
ejpam-1871	237	23	)	)	PUNCT
ejpam-1871	237	24	,	,	PUNCT
ejpam-1871	237	25	.	.	PUNCT
ejpam-1871	237	26	.	.	PUNCT
ejpam-1871	238	1	.	.	PUNCT
ejpam-1871	239	1	,	,	PUNCT
ejpam-1871	239	2	fαn−1	fαn−1	PROPN
ejpam-1871	239	3	(	(	PUNCT
ejpam-1871	239	4	sn−1an−1)≤	sn−1an−1)≤	PROPN
ejpam-1871	239	5	fαn−1	fαn−1	PROPN
ejpam-1871	239	6	(	(	PUNCT
ejpam-1871	239	7	snan	snan	PROPN
ejpam-1871	239	8	)	)	PUNCT
ejpam-1871	239	9	,	,	PUNCT
ejpam-1871	239	10	fα(snan)≤	fα(snan)≤	NOUN
ejpam-1871	239	11	a′α	a′α	ADJ
ejpam-1871	239	12	.	.	PUNCT
ejpam-1871	240	1	since	since	SCONJ
ejpam-1871	240	2	fα1	fα1	NOUN
ejpam-1871	240	3	,	,	PUNCT
ejpam-1871	240	4	.	.	PUNCT
ejpam-1871	240	5	.	.	PUNCT
ejpam-1871	240	6	.	.	PUNCT
ejpam-1871	241	1	,	,	PUNCT
ejpam-1871	241	2	fαn−1	fαn−1	PROPN
ejpam-1871	241	3	are	be	AUX
ejpam-1871	241	4	regular	regular	ADJ
ejpam-1871	241	5	monomorphisms	monomorphism	NOUN
ejpam-1871	241	6	,	,	PUNCT
ejpam-1871	241	7	s1a1	s1a1	X
ejpam-1871	241	8	≤	≤	NUM
ejpam-1871	241	9	s2a2	s2a2	PROPN
ejpam-1871	241	10	,	,	PUNCT
ejpam-1871	241	11	.	.	PUNCT
ejpam-1871	241	12	.	.	PUNCT
ejpam-1871	242	1	.	.	PUNCT
ejpam-1871	243	1	,	,	PUNCT
ejpam-1871	243	2	sn−1an−1	sn−1an−1	PROPN
ejpam-1871	243	3	≤	≤	NUM
ejpam-1871	243	4	snan	snan	NOUN
ejpam-1871	243	5	,	,	PUNCT
ejpam-1871	243	6	whence	whence	ADP
ejpam-1871	243	7	aα	aα	NOUN
ejpam-1871	243	8	≤	≤	PROPN
ejpam-1871	243	9	fα(s1a1)≤	fα(s1a1)≤	VERB
ejpam-1871	243	10	fα(s2a2)≤	fα(s2a2)≤	PROPN
ejpam-1871	243	11	fα(s3a3)≤	fα(s3a3)≤	ADV
ejpam-1871	243	12	.	.	PUNCT
ejpam-1871	243	13	.	.	PUNCT
ejpam-1871	244	1	.≤	.≤	PUNCT
ejpam-1871	245	1	fα(sn−1an−1)≤	fα(sn−1an−1)≤	PROPN
ejpam-1871	245	2	fα(snan)≤	fα(snan)≤	NOUN
ejpam-1871	245	3	a′α	a′α	ADV
ejpam-1871	245	4	,	,	PUNCT
ejpam-1871	245	5	as	as	SCONJ
ejpam-1871	245	6	required	require	VERB
ejpam-1871	245	7	.	.	PUNCT
ejpam-1871	246	1	h.	h.	PROPN
ejpam-1871	246	2	rasouli	rasouli	PROPN
ejpam-1871	246	3	/	/	SYM
ejpam-1871	246	4	eur	eur	PROPN
ejpam-1871	246	5	.	.	PUNCT
ejpam-1871	247	1	j.	j.	PROPN
ejpam-1871	247	2	pure	pure	PROPN
ejpam-1871	247	3	appl	appl	PROPN
ejpam-1871	247	4	.	.	PROPN
ejpam-1871	247	5	math	math	PROPN
ejpam-1871	247	6	,	,	PUNCT
ejpam-1871	247	7	7	7	NUM
ejpam-1871	247	8	(	(	PUNCT
ejpam-1871	247	9	2014	2014	NUM
ejpam-1871	247	10	)	)	PUNCT
ejpam-1871	247	11	,	,	PUNCT
ejpam-1871	247	12	166	166	NUM
ejpam-1871	247	13	-	-	SYM
ejpam-1871	247	14	178	178	NUM
ejpam-1871	247	15	173	173	NUM
ejpam-1871	247	16	corollary	corollary	ADJ
ejpam-1871	247	17	1	1	NUM
ejpam-1871	247	18	.	.	PUNCT
ejpam-1871	248	1	every	every	DET
ejpam-1871	248	2	multiple	multiple	ADJ
ejpam-1871	248	3	pushout	pushout	NOUN
ejpam-1871	248	4	of	of	ADP
ejpam-1871	248	5	regular	regular	ADJ
ejpam-1871	248	6	monomorphisms	monomorphism	NOUN
ejpam-1871	248	7	(	(	PUNCT
ejpam-1871	248	8	the	the	DET
ejpam-1871	248	9	diagonal	diagonal	ADJ
ejpam-1871	248	10	maps	map	NOUN
ejpam-1871	248	11	on	on	ADP
ejpam-1871	248	12	the	the	DET
ejpam-1871	248	13	multiple	multiple	ADJ
ejpam-1871	248	14	pushout	pushout	NOUN
ejpam-1871	248	15	diagram	diagram	NOUN
ejpam-1871	248	16	)	)	PUNCT
ejpam-1871	248	17	is	be	AUX
ejpam-1871	248	18	a	a	DET
ejpam-1871	248	19	regular	regular	ADJ
ejpam-1871	248	20	monomorphism	monomorphism	NOUN
ejpam-1871	248	21	.	.	PUNCT
ejpam-1871	249	1	proof	proof	NOUN
ejpam-1871	249	2	.	.	PUNCT
ejpam-1871	250	1	apply	apply	VERB
ejpam-1871	250	2	lemma	lemma	PROPN
ejpam-1871	250	3	1(i	1(i	NUM
ejpam-1871	250	4	)	)	PUNCT
ejpam-1871	250	5	and	and	CCONJ
ejpam-1871	250	6	theorem	theorem	VERB
ejpam-1871	250	7	2	2	NUM
ejpam-1871	250	8	.	.	PUNCT
ejpam-1871	250	9	definition	definition	NOUN
ejpam-1871	250	10	1	1	NUM
ejpam-1871	250	11	.	.	PUNCT
ejpam-1871	251	1	let	let	VERB
ejpam-1871	251	2	e	e	PRON
ejpam-1871	251	3	be	be	AUX
ejpam-1871	251	4	a	a	DET
ejpam-1871	251	5	class	class	NOUN
ejpam-1871	251	6	of	of	ADP
ejpam-1871	251	7	morphisms	morphism	NOUN
ejpam-1871	251	8	of	of	ADP
ejpam-1871	251	9	a	a	DET
ejpam-1871	251	10	category	category	NOUN
ejpam-1871	251	11	c	c	NOUN
ejpam-1871	251	12	.	.	PUNCT
ejpam-1871	252	1	we	we	PRON
ejpam-1871	252	2	say	say	VERB
ejpam-1871	252	3	that	that	SCONJ
ejpam-1871	252	4	c	c	PROPN
ejpam-1871	252	5	has	have	VERB
ejpam-1871	252	6	:	:	PUNCT
ejpam-1871	252	7	i	i	NOUN
ejpam-1871	252	8	)	)	PUNCT
ejpam-1871	252	9	e	e	PROPN
ejpam-1871	252	10	-bounds	-bound	NOUN
ejpam-1871	252	11	if	if	SCONJ
ejpam-1871	252	12	for	for	ADP
ejpam-1871	252	13	every	every	DET
ejpam-1871	252	14	small	small	ADJ
ejpam-1871	252	15	and	and	CCONJ
ejpam-1871	252	16	non	non	ADJ
ejpam-1871	252	17	-	-	ADJ
ejpam-1871	252	18	empty	empty	ADJ
ejpam-1871	252	19	family	family	NOUN
ejpam-1871	252	20	{	{	PUNCT
ejpam-1871	252	21	hα	hα	X
ejpam-1871	252	22	:	:	PUNCT
ejpam-1871	252	23	a→	a→	X
ejpam-1871	252	24	bα}α∈i	bα}α∈i	NOUN
ejpam-1871	252	25	of	of	ADP
ejpam-1871	252	26	e	e	NOUN
ejpam-1871	252	27	-morphisms	-morphism	NOUN
ejpam-1871	252	28	,	,	PUNCT
ejpam-1871	252	29	there	there	PRON
ejpam-1871	252	30	is	be	VERB
ejpam-1871	252	31	an	an	DET
ejpam-1871	252	32	e	e	NOUN
ejpam-1871	252	33	-morphism	-morphism	NOUN
ejpam-1871	252	34	h	h	NOUN
ejpam-1871	252	35	:	:	PUNCT
ejpam-1871	252	36	a→	a→	PROPN
ejpam-1871	252	37	b	b	NOUN
ejpam-1871	252	38	which	which	PRON
ejpam-1871	252	39	factorizes	factorize	VERB
ejpam-1871	252	40	through	through	ADP
ejpam-1871	252	41	all	all	PRON
ejpam-1871	252	42	hα	hα	ADP
ejpam-1871	252	43	’s	’s	NOUN
ejpam-1871	252	44	.	.	PUNCT
ejpam-1871	253	1	ii	ii	X
ejpam-1871	253	2	)	)	PUNCT
ejpam-1871	253	3	e	e	PROPN
ejpam-1871	253	4	-amalgamation	-amalgamation	PROPN
ejpam-1871	253	5	property	property	NOUN
ejpam-1871	253	6	if	if	SCONJ
ejpam-1871	253	7	in	in	ADP
ejpam-1871	253	8	(	(	PUNCT
ejpam-1871	253	9	i	i	NOUN
ejpam-1871	253	10	)	)	PUNCT
ejpam-1871	253	11	,	,	PUNCT
ejpam-1871	253	12	h	h	NOUN
ejpam-1871	253	13	factorizes	factorize	VERB
ejpam-1871	253	14	through	through	ADP
ejpam-1871	253	15	all	all	PRON
ejpam-1871	253	16	hα	hα	NOUN
ejpam-1871	253	17	’s	’s	NOUN
ejpam-1871	253	18	by	by	ADP
ejpam-1871	253	19	e	e	NOUN
ejpam-1871	253	20	-morphisms	-morphism	NOUN
ejpam-1871	253	21	.	.	PUNCT
ejpam-1871	254	1	in	in	ADP
ejpam-1871	254	2	view	view	NOUN
ejpam-1871	254	3	of	of	ADP
ejpam-1871	254	4	corollary	corollary	ADJ
ejpam-1871	254	5	1	1	NUM
ejpam-1871	254	6	,	,	PUNCT
ejpam-1871	254	7	the	the	DET
ejpam-1871	254	8	following	follow	VERB
ejpam-1871	254	9	is	be	AUX
ejpam-1871	254	10	immediate	immediate	ADJ
ejpam-1871	254	11	:	:	PUNCT
ejpam-1871	254	12	proposition	proposition	NOUN
ejpam-1871	254	13	6	6	NUM
ejpam-1871	254	14	.	.	PUNCT
ejpam-1871	255	1	s	s	X
ejpam-1871	255	2	-	-	PUNCT
ejpam-1871	255	3	pos	pos	NOUN
ejpam-1871	255	4	hasm	hasm	NOUN
ejpam-1871	255	5	-amalgamation	-amalgamation	PROPN
ejpam-1871	255	6	property	property	NOUN
ejpam-1871	255	7	and	and	CCONJ
ejpam-1871	255	8	so	so	ADV
ejpam-1871	255	9	also	also	ADV
ejpam-1871	255	10	hasm	hasm	PROPN
ejpam-1871	255	11	-bounds	-bound	NOUN
ejpam-1871	255	12	.	.	PUNCT
ejpam-1871	256	1	finally	finally	ADV
ejpam-1871	256	2	,	,	PUNCT
ejpam-1871	256	3	we	we	PRON
ejpam-1871	256	4	study	study	VERB
ejpam-1871	256	5	directed	direct	VERB
ejpam-1871	256	6	colimit	colimit	NOUN
ejpam-1871	256	7	of	of	ADP
ejpam-1871	256	8	regular	regular	ADJ
ejpam-1871	256	9	monomorphisms	monomorphism	NOUN
ejpam-1871	256	10	in	in	ADP
ejpam-1871	256	11	s	s	NOUN
ejpam-1871	256	12	-	-	PUNCT
ejpam-1871	256	13	pos	pos	NOUN
ejpam-1871	256	14	.	.	PUNCT
ejpam-1871	257	1	recall	recall	VERB
ejpam-1871	257	2	that	that	SCONJ
ejpam-1871	257	3	a	a	DET
ejpam-1871	257	4	directed	direct	VERB
ejpam-1871	257	5	system	system	NOUN
ejpam-1871	257	6	of	of	ADP
ejpam-1871	257	7	s	s	NOUN
ejpam-1871	257	8	-	-	PUNCT
ejpam-1871	257	9	posets	poset	NOUN
ejpam-1871	257	10	and	and	CCONJ
ejpam-1871	257	11	s	s	NOUN
ejpam-1871	257	12	-	-	PUNCT
ejpam-1871	257	13	poset	poset	VERB
ejpam-1871	257	14	maps	map	NOUN
ejpam-1871	257	15	is	be	AUX
ejpam-1871	257	16	a	a	DET
ejpam-1871	257	17	family	family	NOUN
ejpam-1871	257	18	(	(	PUNCT
ejpam-1871	257	19	ai)i∈i	ai)i∈i	NUM
ejpam-1871	257	20	of	of	ADP
ejpam-1871	257	21	s	s	NOUN
ejpam-1871	257	22	-	-	PUNCT
ejpam-1871	257	23	posets	poset	NOUN
ejpam-1871	257	24	indexed	index	VERB
ejpam-1871	257	25	by	by	ADP
ejpam-1871	257	26	an	an	DET
ejpam-1871	257	27	up	up	ADV
ejpam-1871	257	28	-	-	PUNCT
ejpam-1871	257	29	directed	direct	VERB
ejpam-1871	257	30	set	set	NOUN
ejpam-1871	257	31	i	i	PRON
ejpam-1871	257	32	endowed	endow	VERB
ejpam-1871	257	33	by	by	ADP
ejpam-1871	257	34	a	a	DET
ejpam-1871	257	35	family	family	NOUN
ejpam-1871	257	36	(	(	PUNCT
ejpam-1871	257	37	ψi	ψi	ADP
ejpam-1871	257	38	j	j	NOUN
ejpam-1871	257	39	:	:	PUNCT
ejpam-1871	257	40	ai	ai	VERB
ejpam-1871	257	41	→	→	SYM
ejpam-1871	257	42	a	a	DET
ejpam-1871	257	43	j)i≤	j)i≤	NOUN
ejpam-1871	257	44	j∈i	j∈i	PROPN
ejpam-1871	257	45	of	of	ADP
ejpam-1871	257	46	s	s	NOUN
ejpam-1871	257	47	-	-	PUNCT
ejpam-1871	257	48	poset	poset	VERB
ejpam-1871	257	49	maps	map	NOUN
ejpam-1871	257	50	such	such	ADJ
ejpam-1871	257	51	that	that	SCONJ
ejpam-1871	257	52	given	give	VERB
ejpam-1871	257	53	i	i	PRON
ejpam-1871	257	54	≤	≤	NUM
ejpam-1871	257	55	j	j	PROPN
ejpam-1871	257	56	≤	≤	PROPN
ejpam-1871	257	57	k	k	X
ejpam-1871	257	58	∈	∈	PROPN
ejpam-1871	258	1	i	i	PRON
ejpam-1871	258	2	,	,	PUNCT
ejpam-1871	258	3	ψik	ψik	PROPN
ejpam-1871	258	4	=	=	SYM
ejpam-1871	258	5	ψ	ψ	X
ejpam-1871	258	6	jkψi	jkψi	PROPN
ejpam-1871	258	7	j	j	PROPN
ejpam-1871	258	8	,	,	PUNCT
ejpam-1871	258	9	and	and	CCONJ
ejpam-1871	258	10	ψii	ψii	VERB
ejpam-1871	258	11	=	=	SYM
ejpam-1871	259	1	i	i	PROPN
ejpam-1871	259	2	d.	d.	PROPN
ejpam-1871	259	3	also	also	ADV
ejpam-1871	259	4	the	the	DET
ejpam-1871	259	5	pair	pair	NOUN
ejpam-1871	259	6	(	(	PUNCT
ejpam-1871	259	7	l	l	NOUN
ejpam-1871	259	8	im−→ai	im−→ai	NUM
ejpam-1871	259	9	,	,	PUNCT
ejpam-1871	259	10	{	{	PUNCT
ejpam-1871	259	11	αi	αi	VERB
ejpam-1871	259	12	:	:	PUNCT
ejpam-1871	259	13	ai	ai	VERB
ejpam-1871	259	14	→	→	SYM
ejpam-1871	259	15	l	l	NOUN
ejpam-1871	259	16	im−→ai	im−→ai	NUM
ejpam-1871	259	17	}	}	PUNCT
ejpam-1871	259	18	)	)	PUNCT
ejpam-1871	259	19	or	or	CCONJ
ejpam-1871	259	20	in	in	ADP
ejpam-1871	259	21	abbreviation	abbreviation	NOUN
ejpam-1871	259	22	,	,	PUNCT
ejpam-1871	259	23	l	l	PROPN
ejpam-1871	259	24	im−→ai	im−→ai	PRON
ejpam-1871	259	25	is	be	AUX
ejpam-1871	259	26	called	call	VERB
ejpam-1871	259	27	the	the	DET
ejpam-1871	259	28	directed	direct	VERB
ejpam-1871	259	29	colimit	colimit	NOUN
ejpam-1871	259	30	(	(	PUNCT
ejpam-1871	259	31	or	or	CCONJ
ejpam-1871	259	32	direct	direct	ADJ
ejpam-1871	259	33	limit	limit	NOUN
ejpam-1871	259	34	)	)	PUNCT
ejpam-1871	259	35	of	of	ADP
ejpam-1871	259	36	the	the	DET
ejpam-1871	259	37	directed	direct	VERB
ejpam-1871	259	38	system	system	NOUN
ejpam-1871	259	39	(	(	PUNCT
ejpam-1871	259	40	(	(	PUNCT
ejpam-1871	259	41	ai)i∈i	ai)i∈i	NUM
ejpam-1871	259	42	,	,	PUNCT
ejpam-1871	259	43	(	(	PUNCT
ejpam-1871	259	44	ψi	ψi	ADP
ejpam-1871	259	45	j)i≤	j)i≤	PROPN
ejpam-1871	259	46	j	j	PROPN
ejpam-1871	259	47	)	)	PUNCT
ejpam-1871	259	48	if	if	SCONJ
ejpam-1871	259	49	for	for	ADP
ejpam-1871	259	50	every	every	DET
ejpam-1871	259	51	i	i	NOUN
ejpam-1871	259	52	≤	≤	PROPN
ejpam-1871	259	53	j	j	PROPN
ejpam-1871	259	54	∈	∈	PROPN
ejpam-1871	260	1	i	i	PRON
ejpam-1871	260	2	,	,	PUNCT
ejpam-1871	260	3	α	α	PROPN
ejpam-1871	260	4	jψi	jψi	PROPN
ejpam-1871	260	5	j	j	PROPN
ejpam-1871	260	6	=	=	PUNCT
ejpam-1871	260	7	αi	αi	VERB
ejpam-1871	260	8	,	,	PUNCT
ejpam-1871	260	9	and	and	CCONJ
ejpam-1871	260	10	for	for	ADP
ejpam-1871	260	11	every	every	DET
ejpam-1871	260	12	(	(	PUNCT
ejpam-1871	260	13	b	b	NOUN
ejpam-1871	260	14	,	,	PUNCT
ejpam-1871	260	15	fi	fi	NOUN
ejpam-1871	260	16	:	:	PUNCT
ejpam-1871	260	17	ai	ai	VERB
ejpam-1871	260	18	→	→	SYM
ejpam-1871	260	19	b	b	NOUN
ejpam-1871	260	20	)	)	PUNCT
ejpam-1871	260	21	with	with	ADP
ejpam-1871	260	22	f	f	PROPN
ejpam-1871	260	23	jψi	jψi	PROPN
ejpam-1871	260	24	j	j	PROPN
ejpam-1871	261	1	=	=	PROPN
ejpam-1871	261	2	fi	fi	PROPN
ejpam-1871	261	3	,	,	PUNCT
ejpam-1871	261	4	i	i	PRON
ejpam-1871	262	1	≤	≤	X
ejpam-1871	262	2	j	j	PROPN
ejpam-1871	263	1	∈	∈	PROPN
ejpam-1871	264	1	i	i	PRON
ejpam-1871	264	2	,	,	PUNCT
ejpam-1871	264	3	there	there	PRON
ejpam-1871	264	4	exists	exist	VERB
ejpam-1871	264	5	a	a	DET
ejpam-1871	264	6	unique	unique	ADJ
ejpam-1871	264	7	s	s	NOUN
ejpam-1871	264	8	-	-	PUNCT
ejpam-1871	264	9	poset	poset	VERB
ejpam-1871	264	10	map	map	NOUN
ejpam-1871	264	11	ν	ν	NOUN
ejpam-1871	264	12	:	:	PUNCT
ejpam-1871	264	13	l	l	NOUN
ejpam-1871	264	14	im−→ai	im−→ai	NUM
ejpam-1871	264	15	→	→	SYM
ejpam-1871	264	16	b	b	X
ejpam-1871	264	17	such	such	ADJ
ejpam-1871	264	18	that	that	DET
ejpam-1871	264	19	ναi	ναi	NOUN
ejpam-1871	264	20	=	=	ADJ
ejpam-1871	264	21	fi	fi	NOUN
ejpam-1871	264	22	,	,	PUNCT
ejpam-1871	264	23	for	for	ADP
ejpam-1871	264	24	every	every	DET
ejpam-1871	264	25	i	i	NOUN
ejpam-1871	264	26	∈	∈	PROPN
ejpam-1871	265	1	i	i	PRON
ejpam-1871	265	2	.	.	PUNCT
ejpam-1871	266	1	recall	recall	VERB
ejpam-1871	266	2	from	from	ADP
ejpam-1871	266	3	[	[	X
ejpam-1871	266	4	7	7	X
ejpam-1871	266	5	]	]	PUNCT
ejpam-1871	266	6	that	that	SCONJ
ejpam-1871	266	7	the	the	DET
ejpam-1871	266	8	directed	direct	VERB
ejpam-1871	266	9	colimit	colimit	NOUN
ejpam-1871	266	10	of	of	ADP
ejpam-1871	266	11	a	a	DET
ejpam-1871	266	12	directed	direct	VERB
ejpam-1871	266	13	system	system	NOUN
ejpam-1871	266	14	(	(	PUNCT
ejpam-1871	266	15	(	(	PUNCT
ejpam-1871	266	16	ai)i∈i	ai)i∈i	NUM
ejpam-1871	266	17	,	,	PUNCT
ejpam-1871	266	18	(	(	PUNCT
ejpam-1871	266	19	ψi	ψi	ADP
ejpam-1871	266	20	j)i≤	j)i≤	PROPN
ejpam-1871	266	21	j	j	PROPN
ejpam-1871	266	22	)	)	PUNCT
ejpam-1871	266	23	of	of	ADP
ejpam-1871	266	24	s	s	NOUN
ejpam-1871	266	25	-	-	PUNCT
ejpam-1871	266	26	posets	poset	NOUN
ejpam-1871	266	27	exists	exist	VERB
ejpam-1871	266	28	,	,	PUNCT
ejpam-1871	266	29	and	and	CCONJ
ejpam-1871	266	30	may	may	AUX
ejpam-1871	266	31	be	be	AUX
ejpam-1871	266	32	represented	represent	VERB
ejpam-1871	266	33	as	as	ADP
ejpam-1871	266	34	(	(	PUNCT
ejpam-1871	266	35	a	a	PRON
ejpam-1871	266	36	/	/	SYM
ejpam-1871	266	37	θ	θ	NOUN
ejpam-1871	266	38	,	,	PUNCT
ejpam-1871	266	39	(	(	PUNCT
ejpam-1871	266	40	ψi	ψi	ADP
ejpam-1871	266	41	:	:	PUNCT
ejpam-1871	266	42	ai	ai	VERB
ejpam-1871	266	43	→	→	SYM
ejpam-1871	266	44	a	a	X
ejpam-1871	266	45	/	/	SYM
ejpam-1871	266	46	θ	θ	NOUN
ejpam-1871	266	47	)	)	PUNCT
ejpam-1871	266	48	i∈i	i∈i	ADJ
ejpam-1871	266	49	)	)	PUNCT
ejpam-1871	266	50	,	,	PUNCT
ejpam-1871	266	51	where	where	SCONJ
ejpam-1871	266	52	i	i	PRON
ejpam-1871	266	53	)	)	PUNCT
ejpam-1871	266	54	a=	a=	VERB
ejpam-1871	266	55	∐	∐	ADV
ejpam-1871	266	56	ai	ai	VERB
ejpam-1871	266	57	;	;	PUNCT
ejpam-1871	266	58	ii	ii	NUM
ejpam-1871	266	59	)	)	PUNCT
ejpam-1871	266	60	aθa′(a	aθa′(a	NOUN
ejpam-1871	266	61	∈	∈	PROPN
ejpam-1871	266	62	ai	ai	VERB
ejpam-1871	266	63	,	,	PUNCT
ejpam-1871	266	64	a′	a′	PROPN
ejpam-1871	266	65	∈	∈	PROPN
ejpam-1871	266	66	a	a	DET
ejpam-1871	266	67	j	j	NOUN
ejpam-1871	266	68	)	)	PUNCT
ejpam-1871	267	1	if	if	SCONJ
ejpam-1871	267	2	and	and	CCONJ
ejpam-1871	267	3	only	only	ADV
ejpam-1871	267	4	if	if	SCONJ
ejpam-1871	267	5	∃k	∃k	PROPN
ejpam-1871	267	6	≥	≥	NOUN
ejpam-1871	267	7	i	i	NOUN
ejpam-1871	267	8	,	,	PUNCT
ejpam-1871	267	9	j	j	PROPN
ejpam-1871	267	10	:	:	PUNCT
ejpam-1871	267	11	ψik(a	ψik(a	X
ejpam-1871	267	12	)	)	PUNCT
ejpam-1871	268	1	=	=	NOUN
ejpam-1871	268	2	ψ	ψ	X
ejpam-1871	268	3	jk(a′	jk(a′	NOUN
ejpam-1871	268	4	)	)	PUNCT
ejpam-1871	268	5	;	;	PUNCT
ejpam-1871	268	6	iii	iii	X
ejpam-1871	268	7	)	)	PUNCT
ejpam-1871	269	1	[	[	X
ejpam-1871	269	2	a]θ	a]θ	X
ejpam-1871	269	3	≤	≤	NOUN
ejpam-1871	270	1	[	[	PUNCT
ejpam-1871	270	2	a′]θ	a′]θ	NUM
ejpam-1871	270	3	(	(	PUNCT
ejpam-1871	270	4	a	a	DET
ejpam-1871	270	5	∈	∈	NOUN
ejpam-1871	270	6	ai	ai	VERB
ejpam-1871	270	7	,	,	PUNCT
ejpam-1871	270	8	a′	a′	PROPN
ejpam-1871	270	9	∈	∈	PROPN
ejpam-1871	270	10	a	a	DET
ejpam-1871	270	11	j	j	NOUN
ejpam-1871	270	12	)	)	PUNCT
ejpam-1871	271	1	if	if	SCONJ
ejpam-1871	271	2	and	and	CCONJ
ejpam-1871	271	3	only	only	ADV
ejpam-1871	271	4	if	if	SCONJ
ejpam-1871	271	5	∃k	∃k	PROPN
ejpam-1871	271	6	≥	≥	NOUN
ejpam-1871	271	7	i	i	NOUN
ejpam-1871	271	8	,	,	PUNCT
ejpam-1871	271	9	j	j	PROPN
ejpam-1871	271	10	:	:	PUNCT
ejpam-1871	271	11	ψik(a)≤ψ	ψik(a)≤ψ	PROPN
ejpam-1871	271	12	jk(a′	jk(a′	PROPN
ejpam-1871	271	13	)	)	PUNCT
ejpam-1871	271	14	;	;	PUNCT
ejpam-1871	271	15	iv	iv	X
ejpam-1871	271	16	)	)	PUNCT
ejpam-1871	271	17	for	for	ADP
ejpam-1871	271	18	each	each	DET
ejpam-1871	271	19	i	i	PRON
ejpam-1871	271	20	∈	∈	PROPN
ejpam-1871	271	21	i	i	PRON
ejpam-1871	271	22	and	and	CCONJ
ejpam-1871	271	23	a	a	DET
ejpam-1871	271	24	∈	∈	NOUN
ejpam-1871	271	25	ai	ai	VERB
ejpam-1871	271	26	,	,	PUNCT
ejpam-1871	271	27	ψi(a	ψi(a	PUNCT
ejpam-1871	271	28	)	)	PUNCT
ejpam-1871	271	29	=	=	PUNCT
ejpam-1871	272	1	[	[	X
ejpam-1871	272	2	a]θ	a]θ	X
ejpam-1871	272	3	.	.	PUNCT
ejpam-1871	273	1	theorem	theorem	NOUN
ejpam-1871	273	2	3	3	X
ejpam-1871	273	3	.	.	PUNCT
ejpam-1871	274	1	let	let	VERB
ejpam-1871	274	2	i	i	PRON
ejpam-1871	274	3	be	be	AUX
ejpam-1871	274	4	an	an	DET
ejpam-1871	274	5	up	up	ADV
ejpam-1871	274	6	-	-	PUNCT
ejpam-1871	274	7	directed	direct	VERB
ejpam-1871	274	8	set	set	NOUN
ejpam-1871	274	9	and	and	CCONJ
ejpam-1871	274	10	{	{	PUNCT
ejpam-1871	274	11	hα	hα	X
ejpam-1871	274	12	:	:	PUNCT
ejpam-1871	274	13	aα→	aα→	ADJ
ejpam-1871	275	1	bα	bα	VERB
ejpam-1871	276	1	|	|	ADV
ejpam-1871	276	2	α	α	NOUN
ejpam-1871	276	3	∈	∈	PROPN
ejpam-1871	277	1	i	i	PRON
ejpam-1871	277	2	}	}	PUNCT
ejpam-1871	277	3	be	be	VERB
ejpam-1871	277	4	a	a	DET
ejpam-1871	277	5	directed	direct	VERB
ejpam-1871	277	6	family	family	NOUN
ejpam-1871	277	7	of	of	ADP
ejpam-1871	277	8	regular	regular	ADJ
ejpam-1871	277	9	monomorphisms	monomorphism	NOUN
ejpam-1871	277	10	.	.	PUNCT
ejpam-1871	278	1	then	then	ADV
ejpam-1871	278	2	the	the	DET
ejpam-1871	278	3	directed	direct	VERB
ejpam-1871	278	4	colimit	colimit	NOUN
ejpam-1871	278	5	homomorphism	homomorphism	NOUN
ejpam-1871	278	6	induced	induce	VERB
ejpam-1871	278	7	by	by	ADP
ejpam-1871	278	8	h	h	NOUN
ejpam-1871	278	9	:	:	PUNCT
ejpam-1871	278	10	l	l	NOUN
ejpam-1871	278	11	im−→aα	im−→aα	PROPN
ejpam-1871	278	12	→	→	SYM
ejpam-1871	278	13	l	l	NOUN
ejpam-1871	278	14	im−→bα	im−→bα	PROPN
ejpam-1871	278	15	is	be	AUX
ejpam-1871	278	16	a	a	DET
ejpam-1871	278	17	regular	regular	ADJ
ejpam-1871	278	18	monomorphism	monomorphism	NOUN
ejpam-1871	278	19	.	.	PUNCT
ejpam-1871	279	1	proof	proof	NOUN
ejpam-1871	279	2	.	.	PUNCT
ejpam-1871	280	1	let	let	VERB
ejpam-1871	280	2	(	(	PUNCT
ejpam-1871	280	3	l	l	NOUN
ejpam-1871	280	4	im−→aα	im−→aα	NOUN
ejpam-1871	280	5	,	,	PUNCT
ejpam-1871	280	6	fα	fα	NOUN
ejpam-1871	280	7	)	)	PUNCT
ejpam-1871	280	8	,	,	PUNCT
ejpam-1871	280	9	(	(	PUNCT
ejpam-1871	280	10	l	l	PROPN
ejpam-1871	280	11	im−→bα	im−→bα	PROPN
ejpam-1871	280	12	,	,	PUNCT
ejpam-1871	280	13	gα	gα	NOUN
ejpam-1871	280	14	)	)	PUNCT
ejpam-1871	280	15	be	be	AUX
ejpam-1871	280	16	directed	direct	VERB
ejpam-1871	280	17	colimits	colimit	NOUN
ejpam-1871	280	18	of	of	ADP
ejpam-1871	280	19	the	the	DET
ejpam-1871	280	20	directed	direct	VERB
ejpam-1871	280	21	systems	system	NOUN
ejpam-1871	280	22	(	(	PUNCT
ejpam-1871	280	23	(	(	PUNCT
ejpam-1871	280	24	aα)α∈i	aα)α∈i	NUM
ejpam-1871	280	25	,	,	PUNCT
ejpam-1871	280	26	(	(	PUNCT
ejpam-1871	280	27	ψαβ)α≤β	ψαβ)α≤β	NUM
ejpam-1871	280	28	)	)	PUNCT
ejpam-1871	280	29	and	and	CCONJ
ejpam-1871	280	30	(	(	PUNCT
ejpam-1871	280	31	(	(	PUNCT
ejpam-1871	280	32	bα)α∈i	bα)α∈i	X
ejpam-1871	280	33	,	,	PUNCT
ejpam-1871	280	34	(	(	PUNCT
ejpam-1871	280	35	ϕαβ)α≤β	ϕαβ)α≤β	PROPN
ejpam-1871	280	36	)	)	PUNCT
ejpam-1871	280	37	,	,	PUNCT
ejpam-1871	280	38	respectively	respectively	ADV
ejpam-1871	280	39	.	.	PUNCT
ejpam-1871	281	1	suppose	suppose	VERB
ejpam-1871	281	2	{	{	PUNCT
ejpam-1871	281	3	hα	hα	X
ejpam-1871	281	4	:	:	PUNCT
ejpam-1871	281	5	aα	aα	NOUN
ejpam-1871	281	6	→	→	SYM
ejpam-1871	281	7	bα	bα	NOUN
ejpam-1871	282	1	|	|	ADV
ejpam-1871	282	2	α	α	NOUN
ejpam-1871	282	3	∈	∈	PROPN
ejpam-1871	283	1	i	i	PRON
ejpam-1871	283	2	}	}	PUNCT
ejpam-1871	283	3	is	be	AUX
ejpam-1871	283	4	a	a	DET
ejpam-1871	283	5	directed	direct	VERB
ejpam-1871	283	6	family	family	NOUN
ejpam-1871	283	7	of	of	ADP
ejpam-1871	283	8	regular	regular	ADJ
ejpam-1871	283	9	monomorphisms	monomorphism	NOUN
ejpam-1871	283	10	such	such	ADJ
ejpam-1871	283	11	that	that	PRON
ejpam-1871	283	12	for	for	ADP
ejpam-1871	283	13	every	every	DET
ejpam-1871	283	14	α	α	NOUN
ejpam-1871	283	15	≤	≤	ADJ
ejpam-1871	283	16	β	β	X
ejpam-1871	283	17	,	,	PUNCT
ejpam-1871	283	18	fβψαβ	fβψαβ	NOUN
ejpam-1871	283	19	=	=	PUNCT
ejpam-1871	283	20	fα	fα	NOUN
ejpam-1871	283	21	and	and	CCONJ
ejpam-1871	283	22	gβϕαβ	gβϕαβ	VERB
ejpam-1871	283	23	=	=	PUNCT
ejpam-1871	283	24	gα	gα	NOUN
ejpam-1871	283	25	.	.	PUNCT
ejpam-1871	284	1	then	then	ADV
ejpam-1871	284	2	gβhβψαβ	gβhβψαβ	VERB
ejpam-1871	284	3	=	=	X
ejpam-1871	284	4	gβϕαβhα	gβϕαβhα	NOUN
ejpam-1871	284	5	=	=	NOUN
ejpam-1871	284	6	gαhα	gαhα	ADJ
ejpam-1871	284	7	.	.	PUNCT
ejpam-1871	285	1	thus	thus	ADV
ejpam-1871	285	2	h	h	NOUN
ejpam-1871	285	3	=	=	SYM
ejpam-1871	285	4	l	l	NOUN
ejpam-1871	285	5	im−→hα	im−→hα	NOUN
ejpam-1871	285	6	exists	exist	VERB
ejpam-1871	285	7	by	by	ADP
ejpam-1871	285	8	the	the	DET
ejpam-1871	285	9	universal	universal	ADJ
ejpam-1871	285	10	property	property	NOUN
ejpam-1871	285	11	of	of	ADP
ejpam-1871	285	12	colimits	colimit	NOUN
ejpam-1871	285	13	.	.	PUNCT
ejpam-1871	286	1	consider	consider	VERB
ejpam-1871	286	2	l	l	NOUN
ejpam-1871	286	3	im−→aα	im−→aα	NOUN
ejpam-1871	286	4	=	=	PUNCT
ejpam-1871	286	5	(	(	PUNCT
ejpam-1871	286	6	∐	∐	ADV
ejpam-1871	286	7	α	α	NOUN
ejpam-1871	286	8	aα)/ρ	aα)/ρ	NOUN
ejpam-1871	286	9	and	and	CCONJ
ejpam-1871	286	10	l	l	NOUN
ejpam-1871	286	11	im−→bα	im−→bα	NOUN
ejpam-1871	287	1	=	=	PUNCT
ejpam-1871	287	2	(	(	PUNCT
ejpam-1871	287	3	∐	∐	ADV
ejpam-1871	287	4	α	α	NOUN
ejpam-1871	287	5	bα)/ρ′.	bα)/ρ′.	PROPN
ejpam-1871	287	6	let	let	VERB
ejpam-1871	287	7	h[aα]ρ	h[aα]ρ	NOUN
ejpam-1871	287	8	≤	≤	NUM
ejpam-1871	287	9	h[aβ]ρ	h[aβ]ρ	PROPN
ejpam-1871	287	10	.	.	PUNCT
ejpam-1871	288	1	then	then	ADV
ejpam-1871	288	2	we	we	PRON
ejpam-1871	288	3	have	have	VERB
ejpam-1871	288	4	[	[	X
ejpam-1871	288	5	hα(aα)]ρ′	hα(aα)]ρ′	PROPN
ejpam-1871	288	6	=	=	SYM
ejpam-1871	288	7	gαhα(aα	gαhα(aα	PROPN
ejpam-1871	288	8	)	)	PUNCT
ejpam-1871	288	9	=	=	SYM
ejpam-1871	288	10	hfα(aα	hfα(aα	X
ejpam-1871	288	11	)	)	PUNCT
ejpam-1871	288	12	=	=	SYM
ejpam-1871	288	13	h[aα]ρ	h[aα]ρ	NOUN
ejpam-1871	288	14	≤	≤	NUM
ejpam-1871	288	15	h.	h.	PROPN
ejpam-1871	288	16	rasouli	rasouli	PROPN
ejpam-1871	288	17	/	/	SYM
ejpam-1871	288	18	eur	eur	PROPN
ejpam-1871	288	19	.	.	PUNCT
ejpam-1871	289	1	j.	j.	PROPN
ejpam-1871	289	2	pure	pure	PROPN
ejpam-1871	289	3	appl	appl	PROPN
ejpam-1871	289	4	.	.	PROPN
ejpam-1871	289	5	math	math	PROPN
ejpam-1871	289	6	,	,	PUNCT
ejpam-1871	289	7	7	7	NUM
ejpam-1871	289	8	(	(	PUNCT
ejpam-1871	289	9	2014	2014	NUM
ejpam-1871	289	10	)	)	PUNCT
ejpam-1871	289	11	,	,	PUNCT
ejpam-1871	289	12	166	166	NUM
ejpam-1871	289	13	-	-	SYM
ejpam-1871	289	14	178	178	NUM
ejpam-1871	289	15	174	174	NUM
ejpam-1871	289	16	h[aβ]ρ	h[aβ]ρ	NOUN
ejpam-1871	289	17	=	=	SYM
ejpam-1871	289	18	hfβ(aβ	hfβ(aβ	NOUN
ejpam-1871	289	19	)	)	PUNCT
ejpam-1871	289	20	=	=	SYM
ejpam-1871	289	21	gβhβ(aβ	gβhβ(aβ	PROPN
ejpam-1871	289	22	)	)	PUNCT
ejpam-1871	289	23	=	=	PUNCT
ejpam-1871	290	1	[	[	X
ejpam-1871	290	2	hβ(aβ)]ρ′	hβ(aβ)]ρ′	PROPN
ejpam-1871	290	3	.	.	PUNCT
ejpam-1871	291	1	therefore	therefore	ADV
ejpam-1871	291	2	,	,	PUNCT
ejpam-1871	291	3	hα(aα)≤ρ′	hα(aα)≤ρ′	PROPN
ejpam-1871	291	4	hβ(aβ	hβ(aβ	PROPN
ejpam-1871	291	5	)	)	PUNCT
ejpam-1871	292	1	and	and	CCONJ
ejpam-1871	292	2	hence	hence	ADV
ejpam-1871	292	3	there	there	PRON
ejpam-1871	292	4	exists	exist	VERB
ejpam-1871	292	5	γ	γ	X
ejpam-1871	292	6	∈	∈	PROPN
ejpam-1871	292	7	i	i	PRON
ejpam-1871	292	8	such	such	ADJ
ejpam-1871	292	9	that	that	SCONJ
ejpam-1871	292	10	γ≥	γ≥	PROPN
ejpam-1871	292	11	α	α	NOUN
ejpam-1871	292	12	,	,	PUNCT
ejpam-1871	292	13	β	β	X
ejpam-1871	292	14	and	and	CCONJ
ejpam-1871	292	15	ϕαγhα(aα	ϕαγhα(aα	ADJ
ejpam-1871	292	16	)	)	PUNCT
ejpam-1871	292	17	≤	≤	NUM
ejpam-1871	292	18	ϕβγhβ(aβ	ϕβγhβ(aβ	NOUN
ejpam-1871	292	19	)	)	PUNCT
ejpam-1871	292	20	.	.	PUNCT
ejpam-1871	293	1	this	this	PRON
ejpam-1871	293	2	implies	imply	VERB
ejpam-1871	293	3	that	that	SCONJ
ejpam-1871	293	4	hγψαγ(aα	hγψαγ(aα	ADJ
ejpam-1871	293	5	)	)	PUNCT
ejpam-1871	293	6	≤	≤	NUM
ejpam-1871	293	7	hγψβγ(aβ	hγψβγ(aβ	NOUN
ejpam-1871	293	8	)	)	PUNCT
ejpam-1871	293	9	.	.	PUNCT
ejpam-1871	294	1	now	now	ADV
ejpam-1871	294	2	,	,	PUNCT
ejpam-1871	294	3	since	since	SCONJ
ejpam-1871	294	4	hγ	hγ	PRON
ejpam-1871	294	5	is	be	AUX
ejpam-1871	294	6	a	a	DET
ejpam-1871	294	7	regular	regular	ADJ
ejpam-1871	294	8	monomorphism	monomorphism	NOUN
ejpam-1871	294	9	by	by	ADP
ejpam-1871	294	10	hypothesis	hypothesis	NOUN
ejpam-1871	294	11	,	,	PUNCT
ejpam-1871	294	12	we	we	PRON
ejpam-1871	294	13	get	get	VERB
ejpam-1871	294	14	ψαγ(aα	ψαγ(aα	ADJ
ejpam-1871	294	15	)	)	PUNCT
ejpam-1871	294	16	≤	≤	NUM
ejpam-1871	294	17	ψβγ(aβ	ψβγ(aβ	NOUN
ejpam-1871	294	18	)	)	PUNCT
ejpam-1871	294	19	which	which	PRON
ejpam-1871	294	20	gives	give	VERB
ejpam-1871	294	21	that	that	DET
ejpam-1871	294	22	aα	aα	NOUN
ejpam-1871	294	23	≤ρ	≤ρ	NOUN
ejpam-1871	294	24	aβ	aβ	INTJ
ejpam-1871	294	25	.	.	PUNCT
ejpam-1871	295	1	consequently	consequently	ADV
ejpam-1871	295	2	,	,	PUNCT
ejpam-1871	295	3	[	[	X
ejpam-1871	295	4	aα]ρ	aα]ρ	NOUN
ejpam-1871	295	5	≤	≤	VERB
ejpam-1871	296	1	[	[	X
ejpam-1871	296	2	aβ]ρ	aβ]ρ	ADJ
ejpam-1871	296	3	and	and	CCONJ
ejpam-1871	296	4	hence	hence	ADV
ejpam-1871	296	5	h	h	NOUN
ejpam-1871	296	6	is	be	AUX
ejpam-1871	296	7	a	a	DET
ejpam-1871	296	8	regular	regular	ADJ
ejpam-1871	296	9	monomorphism	monomorphism	NOUN
ejpam-1871	296	10	.	.	PUNCT
ejpam-1871	297	1	corollary	corollary	ADJ
ejpam-1871	297	2	2	2	NUM
ejpam-1871	297	3	.	.	PUNCT
ejpam-1871	298	1	s	s	X
ejpam-1871	298	2	-	-	PUNCT
ejpam-1871	298	3	pos	pos	NOUN
ejpam-1871	298	4	hasm	hasm	NOUN
ejpam-1871	298	5	-directed	-directe	VERB
ejpam-1871	298	6	colimits	colimit	NOUN
ejpam-1871	298	7	.	.	PUNCT
ejpam-1871	299	1	proof	proof	NOUN
ejpam-1871	299	2	.	.	PUNCT
ejpam-1871	300	1	assume	assume	VERB
ejpam-1871	300	2	that	that	SCONJ
ejpam-1871	300	3	(	(	PUNCT
ejpam-1871	300	4	l	l	PROPN
ejpam-1871	300	5	im−→bα	im−→bα	PROPN
ejpam-1871	300	6	,	,	PUNCT
ejpam-1871	300	7	gα	gα	NOUN
ejpam-1871	300	8	)	)	PUNCT
ejpam-1871	300	9	is	be	AUX
ejpam-1871	300	10	the	the	DET
ejpam-1871	300	11	directed	direct	VERB
ejpam-1871	300	12	colimit	colimit	NOUN
ejpam-1871	300	13	of	of	ADP
ejpam-1871	300	14	the	the	DET
ejpam-1871	300	15	directed	direct	VERB
ejpam-1871	300	16	system	system	NOUN
ejpam-1871	300	17	(	(	PUNCT
ejpam-1871	300	18	(	(	PUNCT
ejpam-1871	300	19	bα)α∈i	bα)α∈i	X
ejpam-1871	300	20	,	,	PUNCT
ejpam-1871	300	21	(	(	PUNCT
ejpam-1871	300	22	ϕαβ)α≤β	ϕαβ)α≤β	PROPN
ejpam-1871	300	23	)	)	PUNCT
ejpam-1871	300	24	,	,	PUNCT
ejpam-1871	300	25	and	and	CCONJ
ejpam-1871	300	26	{	{	PUNCT
ejpam-1871	300	27	hα	hα	PART
ejpam-1871	300	28	:	:	PUNCT
ejpam-1871	300	29	a→	a→	PUNCT
ejpam-1871	300	30	bα	bα	VERB
ejpam-1871	301	1	|	|	ADV
ejpam-1871	301	2	α	α	NOUN
ejpam-1871	301	3	∈	∈	PROPN
ejpam-1871	302	1	i	i	PRON
ejpam-1871	302	2	}	}	PUNCT
ejpam-1871	302	3	is	be	AUX
ejpam-1871	302	4	a	a	DET
ejpam-1871	302	5	directed	direct	VERB
ejpam-1871	302	6	family	family	NOUN
ejpam-1871	302	7	of	of	ADP
ejpam-1871	302	8	regular	regular	ADJ
ejpam-1871	302	9	monomorphisms	monomorphism	NOUN
ejpam-1871	302	10	such	such	ADJ
ejpam-1871	302	11	that	that	DET
ejpam-1871	302	12	gβϕαβ	gβϕαβ	NOUN
ejpam-1871	302	13	=	=	SYM
ejpam-1871	302	14	gα	gα	NOUN
ejpam-1871	302	15	,	,	PUNCT
ejpam-1871	302	16	for	for	ADP
ejpam-1871	302	17	every	every	DET
ejpam-1871	302	18	α	α	NOUN
ejpam-1871	302	19	≤	≤	NUM
ejpam-1871	302	20	β	β	X
ejpam-1871	302	21	.	.	PUNCT
ejpam-1871	303	1	let	let	VERB
ejpam-1871	303	2	h	h	NOUN
ejpam-1871	303	3	:	:	PUNCT
ejpam-1871	303	4	a→	a→	PUNCT
ejpam-1871	303	5	l	l	NOUN
ejpam-1871	303	6	im−→bα	im−→bα	PROPN
ejpam-1871	303	7	be	be	AUX
ejpam-1871	303	8	the	the	DET
ejpam-1871	303	9	directed	direct	VERB
ejpam-1871	303	10	colimit	colimit	NOUN
ejpam-1871	303	11	of	of	ADP
ejpam-1871	303	12	regular	regular	ADJ
ejpam-1871	303	13	monomorphisms	monomorphism	NOUN
ejpam-1871	303	14	hα	hα	ADP
ejpam-1871	303	15	:	:	PUNCT
ejpam-1871	303	16	a→	a→	PROPN
ejpam-1871	303	17	bα	bα	PROPN
ejpam-1871	303	18	,	,	PUNCT
ejpam-1871	303	19	α	α	PROPN
ejpam-1871	304	1	∈	∈	PROPN
ejpam-1871	305	1	i	i	PRON
ejpam-1871	305	2	.	.	PUNCT
ejpam-1871	305	3	recall	recall	VERB
ejpam-1871	305	4	that	that	SCONJ
ejpam-1871	305	5	h=	h=	PRON
ejpam-1871	305	6	l	l	NOUN
ejpam-1871	305	7	im−→hα	im−→hα	NOUN
ejpam-1871	305	8	=	=	PUNCT
ejpam-1871	305	9	gαhα	gαhα	ADJ
ejpam-1871	305	10	=	=	SYM
ejpam-1871	305	11	gβhβ	gβhβ	PROPN
ejpam-1871	305	12	=	=	SYM
ejpam-1871	305	13	gγhγ	gγhγ	NOUN
ejpam-1871	306	1	=	=	X
ejpam-1871	307	1	.	.	PUNCT
ejpam-1871	307	2	.	.	PUNCT
ejpam-1871	307	3	.	.	PUNCT
ejpam-1871	307	4	.	.	PUNCT
ejpam-1871	308	1	now	now	ADV
ejpam-1871	308	2	,	,	PUNCT
ejpam-1871	308	3	take	take	VERB
ejpam-1871	308	4	σ	σ	NOUN
ejpam-1871	308	5	=	=	NOUN
ejpam-1871	308	6	:	:	PUNCT
ejpam-1871	308	7	{	{	PUNCT
ejpam-1871	308	8	i	i	NOUN
ejpam-1871	308	9	d	d	PROPN
ejpam-1871	308	10	:	:	PUNCT
ejpam-1871	308	11	aα→	aα→	VERB
ejpam-1871	309	1	aγ	aγ	INTJ
ejpam-1871	309	2	|	|	ADV
ejpam-1871	310	1	α	α	NOUN
ejpam-1871	311	1	∈	∈	PROPN
ejpam-1871	312	1	i	i	PRON
ejpam-1871	312	2	−	−	PROPN
ejpam-1871	312	3	{	{	PUNCT
ejpam-1871	312	4	γ	γ	X
ejpam-1871	312	5	}	}	PUNCT
ejpam-1871	312	6	,	,	PUNCT
ejpam-1871	312	7	aα	aα	NOUN
ejpam-1871	312	8	=	=	PUNCT
ejpam-1871	312	9	a=	a=	VERB
ejpam-1871	312	10	aγ	aγ	ADP
ejpam-1871	312	11	}	}	PUNCT
ejpam-1871	312	12	.	.	PUNCT
ejpam-1871	313	1	it	it	PRON
ejpam-1871	313	2	is	be	AUX
ejpam-1871	313	3	clear	clear	ADJ
ejpam-1871	313	4	that	that	SCONJ
ejpam-1871	313	5	σ	σ	PROPN
ejpam-1871	313	6	is	be	AUX
ejpam-1871	313	7	a	a	DET
ejpam-1871	313	8	directed	direct	VERB
ejpam-1871	313	9	system	system	NOUN
ejpam-1871	313	10	and	and	CCONJ
ejpam-1871	313	11	l	l	NOUN
ejpam-1871	313	12	im−→aα	im−→aα	NOUN
ejpam-1871	313	13	=	=	PRON
ejpam-1871	313	14	∐	∐	X
ejpam-1871	313	15	aα	aα	NOUN
ejpam-1871	313	16	.	.	PUNCT
ejpam-1871	314	1	by	by	ADP
ejpam-1871	314	2	theorem	theorem	NOUN
ejpam-1871	314	3	3	3	NUM
ejpam-1871	314	4	,	,	PUNCT
ejpam-1871	314	5	the	the	DET
ejpam-1871	314	6	induced	induce	VERB
ejpam-1871	314	7	directed	direct	VERB
ejpam-1871	314	8	colimit	colimit	NOUN
ejpam-1871	314	9	homomorphism	homomorphism	PROPN
ejpam-1871	314	10	h′	h′	PROPN
ejpam-1871	314	11	:	:	PUNCT
ejpam-1871	314	12	∐	∐	PROPN
ejpam-1871	314	13	aα	aα	NOUN
ejpam-1871	314	14	→	→	SYM
ejpam-1871	314	15	l	l	NOUN
ejpam-1871	314	16	im−→bα	im−→bα	NOUN
ejpam-1871	314	17	is	be	AUX
ejpam-1871	314	18	a	a	DET
ejpam-1871	314	19	regular	regular	ADJ
ejpam-1871	314	20	monomorphism	monomorphism	NOUN
ejpam-1871	314	21	.	.	PUNCT
ejpam-1871	315	1	on	on	ADP
ejpam-1871	315	2	the	the	DET
ejpam-1871	315	3	other	other	ADJ
ejpam-1871	315	4	hand	hand	NOUN
ejpam-1871	315	5	,	,	PUNCT
ejpam-1871	315	6	obviously	obviously	ADV
ejpam-1871	315	7	the	the	DET
ejpam-1871	315	8	canonical	canonical	ADJ
ejpam-1871	315	9	map	map	NOUN
ejpam-1871	315	10	iα	iα	VERB
ejpam-1871	315	11	:	:	PUNCT
ejpam-1871	315	12	aα→	aα→	X
ejpam-1871	315	13	∐	∐	ADJ
ejpam-1871	315	14	aα	aα	PROPN
ejpam-1871	315	15	is	be	AUX
ejpam-1871	315	16	also	also	ADV
ejpam-1871	315	17	a	a	DET
ejpam-1871	315	18	regular	regular	ADJ
ejpam-1871	315	19	monomorphism	monomorphism	NOUN
ejpam-1871	315	20	.	.	PUNCT
ejpam-1871	316	1	hence	hence	ADV
ejpam-1871	316	2	,	,	PUNCT
ejpam-1871	316	3	in	in	ADP
ejpam-1871	316	4	view	view	NOUN
ejpam-1871	316	5	of	of	ADP
ejpam-1871	316	6	lemma	lemma	PROPN
ejpam-1871	316	7	1	1	NUM
ejpam-1871	316	8	(	(	PUNCT
ejpam-1871	316	9	i	i	NOUN
ejpam-1871	316	10	)	)	PUNCT
ejpam-1871	316	11	,	,	PUNCT
ejpam-1871	316	12	h=	h=	VERB
ejpam-1871	316	13	h′iα	h′iα	ADV
ejpam-1871	316	14	:	:	PUNCT
ejpam-1871	316	15	aα	aα	NOUN
ejpam-1871	316	16	=	=	SYM
ejpam-1871	316	17	a→	a→	PUNCT
ejpam-1871	316	18	l	l	NOUN
ejpam-1871	316	19	im−→bα	im−→bα	PROPN
ejpam-1871	316	20	is	be	AUX
ejpam-1871	316	21	a	a	DET
ejpam-1871	316	22	regular	regular	ADJ
ejpam-1871	316	23	monomorphism	monomorphism	NOUN
ejpam-1871	316	24	.	.	PUNCT
ejpam-1871	317	1	definition	definition	NOUN
ejpam-1871	317	2	2	2	NUM
ejpam-1871	317	3	.	.	PUNCT
ejpam-1871	318	1	let	let	VERB
ejpam-1871	318	2	e	e	PRON
ejpam-1871	318	3	be	be	AUX
ejpam-1871	318	4	a	a	DET
ejpam-1871	318	5	class	class	NOUN
ejpam-1871	318	6	of	of	ADP
ejpam-1871	318	7	morphisms	morphism	NOUN
ejpam-1871	318	8	of	of	ADP
ejpam-1871	318	9	a	a	DET
ejpam-1871	318	10	category	category	NOUN
ejpam-1871	318	11	c	c	NOUN
ejpam-1871	318	12	.	.	PUNCT
ejpam-1871	319	1	we	we	PRON
ejpam-1871	319	2	say	say	VERB
ejpam-1871	319	3	that	that	SCONJ
ejpam-1871	319	4	c	c	PROPN
ejpam-1871	319	5	fulfills	fulfill	VERB
ejpam-1871	319	6	the	the	DET
ejpam-1871	319	7	e	e	NOUN
ejpam-1871	319	8	-chain	-chain	PROPN
ejpam-1871	319	9	condition	condition	NOUN
ejpam-1871	319	10	if	if	SCONJ
ejpam-1871	319	11	for	for	ADP
ejpam-1871	319	12	every	every	DET
ejpam-1871	319	13	directed	direct	VERB
ejpam-1871	319	14	system	system	NOUN
ejpam-1871	319	15	(	(	PUNCT
ejpam-1871	319	16	(	(	PUNCT
ejpam-1871	319	17	aα)α∈i	aα)α∈i	NUM
ejpam-1871	319	18	,	,	PUNCT
ejpam-1871	319	19	(	(	PUNCT
ejpam-1871	319	20	ϕαβ)α≤β∈i	ϕαβ)α≤β∈i	X
ejpam-1871	319	21	)	)	PUNCT
ejpam-1871	319	22	whose	whose	DET
ejpam-1871	319	23	index	index	NOUN
ejpam-1871	319	24	set	set	VERB
ejpam-1871	319	25	i	i	PRON
ejpam-1871	319	26	is	be	AUX
ejpam-1871	319	27	a	a	DET
ejpam-1871	319	28	well	well	ADV
ejpam-1871	319	29	-	-	PUNCT
ejpam-1871	319	30	ordered	order	VERB
ejpam-1871	319	31	chain	chain	NOUN
ejpam-1871	319	32	with	with	ADP
ejpam-1871	319	33	the	the	DET
ejpam-1871	319	34	least	least	ADJ
ejpam-1871	319	35	element	element	NOUN
ejpam-1871	319	36	0	0	NUM
ejpam-1871	319	37	,	,	PUNCT
ejpam-1871	319	38	and	and	CCONJ
ejpam-1871	319	39	ϕ0α	ϕ0α	NUM
ejpam-1871	319	40	∈	∈	PROPN
ejpam-1871	319	41	e	e	NOUN
ejpam-1871	319	42	for	for	ADP
ejpam-1871	319	43	all	all	DET
ejpam-1871	319	44	α	α	NOUN
ejpam-1871	319	45	,	,	PUNCT
ejpam-1871	319	46	there	there	PRON
ejpam-1871	319	47	is	be	VERB
ejpam-1871	319	48	a	a	DET
ejpam-1871	319	49	(	(	PUNCT
ejpam-1871	319	50	so	so	ADV
ejpam-1871	319	51	called	call	VERB
ejpam-1871	319	52	“	"	PUNCT
ejpam-1871	319	53	upper	upper	ADJ
ejpam-1871	319	54	bound	bind	VERB
ejpam-1871	319	55	"	"	PUNCT
ejpam-1871	319	56	)	)	PUNCT
ejpam-1871	319	57	family	family	NOUN
ejpam-1871	319	58	(	(	PUNCT
ejpam-1871	319	59	gα	gα	ADP
ejpam-1871	319	60	:	:	PUNCT
ejpam-1871	319	61	aα→	aα→	X
ejpam-1871	319	62	a)α∈i	a)α∈i	NOUN
ejpam-1871	319	63	with	with	ADP
ejpam-1871	319	64	g0	g0	PROPN
ejpam-1871	319	65	∈	∈	PROPN
ejpam-1871	319	66	e	e	PROPN
ejpam-1871	319	67	and	and	CCONJ
ejpam-1871	319	68	gβϕαβ	gβϕαβ	PROPN
ejpam-1871	319	69	=	=	SYM
ejpam-1871	319	70	gα	gα	NOUN
ejpam-1871	319	71	.	.	PUNCT
ejpam-1871	319	72	proposition	proposition	NOUN
ejpam-1871	319	73	7	7	NUM
ejpam-1871	319	74	.	.	PUNCT
ejpam-1871	319	75	s	s	X
ejpam-1871	319	76	-	-	PUNCT
ejpam-1871	319	77	pos	pos	NOUN
ejpam-1871	319	78	fulfills	fulfill	VERB
ejpam-1871	319	79	them	they	PRON
ejpam-1871	319	80	-chain	-chain	ADJ
ejpam-1871	319	81	condition	condition	NOUN
ejpam-1871	319	82	.	.	PUNCT
ejpam-1871	320	1	proof	proof	NOUN
ejpam-1871	320	2	.	.	PUNCT
ejpam-1871	321	1	take	take	VERB
ejpam-1871	321	2	a=	a=	ADV
ejpam-1871	321	3	l	l	NOUN
ejpam-1871	321	4	im−→αaα	im−→αaα	ADV
ejpam-1871	321	5	and	and	CCONJ
ejpam-1871	321	6	let	let	VERB
ejpam-1871	321	7	gα	gα	VERB
ejpam-1871	321	8	:	:	PUNCT
ejpam-1871	321	9	aα→	aα→	DET
ejpam-1871	321	10	a	a	DET
ejpam-1871	321	11	be	be	AUX
ejpam-1871	321	12	the	the	DET
ejpam-1871	321	13	colimit	colimit	NOUN
ejpam-1871	321	14	maps	map	NOUN
ejpam-1871	321	15	.	.	PUNCT
ejpam-1871	322	1	then	then	ADV
ejpam-1871	322	2	,	,	PUNCT
ejpam-1871	322	3	applying	apply	VERB
ejpam-1871	322	4	corollary	corollary	NOUN
ejpam-1871	322	5	2	2	NUM
ejpam-1871	322	6	,	,	PUNCT
ejpam-1871	322	7	we	we	PRON
ejpam-1871	322	8	get	get	VERB
ejpam-1871	322	9	the	the	DET
ejpam-1871	322	10	result	result	NOUN
ejpam-1871	322	11	.	.	PUNCT
ejpam-1871	323	1	3	3	X
ejpam-1871	323	2	.	.	X
ejpam-1871	323	3	comparison	comparison	NOUN
ejpam-1871	323	4	of	of	ADP
ejpam-1871	323	5	categorical	categorical	ADJ
ejpam-1871	323	6	properties	property	NOUN
ejpam-1871	323	7	of	of	ADP
ejpam-1871	323	8	monomorphisms	monomorphism	NOUN
ejpam-1871	323	9	and	and	CCONJ
ejpam-1871	323	10	regular	regular	ADJ
ejpam-1871	323	11	monomorphisms	monomorphism	NOUN
ejpam-1871	323	12	in	in	ADP
ejpam-1871	323	13	this	this	DET
ejpam-1871	323	14	section	section	NOUN
ejpam-1871	323	15	some	some	DET
ejpam-1871	323	16	category	category	NOUN
ejpam-1871	323	17	-	-	PUNCT
ejpam-1871	323	18	theoretic	theoretic	NOUN
ejpam-1871	323	19	notions	notion	NOUN
ejpam-1871	323	20	relative	relative	ADJ
ejpam-1871	323	21	to	to	ADP
ejpam-1871	323	22	monomorphisms	monomorphism	NOUN
ejpam-1871	323	23	and	and	CCONJ
ejpam-1871	323	24	regular	regular	ADJ
ejpam-1871	323	25	monomorphisms	monomorphism	NOUN
ejpam-1871	323	26	in	in	ADP
ejpam-1871	323	27	pos	pos	NOUN
ejpam-1871	323	28	and	and	CCONJ
ejpam-1871	323	29	s	s	NOUN
ejpam-1871	323	30	-	-	PUNCT
ejpam-1871	323	31	pos	pos	NOUN
ejpam-1871	323	32	is	be	AUX
ejpam-1871	323	33	studied	study	VERB
ejpam-1871	323	34	.	.	PUNCT
ejpam-1871	324	1	we	we	PRON
ejpam-1871	324	2	show	show	VERB
ejpam-1871	324	3	that	that	SCONJ
ejpam-1871	324	4	these	these	DET
ejpam-1871	324	5	morphisms	morphism	NOUN
ejpam-1871	324	6	have	have	VERB
ejpam-1871	324	7	a	a	DET
ejpam-1871	324	8	different	different	ADJ
ejpam-1871	324	9	behaviour	behaviour	NOUN
ejpam-1871	324	10	with	with	ADP
ejpam-1871	324	11	some	some	DET
ejpam-1871	324	12	categorical	categorical	ADJ
ejpam-1871	324	13	properties	property	NOUN
ejpam-1871	324	14	.	.	PUNCT
ejpam-1871	325	1	first	first	ADV
ejpam-1871	325	2	notice	notice	VERB
ejpam-1871	325	3	that	that	SCONJ
ejpam-1871	325	4	using	use	VERB
ejpam-1871	325	5	similar	similar	ADJ
ejpam-1871	325	6	arguments	argument	NOUN
ejpam-1871	325	7	in	in	ADP
ejpam-1871	325	8	proofs	proof	NOUN
ejpam-1871	325	9	of	of	ADP
ejpam-1871	325	10	results	result	NOUN
ejpam-1871	325	11	in	in	ADP
ejpam-1871	325	12	section	section	NOUN
ejpam-1871	325	13	2	2	NUM
ejpam-1871	325	14	for	for	ADP
ejpam-1871	325	15	the	the	DET
ejpam-1871	325	16	class	class	NOUN
ejpam-1871	325	17	of	of	ADP
ejpam-1871	325	18	monomorphisms	monomorphism	NOUN
ejpam-1871	325	19	,	,	PUNCT
ejpam-1871	325	20	some	some	DET
ejpam-1871	325	21	properties	property	NOUN
ejpam-1871	325	22	regarding	regard	VERB
ejpam-1871	325	23	composition	composition	NOUN
ejpam-1871	325	24	closed	close	VERB
ejpam-1871	325	25	,	,	PUNCT
ejpam-1871	325	26	limits	limit	NOUN
ejpam-1871	325	27	(	(	PUNCT
ejpam-1871	325	28	products	product	NOUN
ejpam-1871	325	29	and	and	CCONJ
ejpam-1871	325	30	pullbacks	pullback	NOUN
ejpam-1871	325	31	)	)	PUNCT
ejpam-1871	325	32	,	,	PUNCT
ejpam-1871	325	33	colimits	colimit	NOUN
ejpam-1871	325	34	(	(	PUNCT
ejpam-1871	325	35	coproducts	coproduct	NOUN
ejpam-1871	325	36	and	and	CCONJ
ejpam-1871	325	37	direct	direct	ADJ
ejpam-1871	325	38	sums	sum	NOUN
ejpam-1871	325	39	)	)	PUNCT
ejpam-1871	325	40	and	and	CCONJ
ejpam-1871	325	41	directed	direct	VERB
ejpam-1871	325	42	colimits	colimit	NOUN
ejpam-1871	325	43	hold	hold	VERB
ejpam-1871	325	44	in	in	ADP
ejpam-1871	325	45	pos	pos	NOUN
ejpam-1871	325	46	and	and	CCONJ
ejpam-1871	325	47	s	s	NOUN
ejpam-1871	325	48	-	-	PUNCT
ejpam-1871	325	49	pos	pos	NOUN
ejpam-1871	325	50	.	.	PUNCT
ejpam-1871	326	1	about	about	ADP
ejpam-1871	326	2	factorization	factorization	NOUN
ejpam-1871	326	3	diagonalization	diagonalization	NOUN
ejpam-1871	326	4	property	property	NOUN
ejpam-1871	326	5	,	,	PUNCT
ejpam-1871	326	6	note	note	VERB
ejpam-1871	326	7	the	the	DET
ejpam-1871	326	8	following	following	NOUN
ejpam-1871	326	9	:	:	PUNCT
ejpam-1871	326	10	h.	h.	PROPN
ejpam-1871	326	11	rasouli	rasouli	PROPN
ejpam-1871	326	12	/	/	SYM
ejpam-1871	326	13	eur	eur	PROPN
ejpam-1871	326	14	.	.	PUNCT
ejpam-1871	327	1	j.	j.	PROPN
ejpam-1871	327	2	pure	pure	PROPN
ejpam-1871	327	3	appl	appl	PROPN
ejpam-1871	327	4	.	.	PROPN
ejpam-1871	327	5	math	math	PROPN
ejpam-1871	327	6	,	,	PUNCT
ejpam-1871	327	7	7	7	NUM
ejpam-1871	327	8	(	(	PUNCT
ejpam-1871	327	9	2014	2014	NUM
ejpam-1871	327	10	)	)	PUNCT
ejpam-1871	327	11	,	,	PUNCT
ejpam-1871	327	12	166	166	NUM
ejpam-1871	327	13	-	-	SYM
ejpam-1871	327	14	178	178	NUM
ejpam-1871	327	15	175	175	NUM
ejpam-1871	327	16	remark	remark	NOUN
ejpam-1871	327	17	2	2	NUM
ejpam-1871	327	18	.	.	PUNCT
ejpam-1871	327	19	s	s	X
ejpam-1871	327	20	-	-	PUNCT
ejpam-1871	327	21	pos	pos	NOUN
ejpam-1871	327	22	does	do	AUX
ejpam-1871	327	23	not	not	PART
ejpam-1871	327	24	generally	generally	ADV
ejpam-1871	327	25	have	have	VERB
ejpam-1871	327	26	(	(	PUNCT
ejpam-1871	327	27	e	e	NOUN
ejpam-1871	327	28	,	,	PUNCT
ejpam-1871	327	29	m	m	VERB
ejpam-1871	327	30	ono)-factorization	ono)-factorization	NOUN
ejpam-1871	327	31	diagonalization	diagonalization	NOUN
ejpam-1871	327	32	property	property	NOUN
ejpam-1871	327	33	,	,	PUNCT
ejpam-1871	327	34	where	where	SCONJ
ejpam-1871	327	35	e	e	PROPN
ejpam-1871	327	36	andm	andm	PROPN
ejpam-1871	327	37	ono	ono	PROPN
ejpam-1871	327	38	are	be	AUX
ejpam-1871	327	39	the	the	DET
ejpam-1871	327	40	classes	class	NOUN
ejpam-1871	327	41	of	of	ADP
ejpam-1871	327	42	epimorphisms	epimorphism	NOUN
ejpam-1871	327	43	and	and	CCONJ
ejpam-1871	327	44	monomorphisms	monomorphism	NOUN
ejpam-1871	327	45	,	,	PUNCT
ejpam-1871	327	46	respectively	respectively	ADV
ejpam-1871	327	47	.	.	PUNCT
ejpam-1871	328	1	in	in	ADP
ejpam-1871	328	2	fact	fact	NOUN
ejpam-1871	328	3	,	,	PUNCT
ejpam-1871	328	4	although	although	SCONJ
ejpam-1871	328	5	each	each	DET
ejpam-1871	328	6	s	s	NOUN
ejpam-1871	328	7	-	-	PUNCT
ejpam-1871	328	8	poset	poset	VERB
ejpam-1871	328	9	morphism	morphism	NOUN
ejpam-1871	328	10	f	f	PROPN
ejpam-1871	328	11	has	have	VERB
ejpam-1871	328	12	a	a	DET
ejpam-1871	328	13	factorization	factorization	NOUN
ejpam-1871	328	14	as	as	ADP
ejpam-1871	328	15	f	f	PROPN
ejpam-1871	328	16	=	=	SYM
ejpam-1871	328	17	me	me	PROPN
ejpam-1871	328	18	,	,	PUNCT
ejpam-1871	328	19	where	where	SCONJ
ejpam-1871	328	20	m	m	VERB
ejpam-1871	328	21	∈m	∈m	NOUN
ejpam-1871	328	22	ono	ono	PROPN
ejpam-1871	328	23	,	,	PUNCT
ejpam-1871	328	24	e	e	PROPN
ejpam-1871	328	25	∈	∈	PROPN
ejpam-1871	328	26	e	e	X
ejpam-1871	328	27	(	(	PUNCT
ejpam-1871	328	28	see	see	VERB
ejpam-1871	328	29	the	the	DET
ejpam-1871	328	30	proof	proof	NOUN
ejpam-1871	328	31	of	of	ADP
ejpam-1871	328	32	proposition	proposition	NOUN
ejpam-1871	328	33	1	1	NUM
ejpam-1871	328	34	)	)	PUNCT
ejpam-1871	328	35	,	,	PUNCT
ejpam-1871	328	36	there	there	PRON
ejpam-1871	328	37	exist	exist	VERB
ejpam-1871	328	38	e	e	X
ejpam-1871	328	39	∈	∈	PROPN
ejpam-1871	328	40	e	e	NOUN
ejpam-1871	328	41	and	and	CCONJ
ejpam-1871	328	42	m	m	PROPN
ejpam-1871	328	43	∈	∈	PROPN
ejpam-1871	328	44	m	m	VERB
ejpam-1871	328	45	ono	ono	NOUN
ejpam-1871	328	46	such	such	ADJ
ejpam-1871	328	47	that	that	SCONJ
ejpam-1871	328	48	e	e	NOUN
ejpam-1871	328	49	is	be	AUX
ejpam-1871	328	50	not	not	PART
ejpam-1871	328	51	vertical	vertical	ADJ
ejpam-1871	328	52	on	on	ADP
ejpam-1871	328	53	m.	m.	NOUN
ejpam-1871	328	54	to	to	PART
ejpam-1871	328	55	see	see	VERB
ejpam-1871	328	56	this	this	PRON
ejpam-1871	328	57	,	,	PUNCT
ejpam-1871	328	58	for	for	ADP
ejpam-1871	328	59	a	a	DET
ejpam-1871	328	60	pomonoid	pomonoid	NOUN
ejpam-1871	328	61	s	s	PART
ejpam-1871	328	62	,	,	PUNCT
ejpam-1871	328	63	consider	consider	VERB
ejpam-1871	328	64	the	the	DET
ejpam-1871	328	65	s	s	NOUN
ejpam-1871	328	66	-	-	PUNCT
ejpam-1871	328	67	posets	poset	NOUN
ejpam-1871	328	68	a=	a=	VERB
ejpam-1871	328	69	1	1	NUM
ejpam-1871	328	70	t	t	NOUN
ejpam-1871	328	71	1	1	NUM
ejpam-1871	328	72	=	=	SYM
ejpam-1871	328	73	{	{	PUNCT
ejpam-1871	328	74	a	a	PRON
ejpam-1871	328	75	,	,	PUNCT
ejpam-1871	328	76	b	b	NOUN
ejpam-1871	328	77	}	}	PUNCT
ejpam-1871	328	78	,	,	PUNCT
ejpam-1871	328	79	b	b	X
ejpam-1871	328	80	=	=	SYM
ejpam-1871	328	81	2	2	NUM
ejpam-1871	328	82	=	=	SYM
ejpam-1871	328	83	(	(	PUNCT
ejpam-1871	328	84	{	{	PUNCT
ejpam-1871	328	85	a	a	PROPN
ejpam-1871	328	86	,	,	PUNCT
ejpam-1871	328	87	b	b	NOUN
ejpam-1871	328	88	}	}	PUNCT
ejpam-1871	328	89	,	,	PUNCT
ejpam-1871	328	90	a≤	a≤	DET
ejpam-1871	328	91	b	b	NOUN
ejpam-1871	328	92	)	)	PUNCT
ejpam-1871	328	93	,	,	PUNCT
ejpam-1871	328	94	c	c	NOUN
ejpam-1871	328	95	=	=	SYM
ejpam-1871	328	96	2	2	NUM
ejpam-1871	328	97	t	t	NOUN
ejpam-1871	328	98	1	1	NUM
ejpam-1871	328	99	=	=	SYM
ejpam-1871	328	100	(	(	PUNCT
ejpam-1871	328	101	{	{	PUNCT
ejpam-1871	328	102	a	a	PRON
ejpam-1871	328	103	,	,	PUNCT
ejpam-1871	328	104	b	b	NOUN
ejpam-1871	328	105	,	,	PUNCT
ejpam-1871	328	106	c	c	NOUN
ejpam-1871	328	107	}	}	PUNCT
ejpam-1871	328	108	,	,	PUNCT
ejpam-1871	328	109	a≤	a≤	DET
ejpam-1871	328	110	b	b	NOUN
ejpam-1871	328	111	)	)	PUNCT
ejpam-1871	328	112	and	and	CCONJ
ejpam-1871	328	113	d	d	NOUN
ejpam-1871	328	114	=	=	SYM
ejpam-1871	328	115	3	3	NUM
ejpam-1871	328	116	=	=	SYM
ejpam-1871	328	117	(	(	PUNCT
ejpam-1871	328	118	{	{	PUNCT
ejpam-1871	328	119	a	a	PRON
ejpam-1871	328	120	,	,	PUNCT
ejpam-1871	328	121	b	b	NOUN
ejpam-1871	328	122	,	,	PUNCT
ejpam-1871	328	123	c	c	NOUN
ejpam-1871	328	124	}	}	PUNCT
ejpam-1871	328	125	,	,	PUNCT
ejpam-1871	328	126	a≤	a≤	VERB
ejpam-1871	328	127	b≤	b≤	PROPN
ejpam-1871	328	128	c	c	NOUN
ejpam-1871	328	129	)	)	PUNCT
ejpam-1871	328	130	with	with	ADP
ejpam-1871	328	131	trivial	trivial	ADJ
ejpam-1871	328	132	actions	action	NOUN
ejpam-1871	328	133	of	of	ADP
ejpam-1871	328	134	s.	s.	PROPN
ejpam-1871	328	135	take	take	VERB
ejpam-1871	328	136	the	the	DET
ejpam-1871	328	137	inclusion	inclusion	NOUN
ejpam-1871	328	138	maps	map	NOUN
ejpam-1871	328	139	e	e	NOUN
ejpam-1871	328	140	:	:	PUNCT
ejpam-1871	328	141	a	a	DET
ejpam-1871	328	142	,	,	PUNCT
ejpam-1871	328	143	→	→	SYM
ejpam-1871	328	144	b	b	PROPN
ejpam-1871	328	145	and	and	CCONJ
ejpam-1871	328	146	m	m	PRON
ejpam-1871	328	147	:	:	PUNCT
ejpam-1871	329	1	c	c	X
ejpam-1871	329	2	,	,	PUNCT
ejpam-1871	329	3	→	→	SYM
ejpam-1871	329	4	d.	d.	PROPN
ejpam-1871	329	5	clearly	clearly	ADV
ejpam-1871	329	6	,	,	PUNCT
ejpam-1871	329	7	m	m	PROPN
ejpam-1871	329	8	∈	∈	PROPN
ejpam-1871	329	9	m	m	NOUN
ejpam-1871	329	10	ono	ono	PROPN
ejpam-1871	329	11	and	and	CCONJ
ejpam-1871	329	12	e	e	NOUN
ejpam-1871	329	13	∈	∈	PROPN
ejpam-1871	329	14	e	e	X
ejpam-1871	329	15	.	.	PUNCT
ejpam-1871	330	1	we	we	PRON
ejpam-1871	330	2	show	show	VERB
ejpam-1871	330	3	that	that	SCONJ
ejpam-1871	330	4	e	e	NOUN
ejpam-1871	330	5	is	be	AUX
ejpam-1871	330	6	not	not	PART
ejpam-1871	330	7	vertical	vertical	ADJ
ejpam-1871	330	8	on	on	ADP
ejpam-1871	330	9	m.	m.	NOUN
ejpam-1871	330	10	for	for	ADP
ejpam-1871	330	11	this	this	PRON
ejpam-1871	330	12	,	,	PUNCT
ejpam-1871	330	13	define	define	VERB
ejpam-1871	330	14	the	the	DET
ejpam-1871	330	15	morphisms	morphism	NOUN
ejpam-1871	330	16	u	u	NOUN
ejpam-1871	330	17	:	:	PUNCT
ejpam-1871	330	18	a	a	DET
ejpam-1871	330	19	→	→	SYM
ejpam-1871	330	20	c	c	NOUN
ejpam-1871	330	21	and	and	CCONJ
ejpam-1871	330	22	v	v	X
ejpam-1871	330	23	:	:	PUNCT
ejpam-1871	330	24	b	b	X
ejpam-1871	330	25	→	→	SYM
ejpam-1871	330	26	d	d	NOUN
ejpam-1871	330	27	by	by	ADP
ejpam-1871	330	28	u(a	u(a	NOUN
ejpam-1871	330	29	)	)	PUNCT
ejpam-1871	330	30	=	=	SYM
ejpam-1871	330	31	v(a	v(a	X
ejpam-1871	330	32	)	)	PUNCT
ejpam-1871	330	33	=	=	SYM
ejpam-1871	330	34	b	b	PROPN
ejpam-1871	330	35	,	,	PUNCT
ejpam-1871	330	36	u(b	u(b	NUM
ejpam-1871	330	37	)	)	PUNCT
ejpam-1871	330	38	=	=	SYM
ejpam-1871	330	39	v(b	v(b	PROPN
ejpam-1871	330	40	)	)	PUNCT
ejpam-1871	330	41	=	=	SYM
ejpam-1871	330	42	c.	c.	NOUN
ejpam-1871	330	43	consider	consider	VERB
ejpam-1871	330	44	the	the	DET
ejpam-1871	330	45	following	follow	VERB
ejpam-1871	330	46	commutative	commutative	ADJ
ejpam-1871	330	47	diagram	diagram	NOUN
ejpam-1871	330	48	a	a	DET
ejpam-1871	330	49	u	u	PROPN
ejpam-1871	330	50	�	�	PROPN
ejpam-1871	330	51	�	�	PROPN
ejpam-1871	330	52	e	e	PROPN
ejpam-1871	330	53	//	//	PROPN
ejpam-1871	330	54	b	b	PROPN
ejpam-1871	330	55	v	v	NUM
ejpam-1871	330	56	�	�	PROPN
ejpam-1871	330	57	�	�	PROPN
ejpam-1871	330	58	c	c	PROPN
ejpam-1871	330	59	m	m	PROPN
ejpam-1871	330	60	//	//	PROPN
ejpam-1871	331	1	d	d	X
ejpam-1871	331	2	one	one	PRON
ejpam-1871	331	3	can	can	AUX
ejpam-1871	331	4	easily	easily	ADV
ejpam-1871	331	5	check	check	VERB
ejpam-1871	331	6	that	that	SCONJ
ejpam-1871	331	7	there	there	PRON
ejpam-1871	331	8	is	be	VERB
ejpam-1871	331	9	no	no	DET
ejpam-1871	331	10	morphism	morphism	NOUN
ejpam-1871	331	11	d	d	NOUN
ejpam-1871	331	12	:	:	PUNCT
ejpam-1871	331	13	b→	b→	PROPN
ejpam-1871	331	14	c	c	NOUN
ejpam-1871	331	15	such	such	ADJ
ejpam-1871	331	16	that	that	PRON
ejpam-1871	331	17	de	de	X
ejpam-1871	331	18	=	=	SYM
ejpam-1871	331	19	u.	u.	VERB
ejpam-1871	331	20	the	the	DET
ejpam-1871	331	21	following	follow	VERB
ejpam-1871	331	22	example	example	NOUN
ejpam-1871	331	23	shows	show	VERB
ejpam-1871	331	24	that	that	SCONJ
ejpam-1871	331	25	,	,	PUNCT
ejpam-1871	331	26	in	in	ADP
ejpam-1871	331	27	contrast	contrast	NOUN
ejpam-1871	331	28	to	to	ADP
ejpam-1871	331	29	some	some	DET
ejpam-1871	331	30	categories	category	NOUN
ejpam-1871	331	31	such	such	ADJ
ejpam-1871	331	32	as	as	ADP
ejpam-1871	331	33	s	s	NOUN
ejpam-1871	331	34	-	-	NOUN
ejpam-1871	331	35	act	act	NOUN
ejpam-1871	331	36	,	,	PUNCT
ejpam-1871	331	37	for	for	ADP
ejpam-1871	331	38	a	a	DET
ejpam-1871	331	39	monoid	monoid	NOUN
ejpam-1871	331	40	s	s	NOUN
ejpam-1871	331	41	,	,	PUNCT
ejpam-1871	331	42	pushouts	pushout	NOUN
ejpam-1871	331	43	do	do	AUX
ejpam-1871	331	44	not	not	PART
ejpam-1871	331	45	transfer	transfer	VERB
ejpam-1871	331	46	monomorphisms	monomorphism	NOUN
ejpam-1871	331	47	in	in	ADP
ejpam-1871	331	48	s	s	NOUN
ejpam-1871	331	49	-	-	PUNCT
ejpam-1871	331	50	pos	pos	NOUN
ejpam-1871	331	51	(	(	PUNCT
ejpam-1871	331	52	see	see	VERB
ejpam-1871	331	53	[	[	X
ejpam-1871	331	54	4	4	NUM
ejpam-1871	331	55	,	,	PUNCT
ejpam-1871	331	56	theorem	theorem	ADJ
ejpam-1871	331	57	3.2(1	3.2(1	NUM
ejpam-1871	331	58	)	)	PUNCT
ejpam-1871	331	59	]	]	PUNCT
ejpam-1871	331	60	)	)	PUNCT
ejpam-1871	331	61	.	.	PUNCT
ejpam-1871	332	1	example	example	NOUN
ejpam-1871	333	1	1	1	NUM
ejpam-1871	333	2	.	.	X
ejpam-1871	333	3	for	for	ADP
ejpam-1871	333	4	a	a	DET
ejpam-1871	333	5	pomonoid	pomonoid	NOUN
ejpam-1871	333	6	s	s	PART
ejpam-1871	333	7	,	,	PUNCT
ejpam-1871	333	8	consider	consider	VERB
ejpam-1871	333	9	the	the	DET
ejpam-1871	333	10	s	s	NOUN
ejpam-1871	333	11	-	-	PUNCT
ejpam-1871	333	12	posets	poset	NOUN
ejpam-1871	333	13	a=	a=	NOUN
ejpam-1871	333	14	1t1=	1t1=	NUM
ejpam-1871	333	15	{	{	PUNCT
ejpam-1871	333	16	a	a	DET
ejpam-1871	333	17	,	,	PUNCT
ejpam-1871	333	18	b	b	NOUN
ejpam-1871	333	19	}	}	PUNCT
ejpam-1871	333	20	,	,	PUNCT
ejpam-1871	333	21	b	b	X
ejpam-1871	333	22	=	=	SYM
ejpam-1871	333	23	2=	2=	NUM
ejpam-1871	333	24	(	(	PUNCT
ejpam-1871	333	25	{	{	PUNCT
ejpam-1871	333	26	a	a	PRON
ejpam-1871	333	27	,	,	PUNCT
ejpam-1871	333	28	b	b	NOUN
ejpam-1871	333	29	}	}	PUNCT
ejpam-1871	333	30	,	,	PUNCT
ejpam-1871	333	31	a≤	a≤	DET
ejpam-1871	333	32	b	b	NOUN
ejpam-1871	333	33	)	)	PUNCT
ejpam-1871	333	34	and	and	CCONJ
ejpam-1871	333	35	c	c	NOUN
ejpam-1871	333	36	=	=	SYM
ejpam-1871	333	37	2	2	NUM
ejpam-1871	333	38	t	t	NOUN
ejpam-1871	333	39	1	1	NUM
ejpam-1871	333	40	=	=	SYM
ejpam-1871	333	41	(	(	PUNCT
ejpam-1871	333	42	{	{	PUNCT
ejpam-1871	333	43	a	a	PRON
ejpam-1871	333	44	,	,	PUNCT
ejpam-1871	333	45	b	b	NOUN
ejpam-1871	333	46	,	,	PUNCT
ejpam-1871	333	47	c	c	NOUN
ejpam-1871	333	48	}	}	PUNCT
ejpam-1871	333	49	,	,	PUNCT
ejpam-1871	333	50	a≤	a≤	ADP
ejpam-1871	333	51	c	c	NOUN
ejpam-1871	333	52	)	)	PUNCT
ejpam-1871	333	53	with	with	ADP
ejpam-1871	333	54	trivial	trivial	ADJ
ejpam-1871	333	55	actions	action	NOUN
ejpam-1871	333	56	of	of	ADP
ejpam-1871	333	57	s	s	PROPN
ejpam-1871	333	58	,	,	PUNCT
ejpam-1871	333	59	and	and	CCONJ
ejpam-1871	333	60	also	also	ADV
ejpam-1871	333	61	the	the	DET
ejpam-1871	333	62	inclusion	inclusion	NOUN
ejpam-1871	334	1	i	i	PRON
ejpam-1871	334	2	:	:	PUNCT
ejpam-1871	334	3	a	a	DET
ejpam-1871	334	4	,	,	PUNCT
ejpam-1871	334	5	→	→	SYM
ejpam-1871	334	6	b	b	NOUN
ejpam-1871	334	7	and	and	CCONJ
ejpam-1871	334	8	the	the	DET
ejpam-1871	334	9	homomorphism	homomorphism	PROPN
ejpam-1871	334	10	j	j	PROPN
ejpam-1871	334	11	:	:	PUNCT
ejpam-1871	334	12	a→	a→	PUNCT
ejpam-1871	334	13	c	c	NOUN
ejpam-1871	334	14	given	give	VERB
ejpam-1871	334	15	by	by	ADP
ejpam-1871	334	16	j(a	j(a	NOUN
ejpam-1871	334	17	)	)	PUNCT
ejpam-1871	335	1	=	=	SYM
ejpam-1871	335	2	c	c	X
ejpam-1871	335	3	,	,	PUNCT
ejpam-1871	335	4	j(b	j(b	NOUN
ejpam-1871	335	5	)	)	PUNCT
ejpam-1871	335	6	=	=	VERB
ejpam-1871	336	1	a.	a.	NOUN
ejpam-1871	336	2	the	the	DET
ejpam-1871	336	3	pushout	pushout	NOUN
ejpam-1871	336	4	of	of	ADP
ejpam-1871	336	5	i	i	PRON
ejpam-1871	336	6	and	and	CCONJ
ejpam-1871	336	7	j	j	PROPN
ejpam-1871	336	8	is	be	AUX
ejpam-1871	336	9	described	describe	VERB
ejpam-1871	336	10	as	as	ADP
ejpam-1871	336	11	�	�	PROPN
ejpam-1871	336	12	q	q	PROPN
ejpam-1871	337	1	=	=	PUNCT
ejpam-1871	337	2	(	(	PUNCT
ejpam-1871	337	3	b	b	PROPN
ejpam-1871	337	4	t	t	PROPN
ejpam-1871	337	5	c)/θ	c)/θ	NOUN
ejpam-1871	337	6	(	(	PUNCT
ejpam-1871	337	7	h	h	NOUN
ejpam-1871	337	8	)	)	PUNCT
ejpam-1871	337	9	,	,	PUNCT
ejpam-1871	337	10	qb	qb	PROPN
ejpam-1871	337	11	=	=	PUNCT
ejpam-1871	337	12	πib	πib	PROPN
ejpam-1871	337	13	,	,	PUNCT
ejpam-1871	337	14	qc	qc	PROPN
ejpam-1871	337	15	=	=	SYM
ejpam-1871	337	16	πic	πic	PROPN
ejpam-1871	337	17	�	�	PROPN
ejpam-1871	337	18	where	where	SCONJ
ejpam-1871	337	19	θ	θ	PROPN
ejpam-1871	337	20	(	(	PUNCT
ejpam-1871	337	21	h	h	NOUN
ejpam-1871	337	22	)	)	PUNCT
ejpam-1871	337	23	is	be	AUX
ejpam-1871	337	24	the	the	DET
ejpam-1871	337	25	s	s	NOUN
ejpam-1871	337	26	-	-	PUNCT
ejpam-1871	337	27	poset	poset	ADJ
ejpam-1871	337	28	congruence	congruence	NOUN
ejpam-1871	337	29	on	on	ADP
ejpam-1871	337	30	b	b	PROPN
ejpam-1871	337	31	t	t	PROPN
ejpam-1871	337	32	c	c	AUX
ejpam-1871	337	33	generated	generate	VERB
ejpam-1871	337	34	by	by	ADP
ejpam-1871	337	35	h	h	PROPN
ejpam-1871	337	36	=	=	PRON
ejpam-1871	337	37	{	{	PUNCT
ejpam-1871	337	38	(	(	PUNCT
ejpam-1871	337	39	(	(	PUNCT
ejpam-1871	337	40	1	1	NUM
ejpam-1871	337	41	,	,	PUNCT
ejpam-1871	337	42	a	a	NOUN
ejpam-1871	337	43	)	)	PUNCT
ejpam-1871	337	44	,	,	PUNCT
ejpam-1871	337	45	(	(	PUNCT
ejpam-1871	337	46	2	2	NUM
ejpam-1871	337	47	,	,	PUNCT
ejpam-1871	337	48	c	c	NOUN
ejpam-1871	337	49	)	)	PUNCT
ejpam-1871	337	50	)	)	PUNCT
ejpam-1871	337	51	,	,	PUNCT
ejpam-1871	337	52	(	(	PUNCT
ejpam-1871	337	53	(	(	PUNCT
ejpam-1871	337	54	1	1	NUM
ejpam-1871	337	55	,	,	PUNCT
ejpam-1871	337	56	b	b	NOUN
ejpam-1871	337	57	)	)	PUNCT
ejpam-1871	337	58	,	,	PUNCT
ejpam-1871	337	59	(	(	PUNCT
ejpam-1871	337	60	2	2	NUM
ejpam-1871	337	61	,	,	PUNCT
ejpam-1871	337	62	a	a	PRON
ejpam-1871	337	63	)	)	PUNCT
ejpam-1871	337	64	)	)	PUNCT
ejpam-1871	337	65	}	}	PUNCT
ejpam-1871	337	66	,	,	PUNCT
ejpam-1871	337	67	π	π	X
ejpam-1871	337	68	:	:	PUNCT
ejpam-1871	337	69	b	b	X
ejpam-1871	337	70	t	t	X
ejpam-1871	337	71	c	c	PROPN
ejpam-1871	337	72	→q	→q	PUNCT
ejpam-1871	337	73	is	be	AUX
ejpam-1871	337	74	the	the	DET
ejpam-1871	337	75	natural	natural	ADJ
ejpam-1871	337	76	map	map	NOUN
ejpam-1871	337	77	,	,	PUNCT
ejpam-1871	337	78	and	and	CCONJ
ejpam-1871	337	79	ib	ib	INTJ
ejpam-1871	337	80	,	,	PUNCT
ejpam-1871	337	81	ic	ic	PROPN
ejpam-1871	337	82	are	be	AUX
ejpam-1871	337	83	the	the	DET
ejpam-1871	337	84	coproduct	coproduct	NOUN
ejpam-1871	337	85	injections	injection	NOUN
ejpam-1871	337	86	.	.	PUNCT
ejpam-1871	338	1	we	we	PRON
ejpam-1871	338	2	claim	claim	VERB
ejpam-1871	338	3	that	that	SCONJ
ejpam-1871	338	4	[	[	X
ejpam-1871	338	5	(	(	PUNCT
ejpam-1871	338	6	2	2	NUM
ejpam-1871	338	7	,	,	PUNCT
ejpam-1871	338	8	a	a	NOUN
ejpam-1871	338	9	)	)	PUNCT
ejpam-1871	338	10	]	]	PUNCT
ejpam-1871	339	1	=	=	PUNCT
ejpam-1871	340	1	[	[	X
ejpam-1871	340	2	(	(	PUNCT
ejpam-1871	340	3	2	2	NUM
ejpam-1871	340	4	,	,	PUNCT
ejpam-1871	340	5	c	c	NOUN
ejpam-1871	340	6	)	)	PUNCT
ejpam-1871	340	7	]	]	PUNCT
ejpam-1871	340	8	.	.	PUNCT
ejpam-1871	341	1	first	first	ADV
ejpam-1871	341	2	note	note	VERB
ejpam-1871	341	3	that	that	SCONJ
ejpam-1871	341	4	since	since	SCONJ
ejpam-1871	341	5	a	a	DET
ejpam-1871	341	6	≤	≤	NUM
ejpam-1871	341	7	c	c	NOUN
ejpam-1871	341	8	in	in	ADP
ejpam-1871	341	9	c	c	PROPN
ejpam-1871	341	10	,	,	PUNCT
ejpam-1871	341	11	(	(	PUNCT
ejpam-1871	341	12	2	2	NUM
ejpam-1871	341	13	,	,	PUNCT
ejpam-1871	341	14	a	a	PRON
ejpam-1871	341	15	)	)	PUNCT
ejpam-1871	341	16	≤	≤	NOUN
ejpam-1871	341	17	(	(	PUNCT
ejpam-1871	341	18	2	2	NUM
ejpam-1871	341	19	,	,	PUNCT
ejpam-1871	341	20	c	c	NOUN
ejpam-1871	341	21	)	)	PUNCT
ejpam-1871	341	22	in	in	ADP
ejpam-1871	341	23	b	b	PROPN
ejpam-1871	341	24	t	t	PROPN
ejpam-1871	341	25	c	c	NOUN
ejpam-1871	341	26	which	which	PRON
ejpam-1871	341	27	implies	imply	VERB
ejpam-1871	341	28	that	that	SCONJ
ejpam-1871	341	29	[	[	X
ejpam-1871	341	30	(	(	PUNCT
ejpam-1871	341	31	2	2	NUM
ejpam-1871	341	32	,	,	PUNCT
ejpam-1871	341	33	a)]≤	a)]≤	PROPN
ejpam-1871	341	34	[	[	X
ejpam-1871	341	35	(	(	PUNCT
ejpam-1871	341	36	2	2	NUM
ejpam-1871	341	37	,	,	PUNCT
ejpam-1871	341	38	c	c	NOUN
ejpam-1871	341	39	)	)	PUNCT
ejpam-1871	341	40	]	]	PUNCT
ejpam-1871	341	41	.	.	PUNCT
ejpam-1871	342	1	on	on	ADP
ejpam-1871	342	2	the	the	DET
ejpam-1871	342	3	other	other	ADJ
ejpam-1871	342	4	hand	hand	NOUN
ejpam-1871	342	5	,	,	PUNCT
ejpam-1871	342	6	(	(	PUNCT
ejpam-1871	342	7	2	2	NUM
ejpam-1871	342	8	,	,	PUNCT
ejpam-1871	342	9	c)≤h∪h−1	c)≤h∪h−1	PRON
ejpam-1871	342	10	(	(	PUNCT
ejpam-1871	342	11	2	2	NUM
ejpam-1871	342	12	,	,	PUNCT
ejpam-1871	342	13	a	a	PRON
ejpam-1871	342	14	)	)	PUNCT
ejpam-1871	342	15	because	because	SCONJ
ejpam-1871	342	16	we	we	PRON
ejpam-1871	342	17	have	have	VERB
ejpam-1871	342	18	(	(	PUNCT
ejpam-1871	342	19	2	2	NUM
ejpam-1871	342	20	,	,	PUNCT
ejpam-1871	342	21	c)≤	c)≤	NOUN
ejpam-1871	342	22	(	(	PUNCT
ejpam-1871	342	23	2	2	NUM
ejpam-1871	342	24	,	,	PUNCT
ejpam-1871	342	25	c)h−1(1	c)h−1(1	NOUN
ejpam-1871	342	26	,	,	PUNCT
ejpam-1871	342	27	a)≤	a)≤	X
ejpam-1871	342	28	(	(	PUNCT
ejpam-1871	342	29	1	1	NUM
ejpam-1871	342	30	,	,	PUNCT
ejpam-1871	342	31	b)h(2	b)h(2	NOUN
ejpam-1871	342	32	,	,	PUNCT
ejpam-1871	342	33	a)≤	a)≤	X
ejpam-1871	342	34	(	(	PUNCT
ejpam-1871	342	35	2	2	NUM
ejpam-1871	342	36	,	,	PUNCT
ejpam-1871	342	37	a	a	PRON
ejpam-1871	342	38	)	)	PUNCT
ejpam-1871	342	39	.	.	PUNCT
ejpam-1871	343	1	this	this	PRON
ejpam-1871	343	2	gives	give	VERB
ejpam-1871	343	3	that	that	SCONJ
ejpam-1871	343	4	[	[	X
ejpam-1871	343	5	(	(	PUNCT
ejpam-1871	343	6	2	2	NUM
ejpam-1871	343	7	,	,	PUNCT
ejpam-1871	343	8	c)]≤	c)]≤	NOUN
ejpam-1871	343	9	[	[	X
ejpam-1871	343	10	(	(	PUNCT
ejpam-1871	343	11	2	2	NUM
ejpam-1871	343	12	,	,	PUNCT
ejpam-1871	343	13	a	a	NOUN
ejpam-1871	343	14	)	)	PUNCT
ejpam-1871	343	15	]	]	PUNCT
ejpam-1871	343	16	.	.	PUNCT
ejpam-1871	344	1	therefore	therefore	ADV
ejpam-1871	344	2	,	,	PUNCT
ejpam-1871	344	3	qc(a	qc(a	NOUN
ejpam-1871	344	4	)	)	PUNCT
ejpam-1871	344	5	=	=	PUNCT
ejpam-1871	345	1	[	[	X
ejpam-1871	345	2	(	(	PUNCT
ejpam-1871	345	3	2	2	NUM
ejpam-1871	345	4	,	,	PUNCT
ejpam-1871	345	5	a	a	NOUN
ejpam-1871	345	6	)	)	PUNCT
ejpam-1871	345	7	]	]	PUNCT
ejpam-1871	346	1	=	=	PUNCT
ejpam-1871	347	1	[	[	X
ejpam-1871	347	2	(	(	PUNCT
ejpam-1871	347	3	2	2	NUM
ejpam-1871	347	4	,	,	PUNCT
ejpam-1871	347	5	c	c	NOUN
ejpam-1871	347	6	)	)	PUNCT
ejpam-1871	347	7	]	]	PUNCT
ejpam-1871	348	1	=	=	SYM
ejpam-1871	348	2	qc(c	qc(c	PROPN
ejpam-1871	348	3	)	)	PUNCT
ejpam-1871	348	4	,	,	PUNCT
ejpam-1871	348	5	which	which	PRON
ejpam-1871	348	6	shows	show	VERB
ejpam-1871	348	7	that	that	SCONJ
ejpam-1871	348	8	qc	qc	PROPN
ejpam-1871	348	9	is	be	AUX
ejpam-1871	348	10	not	not	PART
ejpam-1871	348	11	a	a	DET
ejpam-1871	348	12	monomorphism	monomorphism	NOUN
ejpam-1871	348	13	.	.	PUNCT
ejpam-1871	349	1	injectivity	injectivity	NOUN
ejpam-1871	349	2	and	and	CCONJ
ejpam-1871	349	3	absolute	absolute	ADJ
ejpam-1871	349	4	retractness	retractness	NOUN
ejpam-1871	349	5	relative	relative	ADJ
ejpam-1871	349	6	to	to	ADP
ejpam-1871	349	7	a	a	DET
ejpam-1871	349	8	class	class	NOUN
ejpam-1871	349	9	of	of	ADP
ejpam-1871	349	10	morphisms	morphism	NOUN
ejpam-1871	349	11	of	of	ADP
ejpam-1871	349	12	a	a	DET
ejpam-1871	349	13	category	category	NOUN
ejpam-1871	349	14	are	be	AUX
ejpam-1871	349	15	two	two	NUM
ejpam-1871	349	16	category	category	NOUN
ejpam-1871	349	17	-	-	PUNCT
ejpam-1871	349	18	theoretic	theoretic	NOUN
ejpam-1871	349	19	close	close	ADJ
ejpam-1871	349	20	notions	notion	NOUN
ejpam-1871	349	21	,	,	PUNCT
ejpam-1871	349	22	which	which	PRON
ejpam-1871	349	23	usually	usually	ADV
ejpam-1871	349	24	coincide	coincide	VERB
ejpam-1871	349	25	under	under	ADP
ejpam-1871	349	26	some	some	DET
ejpam-1871	349	27	conditions	condition	NOUN
ejpam-1871	349	28	(	(	PUNCT
ejpam-1871	349	29	cf	cf	NOUN
ejpam-1871	349	30	.	.	PUNCT
ejpam-1871	350	1	[	[	X
ejpam-1871	350	2	4	4	NUM
ejpam-1871	350	3	]	]	NUM
ejpam-1871	350	4	)	)	PUNCT
ejpam-1871	350	5	.	.	PUNCT
ejpam-1871	351	1	recall	recall	VERB
ejpam-1871	351	2	from	from	ADP
ejpam-1871	351	3	[	[	X
ejpam-1871	351	4	3	3	X
ejpam-1871	351	5	]	]	PUNCT
ejpam-1871	351	6	that	that	SCONJ
ejpam-1871	351	7	in	in	ADP
ejpam-1871	351	8	the	the	DET
ejpam-1871	351	9	category	category	NOUN
ejpam-1871	351	10	pos	pos	NOUN
ejpam-1871	351	11	of	of	ADP
ejpam-1871	351	12	posets	poset	NOUN
ejpam-1871	351	13	and	and	CCONJ
ejpam-1871	351	14	order	order	NOUN
ejpam-1871	351	15	-	-	PUNCT
ejpam-1871	351	16	preserving	preserve	VERB
ejpam-1871	351	17	maps	map	NOUN
ejpam-1871	351	18	,	,	PUNCT
ejpam-1871	351	19	these	these	DET
ejpam-1871	351	20	concepts	concept	NOUN
ejpam-1871	351	21	with	with	ADP
ejpam-1871	351	22	respect	respect	NOUN
ejpam-1871	351	23	to	to	ADP
ejpam-1871	351	24	regular	regular	ADJ
ejpam-1871	351	25	monomorphisms	monomorphism	NOUN
ejpam-1871	351	26	(	(	PUNCT
ejpam-1871	351	27	order	order	NOUN
ejpam-1871	351	28	-	-	PUNCT
ejpam-1871	351	29	embeddings	embedding	NOUN
ejpam-1871	351	30	)	)	PUNCT
ejpam-1871	351	31	are	be	AUX
ejpam-1871	351	32	the	the	DET
ejpam-1871	351	33	same	same	ADJ
ejpam-1871	351	34	,	,	PUNCT
ejpam-1871	351	35	which	which	PRON
ejpam-1871	351	36	are	be	AUX
ejpam-1871	351	37	exactly	exactly	ADV
ejpam-1871	351	38	complete	complete	ADJ
ejpam-1871	351	39	posets	poset	NOUN
ejpam-1871	351	40	.	.	PUNCT
ejpam-1871	352	1	here	here	ADV
ejpam-1871	352	2	we	we	PRON
ejpam-1871	352	3	show	show	VERB
ejpam-1871	352	4	that	that	SCONJ
ejpam-1871	352	5	absolute	absolute	ADJ
ejpam-1871	352	6	retractness	retractness	NOUN
ejpam-1871	352	7	is	be	AUX
ejpam-1871	352	8	actually	actually	ADV
ejpam-1871	352	9	a	a	DET
ejpam-1871	352	10	different	different	ADJ
ejpam-1871	352	11	notion	notion	NOUN
ejpam-1871	352	12	to	to	PART
ejpam-1871	352	13	injectivity	injectivity	PROPN
ejpam-1871	352	14	h.	h.	PROPN
ejpam-1871	352	15	rasouli	rasouli	PROPN
ejpam-1871	352	16	/	/	SYM
ejpam-1871	352	17	eur	eur	PROPN
ejpam-1871	352	18	.	.	PUNCT
ejpam-1871	353	1	j.	j.	PROPN
ejpam-1871	353	2	pure	pure	PROPN
ejpam-1871	353	3	appl	appl	PROPN
ejpam-1871	353	4	.	.	PROPN
ejpam-1871	353	5	math	math	PROPN
ejpam-1871	353	6	,	,	PUNCT
ejpam-1871	353	7	7	7	NUM
ejpam-1871	353	8	(	(	PUNCT
ejpam-1871	353	9	2014	2014	NUM
ejpam-1871	353	10	)	)	PUNCT
ejpam-1871	353	11	,	,	PUNCT
ejpam-1871	353	12	166	166	NUM
ejpam-1871	353	13	-	-	SYM
ejpam-1871	353	14	178	178	NUM
ejpam-1871	353	15	176	176	NUM
ejpam-1871	353	16	of	of	ADP
ejpam-1871	353	17	posets	poset	NOUN
ejpam-1871	353	18	relative	relative	ADJ
ejpam-1871	353	19	to	to	ADP
ejpam-1871	353	20	monomorphisms	monomorphism	NOUN
ejpam-1871	353	21	(	(	PUNCT
ejpam-1871	353	22	one	one	NUM
ejpam-1871	353	23	-	-	PUNCT
ejpam-1871	353	24	one	one	NUM
ejpam-1871	353	25	monotone	monotone	ADJ
ejpam-1871	353	26	maps	map	NOUN
ejpam-1871	353	27	)	)	PUNCT
ejpam-1871	353	28	.	.	PUNCT
ejpam-1871	354	1	more	more	ADV
ejpam-1871	354	2	precisely	precisely	ADV
ejpam-1871	354	3	,	,	PUNCT
ejpam-1871	354	4	there	there	PRON
ejpam-1871	354	5	exists	exist	VERB
ejpam-1871	354	6	no	no	DET
ejpam-1871	354	7	non	non	ADJ
ejpam-1871	354	8	-	-	ADJ
ejpam-1871	354	9	trivial	trivial	ADJ
ejpam-1871	354	10	injective	injective	ADJ
ejpam-1871	354	11	poset	poset	NOUN
ejpam-1871	354	12	,	,	PUNCT
ejpam-1871	354	13	but	but	CCONJ
ejpam-1871	354	14	we	we	PRON
ejpam-1871	354	15	show	show	VERB
ejpam-1871	354	16	that	that	SCONJ
ejpam-1871	354	17	absolute	absolute	ADJ
ejpam-1871	354	18	retract	retract	NOUN
ejpam-1871	354	19	posets	poset	NOUN
ejpam-1871	354	20	are	be	AUX
ejpam-1871	354	21	exactly	exactly	ADV
ejpam-1871	354	22	complete	complete	ADJ
ejpam-1871	354	23	chains	chain	NOUN
ejpam-1871	354	24	.	.	PUNCT
ejpam-1871	355	1	let	let	VERB
ejpam-1871	355	2	us	we	PRON
ejpam-1871	355	3	first	first	ADV
ejpam-1871	355	4	recall	recall	VERB
ejpam-1871	355	5	some	some	DET
ejpam-1871	355	6	definitions	definition	NOUN
ejpam-1871	355	7	.	.	PUNCT
ejpam-1871	356	1	a	a	DET
ejpam-1871	356	2	poset	poset	NOUN
ejpam-1871	356	3	p	p	NOUN
ejpam-1871	356	4	is	be	AUX
ejpam-1871	356	5	called	call	VERB
ejpam-1871	356	6	(	(	PUNCT
ejpam-1871	356	7	regular	regular	ADJ
ejpam-1871	356	8	)	)	PUNCT
ejpam-1871	356	9	absolute	absolute	ADJ
ejpam-1871	356	10	retract	retract	NOUN
ejpam-1871	356	11	if	if	SCONJ
ejpam-1871	356	12	each	each	DET
ejpam-1871	356	13	(	(	PUNCT
ejpam-1871	356	14	regular	regular	ADJ
ejpam-1871	356	15	)	)	PUNCT
ejpam-1871	356	16	monomorphism	monomorphism	NOUN
ejpam-1871	357	1	f	f	X
ejpam-1871	357	2	:	:	PUNCT
ejpam-1871	357	3	p	p	X
ejpam-1871	357	4	→q	→q	PUNCT
ejpam-1871	357	5	in	in	ADP
ejpam-1871	357	6	pos	pos	NOUN
ejpam-1871	357	7	is	be	AUX
ejpam-1871	357	8	a	a	DET
ejpam-1871	357	9	section	section	NOUN
ejpam-1871	357	10	.	.	PUNCT
ejpam-1871	358	1	notice	notice	VERB
ejpam-1871	358	2	that	that	SCONJ
ejpam-1871	358	3	,	,	PUNCT
ejpam-1871	358	4	using	use	VERB
ejpam-1871	358	5	zorn	zorn	PROPN
ejpam-1871	358	6	’s	’s	PART
ejpam-1871	358	7	lemma	lemma	PROPN
ejpam-1871	358	8	,	,	PUNCT
ejpam-1871	358	9	there	there	PRON
ejpam-1871	358	10	exists	exist	VERB
ejpam-1871	358	11	a	a	DET
ejpam-1871	358	12	total	total	ADJ
ejpam-1871	358	13	order	order	NOUN
ejpam-1871	358	14	�	�	PROPN
ejpam-1871	358	15	on	on	ADP
ejpam-1871	358	16	a	a	DET
ejpam-1871	358	17	poset	poset	NOUN
ejpam-1871	358	18	(	(	PUNCT
ejpam-1871	358	19	p,≤	p,≤	NOUN
ejpam-1871	358	20	)	)	PUNCT
ejpam-1871	358	21	which	which	PRON
ejpam-1871	358	22	is	be	AUX
ejpam-1871	358	23	compatible	compatible	ADJ
ejpam-1871	358	24	with	with	ADP
ejpam-1871	358	25	the	the	DET
ejpam-1871	358	26	partial	partial	ADJ
ejpam-1871	358	27	order	order	NOUN
ejpam-1871	358	28	≤	≤	NUM
ejpam-1871	358	29	;	;	PUNCT
ejpam-1871	358	30	this	this	PRON
ejpam-1871	358	31	means	mean	VERB
ejpam-1871	358	32	a	a	DET
ejpam-1871	358	33	≤	≤	NUM
ejpam-1871	358	34	b	b	NOUN
ejpam-1871	358	35	implies	imply	VERB
ejpam-1871	358	36	that	that	SCONJ
ejpam-1871	358	37	a	a	DET
ejpam-1871	358	38	�	�	PROPN
ejpam-1871	358	39	b	b	PROPN
ejpam-1871	358	40	,	,	PUNCT
ejpam-1871	358	41	for	for	ADP
ejpam-1871	358	42	every	every	DET
ejpam-1871	358	43	a	a	PROPN
ejpam-1871	358	44	,	,	PUNCT
ejpam-1871	358	45	b	b	PROPN
ejpam-1871	358	46	∈	∈	PROPN
ejpam-1871	358	47	p	p	X
ejpam-1871	358	48	(	(	PUNCT
ejpam-1871	358	49	see	see	VERB
ejpam-1871	358	50	[	[	X
ejpam-1871	358	51	14	14	NUM
ejpam-1871	358	52	]	]	SYM
ejpam-1871	358	53	)	)	PUNCT
ejpam-1871	358	54	.	.	PUNCT
ejpam-1871	359	1	in	in	ADP
ejpam-1871	359	2	the	the	DET
ejpam-1871	359	3	following	follow	VERB
ejpam-1871	359	4	result	result	NOUN
ejpam-1871	359	5	,	,	PUNCT
ejpam-1871	359	6	all	all	DET
ejpam-1871	359	7	absolute	absolute	ADJ
ejpam-1871	359	8	retract	retract	NOUN
ejpam-1871	359	9	posets	poset	NOUN
ejpam-1871	359	10	is	be	AUX
ejpam-1871	359	11	characterized	characterize	VERB
ejpam-1871	359	12	.	.	PUNCT
ejpam-1871	360	1	theorem	theorem	ADJ
ejpam-1871	360	2	4	4	NUM
ejpam-1871	360	3	(	(	PUNCT
ejpam-1871	360	4	characterization	characterization	NOUN
ejpam-1871	360	5	of	of	ADP
ejpam-1871	360	6	absolute	absolute	ADJ
ejpam-1871	360	7	retract	retract	ADJ
ejpam-1871	360	8	objects	object	NOUN
ejpam-1871	360	9	in	in	ADP
ejpam-1871	360	10	pos	pos	NOUN
ejpam-1871	360	11	)	)	PUNCT
ejpam-1871	360	12	.	.	PUNCT
ejpam-1871	361	1	let	let	VERB
ejpam-1871	361	2	p	p	PRON
ejpam-1871	361	3	be	be	AUX
ejpam-1871	361	4	a	a	DET
ejpam-1871	361	5	poset	poset	NOUN
ejpam-1871	361	6	.	.	PUNCT
ejpam-1871	362	1	then	then	ADV
ejpam-1871	362	2	p	p	NOUN
ejpam-1871	362	3	is	be	AUX
ejpam-1871	362	4	absolute	absolute	ADJ
ejpam-1871	362	5	retract	retract	NOUN
ejpam-1871	362	6	if	if	SCONJ
ejpam-1871	362	7	and	and	CCONJ
ejpam-1871	362	8	only	only	ADV
ejpam-1871	362	9	if	if	SCONJ
ejpam-1871	362	10	it	it	PRON
ejpam-1871	362	11	is	be	AUX
ejpam-1871	362	12	a	a	DET
ejpam-1871	362	13	complete	complete	ADJ
ejpam-1871	362	14	chain	chain	NOUN
ejpam-1871	362	15	.	.	PUNCT
ejpam-1871	363	1	proof	proof	NOUN
ejpam-1871	363	2	.	.	PUNCT
ejpam-1871	364	1	assume	assume	VERB
ejpam-1871	364	2	that	that	SCONJ
ejpam-1871	364	3	(	(	PUNCT
ejpam-1871	364	4	p,≤	p,≤	NOUN
ejpam-1871	364	5	)	)	PUNCT
ejpam-1871	364	6	is	be	AUX
ejpam-1871	364	7	an	an	DET
ejpam-1871	364	8	absolute	absolute	ADJ
ejpam-1871	364	9	retract	retract	NOUN
ejpam-1871	364	10	poset	poset	NOUN
ejpam-1871	364	11	.	.	PUNCT
ejpam-1871	365	1	this	this	PRON
ejpam-1871	365	2	clearly	clearly	ADV
ejpam-1871	365	3	implies	imply	VERB
ejpam-1871	365	4	that	that	SCONJ
ejpam-1871	365	5	p	p	PROPN
ejpam-1871	365	6	is	be	AUX
ejpam-1871	365	7	regular	regular	ADJ
ejpam-1871	365	8	absolute	absolute	ADJ
ejpam-1871	365	9	retract	retract	NOUN
ejpam-1871	365	10	and	and	CCONJ
ejpam-1871	365	11	then	then	ADV
ejpam-1871	365	12	complete	complete	VERB
ejpam-1871	365	13	by	by	ADP
ejpam-1871	365	14	[	[	X
ejpam-1871	365	15	3	3	NUM
ejpam-1871	365	16	,	,	PUNCT
ejpam-1871	365	17	proposition	proposition	NOUN
ejpam-1871	365	18	1	1	NUM
ejpam-1871	365	19	]	]	PUNCT
ejpam-1871	365	20	.	.	PUNCT
ejpam-1871	366	1	to	to	PART
ejpam-1871	366	2	show	show	VERB
ejpam-1871	366	3	that	that	SCONJ
ejpam-1871	366	4	p	p	NOUN
ejpam-1871	366	5	is	be	AUX
ejpam-1871	366	6	a	a	DET
ejpam-1871	366	7	chain	chain	NOUN
ejpam-1871	366	8	,	,	PUNCT
ejpam-1871	366	9	consider	consider	VERB
ejpam-1871	366	10	a	a	DET
ejpam-1871	366	11	compatible	compatible	ADJ
ejpam-1871	366	12	total	total	ADJ
ejpam-1871	366	13	order	order	NOUN
ejpam-1871	366	14	�	�	PROPN
ejpam-1871	366	15	on	on	ADP
ejpam-1871	366	16	p.	p.	NOUN
ejpam-1871	366	17	thus	thus	ADV
ejpam-1871	366	18	the	the	DET
ejpam-1871	366	19	morphism	morphism	NOUN
ejpam-1871	367	1	i	i	PRON
ejpam-1871	367	2	:	:	PUNCT
ejpam-1871	367	3	(	(	PUNCT
ejpam-1871	367	4	p,≤)→	p,≤)→	NOUN
ejpam-1871	367	5	(	(	PUNCT
ejpam-1871	367	6	p	p	PROPN
ejpam-1871	367	7	,	,	PUNCT
ejpam-1871	367	8	�	�	PROPN
ejpam-1871	367	9	)	)	PUNCT
ejpam-1871	367	10	,	,	PUNCT
ejpam-1871	367	11	mapping	map	VERB
ejpam-1871	367	12	the	the	DET
ejpam-1871	367	13	elements	element	NOUN
ejpam-1871	367	14	of	of	ADP
ejpam-1871	367	15	p	p	PRON
ejpam-1871	367	16	identically	identically	ADV
ejpam-1871	367	17	,	,	PUNCT
ejpam-1871	367	18	is	be	AUX
ejpam-1871	367	19	a	a	DET
ejpam-1871	367	20	monomorphism	monomorphism	NOUN
ejpam-1871	367	21	and	and	CCONJ
ejpam-1871	367	22	then	then	ADV
ejpam-1871	367	23	has	have	VERB
ejpam-1871	367	24	a	a	DET
ejpam-1871	367	25	left	left	ADJ
ejpam-1871	367	26	inverse	inverse	NOUN
ejpam-1871	367	27	by	by	ADP
ejpam-1871	367	28	hypothesis	hypothesis	NOUN
ejpam-1871	367	29	.	.	PUNCT
ejpam-1871	368	1	this	this	PRON
ejpam-1871	368	2	obviously	obviously	ADV
ejpam-1871	368	3	implies	imply	VERB
ejpam-1871	368	4	that	that	SCONJ
ejpam-1871	368	5	p	p	PROPN
ejpam-1871	368	6	is	be	AUX
ejpam-1871	368	7	a	a	DET
ejpam-1871	368	8	chain	chain	NOUN
ejpam-1871	368	9	.	.	PUNCT
ejpam-1871	369	1	for	for	ADP
ejpam-1871	369	2	the	the	DET
ejpam-1871	369	3	converse	converse	NOUN
ejpam-1871	369	4	,	,	PUNCT
ejpam-1871	369	5	let	let	VERB
ejpam-1871	369	6	p	p	PRON
ejpam-1871	369	7	be	be	AUX
ejpam-1871	369	8	a	a	DET
ejpam-1871	369	9	complete	complete	ADJ
ejpam-1871	369	10	chain	chain	NOUN
ejpam-1871	369	11	and	and	CCONJ
ejpam-1871	369	12	f	f	NOUN
ejpam-1871	370	1	:	:	PUNCT
ejpam-1871	370	2	p	p	X
ejpam-1871	370	3	→	→	PUNCT
ejpam-1871	370	4	q	q	X
ejpam-1871	370	5	be	be	AUX
ejpam-1871	370	6	a	a	DET
ejpam-1871	370	7	monomorphism	monomorphism	NOUN
ejpam-1871	370	8	in	in	ADP
ejpam-1871	370	9	pos	pos	PROPN
ejpam-1871	370	10	.	.	PUNCT
ejpam-1871	371	1	since	since	SCONJ
ejpam-1871	371	2	p	p	NOUN
ejpam-1871	371	3	is	be	AUX
ejpam-1871	371	4	a	a	DET
ejpam-1871	371	5	chain	chain	NOUN
ejpam-1871	371	6	,	,	PUNCT
ejpam-1871	371	7	f	f	PROPN
ejpam-1871	371	8	is	be	AUX
ejpam-1871	371	9	order	order	NOUN
ejpam-1871	371	10	-	-	PUNCT
ejpam-1871	371	11	embedding	embed	VERB
ejpam-1871	371	12	.	.	PUNCT
ejpam-1871	372	1	on	on	ADP
ejpam-1871	372	2	the	the	DET
ejpam-1871	372	3	other	other	ADJ
ejpam-1871	372	4	hand	hand	NOUN
ejpam-1871	372	5	,	,	PUNCT
ejpam-1871	372	6	since	since	SCONJ
ejpam-1871	372	7	p	p	NOUN
ejpam-1871	372	8	is	be	AUX
ejpam-1871	372	9	complete	complete	ADJ
ejpam-1871	372	10	,	,	PUNCT
ejpam-1871	372	11	it	it	PRON
ejpam-1871	372	12	is	be	AUX
ejpam-1871	372	13	regular	regular	ADJ
ejpam-1871	372	14	absolute	absolute	ADJ
ejpam-1871	372	15	retract	retract	NOUN
ejpam-1871	372	16	by	by	ADP
ejpam-1871	372	17	[	[	X
ejpam-1871	372	18	3	3	NUM
ejpam-1871	372	19	,	,	PUNCT
ejpam-1871	372	20	proposition	proposition	NOUN
ejpam-1871	372	21	1	1	NUM
ejpam-1871	372	22	]	]	PUNCT
ejpam-1871	372	23	.	.	PUNCT
ejpam-1871	373	1	consequently	consequently	ADV
ejpam-1871	373	2	,	,	PUNCT
ejpam-1871	373	3	f	f	PROPN
ejpam-1871	373	4	has	have	VERB
ejpam-1871	373	5	a	a	DET
ejpam-1871	373	6	left	left	ADJ
ejpam-1871	373	7	inverse	inverse	NOUN
ejpam-1871	373	8	and	and	CCONJ
ejpam-1871	373	9	hence	hence	ADV
ejpam-1871	373	10	p	p	PRON
ejpam-1871	373	11	is	be	AUX
ejpam-1871	373	12	absolute	absolute	ADJ
ejpam-1871	373	13	retract	retract	NOUN
ejpam-1871	373	14	.	.	PUNCT
ejpam-1871	374	1	in	in	ADP
ejpam-1871	374	2	what	what	PRON
ejpam-1871	374	3	follows	follow	VERB
ejpam-1871	374	4	,	,	PUNCT
ejpam-1871	374	5	we	we	PRON
ejpam-1871	374	6	study	study	VERB
ejpam-1871	374	7	enough	enough	ADJ
ejpam-1871	374	8	absolute	absolute	ADJ
ejpam-1871	374	9	retractness	retractness	NOUN
ejpam-1871	374	10	of	of	ADP
ejpam-1871	374	11	posets	poset	NOUN
ejpam-1871	374	12	.	.	PUNCT
ejpam-1871	375	1	to	to	ADP
ejpam-1871	375	2	this	this	DET
ejpam-1871	375	3	end	end	NOUN
ejpam-1871	375	4	,	,	PUNCT
ejpam-1871	375	5	we	we	PRON
ejpam-1871	375	6	recall	recall	VERB
ejpam-1871	375	7	some	some	DET
ejpam-1871	375	8	required	required	ADJ
ejpam-1871	375	9	notions	notion	NOUN
ejpam-1871	375	10	.	.	PUNCT
ejpam-1871	376	1	let	let	VERB
ejpam-1871	376	2	p	p	PRON
ejpam-1871	376	3	be	be	AUX
ejpam-1871	376	4	a	a	DET
ejpam-1871	376	5	poset	poset	NOUN
ejpam-1871	376	6	.	.	PUNCT
ejpam-1871	377	1	a	a	DET
ejpam-1871	377	2	poset	poset	NOUN
ejpam-1871	377	3	e	e	NOUN
ejpam-1871	377	4	is	be	AUX
ejpam-1871	377	5	said	say	VERB
ejpam-1871	377	6	to	to	PART
ejpam-1871	377	7	be	be	AUX
ejpam-1871	377	8	an	an	DET
ejpam-1871	377	9	extension	extension	NOUN
ejpam-1871	377	10	of	of	ADP
ejpam-1871	377	11	p	p	NOUN
ejpam-1871	377	12	if	if	SCONJ
ejpam-1871	377	13	p	p	NOUN
ejpam-1871	377	14	is	be	AUX
ejpam-1871	377	15	embedded	embed	VERB
ejpam-1871	377	16	into	into	ADP
ejpam-1871	377	17	e.	e.	PROPN
ejpam-1871	377	18	also	also	ADV
ejpam-1871	377	19	we	we	PRON
ejpam-1871	377	20	say	say	VERB
ejpam-1871	377	21	that	that	SCONJ
ejpam-1871	377	22	e	e	NOUN
ejpam-1871	377	23	is	be	AUX
ejpam-1871	377	24	a	a	DET
ejpam-1871	377	25	monomorphic	monomorphic	ADJ
ejpam-1871	377	26	extension	extension	NOUN
ejpam-1871	377	27	of	of	ADP
ejpam-1871	377	28	p	p	NOUN
ejpam-1871	377	29	if	if	SCONJ
ejpam-1871	377	30	there	there	PRON
ejpam-1871	377	31	exists	exist	VERB
ejpam-1871	377	32	a	a	DET
ejpam-1871	377	33	monomorphism	monomorphism	NOUN
ejpam-1871	377	34	from	from	ADP
ejpam-1871	377	35	p	p	NOUN
ejpam-1871	377	36	to	to	ADP
ejpam-1871	377	37	e.	e.	PROPN
ejpam-1871	377	38	an	an	DET
ejpam-1871	377	39	extension	extension	NOUN
ejpam-1871	377	40	e	e	NOUN
ejpam-1871	377	41	of	of	ADP
ejpam-1871	377	42	p	p	PROPN
ejpam-1871	377	43	is	be	AUX
ejpam-1871	377	44	called	call	VERB
ejpam-1871	377	45	join	join	VERB
ejpam-1871	377	46	dense	dense	ADJ
ejpam-1871	377	47	if	if	SCONJ
ejpam-1871	377	48	each	each	DET
ejpam-1871	377	49	element	element	NOUN
ejpam-1871	377	50	of	of	ADP
ejpam-1871	377	51	e	e	PROPN
ejpam-1871	377	52	is	be	AUX
ejpam-1871	377	53	the	the	DET
ejpam-1871	377	54	join	join	NOUN
ejpam-1871	377	55	of	of	ADP
ejpam-1871	377	56	its	its	PRON
ejpam-1871	377	57	predecessors	predecessor	NOUN
ejpam-1871	377	58	in	in	ADP
ejpam-1871	377	59	p	p	X
ejpam-1871	377	60	,	,	PUNCT
ejpam-1871	377	61	that	that	ADV
ejpam-1871	377	62	is	is	ADV
ejpam-1871	377	63	,	,	PUNCT
ejpam-1871	377	64	e	e	X
ejpam-1871	377	65	=	=	SYM
ejpam-1871	377	66	∨	∨	X
ejpam-1871	377	67	{	{	PUNCT
ejpam-1871	377	68	p	p	NOUN
ejpam-1871	377	69	∈	∈	PROPN
ejpam-1871	377	70	p	p	NOUN
ejpam-1871	377	71	:	:	PUNCT
ejpam-1871	377	72	p	p	X
ejpam-1871	377	73	≤	≤	NUM
ejpam-1871	377	74	e	e	NOUN
ejpam-1871	377	75	}	}	PUNCT
ejpam-1871	377	76	,	,	PUNCT
ejpam-1871	377	77	for	for	ADP
ejpam-1871	377	78	every	every	DET
ejpam-1871	377	79	e	e	PROPN
ejpam-1871	377	80	∈	∈	PROPN
ejpam-1871	377	81	e.	e.	PROPN
ejpam-1871	377	82	meet	meet	PROPN
ejpam-1871	377	83	density	density	NOUN
ejpam-1871	377	84	is	be	AUX
ejpam-1871	377	85	defined	define	VERB
ejpam-1871	377	86	dually	dually	ADV
ejpam-1871	377	87	.	.	PUNCT
ejpam-1871	378	1	the	the	DET
ejpam-1871	378	2	dedekind	dedekind	NOUN
ejpam-1871	378	3	-	-	PUNCT
ejpam-1871	378	4	macneille	macneille	NOUN
ejpam-1871	378	5	completion	completion	NOUN
ejpam-1871	378	6	of	of	ADP
ejpam-1871	378	7	p	p	NOUN
ejpam-1871	378	8	,	,	PUNCT
ejpam-1871	378	9	denoted	denote	VERB
ejpam-1871	378	10	by	by	ADP
ejpam-1871	378	11	dm(p	dm(p	NOUN
ejpam-1871	378	12	)	)	PUNCT
ejpam-1871	378	13	,	,	PUNCT
ejpam-1871	378	14	is	be	AUX
ejpam-1871	378	15	a	a	DET
ejpam-1871	378	16	complete	complete	ADJ
ejpam-1871	378	17	extension	extension	NOUN
ejpam-1871	378	18	of	of	ADP
ejpam-1871	378	19	p	p	PRON
ejpam-1871	378	20	which	which	PRON
ejpam-1871	378	21	is	be	AUX
ejpam-1871	378	22	both	both	PRON
ejpam-1871	378	23	join	join	VERB
ejpam-1871	378	24	and	and	CCONJ
ejpam-1871	378	25	meet	meet	VERB
ejpam-1871	378	26	dense	dense	ADJ
ejpam-1871	378	27	.	.	PUNCT
ejpam-1871	379	1	lemma	lemma	PROPN
ejpam-1871	379	2	2	2	X
ejpam-1871	379	3	.	.	PUNCT
ejpam-1871	380	1	let	let	VERB
ejpam-1871	380	2	p	p	PRON
ejpam-1871	380	3	be	be	AUX
ejpam-1871	380	4	a	a	DET
ejpam-1871	380	5	chain	chain	NOUN
ejpam-1871	380	6	.	.	PUNCT
ejpam-1871	381	1	then	then	ADV
ejpam-1871	381	2	so	so	ADV
ejpam-1871	381	3	is	be	AUX
ejpam-1871	381	4	dm(p	dm(p	NOUN
ejpam-1871	381	5	)	)	PUNCT
ejpam-1871	381	6	.	.	PUNCT
ejpam-1871	382	1	proof	proof	NOUN
ejpam-1871	382	2	.	.	PUNCT
ejpam-1871	383	1	suppose	suppose	VERB
ejpam-1871	383	2	p	p	NOUN
ejpam-1871	383	3	is	be	AUX
ejpam-1871	383	4	a	a	DET
ejpam-1871	383	5	chain	chain	NOUN
ejpam-1871	383	6	,	,	PUNCT
ejpam-1871	383	7	and	and	CCONJ
ejpam-1871	383	8	x	x	X
ejpam-1871	383	9	,	,	PUNCT
ejpam-1871	383	10	y	y	PROPN
ejpam-1871	383	11	∈	∈	PROPN
ejpam-1871	383	12	dm(p	dm(p	NOUN
ejpam-1871	383	13	)	)	PUNCT
ejpam-1871	383	14	,	,	PUNCT
ejpam-1871	383	15	x	x	PROPN
ejpam-1871	383	16	�	�	PROPN
ejpam-1871	383	17	y	y	PROPN
ejpam-1871	383	18	.	.	PUNCT
ejpam-1871	384	1	then	then	ADV
ejpam-1871	384	2	there	there	PRON
ejpam-1871	384	3	exists	exist	VERB
ejpam-1871	384	4	an	an	DET
ejpam-1871	384	5	s	s	NOUN
ejpam-1871	384	6	∈	∈	NOUN
ejpam-1871	384	7	p	p	NOUN
ejpam-1871	384	8	such	such	ADJ
ejpam-1871	384	9	that	that	PRON
ejpam-1871	384	10	s	s	VERB
ejpam-1871	384	11	≤	≤	NOUN
ejpam-1871	384	12	x	x	PUNCT
ejpam-1871	384	13	and	and	CCONJ
ejpam-1871	384	14	s	s	PROPN
ejpam-1871	384	15	�	�	PROPN
ejpam-1871	384	16	y	y	PROPN
ejpam-1871	384	17	(	(	PUNCT
ejpam-1871	384	18	join	join	VERB
ejpam-1871	384	19	density	density	NOUN
ejpam-1871	384	20	)	)	PUNCT
ejpam-1871	384	21	and	and	CCONJ
ejpam-1871	384	22	hence	hence	ADV
ejpam-1871	384	23	also	also	ADV
ejpam-1871	384	24	a	a	DET
ejpam-1871	384	25	t	t	NOUN
ejpam-1871	384	26	∈	∈	PROPN
ejpam-1871	385	1	p	p	NOUN
ejpam-1871	385	2	such	such	ADJ
ejpam-1871	385	3	that	that	SCONJ
ejpam-1871	385	4	t	t	PROPN
ejpam-1871	385	5	≥	≥	NOUN
ejpam-1871	385	6	y	y	PROPN
ejpam-1871	385	7	and	and	CCONJ
ejpam-1871	385	8	s	s	PROPN
ejpam-1871	385	9	�	�	PROPN
ejpam-1871	385	10	t	t	PROPN
ejpam-1871	385	11	(	(	PUNCT
ejpam-1871	385	12	meet	meet	VERB
ejpam-1871	385	13	density	density	NOUN
ejpam-1871	385	14	)	)	PUNCT
ejpam-1871	385	15	.	.	PUNCT
ejpam-1871	386	1	since	since	SCONJ
ejpam-1871	386	2	p	p	NOUN
ejpam-1871	386	3	is	be	AUX
ejpam-1871	386	4	a	a	DET
ejpam-1871	386	5	chain	chain	NOUN
ejpam-1871	386	6	,	,	PUNCT
ejpam-1871	386	7	t	t	PROPN
ejpam-1871	386	8	≤	≤	PROPN
ejpam-1871	386	9	s.	s.	PROPN
ejpam-1871	386	10	thus	thus	ADV
ejpam-1871	386	11	we	we	PRON
ejpam-1871	386	12	get	get	VERB
ejpam-1871	386	13	y	y	PROPN
ejpam-1871	386	14	≤	≤	PROPN
ejpam-1871	386	15	t	t	PROPN
ejpam-1871	386	16	≤	≤	PROPN
ejpam-1871	386	17	s	s	PART
ejpam-1871	386	18	≤	≤	NOUN
ejpam-1871	386	19	x	x	PUNCT
ejpam-1871	386	20	,	,	PUNCT
ejpam-1871	386	21	showing	show	VERB
ejpam-1871	386	22	that	that	DET
ejpam-1871	386	23	dm(p	dm(p	NOUN
ejpam-1871	386	24	)	)	PUNCT
ejpam-1871	386	25	is	be	AUX
ejpam-1871	386	26	a	a	DET
ejpam-1871	386	27	chain	chain	NOUN
ejpam-1871	386	28	.	.	PUNCT
ejpam-1871	387	1	finally	finally	ADV
ejpam-1871	387	2	,	,	PUNCT
ejpam-1871	387	3	the	the	DET
ejpam-1871	387	4	following	following	ADJ
ejpam-1871	387	5	result	result	NOUN
ejpam-1871	387	6	is	be	AUX
ejpam-1871	387	7	obtained	obtain	VERB
ejpam-1871	387	8	:	:	PUNCT
ejpam-1871	387	9	proposition	proposition	NOUN
ejpam-1871	387	10	8	8	NUM
ejpam-1871	387	11	.	.	PUNCT
ejpam-1871	388	1	pos	pos	NOUN
ejpam-1871	388	2	has	have	VERB
ejpam-1871	388	3	enough	enough	ADJ
ejpam-1871	388	4	absolute	absolute	ADJ
ejpam-1871	388	5	retracts	retract	NOUN
ejpam-1871	388	6	:	:	PUNCT
ejpam-1871	388	7	each	each	DET
ejpam-1871	388	8	poset	poset	NOUN
ejpam-1871	388	9	can	can	AUX
ejpam-1871	388	10	be	be	AUX
ejpam-1871	388	11	monomorphically	monomorphically	ADV
ejpam-1871	388	12	extended	extended	ADJ
ejpam-1871	388	13	to	to	ADP
ejpam-1871	388	14	an	an	DET
ejpam-1871	388	15	absolute	absolute	ADJ
ejpam-1871	388	16	retract	retract	NOUN
ejpam-1871	388	17	poset	poset	NOUN
ejpam-1871	388	18	.	.	PUNCT
ejpam-1871	389	1	proof	proof	NOUN
ejpam-1871	389	2	.	.	PUNCT
ejpam-1871	390	1	let	let	VERB
ejpam-1871	390	2	p	p	PRON
ejpam-1871	390	3	be	be	AUX
ejpam-1871	390	4	a	a	DET
ejpam-1871	390	5	poset	poset	NOUN
ejpam-1871	390	6	.	.	PUNCT
ejpam-1871	391	1	in	in	ADP
ejpam-1871	391	2	view	view	NOUN
ejpam-1871	391	3	of	of	ADP
ejpam-1871	391	4	theorem	theorem	NOUN
ejpam-1871	391	5	4	4	NUM
ejpam-1871	391	6	,	,	PUNCT
ejpam-1871	391	7	it	it	PRON
ejpam-1871	391	8	suffices	suffice	VERB
ejpam-1871	391	9	to	to	PART
ejpam-1871	391	10	find	find	VERB
ejpam-1871	391	11	a	a	DET
ejpam-1871	391	12	complete	complete	ADJ
ejpam-1871	391	13	chain	chain	NOUN
ejpam-1871	391	14	as	as	ADP
ejpam-1871	391	15	a	a	DET
ejpam-1871	391	16	monomorphic	monomorphic	ADJ
ejpam-1871	391	17	extension	extension	NOUN
ejpam-1871	391	18	of	of	ADP
ejpam-1871	391	19	p.	p.	NOUN
ejpam-1871	391	20	to	to	PART
ejpam-1871	391	21	see	see	VERB
ejpam-1871	391	22	this	this	PRON
ejpam-1871	391	23	,	,	PUNCT
ejpam-1871	391	24	first	first	ADV
ejpam-1871	391	25	note	note	VERB
ejpam-1871	391	26	that	that	SCONJ
ejpam-1871	391	27	p	p	NOUN
ejpam-1871	391	28	is	be	AUX
ejpam-1871	391	29	embedded	embed	VERB
ejpam-1871	391	30	into	into	ADP
ejpam-1871	391	31	the	the	DET
ejpam-1871	391	32	complete	complete	ADJ
ejpam-1871	391	33	references	reference	NOUN
ejpam-1871	391	34	177	177	NUM
ejpam-1871	391	35	poset	poset	NOUN
ejpam-1871	391	36	dm(p	dm(p	NOUN
ejpam-1871	391	37	)	)	PUNCT
ejpam-1871	391	38	.	.	PUNCT
ejpam-1871	392	1	moreover	moreover	ADV
ejpam-1871	392	2	,	,	PUNCT
ejpam-1871	392	3	dm(p	dm(p	NOUN
ejpam-1871	392	4	)	)	PUNCT
ejpam-1871	392	5	is	be	AUX
ejpam-1871	392	6	monomorphically	monomorphically	ADV
ejpam-1871	392	7	extended	extended	ADJ
ejpam-1871	392	8	to	to	ADP
ejpam-1871	392	9	the	the	DET
ejpam-1871	392	10	chain	chain	NOUN
ejpam-1871	392	11	c	c	NOUN
ejpam-1871	392	12	=	=	SYM
ejpam-1871	392	13	dm(p	dm(p	PROPN
ejpam-1871	392	14	)	)	PUNCT
ejpam-1871	392	15	with	with	ADP
ejpam-1871	392	16	a	a	DET
ejpam-1871	392	17	compatible	compatible	ADJ
ejpam-1871	392	18	total	total	ADJ
ejpam-1871	392	19	order	order	NOUN
ejpam-1871	392	20	.	.	PUNCT
ejpam-1871	393	1	if	if	SCONJ
ejpam-1871	393	2	c	c	PROPN
ejpam-1871	393	3	is	be	AUX
ejpam-1871	393	4	complete	complete	ADJ
ejpam-1871	393	5	,	,	PUNCT
ejpam-1871	393	6	the	the	DET
ejpam-1871	393	7	assertion	assertion	NOUN
ejpam-1871	393	8	holds	hold	VERB
ejpam-1871	393	9	.	.	PUNCT
ejpam-1871	394	1	otherwise	otherwise	ADV
ejpam-1871	394	2	,	,	PUNCT
ejpam-1871	394	3	using	use	VERB
ejpam-1871	394	4	lemma	lemma	PROPN
ejpam-1871	394	5	2	2	NUM
ejpam-1871	394	6	,	,	PUNCT
ejpam-1871	394	7	it	it	PRON
ejpam-1871	394	8	suffices	suffice	VERB
ejpam-1871	394	9	to	to	PART
ejpam-1871	394	10	consider	consider	VERB
ejpam-1871	394	11	the	the	DET
ejpam-1871	394	12	complete	complete	ADJ
ejpam-1871	394	13	chain	chain	NOUN
ejpam-1871	394	14	q	q	NOUN
ejpam-1871	394	15	=	=	PUNCT
ejpam-1871	394	16	dm(c	dm(c	X
ejpam-1871	394	17	)	)	PUNCT
ejpam-1871	394	18	in	in	ADP
ejpam-1871	394	19	which	which	PRON
ejpam-1871	394	20	c	c	NOUN
ejpam-1871	394	21	is	be	AUX
ejpam-1871	394	22	embedded	embed	VERB
ejpam-1871	394	23	.	.	PUNCT
ejpam-1871	395	1	consequently	consequently	ADV
ejpam-1871	395	2	,	,	PUNCT
ejpam-1871	395	3	p	p	PROPN
ejpam-1871	395	4	is	be	AUX
ejpam-1871	395	5	monomorphically	monomorphically	ADV
ejpam-1871	395	6	extended	extended	ADJ
ejpam-1871	395	7	to	to	ADP
ejpam-1871	395	8	the	the	DET
ejpam-1871	395	9	complete	complete	ADJ
ejpam-1871	395	10	chain	chain	NOUN
ejpam-1871	395	11	q	q	NOUN
ejpam-1871	395	12	,	,	PUNCT
ejpam-1871	395	13	as	as	SCONJ
ejpam-1871	395	14	required	require	VERB
ejpam-1871	395	15	.	.	PUNCT
ejpam-1871	396	1	remark	remark	PROPN
ejpam-1871	396	2	3	3	NUM
ejpam-1871	396	3	.	.	PUNCT
ejpam-1871	397	1	in	in	ADP
ejpam-1871	397	2	pos	pos	NOUN
ejpam-1871	397	3	poushouts	poushout	NOUN
ejpam-1871	397	4	do	do	AUX
ejpam-1871	397	5	not	not	PART
ejpam-1871	397	6	transfer	transfer	VERB
ejpam-1871	397	7	monomorphisms	monomorphism	NOUN
ejpam-1871	397	8	,	,	PUNCT
ejpam-1871	397	9	otherwise	otherwise	ADV
ejpam-1871	397	10	,	,	PUNCT
ejpam-1871	397	11	in	in	ADP
ejpam-1871	397	12	view	view	NOUN
ejpam-1871	397	13	of	of	ADP
ejpam-1871	397	14	[	[	X
ejpam-1871	397	15	5	5	NUM
ejpam-1871	397	16	,	,	PUNCT
ejpam-1871	397	17	theorem	theorem	VERB
ejpam-1871	397	18	3.6	3.6	NUM
ejpam-1871	397	19	]	]	PUNCT
ejpam-1871	397	20	and	and	CCONJ
ejpam-1871	397	21	proposition	proposition	NOUN
ejpam-1871	397	22	8	8	NUM
ejpam-1871	397	23	,	,	PUNCT
ejpam-1871	397	24	pos	pos	NOUN
ejpam-1871	397	25	has	have	VERB
ejpam-1871	397	26	enough	enough	ADJ
ejpam-1871	397	27	injectives	injective	NOUN
ejpam-1871	397	28	,	,	PUNCT
ejpam-1871	397	29	a	a	DET
ejpam-1871	397	30	contradiction	contradiction	NOUN
ejpam-1871	397	31	.	.	PUNCT
ejpam-1871	398	1	acknowledgements	acknowledgement	NOUN
ejpam-1871	398	2	i	i	PRON
ejpam-1871	398	3	would	would	AUX
ejpam-1871	398	4	like	like	VERB
ejpam-1871	398	5	to	to	PART
ejpam-1871	398	6	express	express	VERB
ejpam-1871	398	7	my	my	PRON
ejpam-1871	398	8	appreciation	appreciation	NOUN
ejpam-1871	398	9	to	to	ADP
ejpam-1871	398	10	the	the	DET
ejpam-1871	398	11	referee	referee	NOUN
ejpam-1871	398	12	for	for	ADP
ejpam-1871	398	13	carefully	carefully	ADV
ejpam-1871	398	14	reading	read	VERB
ejpam-1871	398	15	the	the	DET
ejpam-1871	398	16	paper	paper	NOUN
ejpam-1871	398	17	.	.	PUNCT
ejpam-1871	399	1	references	reference	NOUN
ejpam-1871	399	2	[	[	X
ejpam-1871	399	3	1	1	NUM
ejpam-1871	399	4	]	]	X
ejpam-1871	399	5	j	j	PROPN
ejpam-1871	399	6	adamek	adamek	PROPN
ejpam-1871	399	7	,	,	PUNCT
ejpam-1871	399	8	h	h	NOUN
ejpam-1871	399	9	herrlich	herrlich	NOUN
ejpam-1871	399	10	,	,	PUNCT
ejpam-1871	399	11	and	and	CCONJ
ejpam-1871	399	12	g	g	PROPN
ejpam-1871	399	13	strecker	strecker	NOUN
ejpam-1871	399	14	.	.	PUNCT
ejpam-1871	400	1	abstract	abstract	ADJ
ejpam-1871	400	2	and	and	CCONJ
ejpam-1871	400	3	concrete	concrete	ADJ
ejpam-1871	400	4	categories	category	NOUN
ejpam-1871	400	5	.	.	PUNCT
ejpam-1871	401	1	john	john	PROPN
ejpam-1871	401	2	wiley	wiley	PROPN
ejpam-1871	401	3	and	and	CCONJ
ejpam-1871	401	4	sons	son	NOUN
ejpam-1871	401	5	,	,	PUNCT
ejpam-1871	401	6	new	new	PROPN
ejpam-1871	401	7	york	york	PROPN
ejpam-1871	401	8	,	,	PUNCT
ejpam-1871	401	9	1990	1990	NUM
ejpam-1871	401	10	.	.	PUNCT
ejpam-1871	402	1	[	[	X
ejpam-1871	402	2	2	2	NUM
ejpam-1871	402	3	]	]	PUNCT
ejpam-1871	402	4	b	b	X
ejpam-1871	402	5	banaschewski	banaschewski	NOUN
ejpam-1871	402	6	.	.	PUNCT
ejpam-1871	403	1	injectivity	injectivity	NOUN
ejpam-1871	403	2	and	and	CCONJ
ejpam-1871	403	3	essential	essential	ADJ
ejpam-1871	403	4	extensions	extension	NOUN
ejpam-1871	403	5	in	in	ADP
ejpam-1871	403	6	equational	equational	ADJ
ejpam-1871	403	7	classes	class	NOUN
ejpam-1871	403	8	of	of	ADP
ejpam-1871	403	9	algebras	algebras	PROPN
ejpam-1871	403	10	.	.	PUNCT
ejpam-1871	404	1	queen	queen	PROPN
ejpam-1871	404	2	’s	’s	PART
ejpam-1871	404	3	papers	paper	NOUN
ejpam-1871	404	4	in	in	ADP
ejpam-1871	404	5	pure	pure	ADJ
ejpam-1871	404	6	and	and	CCONJ
ejpam-1871	404	7	applied	applied	ADJ
ejpam-1871	404	8	mathematics	mathematic	NOUN
ejpam-1871	404	9	,	,	PUNCT
ejpam-1871	404	10	25:131–147	25:131–147	PROPN
ejpam-1871	404	11	,	,	PUNCT
ejpam-1871	404	12	1970	1970	NUM
ejpam-1871	404	13	.	.	PUNCT
ejpam-1871	405	1	[	[	X
ejpam-1871	405	2	3	3	NUM
ejpam-1871	405	3	]	]	SYM
ejpam-1871	405	4	b	b	X
ejpam-1871	405	5	banaschewski	banaschewski	NOUN
ejpam-1871	405	6	and	and	CCONJ
ejpam-1871	405	7	g	g	PROPN
ejpam-1871	405	8	bruns	brun	NOUN
ejpam-1871	405	9	.	.	PUNCT
ejpam-1871	406	1	categorical	categorical	ADJ
ejpam-1871	406	2	characterization	characterization	NOUN
ejpam-1871	406	3	of	of	ADP
ejpam-1871	406	4	the	the	DET
ejpam-1871	406	5	macneille	macneille	PROPN
ejpam-1871	406	6	completion	completion	NOUN
ejpam-1871	406	7	.	.	PUNCT
ejpam-1871	407	1	archiv	archiv	PROPN
ejpam-1871	407	2	der	der	PROPN
ejpam-1871	407	3	mathematik	mathematik	PROPN
ejpam-1871	407	4	,	,	PUNCT
ejpam-1871	407	5	18:369–377	18:369–377	NUM
ejpam-1871	407	6	,	,	PUNCT
ejpam-1871	407	7	1967	1967	NUM
ejpam-1871	407	8	.	.	PUNCT
ejpam-1871	408	1	[	[	X
ejpam-1871	408	2	4	4	NUM
ejpam-1871	408	3	]	]	X
ejpam-1871	408	4	h	h	NOUN
ejpam-1871	408	5	barzegar	barzegar	NOUN
ejpam-1871	408	6	and	and	CCONJ
ejpam-1871	408	7	m	m	PROPN
ejpam-1871	408	8	m	m	PROPN
ejpam-1871	408	9	ebrahimi	ebrahimi	PROPN
ejpam-1871	408	10	.	.	PUNCT
ejpam-1871	409	1	sequentially	sequentially	ADV
ejpam-1871	409	2	pure	pure	ADJ
ejpam-1871	409	3	monomorphisms	monomorphism	NOUN
ejpam-1871	409	4	of	of	ADP
ejpam-1871	409	5	acts	act	NOUN
ejpam-1871	409	6	over	over	ADP
ejpam-1871	409	7	semigroups	semigroup	NOUN
ejpam-1871	409	8	.	.	PUNCT
ejpam-1871	410	1	european	european	ADJ
ejpam-1871	410	2	journal	journal	PROPN
ejpam-1871	410	3	of	of	ADP
ejpam-1871	410	4	pure	pure	ADJ
ejpam-1871	410	5	and	and	CCONJ
ejpam-1871	410	6	applied	applied	ADJ
ejpam-1871	410	7	mathematics	mathematic	NOUN
ejpam-1871	410	8	,	,	PUNCT
ejpam-1871	410	9	4:41–55	4:41–55	NOUN
ejpam-1871	410	10	,	,	PUNCT
ejpam-1871	410	11	2008	2008	NUM
ejpam-1871	410	12	.	.	PUNCT
ejpam-1871	411	1	[	[	X
ejpam-1871	411	2	5	5	NUM
ejpam-1871	411	3	]	]	PUNCT
ejpam-1871	411	4	h	h	NOUN
ejpam-1871	411	5	barzegar	barzegar	NOUN
ejpam-1871	411	6	,	,	PUNCT
ejpam-1871	411	7	m	m	VERB
ejpam-1871	411	8	m	m	VERB
ejpam-1871	411	9	ebrahimi	ebrahimi	ADJ
ejpam-1871	411	10	,	,	PUNCT
ejpam-1871	411	11	and	and	CCONJ
ejpam-1871	411	12	m	m	PROPN
ejpam-1871	411	13	mahmoudi	mahmoudi	NOUN
ejpam-1871	411	14	.	.	PUNCT
ejpam-1871	412	1	essentiality	essentiality	NOUN
ejpam-1871	412	2	and	and	CCONJ
ejpam-1871	412	3	injectivity	injectivity	NOUN
ejpam-1871	412	4	.	.	PUNCT
ejpam-1871	413	1	applied	apply	VERB
ejpam-1871	413	2	categorical	categorical	ADJ
ejpam-1871	413	3	structures	structure	NOUN
ejpam-1871	413	4	,	,	PUNCT
ejpam-1871	413	5	18(1):73–83	18(1):73–83	NUM
ejpam-1871	413	6	,	,	PUNCT
ejpam-1871	413	7	2010	2010	NUM
ejpam-1871	413	8	.	.	PUNCT
ejpam-1871	414	1	[	[	X
ejpam-1871	414	2	6	6	NUM
ejpam-1871	414	3	]	]	PUNCT
ejpam-1871	414	4	t	t	PROPN
ejpam-1871	414	5	s	s	PROPN
ejpam-1871	414	6	blyth	blyth	PROPN
ejpam-1871	414	7	and	and	CCONJ
ejpam-1871	414	8	m	m	PROPN
ejpam-1871	414	9	f	f	PROPN
ejpam-1871	414	10	janowitz	janowitz	PROPN
ejpam-1871	414	11	.	.	PUNCT
ejpam-1871	415	1	residuation	residuation	PROPN
ejpam-1871	415	2	theory	theory	NOUN
ejpam-1871	415	3	.	.	PUNCT
ejpam-1871	416	1	pergamon	pergamon	PROPN
ejpam-1871	416	2	press	press	PROPN
ejpam-1871	416	3	,	,	PUNCT
ejpam-1871	416	4	oxford	oxford	PROPN
ejpam-1871	416	5	,	,	PUNCT
ejpam-1871	416	6	1972	1972	NUM
ejpam-1871	416	7	.	.	PUNCT
ejpam-1871	417	1	[	[	X
ejpam-1871	417	2	7	7	NUM
ejpam-1871	417	3	]	]	X
ejpam-1871	417	4	s	s	VERB
ejpam-1871	417	5	bulman	bulman	NOUN
ejpam-1871	417	6	-	-	PUNCT
ejpam-1871	417	7	fleming	fleming	NOUN
ejpam-1871	417	8	and	and	CCONJ
ejpam-1871	417	9	v	v	ADP
ejpam-1871	417	10	laan	laan	PROPN
ejpam-1871	417	11	.	.	PUNCT
ejpam-1871	417	12	lazard	lazard	PROPN
ejpam-1871	417	13	’s	’s	PART
ejpam-1871	417	14	theorem	theorem	NOUN
ejpam-1871	417	15	for	for	ADP
ejpam-1871	417	16	s	s	NOUN
ejpam-1871	417	17	-	-	NOUN
ejpam-1871	417	18	posets	poset	NOUN
ejpam-1871	417	19	.	.	PUNCT
ejpam-1871	418	1	mathematische	mathematische	PROPN
ejpam-1871	418	2	nachrichten	nachrichten	PROPN
ejpam-1871	418	3	,	,	PUNCT
ejpam-1871	418	4	278(15):1743–1755	278(15):1743–1755	NUM
ejpam-1871	418	5	,	,	PUNCT
ejpam-1871	418	6	2005	2005	NUM
ejpam-1871	418	7	.	.	PUNCT
ejpam-1871	419	1	[	[	X
ejpam-1871	419	2	8	8	NUM
ejpam-1871	419	3	]	]	X
ejpam-1871	419	4	s	s	VERB
ejpam-1871	419	5	bulman	bulman	NOUN
ejpam-1871	419	6	-	-	PUNCT
ejpam-1871	419	7	fleming	fleming	NOUN
ejpam-1871	419	8	and	and	CCONJ
ejpam-1871	419	9	m	m	NOUN
ejpam-1871	419	10	mahmoudi	mahmoudi	NOUN
ejpam-1871	419	11	.	.	PUNCT
ejpam-1871	420	1	the	the	DET
ejpam-1871	420	2	category	category	NOUN
ejpam-1871	420	3	of	of	ADP
ejpam-1871	420	4	s	s	NOUN
ejpam-1871	420	5	-	-	NOUN
ejpam-1871	420	6	posets	poset	NOUN
ejpam-1871	420	7	.	.	PUNCT
ejpam-1871	421	1	semigroup	semigroup	PROPN
ejpam-1871	421	2	forum	forum	PROPN
ejpam-1871	421	3	,	,	PUNCT
ejpam-1871	421	4	71:443–461	71:443–461	PROPN
ejpam-1871	421	5	,	,	PUNCT
ejpam-1871	421	6	2005	2005	NUM
ejpam-1871	421	7	.	.	PUNCT
ejpam-1871	422	1	[	[	X
ejpam-1871	422	2	9	9	NUM
ejpam-1871	422	3	]	]	X
ejpam-1871	422	4	m	m	VERB
ejpam-1871	422	5	m	m	VERB
ejpam-1871	422	6	ebrahimi	ebrahimi	PROPN
ejpam-1871	422	7	,	,	PUNCT
ejpam-1871	422	8	m	m	VERB
ejpam-1871	422	9	mahmoudi	mahmoudi	NOUN
ejpam-1871	422	10	,	,	PUNCT
ejpam-1871	422	11	and	and	CCONJ
ejpam-1871	422	12	h	h	PROPN
ejpam-1871	422	13	rasouli	rasouli	PROPN
ejpam-1871	422	14	.	.	PUNCT
ejpam-1871	423	1	banaschewski	banaschewski	PROPN
ejpam-1871	423	2	’s	’s	PART
ejpam-1871	423	3	theorem	theorem	NOUN
ejpam-1871	423	4	for	for	ADP
ejpam-1871	423	5	s	s	NOUN
ejpam-1871	423	6	-	-	NOUN
ejpam-1871	423	7	posets	poset	NOUN
ejpam-1871	423	8	:	:	PUNCT
ejpam-1871	423	9	regular	regular	ADJ
ejpam-1871	423	10	injectivity	injectivity	NOUN
ejpam-1871	423	11	and	and	CCONJ
ejpam-1871	423	12	completeness	completeness	NOUN
ejpam-1871	423	13	.	.	PUNCT
ejpam-1871	424	1	semigroup	semigroup	PROPN
ejpam-1871	424	2	forum	forum	PROPN
ejpam-1871	424	3	,	,	PUNCT
ejpam-1871	424	4	80:313–324	80:313–324	PROPN
ejpam-1871	424	5	,	,	PUNCT
ejpam-1871	424	6	2010	2010	NUM
ejpam-1871	424	7	.	.	PUNCT
ejpam-1871	425	1	[	[	X
ejpam-1871	425	2	10	10	NUM
ejpam-1871	425	3	]	]	X
ejpam-1871	425	4	m	m	VERB
ejpam-1871	425	5	m	m	VERB
ejpam-1871	425	6	ebrahimi	ebrahimi	PROPN
ejpam-1871	425	7	,	,	PUNCT
ejpam-1871	425	8	m	m	VERB
ejpam-1871	425	9	mahmoudi	mahmoudi	NOUN
ejpam-1871	425	10	,	,	PUNCT
ejpam-1871	425	11	and	and	CCONJ
ejpam-1871	425	12	h	h	PROPN
ejpam-1871	425	13	rasouli	rasouli	PROPN
ejpam-1871	425	14	.	.	PUNCT
ejpam-1871	426	1	characterizing	characterize	VERB
ejpam-1871	426	2	pomonoids	pomonoid	NOUN
ejpam-1871	426	3	s	s	PRON
ejpam-1871	426	4	by	by	ADP
ejpam-1871	426	5	complete	complete	ADJ
ejpam-1871	426	6	s	s	NOUN
ejpam-1871	426	7	-	-	NOUN
ejpam-1871	426	8	posets	poset	NOUN
ejpam-1871	426	9	.	.	PUNCT
ejpam-1871	427	1	cahiers	cahier	NOUN
ejpam-1871	427	2	de	de	ADP
ejpam-1871	427	3	topologie	topologie	PROPN
ejpam-1871	427	4	et	et	PROPN
ejpam-1871	427	5	géométrie	géométrie	VERB
ejpam-1871	427	6	différentielle	différentielle	PROPN
ejpam-1871	427	7	catégoriques	catégorique	NOUN
ejpam-1871	427	8	,	,	PUNCT
ejpam-1871	427	9	li(4):272–281	li(4):272–281	NOUN
ejpam-1871	427	10	,	,	PUNCT
ejpam-1871	427	11	2010	2010	NUM
ejpam-1871	427	12	.	.	PUNCT
ejpam-1871	428	1	[	[	X
ejpam-1871	428	2	11	11	NUM
ejpam-1871	428	3	]	]	X
ejpam-1871	428	4	s	s	VERB
ejpam-1871	428	5	m	m	VERB
ejpam-1871	428	6	fakhruddin	fakhruddin	NOUN
ejpam-1871	428	7	.	.	PUNCT
ejpam-1871	429	1	on	on	ADP
ejpam-1871	429	2	the	the	DET
ejpam-1871	429	3	category	category	NOUN
ejpam-1871	429	4	of	of	ADP
ejpam-1871	429	5	s	s	NOUN
ejpam-1871	429	6	-	-	NOUN
ejpam-1871	429	7	posets	poset	NOUN
ejpam-1871	429	8	.	.	PUNCT
ejpam-1871	430	1	acta	acta	PROPN
ejpam-1871	430	2	scientiarum	scientiarum	PROPN
ejpam-1871	430	3	mathematicarum	mathematicarum	PROPN
ejpam-1871	430	4	(	(	PUNCT
ejpam-1871	430	5	szeged	szeged	PROPN
ejpam-1871	430	6	)	)	PUNCT
ejpam-1871	430	7	,	,	PUNCT
ejpam-1871	430	8	52:85–92	52:85–92	NUM
ejpam-1871	430	9	,	,	PUNCT
ejpam-1871	430	10	1998	1998	NUM
ejpam-1871	430	11	.	.	PUNCT
ejpam-1871	431	1	references	reference	NOUN
ejpam-1871	431	2	178	178	NUM
ejpam-1871	432	1	[	[	X
ejpam-1871	432	2	12	12	NUM
ejpam-1871	432	3	]	]	X
ejpam-1871	432	4	m	m	PROPN
ejpam-1871	432	5	kilp	kilp	PROPN
ejpam-1871	432	6	,	,	PUNCT
ejpam-1871	432	7	u	u	NOUN
ejpam-1871	432	8	knauer	knauer	NOUN
ejpam-1871	432	9	,	,	PUNCT
ejpam-1871	432	10	and	and	CCONJ
ejpam-1871	432	11	a	a	DET
ejpam-1871	432	12	mikhalev	mikhalev	NOUN
ejpam-1871	432	13	.	.	PUNCT
ejpam-1871	433	1	monoids	monoids	PROPN
ejpam-1871	433	2	,	,	PUNCT
ejpam-1871	433	3	acts	act	NOUN
ejpam-1871	433	4	and	and	CCONJ
ejpam-1871	433	5	categories	category	NOUN
ejpam-1871	433	6	.	.	PUNCT
ejpam-1871	434	1	de	de	X
ejpam-1871	434	2	gruyter	gruyter	NOUN
ejpam-1871	434	3	,	,	PUNCT
ejpam-1871	434	4	berlin	berlin	PROPN
ejpam-1871	434	5	,	,	PUNCT
ejpam-1871	434	6	2000	2000	NUM
ejpam-1871	434	7	.	.	PUNCT
ejpam-1871	435	1	[	[	X
ejpam-1871	435	2	13	13	NUM
ejpam-1871	435	3	]	]	SYM
ejpam-1871	435	4	m	m	VERB
ejpam-1871	435	5	mahmoudi	mahmoudi	NOUN
ejpam-1871	435	6	and	and	CCONJ
ejpam-1871	435	7	l	l	PROPN
ejpam-1871	435	8	shahbaz	shahbaz	PROPN
ejpam-1871	435	9	.	.	PUNCT
ejpam-1871	436	1	sequentially	sequentially	ADV
ejpam-1871	436	2	dense	dense	ADJ
ejpam-1871	436	3	essential	essential	ADJ
ejpam-1871	436	4	monomorphisms	monomorphism	NOUN
ejpam-1871	436	5	of	of	ADP
ejpam-1871	436	6	acts	act	NOUN
ejpam-1871	436	7	over	over	ADP
ejpam-1871	436	8	semigroups	semigroup	NOUN
ejpam-1871	436	9	.	.	PUNCT
ejpam-1871	437	1	applied	apply	VERB
ejpam-1871	437	2	categorical	categorical	ADJ
ejpam-1871	437	3	structures	structure	NOUN
ejpam-1871	437	4	,	,	PUNCT
ejpam-1871	437	5	18:461–471	18:461–471	NUM
ejpam-1871	437	6	,	,	PUNCT
ejpam-1871	437	7	2010	2010	NUM
ejpam-1871	437	8	.	.	PUNCT
ejpam-1871	438	1	[	[	X
ejpam-1871	438	2	14	14	NUM
ejpam-1871	438	3	]	]	X
ejpam-1871	438	4	s	s	VERB
ejpam-1871	438	5	roman	roman	NOUN
ejpam-1871	438	6	.	.	PUNCT
ejpam-1871	439	1	lattices	lattice	NOUN
ejpam-1871	439	2	and	and	CCONJ
ejpam-1871	439	3	ordered	order	VERB
ejpam-1871	439	4	sets	set	NOUN
ejpam-1871	439	5	.	.	PUNCT
ejpam-1871	440	1	springer	springer	NOUN
ejpam-1871	440	2	,	,	PUNCT
ejpam-1871	440	3	new	new	PROPN
ejpam-1871	440	4	york	york	PROPN
ejpam-1871	440	5	,	,	PUNCT
ejpam-1871	440	6	2008	2008	NUM
ejpam-1871	440	7	.	.	PUNCT
ejpam-1871	441	1	[	[	X
ejpam-1871	441	2	15	15	NUM
ejpam-1871	441	3	]	]	X
ejpam-1871	441	4	x	x	X
ejpam-1871	441	5	shi	shi	PROPN
ejpam-1871	441	6	.	.	PUNCT
ejpam-1871	442	1	on	on	ADP
ejpam-1871	442	2	flatness	flatness	NOUN
ejpam-1871	442	3	properties	property	NOUN
ejpam-1871	442	4	of	of	ADP
ejpam-1871	442	5	cyclic	cyclic	ADJ
ejpam-1871	442	6	s	s	NOUN
ejpam-1871	442	7	-	-	NOUN
ejpam-1871	442	8	posets	poset	NOUN
ejpam-1871	442	9	.	.	PUNCT
ejpam-1871	443	1	semigroup	semigroup	PROPN
ejpam-1871	443	2	forum	forum	PROPN
ejpam-1871	443	3	,	,	PUNCT
ejpam-1871	443	4	77:248–266	77:248–266	PROPN
ejpam-1871	443	5	,	,	PUNCT
ejpam-1871	443	6	2008	2008	NUM
ejpam-1871	443	7	.	.	PUNCT