id	sid	tid	token	lemma	pos
ejpam-2217	1	1	european	european	PROPN
ejpam-2217	1	2	journal	journal	PROPN
ejpam-2217	1	3	of	of	ADP
ejpam-2217	1	4	pure	pure	ADJ
ejpam-2217	1	5	and	and	CCONJ
ejpam-2217	1	6	applied	apply	VERB
ejpam-2217	1	7	mathematics	mathematic	NOUN
ejpam-2217	1	8	vol	vol	NOUN
ejpam-2217	1	9	.	.	PUNCT
ejpam-2217	2	1	7	7	NUM
ejpam-2217	2	2	,	,	PUNCT
ejpam-2217	2	3	no	no	INTJ
ejpam-2217	2	4	.	.	NOUN
ejpam-2217	2	5	4	4	NUM
ejpam-2217	2	6	,	,	PUNCT
ejpam-2217	2	7	2014	2014	NUM
ejpam-2217	2	8	,	,	PUNCT
ejpam-2217	2	9	412	412	NUM
ejpam-2217	2	10	-	-	SYM
ejpam-2217	2	11	418	418	NUM
ejpam-2217	2	12	issn	issn	PROPN
ejpam-2217	2	13	1307	1307	NUM
ejpam-2217	2	14	-	-	SYM
ejpam-2217	2	15	5543	5543	NUM
ejpam-2217	2	16	–	–	PUNCT
ejpam-2217	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2217	2	18	some	some	DET
ejpam-2217	2	19	relations	relation	NOUN
ejpam-2217	2	20	between	between	ADP
ejpam-2217	2	21	crossed	cross	VERB
ejpam-2217	2	22	modules	module	NOUN
ejpam-2217	2	23	and	and	CCONJ
ejpam-2217	2	24	simplicial	simplicial	ADJ
ejpam-2217	2	25	objects	object	NOUN
ejpam-2217	2	26	in	in	ADP
ejpam-2217	2	27	categories	category	NOUN
ejpam-2217	2	28	of	of	ADP
ejpam-2217	2	29	interest	interest	NOUN
ejpam-2217	2	30	yaşar	yaşar	PROPN
ejpam-2217	2	31	boyacı1,∗	boyacı1,∗	NOUN
ejpam-2217	2	32	,	,	PUNCT
ejpam-2217	2	33	osman	osman	PROPN
ejpam-2217	2	34	avcıoğlu	avcıoğlu	NOUN
ejpam-2217	2	35	2	2	NUM
ejpam-2217	2	36	1	1	NUM
ejpam-2217	2	37	dumlupınar	dumlupınar	NOUN
ejpam-2217	2	38	university	university	NOUN
ejpam-2217	2	39	,	,	PUNCT
ejpam-2217	2	40	faculty	faculty	NOUN
ejpam-2217	2	41	of	of	ADP
ejpam-2217	2	42	education	education	NOUN
ejpam-2217	2	43	,	,	PUNCT
ejpam-2217	2	44	kütahya	kütahya	PROPN
ejpam-2217	2	45	,	,	PUNCT
ejpam-2217	2	46	turkey	turkey	PROPN
ejpam-2217	2	47	2	2	NUM
ejpam-2217	2	48	uşak	uşak	PROPN
ejpam-2217	2	49	university	university	NOUN
ejpam-2217	2	50	,	,	PUNCT
ejpam-2217	2	51	faculty	faculty	NOUN
ejpam-2217	2	52	of	of	ADP
ejpam-2217	2	53	arts	art	NOUN
ejpam-2217	2	54	and	and	CCONJ
ejpam-2217	2	55	sciences	science	NOUN
ejpam-2217	2	56	,	,	PUNCT
ejpam-2217	2	57	uşak	uşak	PROPN
ejpam-2217	2	58	,	,	PUNCT
ejpam-2217	2	59	turkey	turkey	NOUN
ejpam-2217	2	60	abstract	abstract	NOUN
ejpam-2217	2	61	.	.	PUNCT
ejpam-2217	3	1	we	we	PRON
ejpam-2217	3	2	introduce	introduce	VERB
ejpam-2217	3	3	a	a	DET
ejpam-2217	3	4	simplicial	simplicial	ADJ
ejpam-2217	3	5	object	object	NOUN
ejpam-2217	3	6	in	in	ADP
ejpam-2217	3	7	a	a	DET
ejpam-2217	3	8	category	category	NOUN
ejpam-2217	3	9	of	of	ADP
ejpam-2217	3	10	interest	interest	NOUN
ejpam-2217	3	11	and	and	CCONJ
ejpam-2217	3	12	determine	determine	VERB
ejpam-2217	3	13	relations	relation	NOUN
ejpam-2217	3	14	between	between	ADP
ejpam-2217	3	15	crossed	cross	VERB
ejpam-2217	3	16	modules	module	NOUN
ejpam-2217	3	17	and	and	CCONJ
ejpam-2217	3	18	simplicial	simplicial	ADJ
ejpam-2217	3	19	objects	object	NOUN
ejpam-2217	3	20	in	in	ADP
ejpam-2217	3	21	a	a	DET
ejpam-2217	3	22	category	category	NOUN
ejpam-2217	3	23	of	of	ADP
ejpam-2217	3	24	interest	interest	NOUN
ejpam-2217	3	25	.	.	PUNCT
ejpam-2217	4	1	2010	2010	NUM
ejpam-2217	4	2	mathematics	mathematic	NOUN
ejpam-2217	4	3	subject	subject	NOUN
ejpam-2217	4	4	classifications	classification	NOUN
ejpam-2217	4	5	:	:	PUNCT
ejpam-2217	4	6	18b99	18b99	NUM
ejpam-2217	4	7	,	,	PUNCT
ejpam-2217	4	8	18g30	18g30	NUM
ejpam-2217	4	9	,	,	PUNCT
ejpam-2217	4	10	18g50,18g55	18g50,18g55	NUM
ejpam-2217	4	11	key	key	ADJ
ejpam-2217	4	12	words	word	NOUN
ejpam-2217	4	13	and	and	CCONJ
ejpam-2217	4	14	phrases	phrase	NOUN
ejpam-2217	4	15	:	:	PUNCT
ejpam-2217	4	16	category	category	NOUN
ejpam-2217	4	17	of	of	ADP
ejpam-2217	4	18	interest	interest	NOUN
ejpam-2217	4	19	,	,	PUNCT
ejpam-2217	4	20	simplicial	simplicial	ADJ
ejpam-2217	4	21	object	object	NOUN
ejpam-2217	4	22	,	,	PUNCT
ejpam-2217	4	23	crossed	cross	VERB
ejpam-2217	4	24	module	module	NOUN
ejpam-2217	4	25	1	1	NUM
ejpam-2217	4	26	.	.	PUNCT
ejpam-2217	4	27	introduction	introduction	NOUN
ejpam-2217	4	28	categories	category	NOUN
ejpam-2217	4	29	of	of	ADP
ejpam-2217	4	30	interest	interest	NOUN
ejpam-2217	4	31	were	be	AUX
ejpam-2217	4	32	introduced	introduce	VERB
ejpam-2217	4	33	in	in	ADP
ejpam-2217	4	34	order	order	NOUN
ejpam-2217	4	35	to	to	PART
ejpam-2217	4	36	study	study	VERB
ejpam-2217	4	37	properties	property	NOUN
ejpam-2217	4	38	of	of	ADP
ejpam-2217	4	39	different	different	ADJ
ejpam-2217	4	40	algebraic	algebraic	ADJ
ejpam-2217	4	41	categories	category	NOUN
ejpam-2217	4	42	and	and	CCONJ
ejpam-2217	4	43	different	different	ADJ
ejpam-2217	4	44	algebras	algebra	NOUN
ejpam-2217	4	45	simultaneously	simultaneously	ADV
ejpam-2217	4	46	.	.	PUNCT
ejpam-2217	5	1	roughly	roughly	ADV
ejpam-2217	5	2	speaking	speak	VERB
ejpam-2217	5	3	,	,	PUNCT
ejpam-2217	5	4	category	category	NOUN
ejpam-2217	5	5	of	of	ADP
ejpam-2217	5	6	interest	interest	NOUN
ejpam-2217	5	7	can	can	AUX
ejpam-2217	5	8	be	be	AUX
ejpam-2217	5	9	seen	see	VERB
ejpam-2217	5	10	as	as	ADP
ejpam-2217	5	11	a	a	DET
ejpam-2217	5	12	gadget	gadget	NOUN
ejpam-2217	5	13	which	which	PRON
ejpam-2217	5	14	unifies	unify	VERB
ejpam-2217	5	15	many	many	ADJ
ejpam-2217	5	16	algebraic	algebraic	ADJ
ejpam-2217	5	17	constructions	construction	NOUN
ejpam-2217	5	18	.	.	PUNCT
ejpam-2217	6	1	the	the	DET
ejpam-2217	6	2	idea	idea	NOUN
ejpam-2217	6	3	comes	come	VERB
ejpam-2217	6	4	from	from	ADP
ejpam-2217	6	5	p.g	p.g	PROPN
ejpam-2217	6	6	.	.	PROPN
ejpam-2217	6	7	higgins	higgins	PROPN
ejpam-2217	6	8	[	[	X
ejpam-2217	6	9	10	10	NUM
ejpam-2217	6	10	]	]	PUNCT
ejpam-2217	6	11	and	and	CCONJ
ejpam-2217	6	12	the	the	DET
ejpam-2217	6	13	definition	definition	NOUN
ejpam-2217	6	14	is	be	AUX
ejpam-2217	6	15	due	due	ADJ
ejpam-2217	6	16	to	to	ADP
ejpam-2217	6	17	m.	m.	PROPN
ejpam-2217	6	18	barr	barr	PROPN
ejpam-2217	6	19	and	and	CCONJ
ejpam-2217	6	20	g.	g.	PROPN
ejpam-2217	6	21	orzech	orzech	PROPN
ejpam-2217	7	1	[	[	X
ejpam-2217	7	2	11	11	NUM
ejpam-2217	7	3	]	]	PUNCT
ejpam-2217	7	4	.	.	PUNCT
ejpam-2217	8	1	the	the	DET
ejpam-2217	8	2	categories	category	NOUN
ejpam-2217	8	3	of	of	ADP
ejpam-2217	8	4	groups	group	NOUN
ejpam-2217	8	5	,	,	PUNCT
ejpam-2217	8	6	modules	module	NOUN
ejpam-2217	8	7	over	over	ADP
ejpam-2217	8	8	a	a	DET
ejpam-2217	8	9	ring	ring	NOUN
ejpam-2217	8	10	,	,	PUNCT
ejpam-2217	8	11	vector	vector	NOUN
ejpam-2217	8	12	spaces	space	NOUN
ejpam-2217	8	13	,	,	PUNCT
ejpam-2217	8	14	associative	associative	ADJ
ejpam-2217	8	15	algebras	algebra	NOUN
ejpam-2217	8	16	,	,	PUNCT
ejpam-2217	8	17	associative	associative	ADJ
ejpam-2217	8	18	commutative	commutative	ADJ
ejpam-2217	8	19	algebras	algebra	NOUN
ejpam-2217	8	20	,	,	PUNCT
ejpam-2217	8	21	lie	lie	NOUN
ejpam-2217	8	22	algebras	algebra	NOUN
ejpam-2217	8	23	and	and	CCONJ
ejpam-2217	8	24	leibniz	leibniz	PROPN
ejpam-2217	8	25	algebras	algebras	PROPN
ejpam-2217	8	26	are	be	AUX
ejpam-2217	8	27	categories	category	NOUN
ejpam-2217	8	28	of	of	ADP
ejpam-2217	8	29	interest	interest	NOUN
ejpam-2217	8	30	[	[	X
ejpam-2217	8	31	11	11	NUM
ejpam-2217	8	32	]	]	PUNCT
ejpam-2217	8	33	.	.	PUNCT
ejpam-2217	9	1	the	the	DET
ejpam-2217	9	2	categories	category	NOUN
ejpam-2217	9	3	of	of	ADP
ejpam-2217	9	4	crossed	cross	VERB
ejpam-2217	9	5	modules	module	NOUN
ejpam-2217	9	6	and	and	CCONJ
ejpam-2217	9	7	precrossed	precrossed	ADJ
ejpam-2217	9	8	modules	module	NOUN
ejpam-2217	9	9	in	in	ADP
ejpam-2217	9	10	the	the	DET
ejpam-2217	9	11	category	category	NOUN
ejpam-2217	9	12	of	of	ADP
ejpam-2217	9	13	groups	group	NOUN
ejpam-2217	9	14	,	,	PUNCT
ejpam-2217	9	15	respectively	respectively	ADV
ejpam-2217	9	16	,	,	PUNCT
ejpam-2217	9	17	are	be	AUX
ejpam-2217	9	18	equivalent	equivalent	ADJ
ejpam-2217	9	19	to	to	ADP
ejpam-2217	9	20	the	the	DET
ejpam-2217	9	21	categories	category	NOUN
ejpam-2217	9	22	of	of	ADP
ejpam-2217	9	23	interests	interest	NOUN
ejpam-2217	9	24	(	(	PUNCT
ejpam-2217	9	25	see	see	VERB
ejpam-2217	9	26	e.g.	e.g.	ADV
ejpam-2217	9	27	[	[	X
ejpam-2217	9	28	3	3	NUM
ejpam-2217	9	29	,	,	PUNCT
ejpam-2217	9	30	4	4	NUM
ejpam-2217	9	31	]	]	NUM
ejpam-2217	9	32	)	)	PUNCT
ejpam-2217	9	33	.	.	PUNCT
ejpam-2217	10	1	the	the	DET
ejpam-2217	10	2	functorial	functorial	NOUN
ejpam-2217	10	3	relation	relation	NOUN
ejpam-2217	10	4	between	between	ADP
ejpam-2217	10	5	crossed	cross	VERB
ejpam-2217	10	6	modules	module	NOUN
ejpam-2217	10	7	and	and	CCONJ
ejpam-2217	10	8	simplicial	simplicial	ADJ
ejpam-2217	10	9	objects	object	NOUN
ejpam-2217	10	10	with	with	ADP
ejpam-2217	10	11	moore	moore	PROPN
ejpam-2217	10	12	complex	complex	NOUN
ejpam-2217	10	13	of	of	ADP
ejpam-2217	10	14	length	length	NOUN
ejpam-2217	10	15	1	1	NUM
ejpam-2217	10	16	in	in	ADP
ejpam-2217	10	17	groups	group	NOUN
ejpam-2217	10	18	,	,	PUNCT
ejpam-2217	10	19	commutative	commutative	ADJ
ejpam-2217	10	20	algebras	algebra	NOUN
ejpam-2217	10	21	,	,	PUNCT
ejpam-2217	10	22	lie	lie	NOUN
ejpam-2217	10	23	algebras	algebra	NOUN
ejpam-2217	10	24	,	,	PUNCT
ejpam-2217	10	25	leibniz	leibniz	PROPN
ejpam-2217	10	26	n	n	CCONJ
ejpam-2217	10	27	-	-	PUNCT
ejpam-2217	10	28	algebras	algebras	PROPN
ejpam-2217	10	29	were	be	AUX
ejpam-2217	10	30	given	give	VERB
ejpam-2217	10	31	in	in	ADP
ejpam-2217	10	32	[	[	X
ejpam-2217	10	33	1	1	NUM
ejpam-2217	10	34	,	,	PUNCT
ejpam-2217	10	35	2	2	NUM
ejpam-2217	10	36	,	,	PUNCT
ejpam-2217	10	37	5	5	NUM
ejpam-2217	10	38	,	,	PUNCT
ejpam-2217	10	39	8	8	NUM
ejpam-2217	10	40	,	,	PUNCT
ejpam-2217	10	41	9	9	NUM
ejpam-2217	10	42	]	]	PUNCT
ejpam-2217	10	43	.	.	PUNCT
ejpam-2217	11	1	in	in	ADP
ejpam-2217	11	2	this	this	DET
ejpam-2217	11	3	paper	paper	NOUN
ejpam-2217	11	4	,	,	PUNCT
ejpam-2217	11	5	we	we	PRON
ejpam-2217	11	6	will	will	AUX
ejpam-2217	11	7	define	define	VERB
ejpam-2217	11	8	simplicial	simplicial	ADJ
ejpam-2217	11	9	objects	object	NOUN
ejpam-2217	11	10	in	in	ADP
ejpam-2217	11	11	categories	category	NOUN
ejpam-2217	11	12	of	of	ADP
ejpam-2217	11	13	interest	interest	NOUN
ejpam-2217	11	14	and	and	CCONJ
ejpam-2217	11	15	unify	unify	VERB
ejpam-2217	11	16	the	the	DET
ejpam-2217	11	17	stated	state	VERB
ejpam-2217	11	18	results	result	NOUN
ejpam-2217	11	19	under	under	ADP
ejpam-2217	11	20	the	the	DET
ejpam-2217	11	21	name	name	NOUN
ejpam-2217	11	22	of	of	ADP
ejpam-2217	11	23	categories	category	NOUN
ejpam-2217	11	24	of	of	ADP
ejpam-2217	11	25	interest	interest	NOUN
ejpam-2217	11	26	.	.	PUNCT
ejpam-2217	12	1	2	2	X
ejpam-2217	12	2	.	.	X
ejpam-2217	12	3	category	category	NOUN
ejpam-2217	12	4	of	of	ADP
ejpam-2217	12	5	interest	interest	NOUN
ejpam-2217	12	6	we	we	PRON
ejpam-2217	12	7	will	will	AUX
ejpam-2217	12	8	have	have	VERB
ejpam-2217	12	9	the	the	DET
ejpam-2217	12	10	main	main	ADJ
ejpam-2217	12	11	definitions	definition	NOUN
ejpam-2217	12	12	and	and	CCONJ
ejpam-2217	12	13	the	the	DET
ejpam-2217	12	14	statements	statement	NOUN
ejpam-2217	12	15	given	give	VERB
ejpam-2217	12	16	for	for	ADP
ejpam-2217	12	17	category	category	NOUN
ejpam-2217	12	18	of	of	ADP
ejpam-2217	12	19	interest	interest	NOUN
ejpam-2217	12	20	in	in	ADP
ejpam-2217	12	21	[	[	X
ejpam-2217	12	22	4	4	NUM
ejpam-2217	12	23	,	,	PUNCT
ejpam-2217	12	24	7	7	NUM
ejpam-2217	12	25	,	,	PUNCT
ejpam-2217	12	26	11	11	NUM
ejpam-2217	12	27	]	]	PUNCT
ejpam-2217	12	28	.	.	PUNCT
ejpam-2217	13	1	∗corresponding	∗corresponde	VERB
ejpam-2217	13	2	author	author	NOUN
ejpam-2217	13	3	.	.	PUNCT
ejpam-2217	14	1	email	email	NOUN
ejpam-2217	14	2	addresses	address	NOUN
ejpam-2217	14	3	:	:	PUNCT
ejpam-2217	14	4	yasar.boyaci@dpu.edu.tr	yasar.boyaci@dpu.edu.tr	PROPN
ejpam-2217	14	5	(	(	PUNCT
ejpam-2217	14	6	y.	y.	NOUN
ejpam-2217	14	7	boyacı	boyacı	PROPN
ejpam-2217	14	8	)	)	PUNCT
ejpam-2217	14	9	,	,	PUNCT
ejpam-2217	14	10	osman.avcioglu@usak.edu.tr	osman.avcioglu@usak.edu.tr	PROPN
ejpam-2217	14	11	(	(	PUNCT
ejpam-2217	14	12	o.	o.	PROPN
ejpam-2217	14	13	avcıoğlu	avcıoğlu	PROPN
ejpam-2217	14	14	)	)	PUNCT
ejpam-2217	14	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2217	15	1	412	412	NUM
ejpam-2217	15	2	c	c	X
ejpam-2217	15	3	©	©	PROPN
ejpam-2217	15	4	2014	2014	NUM
ejpam-2217	15	5	ejpam	ejpam	NOUN
ejpam-2217	15	6	all	all	DET
ejpam-2217	15	7	rights	right	NOUN
ejpam-2217	15	8	reserved	reserve	VERB
ejpam-2217	15	9	.	.	PUNCT
ejpam-2217	16	1	y.	y.	PROPN
ejpam-2217	16	2	boyacı	boyacı	PROPN
ejpam-2217	16	3	,	,	PUNCT
ejpam-2217	16	4	o.	o.	PROPN
ejpam-2217	16	5	avcıoğlu	avcıoğlu	PROPN
ejpam-2217	16	6	/	/	SYM
ejpam-2217	16	7	eur	eur	PROPN
ejpam-2217	16	8	.	.	PUNCT
ejpam-2217	17	1	j.	j.	PROPN
ejpam-2217	17	2	pure	pure	PROPN
ejpam-2217	17	3	appl	appl	PROPN
ejpam-2217	17	4	.	.	PROPN
ejpam-2217	17	5	math	math	PROPN
ejpam-2217	17	6	,	,	PUNCT
ejpam-2217	17	7	7	7	NUM
ejpam-2217	17	8	(	(	PUNCT
ejpam-2217	17	9	2014	2014	NUM
ejpam-2217	17	10	)	)	PUNCT
ejpam-2217	17	11	,	,	PUNCT
ejpam-2217	17	12	412	412	NUM
ejpam-2217	17	13	-	-	SYM
ejpam-2217	17	14	418	418	NUM
ejpam-2217	17	15	413	413	NUM
ejpam-2217	17	16	let	let	VERB
ejpam-2217	17	17	c	c	PRON
ejpam-2217	17	18	be	be	AUX
ejpam-2217	17	19	a	a	DET
ejpam-2217	17	20	category	category	NOUN
ejpam-2217	17	21	of	of	ADP
ejpam-2217	17	22	groups	group	NOUN
ejpam-2217	17	23	with	with	ADP
ejpam-2217	17	24	a	a	DET
ejpam-2217	17	25	set	set	NOUN
ejpam-2217	17	26	of	of	ADP
ejpam-2217	17	27	operations	operation	NOUN
ejpam-2217	17	28	ω	ω	PROPN
ejpam-2217	17	29	and	and	CCONJ
ejpam-2217	17	30	with	with	ADP
ejpam-2217	17	31	a	a	DET
ejpam-2217	17	32	set	set	NOUN
ejpam-2217	17	33	of	of	ADP
ejpam-2217	17	34	identities	identity	NOUN
ejpam-2217	17	35	e	e	NOUN
ejpam-2217	17	36	,	,	PUNCT
ejpam-2217	17	37	such	such	ADJ
ejpam-2217	17	38	that	that	SCONJ
ejpam-2217	17	39	e	e	NOUN
ejpam-2217	17	40	includes	include	VERB
ejpam-2217	17	41	the	the	DET
ejpam-2217	17	42	group	group	NOUN
ejpam-2217	17	43	laws	law	NOUN
ejpam-2217	17	44	and	and	CCONJ
ejpam-2217	17	45	the	the	DET
ejpam-2217	17	46	following	follow	VERB
ejpam-2217	17	47	conditions	condition	NOUN
ejpam-2217	17	48	hold	hold	VERB
ejpam-2217	17	49	.	.	PUNCT
ejpam-2217	18	1	if	if	SCONJ
ejpam-2217	18	2	ωi	ωi	PROPN
ejpam-2217	18	3	is	be	AUX
ejpam-2217	18	4	the	the	DET
ejpam-2217	18	5	set	set	NOUN
ejpam-2217	18	6	of	of	ADP
ejpam-2217	18	7	i	i	PROPN
ejpam-2217	18	8	-	-	PUNCT
ejpam-2217	18	9	ary	ary	PROPN
ejpam-2217	18	10	operations	operation	NOUN
ejpam-2217	18	11	in	in	ADP
ejpam-2217	18	12	ω	ω	PROPN
ejpam-2217	18	13	,	,	PUNCT
ejpam-2217	18	14	then	then	ADV
ejpam-2217	18	15	:	:	PUNCT
ejpam-2217	18	16	(	(	PUNCT
ejpam-2217	18	17	a	a	X
ejpam-2217	18	18	)	)	PUNCT
ejpam-2217	18	19	ω	ω	NOUN
ejpam-2217	18	20	=	=	PROPN
ejpam-2217	18	21	ω0	ω0	PROPN
ejpam-2217	18	22	∪ω1	∪ω1	NOUN
ejpam-2217	18	23	∪ω2	∪ω2	PROPN
ejpam-2217	18	24	;	;	PUNCT
ejpam-2217	18	25	(	(	PUNCT
ejpam-2217	18	26	b	b	X
ejpam-2217	18	27	)	)	PUNCT
ejpam-2217	18	28	the	the	DET
ejpam-2217	18	29	group	group	NOUN
ejpam-2217	18	30	operations	operation	NOUN
ejpam-2217	18	31	(	(	PUNCT
ejpam-2217	18	32	written	write	VERB
ejpam-2217	18	33	additively	additively	ADV
ejpam-2217	18	34	:	:	PUNCT
ejpam-2217	18	35	0,−,+	0,−,+	X
ejpam-2217	18	36	)	)	PUNCT
ejpam-2217	18	37	are	be	AUX
ejpam-2217	18	38	elements	element	NOUN
ejpam-2217	18	39	of	of	ADP
ejpam-2217	18	40	ω0	ω0	NOUN
ejpam-2217	18	41	,	,	PUNCT
ejpam-2217	18	42	ω1	ω1	PROPN
ejpam-2217	18	43	and	and	CCONJ
ejpam-2217	18	44	ω2	ω2	ADJ
ejpam-2217	18	45	respectively	respectively	ADV
ejpam-2217	18	46	.	.	PUNCT
ejpam-2217	19	1	let	let	VERB
ejpam-2217	19	2	ω′2	ω′2	NOUN
ejpam-2217	19	3	=	=	SYM
ejpam-2217	19	4	ω2	ω2	ADJ
ejpam-2217	19	5	\	\	PROPN
ejpam-2217	19	6	{	{	PUNCT
ejpam-2217	19	7	+	+	NOUN
ejpam-2217	19	8	}	}	PUNCT
ejpam-2217	19	9	,	,	PUNCT
ejpam-2217	19	10	ω′1	ω′1	NOUN
ejpam-2217	19	11	=	=	PROPN
ejpam-2217	19	12	ω1	ω1	PROPN
ejpam-2217	19	13	\	\	PROPN
ejpam-2217	19	14	{	{	PUNCT
ejpam-2217	19	15	−	−	NOUN
ejpam-2217	19	16	}	}	PUNCT
ejpam-2217	19	17	.	.	PUNCT
ejpam-2217	20	1	assume	assume	VERB
ejpam-2217	20	2	that	that	SCONJ
ejpam-2217	20	3	if	if	SCONJ
ejpam-2217	20	4	∗	∗	NOUN
ejpam-2217	20	5	∈	∈	PROPN
ejpam-2217	20	6	ω2	ω2	ADJ
ejpam-2217	20	7	,	,	PUNCT
ejpam-2217	20	8	then	then	ADV
ejpam-2217	20	9	ω′2	ω′2	VERB
ejpam-2217	20	10	contains	contain	VERB
ejpam-2217	20	11	∗	∗	NOUN
ejpam-2217	20	12	◦	◦	NOUN
ejpam-2217	20	13	defined	define	VERB
ejpam-2217	20	14	by	by	ADP
ejpam-2217	20	15	x	x	PROPN
ejpam-2217	20	16	∗	∗	NOUN
ejpam-2217	20	17	◦	◦	NOUN
ejpam-2217	20	18	y	y	NOUN
ejpam-2217	20	19	=	=	SYM
ejpam-2217	20	20	y	y	PROPN
ejpam-2217	20	21	∗	∗	NOUN
ejpam-2217	20	22	x	x	PUNCT
ejpam-2217	20	23	and	and	CCONJ
ejpam-2217	20	24	assume	assume	VERB
ejpam-2217	20	25	ω0	ω0	ADV
ejpam-2217	20	26	=	=	SYM
ejpam-2217	20	27	{	{	PUNCT
ejpam-2217	20	28	0	0	NUM
ejpam-2217	20	29	}	}	PUNCT
ejpam-2217	20	30	;	;	PUNCT
ejpam-2217	20	31	(	(	PUNCT
ejpam-2217	20	32	c	c	X
ejpam-2217	20	33	)	)	PUNCT
ejpam-2217	20	34	for	for	ADP
ejpam-2217	20	35	each	each	DET
ejpam-2217	20	36	∗	∗	NOUN
ejpam-2217	20	37	∈	∈	PROPN
ejpam-2217	20	38	ω′2	ω′2	NOUN
ejpam-2217	20	39	,	,	PUNCT
ejpam-2217	20	40	e	e	PROPN
ejpam-2217	20	41	includes	include	VERB
ejpam-2217	20	42	the	the	DET
ejpam-2217	20	43	identity	identity	NOUN
ejpam-2217	20	44	x	x	NOUN
ejpam-2217	20	45	∗	∗	NOUN
ejpam-2217	20	46	(	(	PUNCT
ejpam-2217	20	47	y	y	PROPN
ejpam-2217	20	48	+	+	PROPN
ejpam-2217	20	49	z	z	X
ejpam-2217	20	50	)	)	PUNCT
ejpam-2217	20	51	=	=	PUNCT
ejpam-2217	21	1	x	x	X
ejpam-2217	21	2	∗	∗	NOUN
ejpam-2217	21	3	y	y	NOUN
ejpam-2217	22	1	+	+	NUM
ejpam-2217	22	2	x	x	SYM
ejpam-2217	22	3	∗	∗	NOUN
ejpam-2217	22	4	z	z	NOUN
ejpam-2217	22	5	;	;	PUNCT
ejpam-2217	22	6	(	(	PUNCT
ejpam-2217	22	7	d	d	X
ejpam-2217	22	8	)	)	PUNCT
ejpam-2217	22	9	for	for	ADP
ejpam-2217	22	10	each	each	DET
ejpam-2217	22	11	ω	ω	PROPN
ejpam-2217	22	12	∈	∈	PROPN
ejpam-2217	22	13	ω′1	ω′1	NOUN
ejpam-2217	22	14	and	and	CCONJ
ejpam-2217	22	15	∗	∗	NOUN
ejpam-2217	22	16	∈	∈	PROPN
ejpam-2217	22	17	ω′2	ω′2	NOUN
ejpam-2217	22	18	,	,	PUNCT
ejpam-2217	22	19	e	e	PROPN
ejpam-2217	22	20	includes	include	VERB
ejpam-2217	22	21	the	the	DET
ejpam-2217	22	22	identities	identity	NOUN
ejpam-2217	22	23	ω(x	ω(x	PUNCT
ejpam-2217	22	24	+	+	PROPN
ejpam-2217	22	25	y	y	X
ejpam-2217	22	26	)	)	PUNCT
ejpam-2217	22	27	=	=	PUNCT
ejpam-2217	22	28	ω(x	ω(x	NOUN
ejpam-2217	22	29	)	)	PUNCT
ejpam-2217	23	1	+	+	CCONJ
ejpam-2217	23	2	ω(y	ω(y	NUM
ejpam-2217	23	3	)	)	PUNCT
ejpam-2217	23	4	and	and	CCONJ
ejpam-2217	23	5	ω(x	ω(x	X
ejpam-2217	23	6	∗	∗	NOUN
ejpam-2217	23	7	y	y	NOUN
ejpam-2217	23	8	)	)	PUNCT
ejpam-2217	24	1	=	=	NOUN
ejpam-2217	24	2	ω(x	ω(x	X
ejpam-2217	24	3	)	)	PUNCT
ejpam-2217	24	4	∗	∗	NOUN
ejpam-2217	24	5	y	y	PROPN
ejpam-2217	24	6	.	.	PUNCT
ejpam-2217	25	1	let	let	VERB
ejpam-2217	25	2	c	c	PRON
ejpam-2217	25	3	be	be	AUX
ejpam-2217	25	4	an	an	DET
ejpam-2217	25	5	object	object	NOUN
ejpam-2217	25	6	of	of	ADP
ejpam-2217	25	7	c	c	PROPN
ejpam-2217	25	8	and	and	CCONJ
ejpam-2217	25	9	x1	x1	PROPN
ejpam-2217	25	10	,	,	PUNCT
ejpam-2217	25	11	x2	x2	PROPN
ejpam-2217	25	12	,	,	PUNCT
ejpam-2217	25	13	x3	x3	PROPN
ejpam-2217	25	14	∈	∈	PROPN
ejpam-2217	26	1	c	c	NOUN
ejpam-2217	26	2	:	:	PUNCT
ejpam-2217	26	3	axiom	axiom	NOUN
ejpam-2217	26	4	1	1	NUM
ejpam-2217	26	5	:	:	PUNCT
ejpam-2217	26	6	x1	x1	PROPN
ejpam-2217	26	7	+	+	CCONJ
ejpam-2217	26	8	(	(	PUNCT
ejpam-2217	26	9	x2	x2	PROPN
ejpam-2217	26	10	∗	∗	NOUN
ejpam-2217	26	11	x3	x3	ADJ
ejpam-2217	26	12	)	)	PUNCT
ejpam-2217	27	1	=	=	SYM
ejpam-2217	27	2	(	(	PUNCT
ejpam-2217	27	3	x2	x2	INTJ
ejpam-2217	27	4	∗	∗	NOUN
ejpam-2217	27	5	x3	x3	PROPN
ejpam-2217	27	6	)	)	PUNCT
ejpam-2217	27	7	+	+	CCONJ
ejpam-2217	28	1	x1	x1	NUM
ejpam-2217	28	2	,	,	PUNCT
ejpam-2217	28	3	for	for	ADP
ejpam-2217	28	4	each	each	DET
ejpam-2217	28	5	∗	∗	NOUN
ejpam-2217	28	6	∈	∈	PROPN
ejpam-2217	28	7	ω′2	ω′2	NOUN
ejpam-2217	28	8	.	.	PUNCT
ejpam-2217	29	1	axiom	axiom	NOUN
ejpam-2217	29	2	2	2	NUM
ejpam-2217	29	3	:	:	PUNCT
ejpam-2217	29	4	for	for	ADP
ejpam-2217	29	5	each	each	DET
ejpam-2217	29	6	ordered	order	VERB
ejpam-2217	29	7	pair	pair	NOUN
ejpam-2217	29	8	(	(	PUNCT
ejpam-2217	29	9	∗,∗	∗,∗	NUM
ejpam-2217	29	10	)	)	PUNCT
ejpam-2217	29	11	∈	∈	NOUN
ejpam-2217	29	12	ω′2	ω′2	VERB
ejpam-2217	29	13	×ω	×ω	ADV
ejpam-2217	29	14	′	′	NUM
ejpam-2217	29	15	2	2	NUM
ejpam-2217	29	16	there	there	PRON
ejpam-2217	29	17	is	be	VERB
ejpam-2217	29	18	a	a	DET
ejpam-2217	29	19	word	word	NOUN
ejpam-2217	29	20	w	w	ADP
ejpam-2217	29	21	such	such	ADJ
ejpam-2217	29	22	that	that	SCONJ
ejpam-2217	29	23	(	(	PUNCT
ejpam-2217	29	24	x1	x1	ADJ
ejpam-2217	29	25	∗	∗	NOUN
ejpam-2217	29	26	x2)∗x3	x2)∗x3	PUNCT
ejpam-2217	30	1	=	=	X
ejpam-2217	30	2	w	w	X
ejpam-2217	30	3	(	(	PUNCT
ejpam-2217	30	4	x1(x2	x1(x2	NOUN
ejpam-2217	30	5	x3	x3	ADJ
ejpam-2217	30	6	)	)	PUNCT
ejpam-2217	30	7	,	,	PUNCT
ejpam-2217	30	8	x1(x3	x1(x3	NUM
ejpam-2217	30	9	x2	x2	PROPN
ejpam-2217	30	10	)	)	PUNCT
ejpam-2217	30	11	,	,	PUNCT
ejpam-2217	30	12	(	(	PUNCT
ejpam-2217	30	13	x2	x2	NOUN
ejpam-2217	30	14	x3)x1	x3)x1	NOUN
ejpam-2217	30	15	,	,	PUNCT
ejpam-2217	30	16	(	(	PUNCT
ejpam-2217	30	17	x3	x3	PROPN
ejpam-2217	30	18	x2)x1	x2)x1	PROPN
ejpam-2217	30	19	,	,	PUNCT
ejpam-2217	30	20	x2(x1	x2(x1	PROPN
ejpam-2217	30	21	x3	x3	PROPN
ejpam-2217	30	22	)	)	PUNCT
ejpam-2217	30	23	,	,	PUNCT
ejpam-2217	30	24	x2(x3	x2(x3	PROPN
ejpam-2217	30	25	x1	x1	PROPN
ejpam-2217	30	26	)	)	PUNCT
ejpam-2217	30	27	,	,	PUNCT
ejpam-2217	30	28	(	(	PUNCT
ejpam-2217	30	29	x1	x1	PROPN
ejpam-2217	30	30	x3)x2	x3)x2	PROPN
ejpam-2217	30	31	,	,	PUNCT
ejpam-2217	30	32	(	(	PUNCT
ejpam-2217	30	33	x3	x3	PROPN
ejpam-2217	30	34	x1)x2	x1)x2	PROPN
ejpam-2217	30	35	)	)	PUNCT
ejpam-2217	30	36	,	,	PUNCT
ejpam-2217	30	37	where	where	SCONJ
ejpam-2217	30	38	each	each	DET
ejpam-2217	30	39	juxtaposition	juxtaposition	NOUN
ejpam-2217	30	40	represents	represent	VERB
ejpam-2217	30	41	an	an	DET
ejpam-2217	30	42	operation	operation	NOUN
ejpam-2217	30	43	in	in	ADP
ejpam-2217	30	44	ω′2	ω′2	NOUN
ejpam-2217	30	45	.	.	PUNCT
ejpam-2217	31	1	definition	definition	NOUN
ejpam-2217	31	2	1	1	NUM
ejpam-2217	31	3	.	.	PUNCT
ejpam-2217	32	1	a	a	DET
ejpam-2217	32	2	category	category	NOUN
ejpam-2217	32	3	of	of	ADP
ejpam-2217	32	4	groups	group	NOUN
ejpam-2217	32	5	with	with	ADP
ejpam-2217	32	6	operations	operation	NOUN
ejpam-2217	32	7	satisfying	satisfy	VERB
ejpam-2217	32	8	axiom	axiom	NOUN
ejpam-2217	32	9	1	1	NUM
ejpam-2217	32	10	and	and	CCONJ
ejpam-2217	32	11	axiom	axiom	NOUN
ejpam-2217	32	12	2	2	NUM
ejpam-2217	32	13	is	be	AUX
ejpam-2217	32	14	called	call	VERB
ejpam-2217	32	15	a	a	DET
ejpam-2217	32	16	category	category	NOUN
ejpam-2217	32	17	of	of	ADP
ejpam-2217	32	18	interest	interest	NOUN
ejpam-2217	32	19	by	by	ADP
ejpam-2217	32	20	orzech	orzech	PROPN
ejpam-2217	32	21	[	[	X
ejpam-2217	32	22	11	11	NUM
ejpam-2217	32	23	]	]	PUNCT
ejpam-2217	32	24	.	.	PUNCT
ejpam-2217	33	1	example	example	NOUN
ejpam-2217	34	1	1	1	NUM
ejpam-2217	34	2	.	.	PUNCT
ejpam-2217	35	1	some	some	DET
ejpam-2217	35	2	examples	example	NOUN
ejpam-2217	35	3	of	of	ADP
ejpam-2217	35	4	categories	category	NOUN
ejpam-2217	35	5	of	of	ADP
ejpam-2217	35	6	interest	interest	NOUN
ejpam-2217	35	7	that	that	PRON
ejpam-2217	35	8	are	be	AUX
ejpam-2217	35	9	given	give	VERB
ejpam-2217	35	10	in	in	ADP
ejpam-2217	35	11	[	[	X
ejpam-2217	35	12	4	4	NUM
ejpam-2217	35	13	]	]	PUNCT
ejpam-2217	35	14	:	:	PUNCT
ejpam-2217	35	15	in	in	ADP
ejpam-2217	35	16	the	the	DET
ejpam-2217	35	17	example	example	NOUN
ejpam-2217	35	18	of	of	ADP
ejpam-2217	35	19	groups	group	NOUN
ejpam-2217	35	20	ω′2	ω′2	VERB
ejpam-2217	35	21	=	=	PUNCT
ejpam-2217	35	22	∅.	∅.	NOUN
ejpam-2217	35	23	in	in	ADP
ejpam-2217	35	24	the	the	DET
ejpam-2217	35	25	case	case	NOUN
ejpam-2217	35	26	of	of	ADP
ejpam-2217	35	27	associative	associative	ADJ
ejpam-2217	35	28	algebras	algebra	NOUN
ejpam-2217	35	29	with	with	ADP
ejpam-2217	35	30	multiplication	multiplication	NOUN
ejpam-2217	35	31	represented	represent	VERB
ejpam-2217	35	32	by	by	ADP
ejpam-2217	35	33	∗	∗	NOUN
ejpam-2217	35	34	,	,	PUNCT
ejpam-2217	35	35	we	we	PRON
ejpam-2217	35	36	have	have	VERB
ejpam-2217	35	37	ω′2	ω′2	NOUN
ejpam-2217	35	38	=	=	SYM
ejpam-2217	35	39	{	{	PUNCT
ejpam-2217	35	40	∗,∗	∗,∗	PROPN
ejpam-2217	35	41	◦	◦	NOUN
ejpam-2217	35	42	}	}	PUNCT
ejpam-2217	35	43	.	.	PUNCT
ejpam-2217	36	1	for	for	ADP
ejpam-2217	36	2	lie	lie	NOUN
ejpam-2217	36	3	algebras	algebras	PROPN
ejpam-2217	36	4	ω′2	ω′2	VERB
ejpam-2217	36	5	=	=	SYM
ejpam-2217	36	6	(	(	PUNCT
ejpam-2217	36	7	[	[	X
ejpam-2217	36	8	,	,	PUNCT
ejpam-2217	36	9	]	]	X
ejpam-2217	36	10	,	,	PUNCT
ejpam-2217	36	11	[	[	X
ejpam-2217	36	12	,	,	PUNCT
ejpam-2217	36	13	]	]	PUNCT
ejpam-2217	36	14	◦	◦	NOUN
ejpam-2217	36	15	)	)	PUNCT
ejpam-2217	36	16	(	(	PUNCT
ejpam-2217	36	17	where	where	SCONJ
ejpam-2217	36	18	[	[	X
ejpam-2217	36	19	a	a	X
ejpam-2217	36	20	,	,	PUNCT
ejpam-2217	36	21	b	b	NOUN
ejpam-2217	36	22	]	]	X
ejpam-2217	36	23	◦	◦	NOUN
ejpam-2217	37	1	=	=	PUNCT
ejpam-2217	38	1	[	[	X
ejpam-2217	38	2	b	b	X
ejpam-2217	38	3	,	,	PUNCT
ejpam-2217	38	4	a	a	PRON
ejpam-2217	38	5	]	]	X
ejpam-2217	38	6	=	=	SYM
ejpam-2217	38	7	−[a	−[a	PROPN
ejpam-2217	38	8	,	,	PUNCT
ejpam-2217	38	9	b	b	NOUN
ejpam-2217	38	10	]	]	X
ejpam-2217	38	11	)	)	PUNCT
ejpam-2217	38	12	.	.	PUNCT
ejpam-2217	39	1	for	for	ADP
ejpam-2217	39	2	leibniz	leibniz	PROPN
ejpam-2217	39	3	algebras	algebras	PROPN
ejpam-2217	39	4	ω′2	ω′2	VERB
ejpam-2217	39	5	=	=	SYM
ejpam-2217	39	6	(	(	PUNCT
ejpam-2217	39	7	[	[	X
ejpam-2217	39	8	,	,	PUNCT
ejpam-2217	39	9	]	]	X
ejpam-2217	39	10	,	,	PUNCT
ejpam-2217	39	11	[	[	X
ejpam-2217	39	12	,	,	PUNCT
ejpam-2217	39	13	]	]	PUNCT
ejpam-2217	39	14	◦	◦	NOUN
ejpam-2217	39	15	)	)	PUNCT
ejpam-2217	39	16	(	(	PUNCT
ejpam-2217	39	17	here	here	ADV
ejpam-2217	39	18	[	[	X
ejpam-2217	39	19	a	a	DET
ejpam-2217	39	20	,	,	PUNCT
ejpam-2217	39	21	b	b	NOUN
ejpam-2217	39	22	]	]	X
ejpam-2217	39	23	◦	◦	NOUN
ejpam-2217	40	1	=	=	PUNCT
ejpam-2217	41	1	[	[	X
ejpam-2217	41	2	b	b	X
ejpam-2217	41	3	,	,	PUNCT
ejpam-2217	41	4	a	a	DET
ejpam-2217	41	5	]	]	X
ejpam-2217	41	6	)	)	PUNCT
ejpam-2217	41	7	.	.	PUNCT
ejpam-2217	42	1	definition	definition	NOUN
ejpam-2217	42	2	2	2	NUM
ejpam-2217	42	3	.	.	PUNCT
ejpam-2217	43	1	let	let	VERB
ejpam-2217	43	2	c	c	PROPN
ejpam-2217	43	3	∈	∈	PROPN
ejpam-2217	43	4	c.	c.	PROPN
ejpam-2217	43	5	a	a	DET
ejpam-2217	43	6	subobject	subobject	NOUN
ejpam-2217	43	7	of	of	ADP
ejpam-2217	43	8	c	c	PROPN
ejpam-2217	43	9	is	be	AUX
ejpam-2217	43	10	called	call	VERB
ejpam-2217	43	11	an	an	DET
ejpam-2217	43	12	ideal	ideal	NOUN
ejpam-2217	43	13	if	if	SCONJ
ejpam-2217	43	14	it	it	PRON
ejpam-2217	43	15	is	be	AUX
ejpam-2217	43	16	the	the	DET
ejpam-2217	43	17	kernel	kernel	NOUN
ejpam-2217	43	18	of	of	ADP
ejpam-2217	43	19	some	some	DET
ejpam-2217	43	20	morphism	morphism	NOUN
ejpam-2217	43	21	.	.	PUNCT
ejpam-2217	44	1	theorem	theorem	NOUN
ejpam-2217	44	2	1	1	X
ejpam-2217	44	3	.	.	PUNCT
ejpam-2217	45	1	let	let	VERB
ejpam-2217	45	2	a	a	PRON
ejpam-2217	45	3	be	be	AUX
ejpam-2217	45	4	a	a	DET
ejpam-2217	45	5	subobject	subobject	NOUN
ejpam-2217	45	6	of	of	ADP
ejpam-2217	45	7	b	b	NOUN
ejpam-2217	45	8	in	in	ADP
ejpam-2217	45	9	c.	c.	PROPN
ejpam-2217	45	10	then	then	ADV
ejpam-2217	45	11	a	a	PRON
ejpam-2217	45	12	is	be	AUX
ejpam-2217	45	13	an	an	DET
ejpam-2217	45	14	ideal	ideal	NOUN
ejpam-2217	45	15	of	of	ADP
ejpam-2217	45	16	b	b	NOUN
ejpam-2217	45	17	if	if	NOUN
ejpam-2217	45	18	and	and	CCONJ
ejpam-2217	45	19	only	only	ADV
ejpam-2217	45	20	if	if	SCONJ
ejpam-2217	45	21	the	the	DET
ejpam-2217	45	22	following	follow	VERB
ejpam-2217	45	23	conditions	condition	NOUN
ejpam-2217	45	24	hold	hold	VERB
ejpam-2217	45	25	:	:	PUNCT
ejpam-2217	45	26	i	i	X
ejpam-2217	45	27	)	)	PUNCT
ejpam-2217	45	28	a	a	PRON
ejpam-2217	45	29	is	be	AUX
ejpam-2217	45	30	a	a	DET
ejpam-2217	45	31	normal	normal	ADJ
ejpam-2217	45	32	subgroup	subgroup	NOUN
ejpam-2217	45	33	of	of	ADP
ejpam-2217	45	34	b	b	PROPN
ejpam-2217	45	35	;	;	PUNCT
ejpam-2217	45	36	ii	ii	NUM
ejpam-2217	45	37	)	)	PUNCT
ejpam-2217	45	38	a	a	DET
ejpam-2217	45	39	∗	∗	NOUN
ejpam-2217	45	40	b	b	X
ejpam-2217	45	41	∈	∈	PROPN
ejpam-2217	45	42	a	a	PRON
ejpam-2217	45	43	,	,	PUNCT
ejpam-2217	45	44	for	for	ADP
ejpam-2217	45	45	all	all	DET
ejpam-2217	45	46	a	a	DET
ejpam-2217	45	47	∈	∈	PROPN
ejpam-2217	45	48	a	a	DET
ejpam-2217	45	49	,	,	PUNCT
ejpam-2217	45	50	b	b	PROPN
ejpam-2217	45	51	∈	∈	PROPN
ejpam-2217	45	52	b	b	PROPN
ejpam-2217	45	53	and	and	CCONJ
ejpam-2217	45	54	∗	∗	NOUN
ejpam-2217	45	55	∈	∈	PROPN
ejpam-2217	45	56	ω′2	ω′2	NOUN
ejpam-2217	45	57	.	.	PUNCT
ejpam-2217	46	1	proof	proof	NOUN
ejpam-2217	46	2	.	.	PUNCT
ejpam-2217	47	1	follows	follow	VERB
ejpam-2217	47	2	from	from	ADP
ejpam-2217	47	3	theorem	theorem	ADJ
ejpam-2217	47	4	1.7	1.7	NUM
ejpam-2217	47	5	given	give	VERB
ejpam-2217	47	6	in	in	ADP
ejpam-2217	47	7	[	[	X
ejpam-2217	47	8	11	11	NUM
ejpam-2217	47	9	]	]	PUNCT
ejpam-2217	47	10	.	.	PUNCT
ejpam-2217	48	1	definition	definition	NOUN
ejpam-2217	48	2	3	3	X
ejpam-2217	48	3	.	.	PUNCT
ejpam-2217	49	1	let	let	VERB
ejpam-2217	49	2	a	a	DET
ejpam-2217	49	3	,	,	PUNCT
ejpam-2217	49	4	b	b	PROPN
ejpam-2217	49	5	∈	∈	PROPN
ejpam-2217	49	6	c.	c.	NOUN
ejpam-2217	49	7	an	an	DET
ejpam-2217	49	8	extension	extension	NOUN
ejpam-2217	49	9	of	of	ADP
ejpam-2217	49	10	b	b	NOUN
ejpam-2217	49	11	by	by	ADP
ejpam-2217	49	12	a	a	PRON
ejpam-2217	49	13	is	be	AUX
ejpam-2217	49	14	a	a	DET
ejpam-2217	49	15	sequence	sequence	NOUN
ejpam-2217	49	16	0	0	NUM
ejpam-2217	49	17	//	//	NOUN
ejpam-2217	50	1	a	a	DET
ejpam-2217	50	2	i	i	PRON
ejpam-2217	50	3	//	//	X
ejpam-2217	50	4	e	e	PROPN
ejpam-2217	50	5	p	p	PROPN
ejpam-2217	50	6	//	//	PROPN
ejpam-2217	50	7	b	b	PROPN
ejpam-2217	50	8	//	//	X
ejpam-2217	50	9	0	0	NUM
ejpam-2217	50	10	(	(	PUNCT
ejpam-2217	50	11	1	1	NUM
ejpam-2217	50	12	)	)	PUNCT
ejpam-2217	50	13	in	in	ADP
ejpam-2217	50	14	which	which	PRON
ejpam-2217	50	15	p	p	NOUN
ejpam-2217	50	16	is	be	AUX
ejpam-2217	50	17	surjective	surjective	ADJ
ejpam-2217	51	1	and	and	CCONJ
ejpam-2217	51	2	i	i	PRON
ejpam-2217	51	3	is	be	AUX
ejpam-2217	51	4	the	the	DET
ejpam-2217	51	5	kernel	kernel	NOUN
ejpam-2217	51	6	of	of	ADP
ejpam-2217	51	7	p.	p.	NOUN
ejpam-2217	52	1	we	we	PRON
ejpam-2217	52	2	say	say	VERB
ejpam-2217	52	3	that	that	SCONJ
ejpam-2217	52	4	an	an	DET
ejpam-2217	52	5	extension	extension	NOUN
ejpam-2217	52	6	is	be	AUX
ejpam-2217	52	7	split	split	VERB
ejpam-2217	52	8	if	if	SCONJ
ejpam-2217	52	9	there	there	PRON
ejpam-2217	52	10	is	be	VERB
ejpam-2217	52	11	a	a	DET
ejpam-2217	52	12	morphism	morphism	NOUN
ejpam-2217	52	13	s	s	PART
ejpam-2217	52	14	:	:	PUNCT
ejpam-2217	52	15	b	b	X
ejpam-2217	52	16	−→	−→	NOUN
ejpam-2217	52	17	e	e	SYM
ejpam-2217	52	18	such	such	ADJ
ejpam-2217	52	19	that	that	DET
ejpam-2217	52	20	ps	ps	NOUN
ejpam-2217	52	21	=	=	SYM
ejpam-2217	52	22	1b	1b	NUM
ejpam-2217	52	23	.	.	PUNCT
ejpam-2217	53	1	y.	y.	PROPN
ejpam-2217	53	2	boyacı	boyacı	PROPN
ejpam-2217	53	3	,	,	PUNCT
ejpam-2217	53	4	o.	o.	PROPN
ejpam-2217	53	5	avcıoğlu	avcıoğlu	PROPN
ejpam-2217	53	6	/	/	SYM
ejpam-2217	53	7	eur	eur	PROPN
ejpam-2217	53	8	.	.	PUNCT
ejpam-2217	54	1	j.	j.	PROPN
ejpam-2217	54	2	pure	pure	PROPN
ejpam-2217	54	3	appl	appl	PROPN
ejpam-2217	54	4	.	.	PROPN
ejpam-2217	54	5	math	math	PROPN
ejpam-2217	54	6	,	,	PUNCT
ejpam-2217	54	7	7	7	NUM
ejpam-2217	54	8	(	(	PUNCT
ejpam-2217	54	9	2014	2014	NUM
ejpam-2217	54	10	)	)	PUNCT
ejpam-2217	54	11	,	,	PUNCT
ejpam-2217	54	12	412	412	NUM
ejpam-2217	54	13	-	-	SYM
ejpam-2217	54	14	418	418	NUM
ejpam-2217	54	15	414	414	NUM
ejpam-2217	54	16	definition	definition	NOUN
ejpam-2217	54	17	4	4	NUM
ejpam-2217	54	18	.	.	PUNCT
ejpam-2217	55	1	for	for	ADP
ejpam-2217	55	2	a	a	DET
ejpam-2217	55	3	,	,	PUNCT
ejpam-2217	55	4	b	b	X
ejpam-2217	55	5	∈	∈	PROPN
ejpam-2217	55	6	c	c	NOUN
ejpam-2217	55	7	we	we	PRON
ejpam-2217	55	8	will	will	AUX
ejpam-2217	55	9	say	say	VERB
ejpam-2217	55	10	that	that	SCONJ
ejpam-2217	55	11	we	we	PRON
ejpam-2217	55	12	have	have	VERB
ejpam-2217	55	13	a	a	DET
ejpam-2217	55	14	set	set	NOUN
ejpam-2217	55	15	of	of	ADP
ejpam-2217	55	16	actions	action	NOUN
ejpam-2217	55	17	of	of	ADP
ejpam-2217	55	18	b	b	NOUN
ejpam-2217	55	19	on	on	ADP
ejpam-2217	55	20	a	a	PRON
ejpam-2217	55	21	,	,	PUNCT
ejpam-2217	55	22	whenever	whenever	SCONJ
ejpam-2217	55	23	there	there	PRON
ejpam-2217	55	24	is	be	VERB
ejpam-2217	55	25	a	a	DET
ejpam-2217	55	26	map	map	NOUN
ejpam-2217	55	27	f∗	f∗	NOUN
ejpam-2217	55	28	:	:	PUNCT
ejpam-2217	56	1	a×	a×	NOUN
ejpam-2217	56	2	b	b	X
ejpam-2217	56	3	−→	−→	NOUN
ejpam-2217	56	4	a	a	PRON
ejpam-2217	56	5	,	,	PUNCT
ejpam-2217	56	6	for	for	ADP
ejpam-2217	56	7	each	each	DET
ejpam-2217	56	8	∗	∗	NOUN
ejpam-2217	56	9	∈	∈	PROPN
ejpam-2217	56	10	ω2	ω2	PROPN
ejpam-2217	56	11	.	.	PUNCT
ejpam-2217	57	1	definition	definition	NOUN
ejpam-2217	57	2	5	5	NUM
ejpam-2217	57	3	.	.	PUNCT
ejpam-2217	57	4	a	a	DET
ejpam-2217	57	5	split	split	ADJ
ejpam-2217	57	6	extension	extension	NOUN
ejpam-2217	57	7	of	of	ADP
ejpam-2217	57	8	b	b	NOUN
ejpam-2217	57	9	by	by	ADP
ejpam-2217	57	10	a	a	DET
ejpam-2217	57	11	induces	induce	NOUN
ejpam-2217	57	12	an	an	DET
ejpam-2217	57	13	action	action	NOUN
ejpam-2217	57	14	of	of	ADP
ejpam-2217	57	15	b	b	NOUN
ejpam-2217	57	16	on	on	ADP
ejpam-2217	57	17	a	a	DET
ejpam-2217	57	18	corresponding	corresponding	NOUN
ejpam-2217	57	19	to	to	ADP
ejpam-2217	57	20	the	the	DET
ejpam-2217	57	21	operations	operation	NOUN
ejpam-2217	57	22	in	in	ADP
ejpam-2217	57	23	c.	c.	NOUN
ejpam-2217	57	24	for	for	ADP
ejpam-2217	57	25	a	a	DET
ejpam-2217	57	26	given	give	VERB
ejpam-2217	57	27	split	split	NOUN
ejpam-2217	57	28	extension	extension	NOUN
ejpam-2217	57	29	(	(	PUNCT
ejpam-2217	57	30	1	1	NUM
ejpam-2217	57	31	)	)	PUNCT
ejpam-2217	57	32	,	,	PUNCT
ejpam-2217	57	33	we	we	PRON
ejpam-2217	57	34	have	have	VERB
ejpam-2217	57	35	b	b	NOUN
ejpam-2217	57	36	·	·	PUNCT
ejpam-2217	57	37	a	a	DET
ejpam-2217	57	38	=	=	NOUN
ejpam-2217	57	39	s(b	s(b	NOUN
ejpam-2217	57	40	)	)	PUNCT
ejpam-2217	58	1	+	+	CCONJ
ejpam-2217	58	2	a−	a−	ADJ
ejpam-2217	58	3	s(b	s(b	NOUN
ejpam-2217	58	4	)	)	PUNCT
ejpam-2217	58	5	,	,	PUNCT
ejpam-2217	58	6	(	(	PUNCT
ejpam-2217	58	7	2	2	X
ejpam-2217	58	8	)	)	PUNCT
ejpam-2217	58	9	b	b	NOUN
ejpam-2217	58	10	∗	∗	NOUN
ejpam-2217	58	11	a	a	DET
ejpam-2217	58	12	=	=	NOUN
ejpam-2217	58	13	s(b	s(b	NOUN
ejpam-2217	58	14	)	)	PUNCT
ejpam-2217	58	15	∗	∗	NOUN
ejpam-2217	58	16	a	a	PRON
ejpam-2217	58	17	,	,	PUNCT
ejpam-2217	58	18	(	(	PUNCT
ejpam-2217	58	19	3	3	NUM
ejpam-2217	58	20	)	)	PUNCT
ejpam-2217	58	21	for	for	ADP
ejpam-2217	58	22	all	all	DET
ejpam-2217	58	23	b	b	PROPN
ejpam-2217	58	24	∈	∈	PROPN
ejpam-2217	58	25	b	b	PROPN
ejpam-2217	58	26	,	,	PUNCT
ejpam-2217	58	27	a	a	DET
ejpam-2217	58	28	∈	∈	PROPN
ejpam-2217	58	29	a	a	PRON
ejpam-2217	58	30	and	and	CCONJ
ejpam-2217	58	31	∗	∗	NOUN
ejpam-2217	58	32	∈	∈	PROPN
ejpam-2217	58	33	ω2	ω2	NOUN
ejpam-2217	58	34	′.	′.	NOUN
ejpam-2217	58	35	actions	action	NOUN
ejpam-2217	58	36	defined	define	VERB
ejpam-2217	58	37	by	by	ADP
ejpam-2217	58	38	(	(	PUNCT
ejpam-2217	58	39	2	2	NUM
ejpam-2217	58	40	)	)	PUNCT
ejpam-2217	58	41	and	and	CCONJ
ejpam-2217	58	42	(	(	PUNCT
ejpam-2217	58	43	3	3	X
ejpam-2217	58	44	)	)	PUNCT
ejpam-2217	58	45	are	be	AUX
ejpam-2217	58	46	called	call	VERB
ejpam-2217	58	47	derived	derived	ADJ
ejpam-2217	58	48	actions	action	NOUN
ejpam-2217	58	49	of	of	ADP
ejpam-2217	58	50	b	b	PROPN
ejpam-2217	58	51	on	on	ADP
ejpam-2217	58	52	a.	a.	NOUN
ejpam-2217	58	53	given	give	VERB
ejpam-2217	58	54	an	an	DET
ejpam-2217	58	55	action	action	NOUN
ejpam-2217	58	56	of	of	ADP
ejpam-2217	58	57	b	b	NOUN
ejpam-2217	58	58	on	on	ADP
ejpam-2217	58	59	a	a	PRON
ejpam-2217	58	60	,	,	PUNCT
ejpam-2217	58	61	the	the	DET
ejpam-2217	58	62	semidirect	semidirect	NOUN
ejpam-2217	58	63	product	product	NOUN
ejpam-2217	58	64	ao	ao	PROPN
ejpam-2217	58	65	b	b	PROPN
ejpam-2217	58	66	is	be	AUX
ejpam-2217	58	67	a	a	DET
ejpam-2217	58	68	universal	universal	ADJ
ejpam-2217	58	69	algebra	algebra	NOUN
ejpam-2217	58	70	whose	whose	DET
ejpam-2217	58	71	underlying	underlying	ADJ
ejpam-2217	58	72	set	set	NOUN
ejpam-2217	58	73	is	be	AUX
ejpam-2217	58	74	a×	a×	PROPN
ejpam-2217	58	75	b	b	PROPN
ejpam-2217	58	76	and	and	CCONJ
ejpam-2217	58	77	the	the	DET
ejpam-2217	58	78	operations	operation	NOUN
ejpam-2217	58	79	are	be	AUX
ejpam-2217	58	80	defined	define	VERB
ejpam-2217	58	81	by	by	ADP
ejpam-2217	58	82	ω(a	ω(a	PROPN
ejpam-2217	58	83	,	,	PUNCT
ejpam-2217	58	84	b	b	NOUN
ejpam-2217	58	85	)	)	PUNCT
ejpam-2217	58	86	=(	=(	NOUN
ejpam-2217	58	87	ω	ω	PROPN
ejpam-2217	58	88	(	(	PUNCT
ejpam-2217	58	89	a	a	NOUN
ejpam-2217	58	90	)	)	PUNCT
ejpam-2217	58	91	,	,	PUNCT
ejpam-2217	58	92	ω	ω	PROPN
ejpam-2217	58	93	(	(	PUNCT
ejpam-2217	58	94	b	b	NOUN
ejpam-2217	58	95	)	)	PUNCT
ejpam-2217	58	96	)	)	PUNCT
ejpam-2217	58	97	,	,	PUNCT
ejpam-2217	58	98	(	(	PUNCT
ejpam-2217	58	99	a′	a′	PROPN
ejpam-2217	58	100	,	,	PUNCT
ejpam-2217	58	101	b′	b′	NUM
ejpam-2217	58	102	)	)	PUNCT
ejpam-2217	59	1	+	+	CCONJ
ejpam-2217	59	2	(	(	PUNCT
ejpam-2217	59	3	a	a	PRON
ejpam-2217	59	4	,	,	PUNCT
ejpam-2217	59	5	b	b	NOUN
ejpam-2217	59	6	)	)	PUNCT
ejpam-2217	59	7	=(	=(	NOUN
ejpam-2217	59	8	a′	a′	NOUN
ejpam-2217	60	1	+	+	SYM
ejpam-2217	60	2	b′	b′	NUM
ejpam-2217	60	3	·	·	PUNCT
ejpam-2217	60	4	a	a	X
ejpam-2217	60	5	,	,	PUNCT
ejpam-2217	60	6	b′	b′	NUM
ejpam-2217	60	7	+	+	CCONJ
ejpam-2217	60	8	b	b	X
ejpam-2217	60	9	)	)	PUNCT
ejpam-2217	60	10	,	,	PUNCT
ejpam-2217	60	11	(	(	PUNCT
ejpam-2217	60	12	a′	a′	PROPN
ejpam-2217	60	13	,	,	PUNCT
ejpam-2217	60	14	b′	b′	NUM
ejpam-2217	60	15	)	)	PUNCT
ejpam-2217	60	16	∗	∗	NOUN
ejpam-2217	60	17	(	(	PUNCT
ejpam-2217	60	18	a	a	PRON
ejpam-2217	60	19	,	,	PUNCT
ejpam-2217	60	20	b	b	NOUN
ejpam-2217	60	21	)	)	PUNCT
ejpam-2217	60	22	=(	=(	NOUN
ejpam-2217	60	23	a′	a′	PROPN
ejpam-2217	60	24	∗	∗	NOUN
ejpam-2217	60	25	a+	a+	PUNCT
ejpam-2217	60	26	a′	a′	PROPN
ejpam-2217	60	27	∗	∗	NOUN
ejpam-2217	60	28	b+	b+	ADP
ejpam-2217	60	29	b′	b′	NUM
ejpam-2217	60	30	∗	∗	NOUN
ejpam-2217	60	31	a	a	PRON
ejpam-2217	60	32	,	,	PUNCT
ejpam-2217	60	33	b′	b′	NUM
ejpam-2217	60	34	∗	∗	NOUN
ejpam-2217	60	35	b	b	NOUN
ejpam-2217	60	36	)	)	PUNCT
ejpam-2217	60	37	,	,	PUNCT
ejpam-2217	60	38	for	for	ADP
ejpam-2217	60	39	all	all	DET
ejpam-2217	60	40	a	a	PRON
ejpam-2217	60	41	,	,	PUNCT
ejpam-2217	60	42	a′	a′	PROPN
ejpam-2217	60	43	∈	∈	PROPN
ejpam-2217	60	44	a	a	DET
ejpam-2217	60	45	,	,	PUNCT
ejpam-2217	60	46	b	b	NOUN
ejpam-2217	60	47	,	,	PUNCT
ejpam-2217	60	48	b′	b′	NUM
ejpam-2217	60	49	∈	∈	PROPN
ejpam-2217	60	50	b.	b.	NOUN
ejpam-2217	60	51	definition	definition	NOUN
ejpam-2217	60	52	6	6	NUM
ejpam-2217	60	53	.	.	PUNCT
ejpam-2217	61	1	a	a	DET
ejpam-2217	61	2	precrossed	precrosse	VERB
ejpam-2217	61	3	module	module	NOUN
ejpam-2217	61	4	in	in	ADP
ejpam-2217	61	5	c	c	PROPN
ejpam-2217	61	6	is	be	AUX
ejpam-2217	61	7	a	a	DET
ejpam-2217	61	8	triple	triple	ADJ
ejpam-2217	61	9	(	(	PUNCT
ejpam-2217	61	10	c1	c1	NOUN
ejpam-2217	61	11	,	,	PUNCT
ejpam-2217	61	12	c0,∂	c0,∂	NUM
ejpam-2217	61	13	)	)	PUNCT
ejpam-2217	61	14	,	,	PUNCT
ejpam-2217	61	15	where	where	SCONJ
ejpam-2217	61	16	c0	c0	NOUN
ejpam-2217	61	17	,	,	PUNCT
ejpam-2217	61	18	c1	c1	PROPN
ejpam-2217	61	19	∈	∈	PROPN
ejpam-2217	61	20	c	c	PROPN
ejpam-2217	61	21	,	,	PUNCT
ejpam-2217	61	22	the	the	DET
ejpam-2217	61	23	object	object	NOUN
ejpam-2217	61	24	c0	c0	NOUN
ejpam-2217	61	25	has	have	VERB
ejpam-2217	61	26	a	a	DET
ejpam-2217	61	27	derived	derived	ADJ
ejpam-2217	61	28	action	action	NOUN
ejpam-2217	61	29	on	on	ADP
ejpam-2217	61	30	c1	c1	PROPN
ejpam-2217	61	31	or	or	CCONJ
ejpam-2217	61	32	shortly	shortly	ADV
ejpam-2217	61	33	c0	c0	PROPN
ejpam-2217	61	34	acts	act	VERB
ejpam-2217	61	35	on	on	ADP
ejpam-2217	61	36	c1	c1	PROPN
ejpam-2217	61	37	and	and	CCONJ
ejpam-2217	61	38	∂	∂	NUM
ejpam-2217	61	39	:	:	PUNCT
ejpam-2217	61	40	c1	c1	PROPN
ejpam-2217	61	41	−→	−→	PROPN
ejpam-2217	61	42	c0	c0	PROPN
ejpam-2217	61	43	is	be	AUX
ejpam-2217	61	44	a	a	DET
ejpam-2217	61	45	morphism	morphism	NOUN
ejpam-2217	61	46	in	in	ADP
ejpam-2217	61	47	c	c	PROPN
ejpam-2217	61	48	with	with	ADP
ejpam-2217	61	49	the	the	DET
ejpam-2217	61	50	conditions	condition	NOUN
ejpam-2217	61	51	:	:	PUNCT
ejpam-2217	61	52	cm	cm	NOUN
ejpam-2217	61	53	1	1	NUM
ejpam-2217	61	54	)	)	PUNCT
ejpam-2217	61	55	∂	∂	NOUN
ejpam-2217	61	56	(	(	PUNCT
ejpam-2217	61	57	c0	c0	PROPN
ejpam-2217	61	58	·	·	PUNCT
ejpam-2217	61	59	c1	c1	PROPN
ejpam-2217	61	60	)	)	PUNCT
ejpam-2217	62	1	=	=	SYM
ejpam-2217	62	2	c0	c0	PROPN
ejpam-2217	62	3	+	+	X
ejpam-2217	62	4	∂	∂	NUM
ejpam-2217	62	5	(	(	PUNCT
ejpam-2217	62	6	c1)−	c1)−	ADJ
ejpam-2217	62	7	c0	c0	NOUN
ejpam-2217	62	8	,	,	PUNCT
ejpam-2217	62	9	∂	∂	NUM
ejpam-2217	62	10	(	(	PUNCT
ejpam-2217	62	11	c0	c0	PROPN
ejpam-2217	62	12	∗	∗	PROPN
ejpam-2217	62	13	c1	c1	PROPN
ejpam-2217	62	14	)	)	PUNCT
ejpam-2217	63	1	=	=	SYM
ejpam-2217	63	2	c0	c0	PROPN
ejpam-2217	63	3	∗	∗	PROPN
ejpam-2217	63	4	∂	∂	NUM
ejpam-2217	63	5	(	(	PUNCT
ejpam-2217	63	6	c1	c1	PROPN
ejpam-2217	63	7	)	)	PUNCT
ejpam-2217	63	8	,	,	PUNCT
ejpam-2217	63	9	for	for	ADP
ejpam-2217	63	10	all	all	DET
ejpam-2217	63	11	c0	c0	PROPN
ejpam-2217	63	12	∈	∈	PROPN
ejpam-2217	63	13	c0	c0	PROPN
ejpam-2217	63	14	,	,	PUNCT
ejpam-2217	63	15	c1	c1	PROPN
ejpam-2217	63	16	∈	∈	PROPN
ejpam-2217	63	17	c1	c1	PROPN
ejpam-2217	63	18	,	,	PUNCT
ejpam-2217	63	19	and	and	CCONJ
ejpam-2217	63	20	∗	∗	NOUN
ejpam-2217	63	21	∈	∈	PROPN
ejpam-2217	63	22	ω2	ω2	PROPN
ejpam-2217	63	23	′.	′.	NOUN
ejpam-2217	63	24	in	in	ADP
ejpam-2217	63	25	addition	addition	NOUN
ejpam-2217	63	26	,	,	PUNCT
ejpam-2217	63	27	if	if	SCONJ
ejpam-2217	63	28	∂	∂	NUM
ejpam-2217	63	29	:	:	PUNCT
ejpam-2217	63	30	c1	c1	PROPN
ejpam-2217	63	31	−→	−→	NOUN
ejpam-2217	63	32	c0	c0	PROPN
ejpam-2217	63	33	satisfies	satisfy	VERB
ejpam-2217	63	34	the	the	DET
ejpam-2217	63	35	conditions	condition	NOUN
ejpam-2217	63	36	cm	cm	NOUN
ejpam-2217	63	37	2	2	NUM
ejpam-2217	63	38	)	)	PUNCT
ejpam-2217	63	39	∂	∂	NOUN
ejpam-2217	63	40	(	(	PUNCT
ejpam-2217	63	41	c1	c1	PROPN
ejpam-2217	63	42	)	)	PUNCT
ejpam-2217	63	43	·	·	PUNCT
ejpam-2217	63	44	c′1	c′1	NOUN
ejpam-2217	63	45	=	=	PROPN
ejpam-2217	63	46	c1	c1	PROPN
ejpam-2217	63	47	+	+	CCONJ
ejpam-2217	63	48	c′1	c′1	NOUN
ejpam-2217	63	49	−	−	PROPN
ejpam-2217	63	50	c1	c1	NOUN
ejpam-2217	63	51	,	,	PUNCT
ejpam-2217	63	52	∂	∂	NUM
ejpam-2217	63	53	(	(	PUNCT
ejpam-2217	63	54	c1	c1	PROPN
ejpam-2217	63	55	)	)	PUNCT
ejpam-2217	63	56	∗	∗	NOUN
ejpam-2217	63	57	c′1	c′1	NOUN
ejpam-2217	63	58	=	=	PROPN
ejpam-2217	63	59	c1	c1	PROPN
ejpam-2217	63	60	∗	∗	NOUN
ejpam-2217	63	61	c′1	c′1	NOUN
ejpam-2217	63	62	,	,	PUNCT
ejpam-2217	63	63	for	for	ADP
ejpam-2217	63	64	all	all	DET
ejpam-2217	63	65	c1	c1	NOUN
ejpam-2217	63	66	,	,	PUNCT
ejpam-2217	63	67	c′1	c′1	NOUN
ejpam-2217	63	68	∈	∈	PROPN
ejpam-2217	63	69	c1	c1	NOUN
ejpam-2217	63	70	,	,	PUNCT
ejpam-2217	63	71	and	and	CCONJ
ejpam-2217	63	72	∗	∗	NOUN
ejpam-2217	63	73	∈	∈	PROPN
ejpam-2217	63	74	ω′2	ω′2	NOUN
ejpam-2217	63	75	,	,	PUNCT
ejpam-2217	63	76	then	then	ADV
ejpam-2217	63	77	the	the	DET
ejpam-2217	63	78	triple	triple	ADJ
ejpam-2217	63	79	(	(	PUNCT
ejpam-2217	63	80	c1	c1	NOUN
ejpam-2217	63	81	,	,	PUNCT
ejpam-2217	63	82	c0,∂	c0,∂	PROPN
ejpam-2217	63	83	)	)	PUNCT
ejpam-2217	63	84	is	be	AUX
ejpam-2217	63	85	called	call	VERB
ejpam-2217	63	86	a	a	DET
ejpam-2217	63	87	crossed	cross	VERB
ejpam-2217	63	88	module	module	NOUN
ejpam-2217	63	89	in	in	ADP
ejpam-2217	63	90	c.	c.	PROPN
ejpam-2217	63	91	definition	definition	NOUN
ejpam-2217	63	92	7	7	NUM
ejpam-2217	63	93	.	.	PUNCT
ejpam-2217	64	1	a	a	DET
ejpam-2217	64	2	morphism	morphism	NOUN
ejpam-2217	64	3	between	between	ADP
ejpam-2217	64	4	two	two	NUM
ejpam-2217	64	5	crossed	cross	VERB
ejpam-2217	64	6	modules	module	NOUN
ejpam-2217	64	7	(	(	PUNCT
ejpam-2217	64	8	c1	c1	NOUN
ejpam-2217	64	9	,	,	PUNCT
ejpam-2217	64	10	c0,∂	c0,∂	NUM
ejpam-2217	64	11	)	)	PUNCT
ejpam-2217	64	12	−→	−→	NOUN
ejpam-2217	64	13	(	(	PUNCT
ejpam-2217	64	14	c	c	NOUN
ejpam-2217	64	15	′1	′1	X
ejpam-2217	64	16	,	,	PUNCT
ejpam-2217	64	17	c	c	PROPN
ejpam-2217	64	18	′0,∂	′0,∂	PROPN
ejpam-2217	64	19	′	′	NUM
ejpam-2217	64	20	)	)	PUNCT
ejpam-2217	64	21	is	be	AUX
ejpam-2217	64	22	a	a	DET
ejpam-2217	64	23	pair	pair	NOUN
ejpam-2217	64	24	of	of	ADP
ejpam-2217	64	25	morphisms	morphism	NOUN
ejpam-2217	64	26	(	(	PUNCT
ejpam-2217	64	27	µ1,µ0	µ1,µ0	X
ejpam-2217	64	28	)	)	PUNCT
ejpam-2217	64	29	in	in	ADP
ejpam-2217	64	30	c	c	PROPN
ejpam-2217	64	31	,	,	PUNCT
ejpam-2217	64	32	µ0	µ0	NOUN
ejpam-2217	64	33	:	:	PUNCT
ejpam-2217	64	34	c0	c0	PROPN
ejpam-2217	64	35	−→	−→	NOUN
ejpam-2217	64	36	c	c	PROPN
ejpam-2217	64	37	′0	′0	NOUN
ejpam-2217	64	38	,	,	PUNCT
ejpam-2217	64	39	µ1	µ1	PROPN
ejpam-2217	64	40	:	:	PUNCT
ejpam-2217	64	41	c1	c1	PROPN
ejpam-2217	64	42	−→	−→	NOUN
ejpam-2217	64	43	c	c	PROPN
ejpam-2217	64	44	′1	′1	NOUN
ejpam-2217	64	45	,	,	PUNCT
ejpam-2217	64	46	such	such	ADJ
ejpam-2217	64	47	that	that	SCONJ
ejpam-2217	64	48	i	i	NOUN
ejpam-2217	64	49	)	)	PUNCT
ejpam-2217	64	50	µ0∂	µ0∂	PROPN
ejpam-2217	64	51	(	(	PUNCT
ejpam-2217	64	52	c	c	NOUN
ejpam-2217	64	53	)	)	PUNCT
ejpam-2217	64	54	=	=	SYM
ejpam-2217	64	55	∂	∂	NUM
ejpam-2217	64	56	′µ1(c	′µ1(c	PROPN
ejpam-2217	64	57	)	)	PUNCT
ejpam-2217	64	58	,	,	PUNCT
ejpam-2217	64	59	ii	ii	PROPN
ejpam-2217	64	60	)	)	PUNCT
ejpam-2217	64	61	µ1(r	µ1(r	PROPN
ejpam-2217	64	62	·	·	PUNCT
ejpam-2217	64	63	c	c	X
ejpam-2217	64	64	)	)	PUNCT
ejpam-2217	64	65	=	=	SYM
ejpam-2217	64	66	µ0(r	µ0(r	PROPN
ejpam-2217	64	67	)	)	PUNCT
ejpam-2217	64	68	·	·	PUNCT
ejpam-2217	64	69	µ1(c	µ1(c	NOUN
ejpam-2217	64	70	)	)	PUNCT
ejpam-2217	64	71	,	,	PUNCT
ejpam-2217	64	72	iii	iii	X
ejpam-2217	64	73	)	)	PUNCT
ejpam-2217	64	74	µ1(r	µ1(r	NOUN
ejpam-2217	64	75	∗	∗	X
ejpam-2217	64	76	c	c	NOUN
ejpam-2217	64	77	)	)	PUNCT
ejpam-2217	64	78	=	=	SYM
ejpam-2217	64	79	µ0(r	µ0(r	PROPN
ejpam-2217	64	80	)	)	PUNCT
ejpam-2217	64	81	∗µ1(c	∗µ1(c	PROPN
ejpam-2217	64	82	)	)	PUNCT
ejpam-2217	64	83	,	,	PUNCT
ejpam-2217	64	84	for	for	ADP
ejpam-2217	64	85	all	all	DET
ejpam-2217	64	86	r	r	NOUN
ejpam-2217	64	87	∈	∈	PROPN
ejpam-2217	64	88	c0	c0	NOUN
ejpam-2217	64	89	,	,	PUNCT
ejpam-2217	64	90	c	c	PROPN
ejpam-2217	64	91	∈	∈	PROPN
ejpam-2217	64	92	c1	c1	PROPN
ejpam-2217	64	93	and	and	CCONJ
ejpam-2217	64	94	∗	∗	NOUN
ejpam-2217	64	95	∈	∈	PROPN
ejpam-2217	64	96	ω2	ω2	PROPN
ejpam-2217	64	97	′.	′.	NOUN
ejpam-2217	64	98	with	with	ADP
ejpam-2217	64	99	this	this	DET
ejpam-2217	64	100	definition	definition	NOUN
ejpam-2217	64	101	,	,	PUNCT
ejpam-2217	64	102	we	we	PRON
ejpam-2217	64	103	have	have	VERB
ejpam-2217	64	104	a	a	DET
ejpam-2217	64	105	category	category	NOUN
ejpam-2217	64	106	whose	whose	DET
ejpam-2217	64	107	objects	object	NOUN
ejpam-2217	64	108	are	be	AUX
ejpam-2217	64	109	crossed	cross	VERB
ejpam-2217	64	110	modules	module	NOUN
ejpam-2217	64	111	and	and	CCONJ
ejpam-2217	64	112	morphisms	morphism	NOUN
ejpam-2217	64	113	are	be	AUX
ejpam-2217	64	114	morphisms	morphism	NOUN
ejpam-2217	64	115	of	of	ADP
ejpam-2217	64	116	crossed	cross	VERB
ejpam-2217	64	117	modules	module	NOUN
ejpam-2217	64	118	defined	define	VERB
ejpam-2217	64	119	above	above	ADV
ejpam-2217	64	120	.	.	PUNCT
ejpam-2217	65	1	the	the	DET
ejpam-2217	65	2	category	category	NOUN
ejpam-2217	65	3	of	of	ADP
ejpam-2217	65	4	crossed	cross	VERB
ejpam-2217	65	5	modules	module	NOUN
ejpam-2217	65	6	will	will	AUX
ejpam-2217	65	7	be	be	AUX
ejpam-2217	65	8	denoted	denote	VERB
ejpam-2217	65	9	by	by	ADP
ejpam-2217	65	10	xmod(c	xmod(c	PROPN
ejpam-2217	65	11	)	)	PUNCT
ejpam-2217	65	12	.	.	PUNCT
ejpam-2217	66	1	y.	y.	PROPN
ejpam-2217	66	2	boyacı	boyacı	PROPN
ejpam-2217	66	3	,	,	PUNCT
ejpam-2217	66	4	o.	o.	PROPN
ejpam-2217	66	5	avcıoğlu	avcıoğlu	PROPN
ejpam-2217	66	6	/	/	SYM
ejpam-2217	66	7	eur	eur	PROPN
ejpam-2217	66	8	.	.	PUNCT
ejpam-2217	67	1	j.	j.	PROPN
ejpam-2217	67	2	pure	pure	PROPN
ejpam-2217	67	3	appl	appl	PROPN
ejpam-2217	67	4	.	.	PROPN
ejpam-2217	67	5	math	math	PROPN
ejpam-2217	67	6	,	,	PUNCT
ejpam-2217	67	7	7	7	NUM
ejpam-2217	67	8	(	(	PUNCT
ejpam-2217	67	9	2014	2014	NUM
ejpam-2217	67	10	)	)	PUNCT
ejpam-2217	67	11	,	,	PUNCT
ejpam-2217	67	12	412	412	NUM
ejpam-2217	67	13	-	-	SYM
ejpam-2217	67	14	418	418	NUM
ejpam-2217	67	15	415	415	NUM
ejpam-2217	67	16	3	3	NUM
ejpam-2217	67	17	.	.	PUNCT
ejpam-2217	67	18	simplicial	simplicial	ADJ
ejpam-2217	67	19	objects	object	NOUN
ejpam-2217	67	20	in	in	ADP
ejpam-2217	67	21	a	a	DET
ejpam-2217	67	22	category	category	NOUN
ejpam-2217	67	23	of	of	ADP
ejpam-2217	67	24	interest	interest	NOUN
ejpam-2217	67	25	let	let	VERB
ejpam-2217	67	26	4	4	NUM
ejpam-2217	67	27	be	be	AUX
ejpam-2217	67	28	the	the	DET
ejpam-2217	67	29	category	category	NOUN
ejpam-2217	67	30	of	of	ADP
ejpam-2217	67	31	finite	finite	ADJ
ejpam-2217	67	32	ordinals	ordinal	NOUN
ejpam-2217	67	33	.	.	PUNCT
ejpam-2217	68	1	a	a	DET
ejpam-2217	68	2	simplicial	simplicial	ADJ
ejpam-2217	68	3	object	object	NOUN
ejpam-2217	68	4	in	in	ADP
ejpam-2217	68	5	a	a	DET
ejpam-2217	68	6	category	category	NOUN
ejpam-2217	68	7	of	of	ADP
ejpam-2217	68	8	interest	interest	NOUN
ejpam-2217	68	9	c	c	NOUN
ejpam-2217	68	10	is	be	AUX
ejpam-2217	68	11	a	a	DET
ejpam-2217	68	12	functor	functor	NOUN
ejpam-2217	68	13	from	from	ADP
ejpam-2217	68	14	the	the	DET
ejpam-2217	68	15	opposite	opposite	ADJ
ejpam-2217	68	16	category	category	NOUN
ejpam-2217	68	17	4op	4op	NOUN
ejpam-2217	68	18	to	to	ADP
ejpam-2217	68	19	c.	c.	PROPN
ejpam-2217	68	20	in	in	ADP
ejpam-2217	68	21	other	other	ADJ
ejpam-2217	68	22	words	word	NOUN
ejpam-2217	68	23	,	,	PUNCT
ejpam-2217	68	24	a	a	DET
ejpam-2217	68	25	simplicial	simplicial	ADJ
ejpam-2217	68	26	object	object	NOUN
ejpam-2217	68	27	c	c	NOUN
ejpam-2217	68	28	in	in	ADP
ejpam-2217	68	29	c	c	PROPN
ejpam-2217	68	30	is	be	AUX
ejpam-2217	68	31	a	a	DET
ejpam-2217	68	32	sequence	sequence	NOUN
ejpam-2217	68	33	c=	c=	NOUN
ejpam-2217	68	34	{	{	PUNCT
ejpam-2217	68	35	c0	c0	PROPN
ejpam-2217	68	36	,	,	PUNCT
ejpam-2217	68	37	c1	c1	PROPN
ejpam-2217	68	38	,	,	PUNCT
ejpam-2217	68	39	.	.	PUNCT
ejpam-2217	68	40	.	.	PUNCT
ejpam-2217	69	1	.	.	PUNCT
ejpam-2217	70	1	,	,	PUNCT
ejpam-2217	70	2	cn	cn	PROPN
ejpam-2217	70	3	,	,	PUNCT
ejpam-2217	70	4	.	.	PUNCT
ejpam-2217	70	5	.	.	PUNCT
ejpam-2217	71	1	.	.	PUNCT
ejpam-2217	71	2	}	}	PUNCT
ejpam-2217	72	1	together	together	ADV
ejpam-2217	72	2	with	with	ADP
ejpam-2217	72	3	face	face	NOUN
ejpam-2217	72	4	and	and	CCONJ
ejpam-2217	72	5	degeneracy	degeneracy	NOUN
ejpam-2217	72	6	maps	map	NOUN
ejpam-2217	73	1	dn	dn	INTJ
ejpam-2217	74	1	i	i	PRON
ejpam-2217	74	2	:	:	PUNCT
ejpam-2217	74	3	cn	cn	INTJ
ejpam-2217	74	4	−→	−→	PROPN
ejpam-2217	74	5	cn−1	cn−1	PROPN
ejpam-2217	74	6	,	,	PUNCT
ejpam-2217	74	7	0≤	0≤	VERB
ejpam-2217	75	1	i	i	VERB
ejpam-2217	75	2	≤	≤	PUNCT
ejpam-2217	75	3	n	n	CCONJ
ejpam-2217	75	4	(	(	PUNCT
ejpam-2217	75	5	n	n	CCONJ
ejpam-2217	75	6	6=	6=	NUM
ejpam-2217	75	7	0	0	NUM
ejpam-2217	75	8	)	)	PUNCT
ejpam-2217	75	9	sn	sn	INTJ
ejpam-2217	76	1	i	i	PRON
ejpam-2217	76	2	:	:	PUNCT
ejpam-2217	76	3	cn	cn	VERB
ejpam-2217	76	4	−→	−→	PROPN
ejpam-2217	76	5	cn+1	cn+1	NOUN
ejpam-2217	76	6	,	,	PUNCT
ejpam-2217	76	7	0≤	0≤	PUNCT
ejpam-2217	77	1	i	i	NOUN
ejpam-2217	77	2	≤	≤	PUNCT
ejpam-2217	77	3	n	n	CCONJ
ejpam-2217	77	4	which	which	PRON
ejpam-2217	77	5	are	be	AUX
ejpam-2217	77	6	homomorphisms	homomorphism	NOUN
ejpam-2217	77	7	of	of	ADP
ejpam-2217	77	8	objects	object	NOUN
ejpam-2217	77	9	in	in	ADP
ejpam-2217	77	10	c	c	NOUN
ejpam-2217	77	11	satisfying	satisfy	VERB
ejpam-2217	77	12	the	the	DET
ejpam-2217	77	13	following	follow	VERB
ejpam-2217	77	14	simplicial	simplicial	ADJ
ejpam-2217	77	15	identities	identity	NOUN
ejpam-2217	77	16	;	;	PUNCT
ejpam-2217	77	17	did	do	VERB
ejpam-2217	77	18	j	j	PROPN
ejpam-2217	78	1	=	=	PUNCT
ejpam-2217	79	1	d	d	PROPN
ejpam-2217	79	2	j−1di	j−1di	PROPN
ejpam-2217	79	3	for	for	ADP
ejpam-2217	79	4	i	i	PRON
ejpam-2217	79	5	<	<	X
ejpam-2217	79	6	j	j	PROPN
ejpam-2217	80	1	dis	dis	PROPN
ejpam-2217	80	2	j	j	PROPN
ejpam-2217	80	3	=	=	PUNCT
ejpam-2217	80	4			PROPN
ejpam-2217	80	5			PRON
ejpam-2217	80	6			PROPN
ejpam-2217	80	7	s	s	PART
ejpam-2217	80	8	j−1di	j−1di	NOUN
ejpam-2217	81	1	i	i	INTJ
ejpam-2217	81	2	d	d	PROPN
ejpam-2217	81	3	s	s	VERB
ejpam-2217	81	4	jdi−1	jdi−1	PROPN
ejpam-2217	81	5	for	for	ADP
ejpam-2217	81	6	i	i	PRON
ejpam-2217	81	7	<	<	X
ejpam-2217	81	8	j	j	PROPN
ejpam-2217	81	9	for	for	ADP
ejpam-2217	81	10	i	i	PROPN
ejpam-2217	82	1	=	=	SYM
ejpam-2217	82	2	j	j	PROPN
ejpam-2217	82	3	or	or	CCONJ
ejpam-2217	82	4	i	i	PRON
ejpam-2217	82	5	=	=	SYM
ejpam-2217	82	6	j	j	PROPN
ejpam-2217	83	1	+	+	CCONJ
ejpam-2217	83	2	1	1	NUM
ejpam-2217	83	3	for	for	ADP
ejpam-2217	83	4	i	i	PRON
ejpam-2217	83	5	>	>	X
ejpam-2217	83	6	j	j	PROPN
ejpam-2217	84	1	+	+	CCONJ
ejpam-2217	84	2	1	1	NUM
ejpam-2217	84	3	sis	sis	NOUN
ejpam-2217	84	4	j	j	PROPN
ejpam-2217	84	5	=	=	SYM
ejpam-2217	84	6	s	s	X
ejpam-2217	84	7	j+1si	j+1si	PROPN
ejpam-2217	84	8	for	for	ADP
ejpam-2217	84	9	i	i	PROPN
ejpam-2217	84	10	≤	≤	NUM
ejpam-2217	84	11	j	j	PROPN
ejpam-2217	84	12	for	for	ADP
ejpam-2217	84	13	0≤	0≤	NUM
ejpam-2217	85	1	i	i	NOUN
ejpam-2217	85	2	≤	≤	PUNCT
ejpam-2217	85	3	n	n	CCONJ
ejpam-2217	85	4	(	(	PUNCT
ejpam-2217	85	5	here	here	ADV
ejpam-2217	85	6	the	the	DET
ejpam-2217	85	7	superscripts	superscript	NOUN
ejpam-2217	85	8	of	of	ADP
ejpam-2217	85	9	maps	map	NOUN
ejpam-2217	85	10	are	be	AUX
ejpam-2217	85	11	dropped	drop	VERB
ejpam-2217	85	12	for	for	ADP
ejpam-2217	85	13	shortness	shortness	NOUN
ejpam-2217	85	14	)	)	PUNCT
ejpam-2217	85	15	.	.	PUNCT
ejpam-2217	86	1	3.1	3.1	NUM
ejpam-2217	86	2	.	.	PUNCT
ejpam-2217	87	1	the	the	DET
ejpam-2217	87	2	moore	moore	PROPN
ejpam-2217	87	3	complex	complex	PROPN
ejpam-2217	87	4	the	the	DET
ejpam-2217	87	5	moore	moore	PROPN
ejpam-2217	87	6	complex	complex	PROPN
ejpam-2217	87	7	nc	nc	PROPN
ejpam-2217	87	8	of	of	ADP
ejpam-2217	87	9	a	a	DET
ejpam-2217	87	10	simplicial	simplicial	ADJ
ejpam-2217	87	11	object	object	NOUN
ejpam-2217	87	12	c	c	NOUN
ejpam-2217	87	13	in	in	ADP
ejpam-2217	87	14	a	a	DET
ejpam-2217	87	15	category	category	NOUN
ejpam-2217	87	16	of	of	ADP
ejpam-2217	87	17	interest	interest	NOUN
ejpam-2217	87	18	c	c	NOUN
ejpam-2217	87	19	is	be	AUX
ejpam-2217	87	20	the	the	DET
ejpam-2217	87	21	complex	complex	ADJ
ejpam-2217	87	22	nc	nc	PROPN
ejpam-2217	87	23	:	:	PUNCT
ejpam-2217	87	24	·	·	PUNCT
ejpam-2217	87	25	·	·	PUNCT
ejpam-2217	87	26	·	·	PUNCT
ejpam-2217	88	1	−→	−→	NOUN
ejpam-2217	88	2	ncn	ncn	NOUN
ejpam-2217	88	3	∂n−→	∂n−→	PROPN
ejpam-2217	88	4	ncn−1	ncn−1	ADJ
ejpam-2217	88	5	∂n−1−→	∂n−1−→	NOUN
ejpam-2217	88	6	·	·	PUNCT
ejpam-2217	88	7	·	·	PUNCT
ejpam-2217	88	8	·	·	PUNCT
ejpam-2217	89	1	∂2−→	∂2−→	PROPN
ejpam-2217	89	2	nc1	nc1	PROPN
ejpam-2217	89	3	∂1−→	∂1−→	PROPN
ejpam-2217	89	4	nc0	nc0	ADV
ejpam-2217	89	5	where	where	SCONJ
ejpam-2217	89	6	nc0	nc0	NOUN
ejpam-2217	89	7	=	=	SYM
ejpam-2217	89	8	c0	c0	X
ejpam-2217	89	9	,	,	PUNCT
ejpam-2217	89	10	ncn	ncn	PROPN
ejpam-2217	89	11	=	=	SYM
ejpam-2217	89	12	n−1	n−1	PROPN
ejpam-2217	89	13	⋂	⋂	PROPN
ejpam-2217	89	14	i=0	i=0	PROPN
ejpam-2217	89	15	kerdi	kerdi	PROPN
ejpam-2217	89	16	and	and	CCONJ
ejpam-2217	89	17	∂n	∂n	PROPN
ejpam-2217	89	18	is	be	AUX
ejpam-2217	89	19	the	the	DET
ejpam-2217	89	20	restriction	restriction	NOUN
ejpam-2217	89	21	of	of	ADP
ejpam-2217	89	22	dn	dn	PROPN
ejpam-2217	89	23	to	to	ADP
ejpam-2217	89	24	ncn	ncn	NOUN
ejpam-2217	89	25	.	.	PUNCT
ejpam-2217	90	1	we	we	PRON
ejpam-2217	90	2	say	say	VERB
ejpam-2217	90	3	that	that	SCONJ
ejpam-2217	90	4	the	the	DET
ejpam-2217	90	5	moore	moore	PROPN
ejpam-2217	90	6	complex	complex	PROPN
ejpam-2217	90	7	nc	nc	PROPN
ejpam-2217	90	8	of	of	ADP
ejpam-2217	90	9	a	a	DET
ejpam-2217	90	10	simplicial	simplicial	ADJ
ejpam-2217	90	11	object	object	NOUN
ejpam-2217	90	12	c	c	NOUN
ejpam-2217	90	13	is	be	AUX
ejpam-2217	90	14	of	of	ADP
ejpam-2217	90	15	length	length	NOUN
ejpam-2217	90	16	k	k	PROPN
ejpam-2217	90	17	if	if	SCONJ
ejpam-2217	90	18	ncn	ncn	PROPN
ejpam-2217	90	19	=	=	NOUN
ejpam-2217	90	20	0	0	PROPN
ejpam-2217	90	21	,	,	PUNCT
ejpam-2217	90	22	for	for	ADP
ejpam-2217	90	23	all	all	DET
ejpam-2217	90	24	n	n	PRON
ejpam-2217	90	25	≥	≥	NOUN
ejpam-2217	90	26	k	k	NOUN
ejpam-2217	91	1	+	+	NOUN
ejpam-2217	91	2	1	1	X
ejpam-2217	91	3	.	.	PUNCT
ejpam-2217	91	4	now	now	ADV
ejpam-2217	91	5	define	define	VERB
ejpam-2217	91	6	a	a	DET
ejpam-2217	91	7	category	category	NOUN
ejpam-2217	91	8	whose	whose	DET
ejpam-2217	91	9	objects	object	NOUN
ejpam-2217	91	10	are	be	AUX
ejpam-2217	91	11	simplicial	simplicial	ADJ
ejpam-2217	91	12	objects	object	NOUN
ejpam-2217	91	13	with	with	ADP
ejpam-2217	91	14	moore	moore	PROPN
ejpam-2217	91	15	complex	complex	NOUN
ejpam-2217	91	16	of	of	ADP
ejpam-2217	91	17	length	length	NOUN
ejpam-2217	91	18	k	k	PROPN
ejpam-2217	91	19	and	and	CCONJ
ejpam-2217	91	20	the	the	DET
ejpam-2217	91	21	morphisms	morphism	NOUN
ejpam-2217	91	22	are	be	AUX
ejpam-2217	91	23	families	family	NOUN
ejpam-2217	91	24	of	of	ADP
ejpam-2217	91	25	homomorphisms	homomorphism	NOUN
ejpam-2217	91	26	compatible	compatible	ADJ
ejpam-2217	91	27	with	with	ADP
ejpam-2217	91	28	face	face	NOUN
ejpam-2217	91	29	and	and	CCONJ
ejpam-2217	91	30	degeneracy	degeneracy	NOUN
ejpam-2217	91	31	maps	map	NOUN
ejpam-2217	91	32	.	.	PUNCT
ejpam-2217	92	1	we	we	PRON
ejpam-2217	92	2	denote	denote	VERB
ejpam-2217	92	3	this	this	DET
ejpam-2217	92	4	category	category	NOUN
ejpam-2217	92	5	by	by	ADP
ejpam-2217	92	6	simp≤k(c	simp≤k(c	NOUN
ejpam-2217	92	7	)	)	PUNCT
ejpam-2217	92	8	.	.	PUNCT
ejpam-2217	93	1	3.2	3.2	NUM
ejpam-2217	93	2	.	.	PUNCT
ejpam-2217	93	3	truncated	truncate	VERB
ejpam-2217	93	4	simplicial	simplicial	ADJ
ejpam-2217	93	5	objects	object	VERB
ejpam-2217	93	6	the	the	DET
ejpam-2217	93	7	following	follow	VERB
ejpam-2217	93	8	terminology	terminology	NOUN
ejpam-2217	93	9	is	be	AUX
ejpam-2217	93	10	adapted	adapt	VERB
ejpam-2217	93	11	from	from	ADP
ejpam-2217	93	12	[	[	X
ejpam-2217	93	13	6	6	NUM
ejpam-2217	93	14	]	]	PUNCT
ejpam-2217	93	15	.	.	PUNCT
ejpam-2217	94	1	details	detail	NOUN
ejpam-2217	94	2	of	of	ADP
ejpam-2217	94	3	the	the	DET
ejpam-2217	94	4	group	group	NOUN
ejpam-2217	94	5	case	case	NOUN
ejpam-2217	94	6	can	can	AUX
ejpam-2217	94	7	be	be	AUX
ejpam-2217	94	8	found	find	VERB
ejpam-2217	94	9	in	in	ADP
ejpam-2217	94	10	[	[	X
ejpam-2217	94	11	6	6	NUM
ejpam-2217	94	12	]	]	PUNCT
ejpam-2217	94	13	.	.	PUNCT
ejpam-2217	95	1	for	for	ADP
ejpam-2217	95	2	each	each	DET
ejpam-2217	95	3	k	k	PROPN
ejpam-2217	95	4	≥	≥	X
ejpam-2217	95	5	0	0	NUM
ejpam-2217	95	6	we	we	PRON
ejpam-2217	95	7	have	have	VERB
ejpam-2217	95	8	a	a	DET
ejpam-2217	95	9	subcategory	subcategory	NOUN
ejpam-2217	95	10	of	of	ADP
ejpam-2217	95	11	4	4	NUM
ejpam-2217	95	12	,	,	PUNCT
ejpam-2217	95	13	denoted	denote	VERB
ejpam-2217	95	14	by	by	ADP
ejpam-2217	95	15	4≤k	4≤k	NUM
ejpam-2217	95	16	obtained	obtain	VERB
ejpam-2217	95	17	by	by	ADP
ejpam-2217	95	18	the	the	DET
ejpam-2217	95	19	objects	object	NOUN
ejpam-2217	95	20	[	[	PUNCT
ejpam-2217	95	21	j	j	NOUN
ejpam-2217	95	22	]	]	X
ejpam-2217	95	23	of	of	ADP
ejpam-2217	95	24	4	4	NUM
ejpam-2217	95	25	with	with	ADP
ejpam-2217	95	26	j	j	PROPN
ejpam-2217	95	27	≤	≤	PROPN
ejpam-2217	95	28	k.	k.	PROPN
ejpam-2217	96	1	a	a	DET
ejpam-2217	96	2	k	k	ADV
ejpam-2217	96	3	-	-	ADJ
ejpam-2217	96	4	truncated	truncate	VERB
ejpam-2217	96	5	simplicial	simplicial	ADJ
ejpam-2217	96	6	object	object	NOUN
ejpam-2217	96	7	is	be	AUX
ejpam-2217	96	8	a	a	DET
ejpam-2217	96	9	functor	functor	NOUN
ejpam-2217	96	10	from	from	ADP
ejpam-2217	96	11	4op	4op	NOUN
ejpam-2217	96	12	≤k	≤k	VERB
ejpam-2217	96	13	to	to	ADP
ejpam-2217	96	14	c.	c.	PROPN
ejpam-2217	96	15	consequently	consequently	ADV
ejpam-2217	96	16	,	,	PUNCT
ejpam-2217	96	17	a	a	DET
ejpam-2217	96	18	k	k	ADV
ejpam-2217	96	19	-	-	ADJ
ejpam-2217	96	20	truncated	truncate	VERB
ejpam-2217	96	21	simplicial	simplicial	ADJ
ejpam-2217	96	22	object	object	NOUN
ejpam-2217	96	23	is	be	AUX
ejpam-2217	96	24	a	a	DET
ejpam-2217	96	25	family	family	NOUN
ejpam-2217	96	26	of	of	ADP
ejpam-2217	96	27	objects	object	NOUN
ejpam-2217	96	28	{	{	PUNCT
ejpam-2217	96	29	c0	c0	NOUN
ejpam-2217	96	30	,	,	PUNCT
ejpam-2217	96	31	c1	c1	PROPN
ejpam-2217	96	32	,	,	PUNCT
ejpam-2217	96	33	.	.	PUNCT
ejpam-2217	96	34	.	.	PUNCT
ejpam-2217	97	1	.	.	PUNCT
ejpam-2217	98	1	,	,	PUNCT
ejpam-2217	98	2	ck	ck	X
ejpam-2217	98	3	}	}	PUNCT
ejpam-2217	98	4	and	and	CCONJ
ejpam-2217	98	5	homomorphism	homomorphism	PROPN
ejpam-2217	98	6	di	di	X
ejpam-2217	98	7	:	:	PUNCT
ejpam-2217	98	8	cn	cn	PROPN
ejpam-2217	98	9	−→	−→	PROPN
ejpam-2217	98	10	cn−1	cn−1	PROPN
ejpam-2217	98	11	,	,	PUNCT
ejpam-2217	98	12	si	si	X
ejpam-2217	98	13	:	:	PUNCT
ejpam-2217	98	14	cn	cn	PROPN
ejpam-2217	98	15	−→	−→	NOUN
ejpam-2217	98	16	cn+1	cn+1	NOUN
ejpam-2217	98	17	,	,	PUNCT
ejpam-2217	98	18	for	for	ADP
ejpam-2217	98	19	each	each	PRON
ejpam-2217	98	20	0≤	0≤	ADJ
ejpam-2217	99	1	i	i	NOUN
ejpam-2217	99	2	≤	≤	PUNCT
ejpam-2217	99	3	n	n	CCONJ
ejpam-2217	99	4	which	which	PRON
ejpam-2217	99	5	satisfy	satisfy	VERB
ejpam-2217	99	6	the	the	DET
ejpam-2217	99	7	simplicial	simplicial	ADJ
ejpam-2217	99	8	identities	identity	NOUN
ejpam-2217	99	9	.	.	PUNCT
ejpam-2217	100	1	we	we	PRON
ejpam-2217	100	2	denote	denote	VERB
ejpam-2217	100	3	the	the	DET
ejpam-2217	100	4	category	category	NOUN
ejpam-2217	100	5	of	of	ADP
ejpam-2217	100	6	k	k	ADV
ejpam-2217	100	7	-	-	ADJ
ejpam-2217	100	8	truncated	truncate	VERB
ejpam-2217	100	9	simplicial	simplicial	ADJ
ejpam-2217	100	10	objects	object	NOUN
ejpam-2217	100	11	by	by	ADP
ejpam-2217	100	12	trksimp(c	trksimp(c	NOUN
ejpam-2217	100	13	)	)	PUNCT
ejpam-2217	100	14	.	.	PUNCT
ejpam-2217	101	1	there	there	PRON
ejpam-2217	101	2	is	be	VERB
ejpam-2217	101	3	a	a	DET
ejpam-2217	101	4	truncation	truncation	NOUN
ejpam-2217	101	5	functor	functor	PROPN
ejpam-2217	101	6	t	t	PROPN
ejpam-2217	101	7	rk	rk	PROPN
ejpam-2217	101	8	from	from	ADP
ejpam-2217	101	9	the	the	DET
ejpam-2217	101	10	category	category	NOUN
ejpam-2217	101	11	simp(c	simp(c	NOUN
ejpam-2217	101	12	)	)	PUNCT
ejpam-2217	101	13	to	to	ADP
ejpam-2217	101	14	the	the	DET
ejpam-2217	101	15	category	category	NOUN
ejpam-2217	101	16	trksimp(c	trksimp(c	NOUN
ejpam-2217	101	17	)	)	PUNCT
ejpam-2217	101	18	given	give	VERB
ejpam-2217	101	19	by	by	ADP
ejpam-2217	101	20	restrictions	restriction	NOUN
ejpam-2217	101	21	.	.	PUNCT
ejpam-2217	102	1	this	this	DET
ejpam-2217	102	2	y.	y.	PROPN
ejpam-2217	102	3	boyacı	boyacı	PROPN
ejpam-2217	102	4	,	,	PUNCT
ejpam-2217	102	5	o.	o.	PROPN
ejpam-2217	102	6	avcıoğlu	avcıoğlu	PROPN
ejpam-2217	102	7	/	/	SYM
ejpam-2217	102	8	eur	eur	PROPN
ejpam-2217	102	9	.	.	PUNCT
ejpam-2217	103	1	j.	j.	PROPN
ejpam-2217	103	2	pure	pure	PROPN
ejpam-2217	103	3	appl	appl	PROPN
ejpam-2217	103	4	.	.	PROPN
ejpam-2217	103	5	math	math	PROPN
ejpam-2217	103	6	,	,	PUNCT
ejpam-2217	103	7	7	7	NUM
ejpam-2217	103	8	(	(	PUNCT
ejpam-2217	103	9	2014	2014	NUM
ejpam-2217	103	10	)	)	PUNCT
ejpam-2217	103	11	,	,	PUNCT
ejpam-2217	103	12	412	412	NUM
ejpam-2217	103	13	-	-	SYM
ejpam-2217	103	14	418	418	NUM
ejpam-2217	103	15	416	416	NUM
ejpam-2217	103	16	truncation	truncation	NOUN
ejpam-2217	103	17	functor	functor	PROPN
ejpam-2217	103	18	has	have	VERB
ejpam-2217	103	19	a	a	DET
ejpam-2217	103	20	left	left	ADJ
ejpam-2217	103	21	adjoint	adjoint	NOUN
ejpam-2217	103	22	stk	stk	PROPN
ejpam-2217	103	23	and	and	CCONJ
ejpam-2217	103	24	a	a	DET
ejpam-2217	103	25	right	right	ADJ
ejpam-2217	103	26	adjoint	adjoint	NOUN
ejpam-2217	103	27	costk	costk	PROPN
ejpam-2217	103	28	called	call	VERB
ejpam-2217	103	29	as	as	ADP
ejpam-2217	103	30	k	k	NOUN
ejpam-2217	103	31	-	-	NOUN
ejpam-2217	103	32	skeleton	skeleton	NOUN
ejpam-2217	103	33	and	and	CCONJ
ejpam-2217	103	34	k	k	NOUN
ejpam-2217	103	35	-	-	NOUN
ejpam-2217	103	36	coskeleton	coskeleton	NOUN
ejpam-2217	103	37	respectively	respectively	ADV
ejpam-2217	103	38	.	.	PUNCT
ejpam-2217	104	1	these	these	DET
ejpam-2217	104	2	adjoints	adjoint	NOUN
ejpam-2217	104	3	can	can	AUX
ejpam-2217	104	4	be	be	AUX
ejpam-2217	104	5	pictured	picture	VERB
ejpam-2217	104	6	as	as	SCONJ
ejpam-2217	104	7	follows	follow	VERB
ejpam-2217	104	8	;	;	PUNCT
ejpam-2217	104	9	trksimp(c	trksimp(c	NUM
ejpam-2217	104	10	)	)	PUNCT
ejpam-2217	104	11	t	t	NOUN
ejpam-2217	104	12	rk←−	rk←−	VERB
ejpam-2217	104	13	−→	−→	ADJ
ejpam-2217	104	14	costk	costk	ADJ
ejpam-2217	104	15	simp(c	simp(c	NOUN
ejpam-2217	104	16	)	)	PUNCT
ejpam-2217	104	17	t	t	NOUN
ejpam-2217	104	18	rk−→	rk−→	PROPN
ejpam-2217	104	19	←−	←−	PROPN
ejpam-2217	104	20	stk	stk	PROPN
ejpam-2217	104	21	trksimp(c	trksimp(c	PROPN
ejpam-2217	104	22	)	)	PUNCT
ejpam-2217	104	23	.	.	PUNCT
ejpam-2217	105	1	see	see	VERB
ejpam-2217	106	1	[	[	X
ejpam-2217	106	2	6	6	NUM
ejpam-2217	106	3	]	]	PUNCT
ejpam-2217	106	4	for	for	ADP
ejpam-2217	106	5	details	detail	NOUN
ejpam-2217	106	6	about	about	ADP
ejpam-2217	106	7	the	the	DET
ejpam-2217	106	8	functors	functors	PROPN
ejpam-2217	106	9	costk	costk	ADJ
ejpam-2217	106	10	and	and	CCONJ
ejpam-2217	106	11	stk	stk	PROPN
ejpam-2217	106	12	.	.	PROPN
ejpam-2217	106	13	theorem	theorem	PROPN
ejpam-2217	106	14	2	2	NUM
ejpam-2217	106	15	.	.	PUNCT
ejpam-2217	107	1	the	the	DET
ejpam-2217	107	2	category	category	NOUN
ejpam-2217	107	3	xmod(c	xmod(c	NOUN
ejpam-2217	107	4	)	)	PUNCT
ejpam-2217	107	5	of	of	ADP
ejpam-2217	107	6	crossed	cross	VERB
ejpam-2217	107	7	modules	module	NOUN
ejpam-2217	107	8	is	be	AUX
ejpam-2217	107	9	naturally	naturally	ADV
ejpam-2217	107	10	equivalent	equivalent	ADJ
ejpam-2217	107	11	to	to	ADP
ejpam-2217	107	12	the	the	DET
ejpam-2217	107	13	category	category	NOUN
ejpam-2217	107	14	simp≤1(c	simp≤1(c	NOUN
ejpam-2217	107	15	)	)	PUNCT
ejpam-2217	107	16	of	of	ADP
ejpam-2217	107	17	simplicial	simplicial	ADJ
ejpam-2217	107	18	objects	object	NOUN
ejpam-2217	107	19	with	with	ADP
ejpam-2217	107	20	moore	moore	PROPN
ejpam-2217	107	21	complex	complex	NOUN
ejpam-2217	107	22	of	of	ADP
ejpam-2217	107	23	length	length	NOUN
ejpam-2217	107	24	1	1	NUM
ejpam-2217	107	25	.	.	PUNCT
ejpam-2217	108	1	proof	proof	NOUN
ejpam-2217	108	2	.	.	PUNCT
ejpam-2217	109	1	let	let	VERB
ejpam-2217	109	2	c	c	PRON
ejpam-2217	109	3	be	be	AUX
ejpam-2217	109	4	a	a	DET
ejpam-2217	109	5	simplicial	simplicial	ADJ
ejpam-2217	109	6	object	object	NOUN
ejpam-2217	109	7	with	with	ADP
ejpam-2217	109	8	moore	moore	PROPN
ejpam-2217	109	9	complex	complex	NOUN
ejpam-2217	109	10	of	of	ADP
ejpam-2217	109	11	length	length	NOUN
ejpam-2217	109	12	1	1	NUM
ejpam-2217	109	13	.	.	PUNCT
ejpam-2217	110	1	take	take	VERB
ejpam-2217	110	2	g	g	NOUN
ejpam-2217	110	3	=	=	NOUN
ejpam-2217	110	4	ker	ker	PROPN
ejpam-2217	110	5	d0	d0	PROPN
ejpam-2217	110	6	and	and	CCONJ
ejpam-2217	110	7	∂	∂	NUM
ejpam-2217	110	8	is	be	AUX
ejpam-2217	110	9	the	the	DET
ejpam-2217	110	10	restriction	restriction	NOUN
ejpam-2217	110	11	of	of	ADP
ejpam-2217	110	12	d1	d1	PROPN
ejpam-2217	110	13	to	to	PART
ejpam-2217	110	14	g.	g.	AUX
ejpam-2217	110	15	define	define	VERB
ejpam-2217	110	16	the	the	DET
ejpam-2217	110	17	actions	action	NOUN
ejpam-2217	110	18	of	of	ADP
ejpam-2217	110	19	c0	c0	NOUN
ejpam-2217	110	20	on	on	ADP
ejpam-2217	110	21	g	g	PROPN
ejpam-2217	110	22	by	by	ADP
ejpam-2217	110	23	c0	c0	PROPN
ejpam-2217	110	24	·	·	PUNCT
ejpam-2217	110	25	g	g	PROPN
ejpam-2217	110	26	=	=	SYM
ejpam-2217	110	27	s0(c0	s0(c0	PROPN
ejpam-2217	110	28	)	)	PUNCT
ejpam-2217	110	29	+	+	CCONJ
ejpam-2217	110	30	g	g	PROPN
ejpam-2217	110	31	−	−	PROPN
ejpam-2217	110	32	s0(c0	s0(c0	NOUN
ejpam-2217	110	33	)	)	PUNCT
ejpam-2217	110	34	,	,	PUNCT
ejpam-2217	110	35	c0	c0	PROPN
ejpam-2217	110	36	∗	∗	VERB
ejpam-2217	110	37	g	g	PROPN
ejpam-2217	110	38	=	=	SYM
ejpam-2217	110	39	s0(c0	s0(c0	NOUN
ejpam-2217	110	40	)	)	PUNCT
ejpam-2217	110	41	∗	∗	NOUN
ejpam-2217	110	42	g	g	NOUN
ejpam-2217	110	43	,	,	PUNCT
ejpam-2217	110	44	for	for	ADP
ejpam-2217	110	45	all	all	DET
ejpam-2217	110	46	c0	c0	PROPN
ejpam-2217	110	47	∈	∈	PROPN
ejpam-2217	110	48	c0	c0	PROPN
ejpam-2217	110	49	and	and	CCONJ
ejpam-2217	110	50	g	g	PROPN
ejpam-2217	110	51	∈	∈	PROPN
ejpam-2217	110	52	g.	g.	NOUN
ejpam-2217	110	53	by	by	ADP
ejpam-2217	110	54	using	use	VERB
ejpam-2217	110	55	this	this	DET
ejpam-2217	110	56	action	action	NOUN
ejpam-2217	110	57	∂	∂	NOUN
ejpam-2217	110	58	:	:	PUNCT
ejpam-2217	110	59	g	g	PROPN
ejpam-2217	110	60	−→	−→	NOUN
ejpam-2217	110	61	c0	c0	PROPN
ejpam-2217	110	62	is	be	AUX
ejpam-2217	110	63	a	a	DET
ejpam-2217	110	64	crossed	cross	VERB
ejpam-2217	110	65	module	module	NOUN
ejpam-2217	110	66	.	.	PUNCT
ejpam-2217	111	1	indeed	indeed	ADV
ejpam-2217	111	2	,	,	PUNCT
ejpam-2217	111	3	cm	cm	NOUN
ejpam-2217	111	4	1	1	NUM
ejpam-2217	111	5	:	:	PUNCT
ejpam-2217	111	6	since	since	SCONJ
ejpam-2217	111	7	d1s0	d1s0	PROPN
ejpam-2217	111	8	=	=	SYM
ejpam-2217	111	9	i	i	PROPN
ejpam-2217	111	10	d	d	PROPN
ejpam-2217	111	11	,	,	PUNCT
ejpam-2217	111	12	we	we	PRON
ejpam-2217	111	13	have	have	VERB
ejpam-2217	111	14	∂	∂	NUM
ejpam-2217	111	15	(	(	PUNCT
ejpam-2217	111	16	c0	c0	PROPN
ejpam-2217	111	17	·	·	PUNCT
ejpam-2217	112	1	g	g	X
ejpam-2217	112	2	)	)	PUNCT
ejpam-2217	112	3	=	=	NOUN
ejpam-2217	112	4	∂	∂	NUM
ejpam-2217	112	5	(	(	PUNCT
ejpam-2217	112	6	s0(c0	s0(c0	NOUN
ejpam-2217	112	7	)	)	PUNCT
ejpam-2217	112	8	+	+	CCONJ
ejpam-2217	112	9	g	g	PROPN
ejpam-2217	112	10	−	−	PROPN
ejpam-2217	112	11	s0(c0	s0(c0	NOUN
ejpam-2217	112	12	)	)	PUNCT
ejpam-2217	112	13	)	)	PUNCT
ejpam-2217	113	1	=	=	NOUN
ejpam-2217	113	2	c0	c0	X
ejpam-2217	113	3	+	+	X
ejpam-2217	113	4	∂	∂	NUM
ejpam-2217	113	5	(	(	PUNCT
ejpam-2217	113	6	g)−	g)−	PROPN
ejpam-2217	113	7	c0	c0	PROPN
ejpam-2217	113	8	,	,	PUNCT
ejpam-2217	113	9	∂	∂	NUM
ejpam-2217	113	10	(	(	PUNCT
ejpam-2217	113	11	c0	c0	PROPN
ejpam-2217	113	12	∗	∗	VERB
ejpam-2217	113	13	g	g	NOUN
ejpam-2217	113	14	)	)	PUNCT
ejpam-2217	113	15	=	=	NOUN
ejpam-2217	113	16	∂	∂	NUM
ejpam-2217	113	17	(	(	PUNCT
ejpam-2217	113	18	s0(c0	s0(c0	NOUN
ejpam-2217	113	19	)	)	PUNCT
ejpam-2217	113	20	∗	∗	NOUN
ejpam-2217	113	21	g	g	NOUN
ejpam-2217	113	22	)	)	PUNCT
ejpam-2217	114	1	=	=	NOUN
ejpam-2217	114	2	c0	c0	X
ejpam-2217	114	3	∗	∗	PROPN
ejpam-2217	114	4	∂	∂	X
ejpam-2217	114	5	(	(	PUNCT
ejpam-2217	114	6	g	g	NOUN
ejpam-2217	114	7	)	)	PUNCT
ejpam-2217	114	8	,	,	PUNCT
ejpam-2217	114	9	for	for	ADP
ejpam-2217	114	10	all	all	DET
ejpam-2217	114	11	c0	c0	PROPN
ejpam-2217	114	12	∈	∈	PROPN
ejpam-2217	114	13	c0	c0	PROPN
ejpam-2217	114	14	and	and	CCONJ
ejpam-2217	114	15	g	g	PROPN
ejpam-2217	114	16	∈	∈	PROPN
ejpam-2217	114	17	g.	g.	PROPN
ejpam-2217	114	18	cm	cm	PROPN
ejpam-2217	114	19	2	2	NUM
ejpam-2217	114	20	:	:	PUNCT
ejpam-2217	114	21	since	since	SCONJ
ejpam-2217	114	22	s0d1	s0d1	NOUN
ejpam-2217	114	23	=	=	SYM
ejpam-2217	114	24	d2s0	d2s0	ADJ
ejpam-2217	114	25	,	,	PUNCT
ejpam-2217	114	26	d2s1	d2s1	X
ejpam-2217	114	27	=	=	SYM
ejpam-2217	114	28	i	i	PROPN
ejpam-2217	114	29	d	d	PROPN
ejpam-2217	114	30	,	,	PUNCT
ejpam-2217	114	31	we	we	PRON
ejpam-2217	114	32	have	have	VERB
ejpam-2217	114	33	∂	∂	NUM
ejpam-2217	114	34	(	(	PUNCT
ejpam-2217	114	35	g	g	PROPN
ejpam-2217	114	36	′	′	NUM
ejpam-2217	114	37	)	)	PUNCT
ejpam-2217	114	38	∗	∗	NOUN
ejpam-2217	114	39	g	g	PROPN
ejpam-2217	114	40	=	=	NOUN
ejpam-2217	114	41	s0d1(g	s0d1(g	PROPN
ejpam-2217	114	42	′	′	NUM
ejpam-2217	114	43	)	)	PUNCT
ejpam-2217	114	44	∗	∗	NOUN
ejpam-2217	114	45	g	g	PROPN
ejpam-2217	114	46	=(	=(	NOUN
ejpam-2217	114	47	s0d1(g	s0d1(g	PROPN
ejpam-2217	114	48	′)−	′)−	PUNCT
ejpam-2217	114	49	g	g	NOUN
ejpam-2217	115	1	′	′	NOUN
ejpam-2217	115	2	+	+	CCONJ
ejpam-2217	115	3	g	g	PROPN
ejpam-2217	115	4	′	′	NUM
ejpam-2217	115	5	)	)	PUNCT
ejpam-2217	116	1	∗	∗	NOUN
ejpam-2217	116	2	g	g	NOUN
ejpam-2217	116	3	=	=	PUNCT
ejpam-2217	116	4	�	�	PROPN
ejpam-2217	116	5	s0d1(g	s0d1(g	PROPN
ejpam-2217	116	6	′)−	′)−	PUNCT
ejpam-2217	116	7	g	g	ADP
ejpam-2217	116	8	′	′	NUM
ejpam-2217	116	9	�	�	PROPN
ejpam-2217	116	10	∗	∗	NOUN
ejpam-2217	116	11	g	g	NOUN
ejpam-2217	116	12	+	+	CCONJ
ejpam-2217	116	13	g	g	NOUN
ejpam-2217	116	14	′	′	NUM
ejpam-2217	116	15	∗	∗	NOUN
ejpam-2217	116	16	g	g	NOUN
ejpam-2217	116	17	=	=	SYM
ejpam-2217	116	18	�	�	PROPN
ejpam-2217	117	1	d2s0	d2s0	ADP
ejpam-2217	117	2	g	g	NOUN
ejpam-2217	117	3	′	′	NUM
ejpam-2217	117	4	−	−	PROPN
ejpam-2217	118	1	d2s1	d2s1	NOUN
ejpam-2217	118	2	g	g	NOUN
ejpam-2217	118	3	′	′	NUM
ejpam-2217	118	4	�	�	PROPN
ejpam-2217	118	5	∗	∗	NOUN
ejpam-2217	118	6	�	�	PROPN
ejpam-2217	118	7	d2s1	d2s1	X
ejpam-2217	118	8	g	g	ADP
ejpam-2217	118	9	�	�	PROPN
ejpam-2217	118	10	+	+	CCONJ
ejpam-2217	118	11	g	g	NOUN
ejpam-2217	118	12	′	′	NUM
ejpam-2217	118	13	∗	∗	NOUN
ejpam-2217	118	14	g	g	PROPN
ejpam-2217	118	15	=	=	PROPN
ejpam-2217	118	16	d2	d2	PROPN
ejpam-2217	118	17	�	�	PROPN
ejpam-2217	118	18	�	�	PROPN
ejpam-2217	118	19	s0	s0	PROPN
ejpam-2217	118	20	g	g	PROPN
ejpam-2217	118	21	′	′	NUM
ejpam-2217	119	1	−	−	PROPN
ejpam-2217	119	2	s1	s1	PROPN
ejpam-2217	119	3	g	g	PROPN
ejpam-2217	119	4	′	′	NUM
ejpam-2217	119	5	�	�	PROPN
ejpam-2217	119	6	∗	∗	NOUN
ejpam-2217	119	7	�	�	PROPN
ejpam-2217	119	8	s1	s1	PROPN
ejpam-2217	119	9	g	g	PROPN
ejpam-2217	119	10	�	�	PROPN
ejpam-2217	119	11	�	�	PROPN
ejpam-2217	119	12	+	+	CCONJ
ejpam-2217	119	13	g	g	NOUN
ejpam-2217	119	14	′	′	NUM
ejpam-2217	119	15	∗	∗	NOUN
ejpam-2217	119	16	g	g	NOUN
ejpam-2217	120	1	=	=	NOUN
ejpam-2217	120	2	g	g	NOUN
ejpam-2217	120	3	′	′	NUM
ejpam-2217	120	4	∗	∗	NOUN
ejpam-2217	120	5	g	g	NOUN
ejpam-2217	120	6	,	,	PUNCT
ejpam-2217	120	7	for	for	ADP
ejpam-2217	120	8	all	all	DET
ejpam-2217	120	9	g	g	NOUN
ejpam-2217	120	10	,	,	PUNCT
ejpam-2217	120	11	g	g	PROPN
ejpam-2217	120	12	′	′	NUM
ejpam-2217	120	13	∈	∈	PROPN
ejpam-2217	120	14	g.	g.	NOUN
ejpam-2217	121	1	by	by	ADP
ejpam-2217	121	2	a	a	DET
ejpam-2217	121	3	similar	similar	ADJ
ejpam-2217	121	4	way	way	NOUN
ejpam-2217	121	5	,	,	PUNCT
ejpam-2217	121	6	we	we	PRON
ejpam-2217	121	7	have	have	VERB
ejpam-2217	121	8	∂	∂	NUM
ejpam-2217	121	9	(	(	PUNCT
ejpam-2217	121	10	g	g	PROPN
ejpam-2217	121	11	′	′	NUM
ejpam-2217	121	12	)	)	PUNCT
ejpam-2217	121	13	·	·	PUNCT
ejpam-2217	122	1	g	g	NOUN
ejpam-2217	122	2	=	=	PUNCT
ejpam-2217	122	3	g	g	NOUN
ejpam-2217	122	4	′	′	NOUN
ejpam-2217	123	1	+	+	CCONJ
ejpam-2217	123	2	g	g	NOUN
ejpam-2217	123	3	−	−	PROPN
ejpam-2217	123	4	g	g	NOUN
ejpam-2217	123	5	′	′	NOUN
ejpam-2217	123	6	for	for	ADP
ejpam-2217	123	7	all	all	DET
ejpam-2217	123	8	g	g	NOUN
ejpam-2217	123	9	,	,	PUNCT
ejpam-2217	124	1	g	g	PROPN
ejpam-2217	124	2	′	′	NUM
ejpam-2217	124	3	∈	∈	PROPN
ejpam-2217	124	4	g.	g.	NOUN
ejpam-2217	125	1	so	so	ADV
ejpam-2217	125	2	we	we	PRON
ejpam-2217	125	3	obtain	obtain	VERB
ejpam-2217	125	4	the	the	DET
ejpam-2217	125	5	functor	functor	PROPN
ejpam-2217	125	6	n1	n1	PROPN
ejpam-2217	125	7	:	:	PUNCT
ejpam-2217	125	8	simp≤1(c	simp≤1(c	NOUN
ejpam-2217	125	9	)	)	PUNCT
ejpam-2217	125	10	−→	−→	NOUN
ejpam-2217	125	11	xmod(c	xmod(c	PROPN
ejpam-2217	125	12	)	)	PUNCT
ejpam-2217	125	13	.	.	PUNCT
ejpam-2217	126	1	references	reference	NOUN
ejpam-2217	126	2	417	417	NUM
ejpam-2217	126	3	conversely	conversely	ADV
ejpam-2217	126	4	,	,	PUNCT
ejpam-2217	126	5	let	let	VERB
ejpam-2217	126	6	∂	∂	NUM
ejpam-2217	126	7	:	:	PUNCT
ejpam-2217	126	8	g	g	PROPN
ejpam-2217	126	9	−→	−→	NOUN
ejpam-2217	126	10	h	h	NOUN
ejpam-2217	126	11	be	be	VERB
ejpam-2217	126	12	a	a	DET
ejpam-2217	126	13	crossed	cross	VERB
ejpam-2217	126	14	module	module	NOUN
ejpam-2217	126	15	.	.	PUNCT
ejpam-2217	127	1	by	by	ADP
ejpam-2217	127	2	using	use	VERB
ejpam-2217	127	3	the	the	DET
ejpam-2217	127	4	action	action	NOUN
ejpam-2217	127	5	of	of	ADP
ejpam-2217	127	6	h	h	NOUN
ejpam-2217	127	7	on	on	ADP
ejpam-2217	127	8	g	g	PROPN
ejpam-2217	127	9	,	,	PUNCT
ejpam-2217	127	10	we	we	PRON
ejpam-2217	127	11	can	can	AUX
ejpam-2217	127	12	form	form	VERB
ejpam-2217	127	13	the	the	DET
ejpam-2217	127	14	semi	semi	ADJ
ejpam-2217	127	15	-	-	ADJ
ejpam-2217	127	16	direct	direct	ADJ
ejpam-2217	127	17	product	product	NOUN
ejpam-2217	127	18	c1	c1	NOUN
ejpam-2217	127	19	:	:	PUNCT
ejpam-2217	128	1	=	=	PUNCT
ejpam-2217	128	2	g	g	NOUN
ejpam-2217	129	1	oh	oh	INTJ
ejpam-2217	129	2	=	=	PUNCT
ejpam-2217	129	3	{	{	PUNCT
ejpam-2217	129	4	(	(	PUNCT
ejpam-2217	129	5	g	g	NOUN
ejpam-2217	129	6	,	,	PUNCT
ejpam-2217	129	7	h	h	NOUN
ejpam-2217	129	8	)	)	PUNCT
ejpam-2217	129	9	:	:	PUNCT
ejpam-2217	130	1	h	h	PROPN
ejpam-2217	130	2	∈	∈	PROPN
ejpam-2217	130	3	h	h	NOUN
ejpam-2217	130	4	,	,	PUNCT
ejpam-2217	130	5	g	g	PROPN
ejpam-2217	130	6	∈	∈	PROPN
ejpam-2217	130	7	g	g	PROPN
ejpam-2217	130	8	}	}	PUNCT
ejpam-2217	130	9	.	.	PUNCT
ejpam-2217	131	1	we	we	PRON
ejpam-2217	131	2	have	have	VERB
ejpam-2217	131	3	the	the	DET
ejpam-2217	131	4	homomorphisms	homomorphism	NOUN
ejpam-2217	131	5	d0	d0	NOUN
ejpam-2217	131	6	:	:	PUNCT
ejpam-2217	131	7	g	g	NOUN
ejpam-2217	131	8	oh	oh	INTJ
ejpam-2217	131	9	−→	−→	NOUN
ejpam-2217	131	10	h	h	NOUN
ejpam-2217	131	11	(	(	PUNCT
ejpam-2217	131	12	g	g	NOUN
ejpam-2217	131	13	,	,	PUNCT
ejpam-2217	131	14	h	h	NOUN
ejpam-2217	131	15	)	)	PUNCT
ejpam-2217	131	16	7−→	7−→	NOUN
ejpam-2217	131	17	h	h	NOUN
ejpam-2217	131	18	d1	d1	NOUN
ejpam-2217	131	19	:	:	PUNCT
ejpam-2217	131	20	g	g	NOUN
ejpam-2217	131	21	oh	oh	INTJ
ejpam-2217	131	22	−→	−→	NOUN
ejpam-2217	131	23	h	h	NOUN
ejpam-2217	131	24	(	(	PUNCT
ejpam-2217	131	25	g	g	NOUN
ejpam-2217	131	26	,	,	PUNCT
ejpam-2217	131	27	h	h	NOUN
ejpam-2217	131	28	)	)	PUNCT
ejpam-2217	131	29	7−→	7−→	NOUN
ejpam-2217	131	30	∂	∂	NOUN
ejpam-2217	131	31	(	(	PUNCT
ejpam-2217	131	32	g	g	NOUN
ejpam-2217	131	33	)	)	PUNCT
ejpam-2217	131	34	+	+	CCONJ
ejpam-2217	131	35	h	h	NOUN
ejpam-2217	131	36	s0	s0	NOUN
ejpam-2217	131	37	:	:	PUNCT
ejpam-2217	132	1	h	h	NOUN
ejpam-2217	132	2	−→	−→	NOUN
ejpam-2217	132	3	g	g	PROPN
ejpam-2217	133	1	oh	oh	INTJ
ejpam-2217	133	2	h	h	NOUN
ejpam-2217	134	1	7−→	7−→	NOUN
ejpam-2217	134	2	(	(	PUNCT
ejpam-2217	134	3	0	0	NUM
ejpam-2217	134	4	,	,	PUNCT
ejpam-2217	134	5	h	h	NOUN
ejpam-2217	134	6	)	)	PUNCT
ejpam-2217	134	7	which	which	PRON
ejpam-2217	134	8	satisfy	satisfy	VERB
ejpam-2217	134	9	the	the	DET
ejpam-2217	134	10	simplicial	simplicial	ADJ
ejpam-2217	134	11	identities	identity	NOUN
ejpam-2217	134	12	.	.	PUNCT
ejpam-2217	135	1	finally	finally	ADV
ejpam-2217	135	2	c1	c1	PROPN
ejpam-2217	135	3	d1,d0	d1,d0	PROPN
ejpam-2217	135	4	�	�	PROPN
ejpam-2217	135	5	s0	s0	PROPN
ejpam-2217	135	6	c0	c0	PROPN
ejpam-2217	135	7	is	be	AUX
ejpam-2217	135	8	a	a	DET
ejpam-2217	135	9	1	1	NUM
ejpam-2217	135	10	-	-	PUNCT
ejpam-2217	135	11	truncated	truncate	VERB
ejpam-2217	135	12	simplicial	simplicial	ADJ
ejpam-2217	135	13	object	object	NOUN
ejpam-2217	135	14	.	.	PUNCT
ejpam-2217	136	1	thus	thus	ADV
ejpam-2217	136	2	we	we	PRON
ejpam-2217	136	3	have	have	VERB
ejpam-2217	136	4	the	the	DET
ejpam-2217	136	5	functor	functor	PROPN
ejpam-2217	136	6	s1	s1	PROPN
ejpam-2217	136	7	:	:	PUNCT
ejpam-2217	136	8	xmod(c	xmod(c	NUM
ejpam-2217	136	9	)	)	PUNCT
ejpam-2217	136	10	−→	−→	NOUN
ejpam-2217	136	11	tr1simp(c	tr1simp(c	NOUN
ejpam-2217	136	12	)	)	PUNCT
ejpam-2217	136	13	.	.	PUNCT
ejpam-2217	137	1	by	by	ADP
ejpam-2217	137	2	using	use	VERB
ejpam-2217	137	3	the	the	DET
ejpam-2217	137	4	functor	functor	PROPN
ejpam-2217	137	5	stk	stk	PROPN
ejpam-2217	137	6	from	from	ADP
ejpam-2217	137	7	the	the	DET
ejpam-2217	137	8	category	category	NOUN
ejpam-2217	137	9	of	of	ADP
ejpam-2217	137	10	k	k	ADV
ejpam-2217	137	11	-	-	ADJ
ejpam-2217	137	12	truncated	truncate	VERB
ejpam-2217	137	13	simplicial	simplicial	ADJ
ejpam-2217	137	14	objects	object	NOUN
ejpam-2217	137	15	to	to	ADP
ejpam-2217	137	16	that	that	PRON
ejpam-2217	137	17	of	of	ADP
ejpam-2217	137	18	simplicial	simplicial	ADJ
ejpam-2217	137	19	objects	object	NOUN
ejpam-2217	137	20	with	with	ADP
ejpam-2217	137	21	moore	moore	PROPN
ejpam-2217	137	22	complex	complex	NOUN
ejpam-2217	137	23	of	of	ADP
ejpam-2217	137	24	length	length	NOUN
ejpam-2217	137	25	1	1	NUM
ejpam-2217	137	26	,	,	PUNCT
ejpam-2217	137	27	we	we	PRON
ejpam-2217	137	28	have	have	AUX
ejpam-2217	137	29	m	m	PRON
ejpam-2217	137	30	:	:	PUNCT
ejpam-2217	137	31	xmod(c	xmod(c	NUM
ejpam-2217	137	32	)	)	PUNCT
ejpam-2217	137	33	−→simp≤1(c	−→simp≤1(c	PROPN
ejpam-2217	137	34	)	)	PUNCT
ejpam-2217	137	35	defined	define	VERB
ejpam-2217	137	36	as	as	ADP
ejpam-2217	137	37	the	the	DET
ejpam-2217	137	38	composition	composition	NOUN
ejpam-2217	137	39	of	of	ADP
ejpam-2217	137	40	s1	s1	PROPN
ejpam-2217	137	41	and	and	CCONJ
ejpam-2217	137	42	st1	st1	PROPN
ejpam-2217	137	43	.	.	PUNCT
ejpam-2217	138	1	finally	finally	ADV
ejpam-2217	138	2	we	we	PRON
ejpam-2217	138	3	have	have	VERB
ejpam-2217	138	4	the	the	DET
ejpam-2217	138	5	natural	natural	ADJ
ejpam-2217	138	6	equivalence	equivalence	NOUN
ejpam-2217	138	7	between	between	ADP
ejpam-2217	138	8	the	the	DET
ejpam-2217	138	9	category	category	NOUN
ejpam-2217	138	10	of	of	ADP
ejpam-2217	138	11	simplicial	simplicial	ADJ
ejpam-2217	138	12	objects	object	NOUN
ejpam-2217	138	13	with	with	ADP
ejpam-2217	138	14	moore	moore	PROPN
ejpam-2217	138	15	complex	complex	NOUN
ejpam-2217	138	16	of	of	ADP
ejpam-2217	138	17	length	length	NOUN
ejpam-2217	138	18	1	1	NUM
ejpam-2217	138	19	and	and	CCONJ
ejpam-2217	138	20	that	that	PRON
ejpam-2217	138	21	of	of	ADP
ejpam-2217	138	22	crossed	cross	VERB
ejpam-2217	138	23	modules	module	NOUN
ejpam-2217	138	24	in	in	ADP
ejpam-2217	138	25	a	a	DET
ejpam-2217	138	26	category	category	NOUN
ejpam-2217	138	27	of	of	ADP
ejpam-2217	138	28	interest	interest	NOUN
ejpam-2217	138	29	c.	c.	PROPN
ejpam-2217	138	30	the	the	DET
ejpam-2217	138	31	main	main	ADJ
ejpam-2217	138	32	result	result	NOUN
ejpam-2217	138	33	of	of	ADP
ejpam-2217	138	34	the	the	DET
ejpam-2217	138	35	paper	paper	NOUN
ejpam-2217	138	36	can	can	AUX
ejpam-2217	138	37	be	be	AUX
ejpam-2217	138	38	diagramized	diagramize	VERB
ejpam-2217	138	39	as	as	ADP
ejpam-2217	138	40	simp≤1(c	simp≤1(c	NOUN
ejpam-2217	138	41	)	)	PUNCT
ejpam-2217	138	42	n	n	CCONJ
ejpam-2217	138	43	�	�	PROPN
ejpam-2217	138	44	m	m	PROPN
ejpam-2217	138	45	xmod(c	xmod(c	PROPN
ejpam-2217	138	46	)	)	PUNCT
ejpam-2217	138	47	.	.	PUNCT
ejpam-2217	139	1	references	reference	NOUN
ejpam-2217	139	2	[	[	X
ejpam-2217	139	3	1	1	NUM
ejpam-2217	139	4	]	]	PUNCT
ejpam-2217	139	5	z	z	NOUN
ejpam-2217	139	6	arvasi	arvasi	NOUN
ejpam-2217	139	7	and	and	CCONJ
ejpam-2217	139	8	i̇	i̇	ADJ
ejpam-2217	139	9	akça	akça	NOUN
ejpam-2217	139	10	.	.	PUNCT
ejpam-2217	140	1	simplicial	simplicial	NOUN
ejpam-2217	140	2	and	and	CCONJ
ejpam-2217	140	3	crossed	cross	VERB
ejpam-2217	140	4	lie	lie	NOUN
ejpam-2217	140	5	algebras	algebra	NOUN
ejpam-2217	140	6	.	.	PUNCT
ejpam-2217	141	1	homology	homology	PROPN
ejpam-2217	141	2	,	,	PUNCT
ejpam-2217	141	3	homotopy	homotopy	NOUN
ejpam-2217	141	4	and	and	CCONJ
ejpam-2217	141	5	applications	application	NOUN
ejpam-2217	141	6	,	,	PUNCT
ejpam-2217	141	7	4(1):43–57	4(1):43–57	NUM
ejpam-2217	141	8	,	,	PUNCT
ejpam-2217	141	9	2002	2002	NUM
ejpam-2217	141	10	.	.	PUNCT
ejpam-2217	142	1	[	[	X
ejpam-2217	142	2	2	2	NUM
ejpam-2217	142	3	]	]	PUNCT
ejpam-2217	142	4	z	z	NOUN
ejpam-2217	142	5	arvasi	arvasi	NOUN
ejpam-2217	142	6	and	and	CCONJ
ejpam-2217	142	7	t	t	PROPN
ejpam-2217	142	8	porter	porter	NOUN
ejpam-2217	142	9	.	.	PUNCT
ejpam-2217	143	1	higher	high	ADJ
ejpam-2217	143	2	dimensional	dimensional	ADJ
ejpam-2217	143	3	peiffer	peiffer	NOUN
ejpam-2217	143	4	elements	element	NOUN
ejpam-2217	143	5	in	in	ADP
ejpam-2217	143	6	simplicial	simplicial	ADJ
ejpam-2217	143	7	commutative	commutative	ADJ
ejpam-2217	143	8	algebras	algebra	NOUN
ejpam-2217	143	9	.	.	PUNCT
ejpam-2217	144	1	theory	theory	NOUN
ejpam-2217	144	2	and	and	CCONJ
ejpam-2217	144	3	applications	application	NOUN
ejpam-2217	144	4	of	of	ADP
ejpam-2217	144	5	categories	category	NOUN
ejpam-2217	144	6	,	,	PUNCT
ejpam-2217	144	7	3(1):1–23	3(1):1–23	NUM
ejpam-2217	144	8	,	,	PUNCT
ejpam-2217	144	9	1997	1997	NUM
ejpam-2217	144	10	.	.	PUNCT
ejpam-2217	145	1	[	[	X
ejpam-2217	145	2	3	3	X
ejpam-2217	145	3	]	]	X
ejpam-2217	145	4	j	j	PROPN
ejpam-2217	145	5	m	m	PROPN
ejpam-2217	145	6	casas	casas	PROPN
ejpam-2217	145	7	,	,	PUNCT
ejpam-2217	145	8	t	t	PROPN
ejpam-2217	145	9	datuashvili	datuashvili	NOUN
ejpam-2217	145	10	,	,	PUNCT
ejpam-2217	145	11	and	and	CCONJ
ejpam-2217	145	12	m	m	PROPN
ejpam-2217	145	13	ladra	ladra	PROPN
ejpam-2217	145	14	.	.	PUNCT
ejpam-2217	145	15	actor	actor	NOUN
ejpam-2217	145	16	of	of	ADP
ejpam-2217	145	17	a	a	DET
ejpam-2217	145	18	precrossed	precrosse	VERB
ejpam-2217	145	19	module	module	NOUN
ejpam-2217	145	20	.	.	PUNCT
ejpam-2217	146	1	communication	communication	NOUN
ejpam-2217	146	2	in	in	ADP
ejpam-2217	146	3	algebra	algebra	PROPN
ejpam-2217	146	4	,	,	PUNCT
ejpam-2217	146	5	37(12):4516–4541	37(12):4516–4541	NUM
ejpam-2217	146	6	,	,	PUNCT
ejpam-2217	146	7	2009	2009	NUM
ejpam-2217	146	8	.	.	PUNCT
ejpam-2217	147	1	references	reference	NOUN
ejpam-2217	147	2	418	418	NUM
ejpam-2217	148	1	[	[	X
ejpam-2217	148	2	4	4	NUM
ejpam-2217	148	3	]	]	X
ejpam-2217	148	4	j	j	PROPN
ejpam-2217	148	5	m	m	PROPN
ejpam-2217	148	6	casas	casas	PROPN
ejpam-2217	148	7	,	,	PUNCT
ejpam-2217	148	8	t	t	PROPN
ejpam-2217	148	9	datuashvili	datuashvili	NOUN
ejpam-2217	148	10	,	,	PUNCT
ejpam-2217	148	11	and	and	CCONJ
ejpam-2217	148	12	m	m	PROPN
ejpam-2217	148	13	ladra	ladra	PROPN
ejpam-2217	148	14	.	.	PUNCT
ejpam-2217	149	1	universal	universal	ADJ
ejpam-2217	149	2	strict	strict	ADJ
ejpam-2217	149	3	general	general	ADJ
ejpam-2217	149	4	actors	actor	NOUN
ejpam-2217	149	5	and	and	CCONJ
ejpam-2217	149	6	actors	actor	NOUN
ejpam-2217	149	7	in	in	ADP
ejpam-2217	149	8	categories	category	NOUN
ejpam-2217	149	9	of	of	ADP
ejpam-2217	149	10	interest	interest	NOUN
ejpam-2217	149	11	.	.	PUNCT
ejpam-2217	150	1	applied	apply	VERB
ejpam-2217	150	2	categorical	categorical	ADJ
ejpam-2217	150	3	structures	structure	NOUN
ejpam-2217	150	4	,	,	PUNCT
ejpam-2217	150	5	18(1):85–114	18(1):85–114	NUM
ejpam-2217	150	6	,	,	PUNCT
ejpam-2217	150	7	2010	2010	NUM
ejpam-2217	150	8	.	.	PUNCT
ejpam-2217	151	1	[	[	X
ejpam-2217	151	2	5	5	X
ejpam-2217	151	3	]	]	PUNCT
ejpam-2217	151	4	j	j	PROPN
ejpam-2217	151	5	m	m	PROPN
ejpam-2217	151	6	casas	casas	PROPN
ejpam-2217	151	7	,	,	PUNCT
ejpam-2217	151	8	e	e	NOUN
ejpam-2217	151	9	khmaladze	khmaladze	NOUN
ejpam-2217	151	10	,	,	PUNCT
ejpam-2217	151	11	and	and	CCONJ
ejpam-2217	151	12	m	m	PROPN
ejpam-2217	151	13	ladra	ladra	PROPN
ejpam-2217	151	14	.	.	PROPN
ejpam-2217	151	15	crossed	cross	VERB
ejpam-2217	151	16	modules	module	NOUN
ejpam-2217	151	17	for	for	ADP
ejpam-2217	151	18	leibniz	leibniz	PROPN
ejpam-2217	151	19	nalgebras	nalgebras	PROPN
ejpam-2217	151	20	.	.	PROPN
ejpam-2217	152	1	forum	forum	PROPN
ejpam-2217	152	2	math	math	PROPN
ejpam-2217	152	3	,	,	PUNCT
ejpam-2217	152	4	20:841–858	20:841–858	NUM
ejpam-2217	152	5	,	,	PUNCT
ejpam-2217	152	6	2008	2008	NUM
ejpam-2217	152	7	.	.	PUNCT
ejpam-2217	153	1	[	[	X
ejpam-2217	153	2	6	6	NUM
ejpam-2217	153	3	]	]	PUNCT
ejpam-2217	153	4	e	e	PROPN
ejpam-2217	153	5	b	b	PROPN
ejpam-2217	153	6	curtis	curtis	PROPN
ejpam-2217	153	7	.	.	PUNCT
ejpam-2217	154	1	simplicial	simplicial	PROPN
ejpam-2217	154	2	homotopy	homotopy	PROPN
ejpam-2217	154	3	theory	theory	NOUN
ejpam-2217	154	4	.	.	PUNCT
ejpam-2217	155	1	advances	advance	NOUN
ejpam-2217	155	2	in	in	ADP
ejpam-2217	155	3	mathematics	mathematic	NOUN
ejpam-2217	155	4	,	,	PUNCT
ejpam-2217	155	5	6(2):107–209	6(2):107–209	NUM
ejpam-2217	155	6	,	,	PUNCT
ejpam-2217	155	7	1971	1971	NUM
ejpam-2217	155	8	.	.	PUNCT
ejpam-2217	156	1	[	[	X
ejpam-2217	156	2	7	7	NUM
ejpam-2217	156	3	]	]	PUNCT
ejpam-2217	156	4	t	t	PROPN
ejpam-2217	156	5	datuashvili	datuashvili	NOUN
ejpam-2217	156	6	.	.	PUNCT
ejpam-2217	157	1	cohomologically	cohomologically	ADV
ejpam-2217	157	2	trivial	trivial	ADJ
ejpam-2217	157	3	internal	internal	ADJ
ejpam-2217	157	4	categories	category	NOUN
ejpam-2217	157	5	in	in	ADP
ejpam-2217	157	6	categories	category	NOUN
ejpam-2217	157	7	of	of	ADP
ejpam-2217	157	8	groups	group	NOUN
ejpam-2217	157	9	with	with	ADP
ejpam-2217	157	10	operations	operation	NOUN
ejpam-2217	157	11	.	.	PUNCT
ejpam-2217	158	1	applied	apply	VERB
ejpam-2217	158	2	categorical	categorical	ADJ
ejpam-2217	158	3	structures	structure	NOUN
ejpam-2217	158	4	,	,	PUNCT
ejpam-2217	158	5	3(3):221–237	3(3):221–237	NUM
ejpam-2217	158	6	,	,	PUNCT
ejpam-2217	158	7	1995	1995	NUM
ejpam-2217	158	8	.	.	PUNCT
ejpam-2217	159	1	[	[	X
ejpam-2217	159	2	8	8	NUM
ejpam-2217	159	3	]	]	X
ejpam-2217	159	4	g	g	PROPN
ejpam-2217	159	5	j	j	PROPN
ejpam-2217	159	6	ellis	ellis	PROPN
ejpam-2217	159	7	.	.	PUNCT
ejpam-2217	160	1	higher	high	ADJ
ejpam-2217	160	2	dimensional	dimensional	ADJ
ejpam-2217	160	3	crossed	cross	VERB
ejpam-2217	160	4	modules	module	NOUN
ejpam-2217	160	5	of	of	ADP
ejpam-2217	160	6	algebras	algebras	PROPN
ejpam-2217	160	7	.	.	PUNCT
ejpam-2217	161	1	journal	journal	PROPN
ejpam-2217	161	2	of	of	ADP
ejpam-2217	161	3	pure	pure	ADJ
ejpam-2217	161	4	and	and	CCONJ
ejpam-2217	161	5	applied	applied	ADJ
ejpam-2217	161	6	algebra	algebra	NOUN
ejpam-2217	161	7	,	,	PUNCT
ejpam-2217	161	8	52(3):277–282	52(3):277–282	PROPN
ejpam-2217	161	9	,	,	PUNCT
ejpam-2217	161	10	1988	1988	NUM
ejpam-2217	161	11	.	.	PUNCT
ejpam-2217	162	1	[	[	X
ejpam-2217	162	2	9	9	NUM
ejpam-2217	162	3	]	]	SYM
ejpam-2217	162	4	g	g	PROPN
ejpam-2217	162	5	j	j	PROPN
ejpam-2217	162	6	ellis	ellis	PROPN
ejpam-2217	162	7	.	.	PUNCT
ejpam-2217	163	1	homotopical	homotopical	ADJ
ejpam-2217	163	2	aspects	aspect	NOUN
ejpam-2217	163	3	of	of	ADP
ejpam-2217	163	4	lie	lie	NOUN
ejpam-2217	163	5	algebras	algebras	PROPN
ejpam-2217	163	6	.	.	PUNCT
ejpam-2217	164	1	journal	journal	PROPN
ejpam-2217	164	2	of	of	ADP
ejpam-2217	164	3	the	the	DET
ejpam-2217	164	4	australian	australian	ADJ
ejpam-2217	164	5	mathematical	mathematical	ADJ
ejpam-2217	164	6	society	society	NOUN
ejpam-2217	164	7	,	,	PUNCT
ejpam-2217	164	8	54(3):393–419	54(3):393–419	PROPN
ejpam-2217	164	9	,	,	PUNCT
ejpam-2217	164	10	1993	1993	NUM
ejpam-2217	164	11	.	.	PUNCT
ejpam-2217	165	1	[	[	X
ejpam-2217	165	2	10	10	NUM
ejpam-2217	165	3	]	]	X
ejpam-2217	165	4	p	p	PROPN
ejpam-2217	165	5	j	j	PROPN
ejpam-2217	165	6	higgins	higgins	PROPN
ejpam-2217	165	7	.	.	PUNCT
ejpam-2217	166	1	groups	group	NOUN
ejpam-2217	166	2	with	with	ADP
ejpam-2217	166	3	multiple	multiple	ADJ
ejpam-2217	166	4	operators	operator	NOUN
ejpam-2217	166	5	.	.	PUNCT
ejpam-2217	167	1	proceedings	proceeding	NOUN
ejpam-2217	167	2	of	of	ADP
ejpam-2217	167	3	the	the	DET
ejpam-2217	167	4	london	london	PROPN
ejpam-2217	167	5	mathematical	mathematical	ADJ
ejpam-2217	167	6	society	society	NOUN
ejpam-2217	167	7	,	,	PUNCT
ejpam-2217	167	8	6(3):366–416	6(3):366–416	NUM
ejpam-2217	167	9	,	,	PUNCT
ejpam-2217	167	10	1956	1956	NUM
ejpam-2217	167	11	.	.	PUNCT
ejpam-2217	168	1	[	[	X
ejpam-2217	168	2	11	11	NUM
ejpam-2217	168	3	]	]	X
ejpam-2217	168	4	g	g	PROPN
ejpam-2217	168	5	orzech	orzech	ADJ
ejpam-2217	168	6	.	.	PUNCT
ejpam-2217	169	1	obstruction	obstruction	NOUN
ejpam-2217	169	2	theory	theory	NOUN
ejpam-2217	169	3	in	in	ADP
ejpam-2217	169	4	algebraic	algebraic	ADJ
ejpam-2217	169	5	categories	category	NOUN
ejpam-2217	169	6	1	1	NUM
ejpam-2217	169	7	and	and	CCONJ
ejpam-2217	169	8	2	2	NUM
ejpam-2217	169	9	.	.	NOUN
ejpam-2217	169	10	journal	journal	NOUN
ejpam-2217	169	11	of	of	ADP
ejpam-2217	169	12	pure	pure	ADJ
ejpam-2217	169	13	and	and	CCONJ
ejpam-2217	169	14	applied	applied	ADJ
ejpam-2217	169	15	algebra	algebra	NOUN
ejpam-2217	169	16	,	,	PUNCT
ejpam-2217	169	17	2(4):287–314	2(4):287–314	NUM
ejpam-2217	169	18	and	and	CCONJ
ejpam-2217	169	19	315–340	315–340	NUM
ejpam-2217	169	20	,	,	PUNCT
ejpam-2217	169	21	1972	1972	NUM
ejpam-2217	169	22	.	.	PUNCT