id	sid	tid	token	lemma	pos
ejpam-6640	1	1	european	european	PROPN
ejpam-6640	1	2	journal	journal	PROPN
ejpam-6640	1	3	of	of	ADP
ejpam-6640	1	4	pure	pure	ADJ
ejpam-6640	1	5	and	and	CCONJ
ejpam-6640	1	6	applied	applied	ADJ
ejpam-6640	1	7	mathematics	mathematic	NOUN
ejpam-6640	1	8	2025	2025	NUM
ejpam-6640	1	9	,	,	PUNCT
ejpam-6640	1	10	vol	vol	NOUN
ejpam-6640	1	11	.	.	PROPN
ejpam-6640	1	12	18	18	NUM
ejpam-6640	1	13	,	,	PUNCT
ejpam-6640	1	14	issue	issue	NOUN
ejpam-6640	1	15	4	4	NUM
ejpam-6640	1	16	,	,	PUNCT
ejpam-6640	1	17	article	article	NOUN
ejpam-6640	1	18	number	number	NOUN
ejpam-6640	1	19	6640	6640	NUM
ejpam-6640	1	20	issn	issn	PROPN
ejpam-6640	1	21	1307	1307	NUM
ejpam-6640	1	22	-	-	SYM
ejpam-6640	1	23	5543	5543	NUM
ejpam-6640	1	24	–	–	PUNCT
ejpam-6640	1	25	ejpam.com	ejpam.com	X
ejpam-6640	1	26	published	publish	VERB
ejpam-6640	1	27	by	by	ADP
ejpam-6640	1	28	new	new	PROPN
ejpam-6640	1	29	york	york	PROPN
ejpam-6640	1	30	business	business	PROPN
ejpam-6640	1	31	global	global	ADJ
ejpam-6640	1	32	exactness	exactness	NOUN
ejpam-6640	1	33	of	of	ADP
ejpam-6640	1	34	the	the	DET
ejpam-6640	1	35	functors	functors	PROPN
ejpam-6640	1	36	homa	homa	PROPN
ejpam-6640	1	37	(	(	PUNCT
ejpam-6640	1	38	x,−	x,−	PROPN
ejpam-6640	1	39	)	)	PUNCT
ejpam-6640	1	40	,	,	PUNCT
ejpam-6640	2	1	homa	homa	NOUN
ejpam-6640	2	2	(	(	PUNCT
ejpam-6640	2	3	−	−	PROPN
ejpam-6640	2	4	,	,	PUNCT
ejpam-6640	2	5	x	x	NOUN
ejpam-6640	2	6	)	)	PUNCT
ejpam-6640	2	7	,	,	PUNCT
ejpam-6640	2	8	homcomp(a	homcomp(a	NOUN
ejpam-6640	2	9	)	)	PUNCT
ejpam-6640	2	10	(	(	PUNCT
ejpam-6640	2	11	x,−	x,−	PROPN
ejpam-6640	2	12	)	)	PUNCT
ejpam-6640	2	13	,	,	PUNCT
ejpam-6640	2	14	homcomp(a	homcomp(a	NOUN
ejpam-6640	2	15	)	)	PUNCT
ejpam-6640	2	16	(	(	PUNCT
ejpam-6640	2	17	−	−	PROPN
ejpam-6640	2	18	,	,	PUNCT
ejpam-6640	2	19	x	x	NOUN
ejpam-6640	2	20	)	)	PUNCT
ejpam-6640	2	21	and	and	CCONJ
ejpam-6640	2	22	the	the	DET
ejpam-6640	2	23	homological	homological	ADJ
ejpam-6640	2	24	functors	functors	PROPN
ejpam-6640	2	25	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	2	26	)	)	PUNCT
ejpam-6640	2	27	and	and	CCONJ
ejpam-6640	2	28	h̃n(−	h̃n(−	PROPN
ejpam-6640	2	29	,	,	PUNCT
ejpam-6640	2	30	x	x	NOUN
ejpam-6640	2	31	)	)	PUNCT
ejpam-6640	2	32	in	in	ADP
ejpam-6640	2	33	a	a	DET
ejpam-6640	2	34	balanced	balanced	ADJ
ejpam-6640	2	35	abelian	abelian	ADJ
ejpam-6640	2	36	category	category	NOUN
ejpam-6640	2	37	ablaye	ablaye	NOUN
ejpam-6640	2	38	diallo1,∗	diallo1,∗	NOUN
ejpam-6640	2	39	,	,	PUNCT
ejpam-6640	2	40	mohamed	mohamed	PROPN
ejpam-6640	2	41	ben	ben	PROPN
ejpam-6640	2	42	faraj	faraj	PROPN
ejpam-6640	2	43	ben	ben	PROPN
ejpam-6640	2	44	maaouia1	maaouia1	PROPN
ejpam-6640	2	45	,	,	PUNCT
ejpam-6640	2	46	mamadou	mamadou	PROPN
ejpam-6640	2	47	sanghare2	sanghare2	NOUN
ejpam-6640	2	48	1	1	NUM
ejpam-6640	2	49	applied	applied	ADJ
ejpam-6640	2	50	mathematics	mathematic	NOUN
ejpam-6640	2	51	,	,	PUNCT
ejpam-6640	2	52	ufr	ufr	PROPN
ejpam-6640	2	53	des	des	PROPN
ejpam-6640	2	54	sciences	science	NOUN
ejpam-6640	2	55	appliquées	appliquées	PROPN
ejpam-6640	2	56	et	et	NOUN
ejpam-6640	2	57	technologie	technologie	PROPN
ejpam-6640	2	58	,	,	PUNCT
ejpam-6640	2	59	université	université	NOUN
ejpam-6640	2	60	gaston	gaston	PROPN
ejpam-6640	2	61	berger	berger	PROPN
ejpam-6640	2	62	,	,	PUNCT
ejpam-6640	2	63	saint	saint	PROPN
ejpam-6640	2	64	-	-	PUNCT
ejpam-6640	2	65	louis	louis	NOUN
ejpam-6640	2	66	,	,	PUNCT
ejpam-6640	2	67	senegal	senegal	NOUN
ejpam-6640	2	68	2	2	NUM
ejpam-6640	2	69	faculté	faculté	X
ejpam-6640	2	70	des	des	PROPN
ejpam-6640	2	71	sciences	sciences	PROPN
ejpam-6640	2	72	et	et	NOUN
ejpam-6640	2	73	techniques	technique	NOUN
ejpam-6640	2	74	,	,	PUNCT
ejpam-6640	2	75	université	université	ADJ
ejpam-6640	2	76	cheikh	cheikh	PROPN
ejpam-6640	2	77	anta	anta	PROPN
ejpam-6640	2	78	diop	diop	PROPN
ejpam-6640	2	79	(	(	PUNCT
ejpam-6640	2	80	ucad	ucad	ADJ
ejpam-6640	2	81	)	)	PUNCT
ejpam-6640	2	82	,	,	PUNCT
ejpam-6640	2	83	dakar	dakar	NOUN
ejpam-6640	2	84	,	,	PUNCT
ejpam-6640	2	85	senegal	senegal	ADJ
ejpam-6640	2	86	abstract	abstract	NOUN
ejpam-6640	2	87	.	.	PUNCT
ejpam-6640	3	1	this	this	DET
ejpam-6640	3	2	article	article	NOUN
ejpam-6640	3	3	presents	present	VERB
ejpam-6640	3	4	several	several	ADJ
ejpam-6640	3	5	results	result	NOUN
ejpam-6640	3	6	concerning	concern	VERB
ejpam-6640	3	7	the	the	DET
ejpam-6640	3	8	exactness	exactness	NOUN
ejpam-6640	3	9	of	of	ADP
ejpam-6640	3	10	covariant	covariant	NOUN
ejpam-6640	3	11	and	and	CCONJ
ejpam-6640	3	12	contravariant	contravariant	PROPN
ejpam-6640	3	13	hom	hom	X
ejpam-6640	3	14	functors	functors	PROPN
ejpam-6640	3	15	and	and	CCONJ
ejpam-6640	3	16	their	their	PRON
ejpam-6640	3	17	derived	derive	VERB
ejpam-6640	3	18	functors	functor	NOUN
ejpam-6640	3	19	in	in	ADP
ejpam-6640	3	20	a	a	DET
ejpam-6640	3	21	balanced	balanced	ADJ
ejpam-6640	3	22	abelian	abelian	ADJ
ejpam-6640	3	23	category	category	NOUN
ejpam-6640	3	24	a	a	X
ejpam-6640	3	25	.	.	PUNCT
ejpam-6640	4	1	in	in	ADP
ejpam-6640	4	2	particular	particular	ADJ
ejpam-6640	4	3	:	:	PUNCT
ejpam-6640	4	4	(	(	PUNCT
ejpam-6640	4	5	i	i	NOUN
ejpam-6640	4	6	)	)	PUNCT
ejpam-6640	4	7	the	the	DET
ejpam-6640	4	8	functors	functors	PROPN
ejpam-6640	4	9	homa	homa	PROPN
ejpam-6640	4	10	(	(	PUNCT
ejpam-6640	4	11	x,−	x,−	PROPN
ejpam-6640	4	12	)	)	PUNCT
ejpam-6640	4	13	and	and	CCONJ
ejpam-6640	4	14	homa	homa	NOUN
ejpam-6640	4	15	(	(	PUNCT
ejpam-6640	4	16	−	−	PROPN
ejpam-6640	4	17	,	,	PUNCT
ejpam-6640	4	18	x	x	X
ejpam-6640	4	19	)	)	PUNCT
ejpam-6640	4	20	are	be	AUX
ejpam-6640	4	21	left	leave	VERB
ejpam-6640	4	22	exact	exact	ADJ
ejpam-6640	4	23	,	,	PUNCT
ejpam-6640	4	24	and	and	CCONJ
ejpam-6640	4	25	become	become	VERB
ejpam-6640	4	26	exact	exact	ADJ
ejpam-6640	4	27	if	if	SCONJ
ejpam-6640	4	28	and	and	CCONJ
ejpam-6640	4	29	only	only	ADV
ejpam-6640	4	30	if	if	SCONJ
ejpam-6640	4	31	x	x	PRON
ejpam-6640	4	32	is	be	AUX
ejpam-6640	4	33	projective	projective	ADJ
ejpam-6640	4	34	(	(	PUNCT
ejpam-6640	4	35	resp	resp	NOUN
ejpam-6640	4	36	.	.	PUNCT
ejpam-6640	4	37	injective	injective	ADJ
ejpam-6640	4	38	)	)	PUNCT
ejpam-6640	4	39	.	.	PUNCT
ejpam-6640	5	1	(	(	PUNCT
ejpam-6640	5	2	ii	ii	X
ejpam-6640	5	3	)	)	PUNCT
ejpam-6640	5	4	the	the	DET
ejpam-6640	5	5	functors	functors	PROPN
ejpam-6640	5	6	homcomp(a	homcomp(a	PROPN
ejpam-6640	5	7	)	)	PUNCT
ejpam-6640	5	8	(	(	PUNCT
ejpam-6640	5	9	x,−	x,−	PROPN
ejpam-6640	5	10	)	)	PUNCT
ejpam-6640	5	11	and	and	CCONJ
ejpam-6640	5	12	homcomp(a	homcomp(a	NOUN
ejpam-6640	5	13	)	)	PUNCT
ejpam-6640	5	14	(	(	PUNCT
ejpam-6640	5	15	−	−	PROPN
ejpam-6640	5	16	,	,	PUNCT
ejpam-6640	5	17	x	x	X
ejpam-6640	5	18	)	)	PUNCT
ejpam-6640	5	19	on	on	ADP
ejpam-6640	5	20	the	the	DET
ejpam-6640	5	21	category	category	NOUN
ejpam-6640	5	22	of	of	ADP
ejpam-6640	5	23	complexes	complex	NOUN
ejpam-6640	5	24	comp(a	comp(a	NOUN
ejpam-6640	5	25	)	)	PUNCT
ejpam-6640	5	26	preserve	preserve	VERB
ejpam-6640	5	27	this	this	DET
ejpam-6640	5	28	behavior	behavior	NOUN
ejpam-6640	5	29	.	.	PUNCT
ejpam-6640	6	1	(	(	PUNCT
ejpam-6640	6	2	iii	iii	X
ejpam-6640	6	3	)	)	PUNCT
ejpam-6640	6	4	the	the	DET
ejpam-6640	6	5	homological	homological	PROPN
ejpam-6640	6	6	functors	functors	PROPN
ejpam-6640	6	7	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	6	8	)	)	PUNCT
ejpam-6640	6	9	and	and	CCONJ
ejpam-6640	6	10	h̃n(−	h̃n(−	PROPN
ejpam-6640	6	11	,	,	PUNCT
ejpam-6640	6	12	x	x	X
ejpam-6640	6	13	)	)	PUNCT
ejpam-6640	6	14	are	be	AUX
ejpam-6640	6	15	constructed	construct	VERB
ejpam-6640	6	16	for	for	ADP
ejpam-6640	6	17	all	all	DET
ejpam-6640	6	18	n	n	PRON
ejpam-6640	6	19	∈	∈	PROPN
ejpam-6640	6	20	z.	z.	X
ejpam-6640	6	21	(	(	PUNCT
ejpam-6640	6	22	iv	iv	X
ejpam-6640	6	23	)	)	PUNCT
ejpam-6640	6	24	for	for	ADP
ejpam-6640	6	25	projective	projective	ADJ
ejpam-6640	6	26	x	x	X
ejpam-6640	6	27	,	,	PUNCT
ejpam-6640	6	28	the	the	DET
ejpam-6640	6	29	connecting	connect	VERB
ejpam-6640	6	30	morphism	morphism	NOUN
ejpam-6640	6	31	λn	λn	PROPN
ejpam-6640	6	32	:	:	PUNCT
ejpam-6640	6	33	h̃n(x,−)((t	h̃n(x,−)((t	PROPN
ejpam-6640	6	34	,	,	PUNCT
ejpam-6640	6	35	γ	γ	NOUN
ejpam-6640	6	36	)	)	PUNCT
ejpam-6640	6	37	)	)	PUNCT
ejpam-6640	6	38	→	→	PUNCT
ejpam-6640	6	39	h̃n+1(x,−)((y	h̃n+1(x,−)((y	PROPN
ejpam-6640	6	40	,	,	PUNCT
ejpam-6640	6	41	α	α	NOUN
ejpam-6640	6	42	)	)	PUNCT
ejpam-6640	6	43	)	)	PUNCT
ejpam-6640	6	44	allows	allow	VERB
ejpam-6640	6	45	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	6	46	)	)	PUNCT
ejpam-6640	6	47	to	to	PART
ejpam-6640	6	48	send	send	VERB
ejpam-6640	6	49	short	short	ADJ
ejpam-6640	6	50	exact	exact	ADJ
ejpam-6640	6	51	sequences	sequence	NOUN
ejpam-6640	6	52	in	in	ADP
ejpam-6640	6	53	comp(a	comp(a	NOUN
ejpam-6640	6	54	)	)	PUNCT
ejpam-6640	6	55	into	into	ADP
ejpam-6640	6	56	long	long	ADJ
ejpam-6640	6	57	exact	exact	ADJ
ejpam-6640	6	58	sequences	sequence	NOUN
ejpam-6640	6	59	in	in	ADP
ejpam-6640	6	60	ab	ab	PROPN
ejpam-6640	6	61	.	.	PUNCT
ejpam-6640	7	1	(	(	PUNCT
ejpam-6640	7	2	v	v	NOUN
ejpam-6640	7	3	)	)	PUNCT
ejpam-6640	7	4	similarly	similarly	ADV
ejpam-6640	7	5	,	,	PUNCT
ejpam-6640	7	6	for	for	ADP
ejpam-6640	7	7	injective	injective	ADJ
ejpam-6640	7	8	x	x	NOUN
ejpam-6640	7	9	,	,	PUNCT
ejpam-6640	7	10	the	the	DET
ejpam-6640	7	11	morphism	morphism	NOUN
ejpam-6640	7	12	δn	δn	NOUN
ejpam-6640	7	13	:	:	PUNCT
ejpam-6640	7	14	h̃n(−	h̃n(−	PROPN
ejpam-6640	7	15	,	,	PUNCT
ejpam-6640	7	16	x)((y	x)((y	PROPN
ejpam-6640	7	17	,	,	PUNCT
ejpam-6640	7	18	α	α	NOUN
ejpam-6640	7	19	)	)	PUNCT
ejpam-6640	7	20	)	)	PUNCT
ejpam-6640	8	1	→	→	SYM
ejpam-6640	8	2	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	8	3	,	,	PUNCT
ejpam-6640	8	4	x)((t	x)((t	PROPN
ejpam-6640	8	5	,	,	PUNCT
ejpam-6640	8	6	γ	γ	NOUN
ejpam-6640	8	7	)	)	PUNCT
ejpam-6640	8	8	)	)	PUNCT
ejpam-6640	8	9	shows	show	VERB
ejpam-6640	8	10	that	that	SCONJ
ejpam-6640	8	11	h̃n(−	h̃n(−	PROPN
ejpam-6640	8	12	,	,	PUNCT
ejpam-6640	8	13	x	x	NOUN
ejpam-6640	8	14	)	)	PUNCT
ejpam-6640	8	15	also	also	ADV
ejpam-6640	8	16	preserves	preserve	VERB
ejpam-6640	8	17	long	long	ADJ
ejpam-6640	8	18	exact	exact	ADJ
ejpam-6640	8	19	sequences	sequence	NOUN
ejpam-6640	8	20	.	.	PUNCT
ejpam-6640	9	1	2020	2020	NUM
ejpam-6640	9	2	mathematics	mathematic	NOUN
ejpam-6640	9	3	subject	subject	NOUN
ejpam-6640	9	4	classifications	classification	NOUN
ejpam-6640	9	5	:	:	PUNCT
ejpam-6640	9	6	16e30	16e30	NUM
ejpam-6640	9	7	,	,	PUNCT
ejpam-6640	9	8	20j05	20j05	NUM
ejpam-6640	9	9	key	key	ADJ
ejpam-6640	9	10	words	word	NOUN
ejpam-6640	9	11	and	and	CCONJ
ejpam-6640	9	12	phrases	phrase	NOUN
ejpam-6640	9	13	:	:	PUNCT
ejpam-6640	9	14	abelian	abelian	ADJ
ejpam-6640	9	15	category	category	NOUN
ejpam-6640	9	16	,	,	PUNCT
ejpam-6640	9	17	balanced	balanced	ADJ
ejpam-6640	9	18	category	category	NOUN
ejpam-6640	9	19	,	,	PUNCT
ejpam-6640	9	20	homological	homological	ADJ
ejpam-6640	9	21	functors	functor	NOUN
ejpam-6640	9	22	,	,	PUNCT
ejpam-6640	9	23	projective	projective	ADJ
ejpam-6640	9	24	object	object	NOUN
ejpam-6640	9	25	,	,	PUNCT
ejpam-6640	9	26	injective	injective	ADJ
ejpam-6640	9	27	object	object	NOUN
ejpam-6640	9	28	,	,	PUNCT
ejpam-6640	9	29	category	category	NOUN
ejpam-6640	9	30	of	of	ADP
ejpam-6640	9	31	abelian	abelian	ADJ
ejpam-6640	9	32	groups	group	NOUN
ejpam-6640	9	33	introduction	introduction	VERB
ejpam-6640	9	34	the	the	DET
ejpam-6640	9	35	main	main	ADJ
ejpam-6640	9	36	objective	objective	NOUN
ejpam-6640	9	37	of	of	ADP
ejpam-6640	9	38	this	this	DET
ejpam-6640	9	39	article	article	NOUN
ejpam-6640	9	40	is	be	AUX
ejpam-6640	9	41	to	to	PART
ejpam-6640	9	42	study	study	VERB
ejpam-6640	9	43	the	the	DET
ejpam-6640	9	44	exactness	exactness	NOUN
ejpam-6640	9	45	of	of	ADP
ejpam-6640	9	46	the	the	DET
ejpam-6640	9	47	functors	functors	PROPN
ejpam-6640	9	48	homa	homa	PROPN
ejpam-6640	9	49	(	(	PUNCT
ejpam-6640	9	50	x,−	x,−	PROPN
ejpam-6640	9	51	)	)	PUNCT
ejpam-6640	9	52	,	,	PUNCT
ejpam-6640	9	53	homa	homa	NOUN
ejpam-6640	9	54	(	(	PUNCT
ejpam-6640	9	55	−	−	PROPN
ejpam-6640	9	56	,	,	PUNCT
ejpam-6640	9	57	x	x	NOUN
ejpam-6640	9	58	)	)	PUNCT
ejpam-6640	9	59	:	:	PUNCT
ejpam-6640	9	60	a	a	DET
ejpam-6640	9	61	−→	−→	PROPN
ejpam-6640	9	62	ab	ab	PROPN
ejpam-6640	9	63	,	,	PUNCT
ejpam-6640	9	64	homcomp(a	homcomp(a	NOUN
ejpam-6640	9	65	)	)	PUNCT
ejpam-6640	9	66	(	(	PUNCT
ejpam-6640	9	67	x,−),homcomp(a	x,−),homcomp(a	PROPN
ejpam-6640	9	68	)	)	PUNCT
ejpam-6640	9	69	(	(	PUNCT
ejpam-6640	9	70	−	−	PROPN
ejpam-6640	9	71	,	,	PUNCT
ejpam-6640	9	72	x	x	NOUN
ejpam-6640	9	73	)	)	PUNCT
ejpam-6640	9	74	:	:	PUNCT
ejpam-6640	9	75	comp(a	comp(a	INTJ
ejpam-6640	9	76	)	)	PUNCT
ejpam-6640	9	77	−→	−→	NOUN
ejpam-6640	9	78	comp(ab	comp(ab	NOUN
ejpam-6640	9	79	)	)	PUNCT
ejpam-6640	9	80	∗corresponding	∗corresponde	VERB
ejpam-6640	9	81	author	author	NOUN
ejpam-6640	9	82	.	.	PUNCT
ejpam-6640	10	1	doi	doi	NOUN
ejpam-6640	10	2	:	:	PUNCT
ejpam-6640	10	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6640	https://doi.org/10.29020/nybg.ejpam.v18i4.6640	PRON
ejpam-6640	10	4	email	email	NOUN
ejpam-6640	10	5	addresses	address	NOUN
ejpam-6640	10	6	:	:	PUNCT
ejpam-6640	10	7	diallo.ablaye@ugb.edu.sn	diallo.ablaye@ugb.edu.sn	PROPN
ejpam-6640	10	8	(	(	PUNCT
ejpam-6640	10	9	a.	a.	PROPN
ejpam-6640	10	10	diallo	diallo	PROPN
ejpam-6640	10	11	)	)	PUNCT
ejpam-6640	10	12	,	,	PUNCT
ejpam-6640	10	13	mohamed-ben.maaouia@ugb.edu.sn	mohamed-ben.maaouia@ugb.edu.sn	PROPN
ejpam-6640	10	14	(	(	PUNCT
ejpam-6640	10	15	m.	m.	PROPN
ejpam-6640	10	16	b.	b.	PROPN
ejpam-6640	10	17	f.	f.	PROPN
ejpam-6640	10	18	b.	b.	PROPN
ejpam-6640	10	19	maaouia	maaouia	PROPN
ejpam-6640	10	20	)	)	PUNCT
ejpam-6640	10	21	,	,	PUNCT
ejpam-6640	10	22	mamadou.sanghare@ucad.edu.sn	mamadou.sanghare@ucad.edu.sn	PROPN
ejpam-6640	10	23	(	(	PUNCT
ejpam-6640	10	24	m.	m.	NOUN
ejpam-6640	10	25	sanghare	sanghare	PROPN
ejpam-6640	10	26	)	)	PUNCT
ejpam-6640	10	27	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6640	10	28	1	1	NUM
ejpam-6640	10	29	copyright	copyright	NOUN
ejpam-6640	10	30	:	:	PUNCT
ejpam-6640	11	1	©	©	PROPN
ejpam-6640	11	2	2025	2025	NUM
ejpam-6640	11	3	the	the	DET
ejpam-6640	11	4	author(s	author(s	NOUN
ejpam-6640	11	5	)	)	PUNCT
ejpam-6640	11	6	.	.	PUNCT
ejpam-6640	12	1	(	(	PUNCT
ejpam-6640	12	2	cc	cc	NOUN
ejpam-6640	12	3	by	by	ADP
ejpam-6640	12	4	-	-	PUNCT
ejpam-6640	12	5	nc	nc	PROPN
ejpam-6640	12	6	4.0	4.0	NUM
ejpam-6640	12	7	)	)	PUNCT
ejpam-6640	12	8	a.	a.	NOUN
ejpam-6640	12	9	diallo	diallo	PROPN
ejpam-6640	12	10	,	,	PUNCT
ejpam-6640	12	11	m.	m.	PROPN
ejpam-6640	12	12	b.	b.	PROPN
ejpam-6640	12	13	f.	f.	PROPN
ejpam-6640	12	14	b.	b.	PROPN
ejpam-6640	12	15	maaouia	maaouia	PROPN
ejpam-6640	12	16	,	,	PUNCT
ejpam-6640	12	17	m.	m.	NOUN
ejpam-6640	12	18	sanghare	sanghare	PROPN
ejpam-6640	12	19	/	/	SYM
ejpam-6640	12	20	eur	eur	PROPN
ejpam-6640	12	21	.	.	PUNCT
ejpam-6640	13	1	j.	j.	PROPN
ejpam-6640	13	2	pure	pure	PROPN
ejpam-6640	13	3	appl	appl	PROPN
ejpam-6640	13	4	.	.	PROPN
ejpam-6640	13	5	math	math	PROPN
ejpam-6640	13	6	,	,	PUNCT
ejpam-6640	13	7	18	18	NUM
ejpam-6640	13	8	(	(	PUNCT
ejpam-6640	13	9	4	4	NUM
ejpam-6640	13	10	)	)	PUNCT
ejpam-6640	13	11	(	(	PUNCT
ejpam-6640	13	12	2025	2025	NUM
ejpam-6640	13	13	)	)	PUNCT
ejpam-6640	13	14	,	,	PUNCT
ejpam-6640	13	15	6640	6640	NUM
ejpam-6640	13	16	2	2	NUM
ejpam-6640	13	17	of	of	ADP
ejpam-6640	13	18	28	28	NUM
ejpam-6640	13	19	and	and	CCONJ
ejpam-6640	13	20	the	the	DET
ejpam-6640	13	21	homological	homological	ADJ
ejpam-6640	13	22	functors	functors	PROPN
ejpam-6640	13	23	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	13	24	)	)	PUNCT
ejpam-6640	13	25	,	,	PUNCT
ejpam-6640	13	26	h̃n(−	h̃n(−	PROPN
ejpam-6640	13	27	,	,	PUNCT
ejpam-6640	13	28	x	x	NOUN
ejpam-6640	13	29	)	)	PUNCT
ejpam-6640	13	30	:	:	PUNCT
ejpam-6640	13	31	comp(a	comp(a	INTJ
ejpam-6640	13	32	)	)	PUNCT
ejpam-6640	13	33	−→	−→	ADP
ejpam-6640	13	34	ab	ab	INTJ
ejpam-6640	13	35	where	where	SCONJ
ejpam-6640	13	36	a	a	PRON
ejpam-6640	13	37	is	be	AUX
ejpam-6640	13	38	a	a	DET
ejpam-6640	13	39	balanced	balanced	ADJ
ejpam-6640	13	40	abelian	abelian	ADJ
ejpam-6640	13	41	category	category	NOUN
ejpam-6640	13	42	,	,	PUNCT
ejpam-6640	13	43	ab	ab	PROPN
ejpam-6640	13	44	the	the	DET
ejpam-6640	13	45	category	category	NOUN
ejpam-6640	13	46	of	of	ADP
ejpam-6640	13	47	abelian	abelian	ADJ
ejpam-6640	13	48	groups	group	NOUN
ejpam-6640	13	49	,	,	PUNCT
ejpam-6640	13	50	and	and	CCONJ
ejpam-6640	13	51	n	n	DET
ejpam-6640	13	52	an	an	DET
ejpam-6640	13	53	integer	integer	NOUN
ejpam-6640	13	54	in	in	ADP
ejpam-6640	13	55	z.	z.	PROPN
ejpam-6640	14	1	this	this	DET
ejpam-6640	14	2	study	study	NOUN
ejpam-6640	14	3	is	be	AUX
ejpam-6640	14	4	motivated	motivate	VERB
ejpam-6640	14	5	by	by	ADP
ejpam-6640	14	6	extending	extend	VERB
ejpam-6640	14	7	the	the	DET
ejpam-6640	14	8	fundamental	fundamental	ADJ
ejpam-6640	14	9	concepts	concept	NOUN
ejpam-6640	14	10	of	of	ADP
ejpam-6640	14	11	homological	homological	ADJ
ejpam-6640	14	12	algebra	algebra	NOUN
ejpam-6640	14	13	from	from	ADP
ejpam-6640	14	14	the	the	DET
ejpam-6640	14	15	category	category	NOUN
ejpam-6640	14	16	of	of	ADP
ejpam-6640	14	17	modules	module	NOUN
ejpam-6640	14	18	to	to	ADP
ejpam-6640	14	19	an	an	DET
ejpam-6640	14	20	arbitrary	arbitrary	ADJ
ejpam-6640	14	21	balanced	balanced	ADJ
ejpam-6640	14	22	abelian	abelian	ADJ
ejpam-6640	14	23	category	category	NOUN
ejpam-6640	14	24	.	.	PUNCT
ejpam-6640	15	1	this	this	DET
ejpam-6640	15	2	generalization	generalization	NOUN
ejpam-6640	15	3	is	be	AUX
ejpam-6640	15	4	not	not	PART
ejpam-6640	15	5	straightforward	straightforward	ADJ
ejpam-6640	15	6	,	,	PUNCT
ejpam-6640	15	7	as	as	SCONJ
ejpam-6640	15	8	evidenced	evidence	VERB
ejpam-6640	15	9	by	by	ADP
ejpam-6640	15	10	the	the	DET
ejpam-6640	15	11	proofs	proof	NOUN
ejpam-6640	15	12	of	of	ADP
ejpam-6640	15	13	the	the	DET
ejpam-6640	15	14	various	various	ADJ
ejpam-6640	15	15	results	result	NOUN
ejpam-6640	15	16	mentioned	mention	VERB
ejpam-6640	15	17	in	in	ADP
ejpam-6640	15	18	the	the	DET
ejpam-6640	15	19	abstract	abstract	NOUN
ejpam-6640	15	20	.	.	PUNCT
ejpam-6640	16	1	furthermore	furthermore	ADV
ejpam-6640	16	2	,	,	PUNCT
ejpam-6640	16	3	this	this	DET
ejpam-6640	16	4	work	work	NOUN
ejpam-6640	16	5	is	be	AUX
ejpam-6640	16	6	inspired	inspire	VERB
ejpam-6640	16	7	by	by	ADP
ejpam-6640	16	8	the	the	DET
ejpam-6640	16	9	exactness	exactness	NOUN
ejpam-6640	16	10	of	of	ADP
ejpam-6640	16	11	the	the	DET
ejpam-6640	16	12	functors	functors	PROPN
ejpam-6640	16	13	homa(x,−	homa(x,−	PROPN
ejpam-6640	16	14	)	)	PUNCT
ejpam-6640	16	15	,	,	PUNCT
ejpam-6640	16	16	homa(−	homa(−	PROPN
ejpam-6640	16	17	,	,	PUNCT
ejpam-6640	16	18	x	x	NOUN
ejpam-6640	16	19	)	)	PUNCT
ejpam-6640	16	20	and	and	CCONJ
ejpam-6640	16	21	the	the	DET
ejpam-6640	16	22	homological	homological	ADJ
ejpam-6640	16	23	functor	functor	NOUN
ejpam-6640	16	24	hn	hn	PROPN
ejpam-6640	16	25	:	:	PUNCT
ejpam-6640	16	26	comp(a	comp(a	NOUN
ejpam-6640	16	27	-	-	PUNCT
ejpam-6640	16	28	mod	mod	ADJ
ejpam-6640	16	29	)	)	PUNCT
ejpam-6640	16	30	−→	−→	PROPN
ejpam-6640	16	31	ab	ab	PROPN
ejpam-6640	16	32	in	in	ADP
ejpam-6640	16	33	the	the	DET
ejpam-6640	16	34	category	category	NOUN
ejpam-6640	16	35	of	of	ADP
ejpam-6640	16	36	left	leave	VERB
ejpam-6640	16	37	a	a	DET
ejpam-6640	16	38	-	-	PUNCT
ejpam-6640	16	39	modules	module	NOUN
ejpam-6640	16	40	a	a	DET
ejpam-6640	16	41	-	-	PUNCT
ejpam-6640	16	42	mod	mod	NOUN
ejpam-6640	16	43	(	(	PUNCT
ejpam-6640	16	44	resp	resp	NOUN
ejpam-6640	16	45	.	.	PUNCT
ejpam-6640	17	1	right	right	ADJ
ejpam-6640	17	2	a	a	DET
ejpam-6640	17	3	-	-	PUNCT
ejpam-6640	17	4	modules	module	NOUN
ejpam-6640	17	5	mod	mod	NOUN
ejpam-6640	17	6	-	-	PUNCT
ejpam-6640	17	7	a	a	NOUN
ejpam-6640	17	8	)	)	PUNCT
ejpam-6640	17	9	and	and	CCONJ
ejpam-6640	17	10	complexes	complex	NOUN
ejpam-6640	17	11	of	of	ADP
ejpam-6640	17	12	left	leave	VERB
ejpam-6640	17	13	a	a	DET
ejpam-6640	17	14	-	-	PUNCT
ejpam-6640	17	15	modules	module	NOUN
ejpam-6640	17	16	(	(	PUNCT
ejpam-6640	17	17	comp(a	comp(a	NOUN
ejpam-6640	17	18	-	-	PUNCT
ejpam-6640	17	19	mod	mod	NOUN
ejpam-6640	17	20	)	)	PUNCT
ejpam-6640	17	21	)	)	PUNCT
ejpam-6640	18	1	(	(	PUNCT
ejpam-6640	18	2	resp	resp	NOUN
ejpam-6640	18	3	.	.	PUNCT
ejpam-6640	19	1	complexes	complex	NOUN
ejpam-6640	19	2	of	of	ADP
ejpam-6640	19	3	right	right	ADJ
ejpam-6640	19	4	a	a	DET
ejpam-6640	19	5	-	-	PUNCT
ejpam-6640	19	6	modules	module	NOUN
ejpam-6640	19	7	comp(mod	comp(mod	NOUN
ejpam-6640	19	8	-	-	PUNCT
ejpam-6640	19	9	a	a	NOUN
ejpam-6640	19	10	)	)	PUNCT
ejpam-6640	19	11	):	):	PUNCT
ejpam-6640	19	12	”	"	PUNCT
ejpam-6640	19	13	the	the	DET
ejpam-6640	19	14	functor	functor	PROPN
ejpam-6640	19	15	and	and	CCONJ
ejpam-6640	19	16	its	its	PRON
ejpam-6640	19	17	relationship	relationship	NOUN
ejpam-6640	19	18	with	with	ADP
ejpam-6640	19	19	homological	homological	ADJ
ejpam-6640	19	20	functor	functor	NOUN
ejpam-6640	19	21	”	"	PUNCT
ejpam-6640	20	1	[	[	X
ejpam-6640	20	2	1	1	NUM
ejpam-6640	20	3	]	]	PUNCT
ejpam-6640	20	4	,	,	PUNCT
ejpam-6640	20	5	”	"	PUNCT
ejpam-6640	20	6	localization	localization	NOUN
ejpam-6640	20	7	,	,	PUNCT
ejpam-6640	20	8	isomorphisms	isomorphism	NOUN
ejpam-6640	20	9	and	and	CCONJ
ejpam-6640	20	10	adjoint	adjoint	VERB
ejpam-6640	20	11	isomorphism	isomorphism	NOUN
ejpam-6640	20	12	in	in	ADP
ejpam-6640	20	13	the	the	DET
ejpam-6640	20	14	category	category	NOUN
ejpam-6640	20	15	comp(amod”[2],”localization	comp(amod”[2],”localization	NOUN
ejpam-6640	20	16	of	of	ADP
ejpam-6640	20	17	hopfian	hopfian	ADJ
ejpam-6640	20	18	and	and	CCONJ
ejpam-6640	20	19	cohopfian	cohopfian	ADJ
ejpam-6640	20	20	objects	object	NOUN
ejpam-6640	20	21	in	in	ADP
ejpam-6640	20	22	the	the	DET
ejpam-6640	20	23	categories	category	NOUN
ejpam-6640	20	24	of	of	ADP
ejpam-6640	20	25	a	a	DET
ejpam-6640	20	26	-	-	PUNCT
ejpam-6640	20	27	mod	mod	ADJ
ejpam-6640	20	28	,	,	PUNCT
ejpam-6640	20	29	agr	agr	X
ejpam-6640	20	30	(	(	PUNCT
ejpam-6640	20	31	a	a	DET
ejpam-6640	20	32	-	-	PUNCT
ejpam-6640	20	33	mod	mod	NOUN
ejpam-6640	20	34	)	)	PUNCT
ejpam-6640	20	35	and	and	CCONJ
ejpam-6640	20	36	comp(agr(a	comp(agr(a	NOUN
ejpam-6640	20	37	-	-	NOUN
ejpam-6640	20	38	mod	mod	ADJ
ejpam-6640	20	39	)	)	PUNCT
ejpam-6640	20	40	)	)	PUNCT
ejpam-6640	20	41	”	"	PUNCT
ejpam-6640	21	1	[	[	X
ejpam-6640	21	2	3	3	NUM
ejpam-6640	21	3	]	]	PUNCT
ejpam-6640	21	4	,	,	PUNCT
ejpam-6640	21	5	”	"	PUNCT
ejpam-6640	21	6	adjunction	adjunction	NOUN
ejpam-6640	21	7	and	and	CCONJ
ejpam-6640	21	8	localization	localization	NOUN
ejpam-6640	21	9	in	in	ADP
ejpam-6640	21	10	the	the	DET
ejpam-6640	21	11	category	category	NOUN
ejpam-6640	21	12	a	a	DET
ejpam-6640	21	13	-	-	PUNCT
ejpam-6640	21	14	alg	alg	NOUN
ejpam-6640	21	15	of	of	ADP
ejpam-6640	21	16	a	a	DET
ejpam-6640	21	17	-	-	PUNCT
ejpam-6640	21	18	algebras	algebra	NOUN
ejpam-6640	21	19	”	"	PUNCT
ejpam-6640	22	1	[	[	X
ejpam-6640	22	2	4	4	NUM
ejpam-6640	22	3	]	]	PUNCT
ejpam-6640	22	4	,	,	PUNCT
ejpam-6640	22	5	”	"	PUNCT
ejpam-6640	22	6	modules	module	NOUN
ejpam-6640	22	7	and	and	CCONJ
ejpam-6640	22	8	rings	ring	NOUN
ejpam-6640	22	9	”	"	PUNCT
ejpam-6640	23	1	[	[	X
ejpam-6640	23	2	5	5	NUM
ejpam-6640	23	3	]	]	PUNCT
ejpam-6640	23	4	,	,	PUNCT
ejpam-6640	23	5	”	"	PUNCT
ejpam-6640	23	6	notes	note	NOUN
ejpam-6640	23	7	on	on	ADP
ejpam-6640	23	8	homological	homological	ADJ
ejpam-6640	23	9	algebras	algebra	NOUN
ejpam-6640	23	10	”	"	PUNCT
ejpam-6640	24	1	[	[	X
ejpam-6640	24	2	6	6	NUM
ejpam-6640	24	3	]	]	PUNCT
ejpam-6640	24	4	,	,	PUNCT
ejpam-6640	24	5	”	"	PUNCT
ejpam-6640	24	6	abelian	abelian	ADJ
ejpam-6640	24	7	categories	category	NOUN
ejpam-6640	24	8	”	"	PUNCT
ejpam-6640	25	1	[	[	X
ejpam-6640	25	2	7	7	NUM
ejpam-6640	25	3	]	]	PUNCT
ejpam-6640	25	4	,	,	PUNCT
ejpam-6640	25	5	”	"	PUNCT
ejpam-6640	25	6	des	des	X
ejpam-6640	25	7	catégories	catégorie	NOUN
ejpam-6640	25	8	abéliennes	abélienne	NOUN
ejpam-6640	25	9	”	"	PUNCT
ejpam-6640	26	1	[	[	X
ejpam-6640	26	2	8	8	NUM
ejpam-6640	26	3	]	]	PUNCT
ejpam-6640	26	4	,	,	PUNCT
ejpam-6640	26	5	”	"	PUNCT
ejpam-6640	26	6	an	an	DET
ejpam-6640	26	7	introduction	introduction	NOUN
ejpam-6640	26	8	to	to	ADP
ejpam-6640	26	9	homological	homological	ADJ
ejpam-6640	26	10	algebra	algebra	NOUN
ejpam-6640	26	11	”	"	PUNCT
ejpam-6640	27	1	[	[	X
ejpam-6640	27	2	9],”an	9],”an	NUM
ejpam-6640	27	3	introduction	introduction	NOUN
ejpam-6640	27	4	to	to	ADP
ejpam-6640	27	5	homological	homological	ADJ
ejpam-6640	27	6	algebra	algebra	NOUN
ejpam-6640	27	7	”	"	PUNCT
ejpam-6640	28	1	[	[	X
ejpam-6640	28	2	10	10	NUM
ejpam-6640	28	3	]	]	PUNCT
ejpam-6640	28	4	and	and	CCONJ
ejpam-6640	28	5	other	other	ADJ
ejpam-6640	28	6	important	important	ADJ
ejpam-6640	28	7	results	result	NOUN
ejpam-6640	28	8	on	on	ADP
ejpam-6640	28	9	abelian	abelian	ADJ
ejpam-6640	28	10	category	category	NOUN
ejpam-6640	28	11	and	and	CCONJ
ejpam-6640	28	12	homological	homological	ADJ
ejpam-6640	28	13	functors	functor	NOUN
ejpam-6640	28	14	by	by	ADP
ejpam-6640	28	15	the	the	DET
ejpam-6640	28	16	autors	autor	NOUN
ejpam-6640	28	17	:	:	PUNCT
ejpam-6640	28	18	elhadjousseynou	elhadjousseynou	NOUN
ejpam-6640	28	19	[	[	X
ejpam-6640	28	20	11	11	NUM
ejpam-6640	28	21	]	]	PUNCT
ejpam-6640	28	22	,	,	PUNCT
ejpam-6640	28	23	joseph	joseph	PROPN
ejpam-6640	28	24	.j	.j	PROPN
ejpam-6640	29	1	rotman	rotman	PROPN
ejpam-6640	30	1	[	[	X
ejpam-6640	30	2	12	12	NUM
ejpam-6640	30	3	]	]	PUNCT
ejpam-6640	30	4	,	,	PUNCT
ejpam-6640	31	1	[	[	X
ejpam-6640	31	2	13	13	NUM
ejpam-6640	31	3	]	]	PUNCT
ejpam-6640	31	4	,	,	PUNCT
ejpam-6640	31	5	bassirou	bassirou	ADJ
ejpam-6640	31	6	dembele	dembele	NOUN
ejpam-6640	32	1	[	[	X
ejpam-6640	32	2	14	14	NUM
ejpam-6640	32	3	]	]	PUNCT
ejpam-6640	32	4	,	,	PUNCT
ejpam-6640	32	5	ahmed	ahmed	PROPN
ejpam-6640	32	6	ould	ould	AUX
ejpam-6640	32	7	chbih	chbih	VERB
ejpam-6640	33	1	[	[	X
ejpam-6640	33	2	15	15	NUM
ejpam-6640	33	3	]	]	PUNCT
ejpam-6640	33	4	,	,	PUNCT
ejpam-6640	33	5	charles	charle	VERB
ejpam-6640	33	6	a	a	DET
ejpam-6640	33	7	weibel	weibel	NOUN
ejpam-6640	34	1	[	[	X
ejpam-6640	34	2	16	16	NUM
ejpam-6640	34	3	]	]	PUNCT
ejpam-6640	34	4	,	,	PUNCT
ejpam-6640	34	5	ahmed	ahmed	PROPN
ejpam-6640	34	6	ould	ould	AUX
ejpam-6640	34	7	chbih	chbih	VERB
ejpam-6640	34	8	et	et	PROPN
ejpam-6640	34	9	al	al	PROPN
ejpam-6640	35	1	[	[	X
ejpam-6640	35	2	17],[18	17],[18	NUM
ejpam-6640	35	3	]	]	PUNCT
ejpam-6640	35	4	and	and	CCONJ
ejpam-6640	35	5	moussa	moussa	PROPN
ejpam-6640	35	6	thiaw	thiaw	NOUN
ejpam-6640	35	7	[	[	X
ejpam-6640	35	8	19	19	NUM
ejpam-6640	35	9	]	]	PUNCT
ejpam-6640	35	10	.	.	PUNCT
ejpam-6640	36	1	thus	thus	ADV
ejpam-6640	36	2	,	,	PUNCT
ejpam-6640	36	3	the	the	DET
ejpam-6640	36	4	article	article	NOUN
ejpam-6640	36	5	is	be	AUX
ejpam-6640	36	6	structured	structure	VERB
ejpam-6640	36	7	as	as	SCONJ
ejpam-6640	36	8	follows	follow	VERB
ejpam-6640	36	9	:	:	PUNCT
ejpam-6640	36	10	in	in	ADP
ejpam-6640	36	11	section	section	NOUN
ejpam-6640	36	12	1	1	NUM
ejpam-6640	36	13	titled	title	VERB
ejpam-6640	36	14	preliminary	preliminary	ADJ
ejpam-6640	36	15	results	result	NOUN
ejpam-6640	36	16	,	,	PUNCT
ejpam-6640	36	17	we	we	PRON
ejpam-6640	36	18	provided	provide	VERB
ejpam-6640	36	19	the	the	DET
ejpam-6640	36	20	following	follow	VERB
ejpam-6640	36	21	definitions	definition	NOUN
ejpam-6640	36	22	:	:	PUNCT
ejpam-6640	36	23	abelian	abelian	ADJ
ejpam-6640	36	24	category	category	NOUN
ejpam-6640	36	25	,	,	PUNCT
ejpam-6640	36	26	balanced	balanced	ADJ
ejpam-6640	36	27	category	category	NOUN
ejpam-6640	36	28	,	,	PUNCT
ejpam-6640	36	29	comp(a	comp(a	NOUN
ejpam-6640	36	30	)	)	PUNCT
ejpam-6640	36	31	,	,	PUNCT
ejpam-6640	36	32	exact	exact	ADJ
ejpam-6640	36	33	sequence	sequence	NOUN
ejpam-6640	36	34	in	in	ADP
ejpam-6640	36	35	comp(a	comp(a	NOUN
ejpam-6640	36	36	)	)	PUNCT
ejpam-6640	36	37	.	.	PUNCT
ejpam-6640	37	1	and	and	CCONJ
ejpam-6640	37	2	we	we	PRON
ejpam-6640	37	3	presented	present	VERB
ejpam-6640	37	4	some	some	DET
ejpam-6640	37	5	preliminary	preliminary	ADJ
ejpam-6640	37	6	results	result	NOUN
ejpam-6640	37	7	.	.	PUNCT
ejpam-6640	38	1	in	in	ADP
ejpam-6640	38	2	section	section	NOUN
ejpam-6640	38	3	2	2	NUM
ejpam-6640	38	4	,	,	PUNCT
ejpam-6640	38	5	titled	title	VERB
ejpam-6640	38	6	the	the	DET
ejpam-6640	38	7	exactness	exactness	NOUN
ejpam-6640	38	8	of	of	ADP
ejpam-6640	38	9	the	the	DET
ejpam-6640	38	10	functors	functors	PROPN
ejpam-6640	38	11	homa	homa	PROPN
ejpam-6640	38	12	(	(	PUNCT
ejpam-6640	38	13	x,−	x,−	PROPN
ejpam-6640	38	14	)	)	PUNCT
ejpam-6640	38	15	and	and	CCONJ
ejpam-6640	38	16	homa	homa	NOUN
ejpam-6640	38	17	(	(	PUNCT
ejpam-6640	38	18	−	−	PROPN
ejpam-6640	38	19	,	,	PUNCT
ejpam-6640	38	20	x	x	NOUN
ejpam-6640	38	21	)	)	PUNCT
ejpam-6640	38	22	,	,	PUNCT
ejpam-6640	38	23	where	where	SCONJ
ejpam-6640	38	24	a	a	PRON
ejpam-6640	38	25	is	be	AUX
ejpam-6640	38	26	a	a	DET
ejpam-6640	38	27	balanced	balanced	ADJ
ejpam-6640	38	28	abelian	abelian	ADJ
ejpam-6640	38	29	category	category	NOUN
ejpam-6640	38	30	and	and	CCONJ
ejpam-6640	38	31	x	x	X
ejpam-6640	38	32	is	be	AUX
ejpam-6640	38	33	an	an	DET
ejpam-6640	38	34	object	object	NOUN
ejpam-6640	38	35	in	in	ADP
ejpam-6640	38	36	a	a	PRON
ejpam-6640	38	37	.	.	PUNCT
ejpam-6640	39	1	the	the	DET
ejpam-6640	39	2	following	follow	VERB
ejpam-6640	39	3	results	result	NOUN
ejpam-6640	39	4	have	have	AUX
ejpam-6640	39	5	been	be	AUX
ejpam-6640	39	6	shown	show	VERB
ejpam-6640	39	7	:	:	PUNCT
ejpam-6640	39	8	(	(	PUNCT
ejpam-6640	39	9	i	i	NOUN
ejpam-6640	39	10	)	)	PUNCT
ejpam-6640	39	11	let	let	VERB
ejpam-6640	39	12	a	a	PRON
ejpam-6640	39	13	be	be	AUX
ejpam-6640	39	14	a	a	DET
ejpam-6640	39	15	balanced	balanced	ADJ
ejpam-6640	39	16	abelian	abelian	ADJ
ejpam-6640	39	17	category	category	NOUN
ejpam-6640	39	18	and	and	CCONJ
ejpam-6640	39	19	x	x	SYM
ejpam-6640	39	20	an	an	DET
ejpam-6640	39	21	object	object	NOUN
ejpam-6640	39	22	in	in	ADP
ejpam-6640	39	23	a	a	PRON
ejpam-6640	39	24	.	.	PUNCT
ejpam-6640	40	1	then	then	ADV
ejpam-6640	40	2	the	the	DET
ejpam-6640	40	3	covariant	covariant	PROPN
ejpam-6640	40	4	functor	functor	PROPN
ejpam-6640	40	5	denoted	denote	VERB
ejpam-6640	40	6	homa	homa	NOUN
ejpam-6640	40	7	(	(	PUNCT
ejpam-6640	40	8	x,−	x,−	PROPN
ejpam-6640	40	9	)	)	PUNCT
ejpam-6640	40	10	:	:	PUNCT
ejpam-6640	40	11	a	a	DET
ejpam-6640	40	12	−→	−→	PROPN
ejpam-6640	40	13	ab	ab	PROPN
ejpam-6640	40	14	,	,	PUNCT
ejpam-6640	40	15	defined	define	VERB
ejpam-6640	40	16	by	by	ADP
ejpam-6640	40	17	:	:	PUNCT
ejpam-6640	40	18	(	(	PUNCT
ejpam-6640	40	19	a	a	X
ejpam-6640	40	20	)	)	PUNCT
ejpam-6640	40	21	∀y	∀y	PROPN
ejpam-6640	40	22	∈	∈	PROPN
ejpam-6640	40	23	ob(a	ob(a	NUM
ejpam-6640	40	24	)	)	PUNCT
ejpam-6640	40	25	,	,	PUNCT
ejpam-6640	40	26	homa	homa	NOUN
ejpam-6640	40	27	(	(	PUNCT
ejpam-6640	40	28	x,−)(y	x,−)(y	PROPN
ejpam-6640	40	29	)	)	PUNCT
ejpam-6640	41	1	=	=	SYM
ejpam-6640	41	2	homa	homa	NOUN
ejpam-6640	41	3	(	(	PUNCT
ejpam-6640	41	4	x	x	X
ejpam-6640	41	5	,	,	PUNCT
ejpam-6640	41	6	y	y	PROPN
ejpam-6640	41	7	)	)	PUNCT
ejpam-6640	41	8	∈	∈	PROPN
ejpam-6640	41	9	ob(ab	ob(ab	PROPN
ejpam-6640	41	10	)	)	PUNCT
ejpam-6640	41	11	;	;	PUNCT
ejpam-6640	41	12	(	(	PUNCT
ejpam-6640	41	13	b	b	X
ejpam-6640	41	14	)	)	PUNCT
ejpam-6640	41	15	∀f	∀f	PROPN
ejpam-6640	41	16	∈	∈	PROPN
ejpam-6640	41	17	homa	homa	NOUN
ejpam-6640	41	18	(	(	PUNCT
ejpam-6640	41	19	y	y	PROPN
ejpam-6640	41	20	,	,	PUNCT
ejpam-6640	41	21	z	z	NOUN
ejpam-6640	41	22	)	)	PUNCT
ejpam-6640	41	23	,	,	PUNCT
ejpam-6640	41	24	homa	homa	NOUN
ejpam-6640	41	25	(	(	PUNCT
ejpam-6640	41	26	x,−)(f	x,−)(f	PROPN
ejpam-6640	41	27	)	)	PUNCT
ejpam-6640	41	28	=	=	SYM
ejpam-6640	41	29	homa	homa	NOUN
ejpam-6640	41	30	(	(	PUNCT
ejpam-6640	41	31	x	x	X
ejpam-6640	41	32	,	,	PUNCT
ejpam-6640	41	33	f	f	X
ejpam-6640	41	34	)	)	PUNCT
ejpam-6640	41	35	=	=	NOUN
ejpam-6640	41	36	f∗	f∗	NOUN
ejpam-6640	41	37	:	:	PUNCT
ejpam-6640	41	38	homa	homa	NOUN
ejpam-6640	41	39	(	(	PUNCT
ejpam-6640	41	40	x	x	X
ejpam-6640	41	41	,	,	PUNCT
ejpam-6640	41	42	y	y	PROPN
ejpam-6640	41	43	)	)	PUNCT
ejpam-6640	41	44	−→	−→	PROPN
ejpam-6640	41	45	homa	homa	NOUN
ejpam-6640	41	46	(	(	PUNCT
ejpam-6640	41	47	x	x	X
ejpam-6640	41	48	,	,	PUNCT
ejpam-6640	41	49	z	z	NOUN
ejpam-6640	41	50	)	)	PUNCT
ejpam-6640	41	51	ϕ	ϕ	PROPN
ejpam-6640	41	52	7−→	7−→	PROPN
ejpam-6640	41	53	f	f	PROPN
ejpam-6640	41	54	◦	◦	NOUN
ejpam-6640	41	55	ϕ	ϕ	NOUN
ejpam-6640	41	56	;	;	PUNCT
ejpam-6640	41	57	is	be	AUX
ejpam-6640	41	58	additive	additive	ADJ
ejpam-6640	41	59	,	,	PUNCT
ejpam-6640	41	60	left	left	ADJ
ejpam-6640	41	61	-	-	PUNCT
ejpam-6640	41	62	exact	exact	NOUN
ejpam-6640	41	63	functor	functor	NOUN
ejpam-6640	42	1	and	and	CCONJ
ejpam-6640	42	2	it	it	PRON
ejpam-6640	42	3	is	be	AUX
ejpam-6640	42	4	exact	exact	ADJ
ejpam-6640	42	5	if	if	SCONJ
ejpam-6640	43	1	and	and	CCONJ
ejpam-6640	43	2	only	only	ADV
ejpam-6640	43	3	if	if	SCONJ
ejpam-6640	43	4	x	x	PRON
ejpam-6640	43	5	is	be	AUX
ejpam-6640	43	6	a	a	DET
ejpam-6640	43	7	projective	projective	ADJ
ejpam-6640	43	8	object	object	NOUN
ejpam-6640	43	9	in	in	ADP
ejpam-6640	43	10	a	a	PRON
ejpam-6640	43	11	.	.	PUNCT
ejpam-6640	44	1	(	(	PUNCT
ejpam-6640	44	2	ii	ii	NOUN
ejpam-6640	44	3	)	)	PUNCT
ejpam-6640	44	4	let	let	VERB
ejpam-6640	44	5	a	a	PRON
ejpam-6640	44	6	be	be	AUX
ejpam-6640	44	7	a	a	DET
ejpam-6640	44	8	balanced	balanced	ADJ
ejpam-6640	44	9	abelian	abelian	ADJ
ejpam-6640	44	10	category	category	NOUN
ejpam-6640	44	11	and	and	CCONJ
ejpam-6640	44	12	x	x	SYM
ejpam-6640	44	13	an	an	DET
ejpam-6640	44	14	object	object	NOUN
ejpam-6640	44	15	in	in	ADP
ejpam-6640	44	16	a	a	PRON
ejpam-6640	44	17	.	.	PUNCT
ejpam-6640	45	1	then	then	ADV
ejpam-6640	45	2	the	the	DET
ejpam-6640	45	3	contravariant	contravariant	PROPN
ejpam-6640	45	4	functor	functor	PROPN
ejpam-6640	45	5	denoted	denote	VERB
ejpam-6640	45	6	homa	homa	NOUN
ejpam-6640	45	7	(	(	PUNCT
ejpam-6640	45	8	−	−	PROPN
ejpam-6640	45	9	,	,	PUNCT
ejpam-6640	45	10	x	x	NOUN
ejpam-6640	45	11	)	)	PUNCT
ejpam-6640	45	12	:	:	PUNCT
ejpam-6640	45	13	a	a	DET
ejpam-6640	45	14	−→	−→	PROPN
ejpam-6640	45	15	ab	ab	PROPN
ejpam-6640	45	16	,	,	PUNCT
ejpam-6640	45	17	defined	define	VERB
ejpam-6640	45	18	by	by	ADP
ejpam-6640	45	19	:	:	PUNCT
ejpam-6640	45	20	(	(	PUNCT
ejpam-6640	45	21	a	a	X
ejpam-6640	45	22	)	)	PUNCT
ejpam-6640	45	23	∀y	∀y	PROPN
ejpam-6640	45	24	∈	∈	PROPN
ejpam-6640	45	25	ob(a	ob(a	NUM
ejpam-6640	45	26	)	)	PUNCT
ejpam-6640	45	27	,	,	PUNCT
ejpam-6640	45	28	homa	homa	NOUN
ejpam-6640	45	29	(	(	PUNCT
ejpam-6640	45	30	−	−	PROPN
ejpam-6640	45	31	,	,	PUNCT
ejpam-6640	45	32	x)(y	x)(y	PUNCT
ejpam-6640	45	33	)	)	PUNCT
ejpam-6640	46	1	=	=	PUNCT
ejpam-6640	46	2	homa	homa	NOUN
ejpam-6640	46	3	(	(	PUNCT
ejpam-6640	46	4	y	y	NOUN
ejpam-6640	46	5	,	,	PUNCT
ejpam-6640	46	6	x	x	NOUN
ejpam-6640	46	7	)	)	PUNCT
ejpam-6640	46	8	∈	∈	PROPN
ejpam-6640	46	9	ob(ab	ob(ab	PROPN
ejpam-6640	46	10	)	)	PUNCT
ejpam-6640	46	11	(	(	PUNCT
ejpam-6640	46	12	b	b	X
ejpam-6640	46	13	)	)	PUNCT
ejpam-6640	46	14	∀f	∀f	PROPN
ejpam-6640	46	15	∈	∈	PROPN
ejpam-6640	46	16	homa	homa	NOUN
ejpam-6640	46	17	(	(	PUNCT
ejpam-6640	46	18	y	y	PROPN
ejpam-6640	46	19	,	,	PUNCT
ejpam-6640	46	20	z	z	NOUN
ejpam-6640	46	21	)	)	PUNCT
ejpam-6640	46	22	,	,	PUNCT
ejpam-6640	46	23	homa	homa	NOUN
ejpam-6640	46	24	(	(	PUNCT
ejpam-6640	46	25	f	f	PROPN
ejpam-6640	46	26	,	,	PUNCT
ejpam-6640	46	27	x	x	NOUN
ejpam-6640	46	28	)	)	PUNCT
ejpam-6640	46	29	=	=	SYM
ejpam-6640	46	30	f∗	f∗	NOUN
ejpam-6640	46	31	:	:	PUNCT
ejpam-6640	46	32	homa	homa	NOUN
ejpam-6640	46	33	(	(	PUNCT
ejpam-6640	46	34	z	z	NOUN
ejpam-6640	46	35	,	,	PUNCT
ejpam-6640	46	36	x	x	NOUN
ejpam-6640	46	37	)	)	PUNCT
ejpam-6640	46	38	−→	−→	ADJ
ejpam-6640	46	39	homa	homa	NOUN
ejpam-6640	46	40	(	(	PUNCT
ejpam-6640	46	41	y	y	NOUN
ejpam-6640	46	42	,	,	PUNCT
ejpam-6640	46	43	x	x	NOUN
ejpam-6640	46	44	)	)	PUNCT
ejpam-6640	46	45	ϕ	ϕ	PROPN
ejpam-6640	46	46	7−→	7−→	PROPN
ejpam-6640	46	47	ϕ	ϕ	PROPN
ejpam-6640	46	48	◦	◦	NOUN
ejpam-6640	46	49	f	f	PROPN
ejpam-6640	46	50	a.	a.	PROPN
ejpam-6640	46	51	diallo	diallo	PROPN
ejpam-6640	46	52	,	,	PUNCT
ejpam-6640	46	53	m.	m.	PROPN
ejpam-6640	46	54	b.	b.	PROPN
ejpam-6640	46	55	f.	f.	PROPN
ejpam-6640	46	56	b.	b.	PROPN
ejpam-6640	46	57	maaouia	maaouia	PROPN
ejpam-6640	46	58	,	,	PUNCT
ejpam-6640	46	59	m.	m.	NOUN
ejpam-6640	46	60	sanghare	sanghare	PROPN
ejpam-6640	46	61	/	/	SYM
ejpam-6640	46	62	eur	eur	PROPN
ejpam-6640	46	63	.	.	PUNCT
ejpam-6640	47	1	j.	j.	PROPN
ejpam-6640	47	2	pure	pure	PROPN
ejpam-6640	47	3	appl	appl	PROPN
ejpam-6640	47	4	.	.	PROPN
ejpam-6640	47	5	math	math	PROPN
ejpam-6640	47	6	,	,	PUNCT
ejpam-6640	47	7	18	18	NUM
ejpam-6640	47	8	(	(	PUNCT
ejpam-6640	47	9	4	4	NUM
ejpam-6640	47	10	)	)	PUNCT
ejpam-6640	47	11	(	(	PUNCT
ejpam-6640	47	12	2025	2025	NUM
ejpam-6640	47	13	)	)	PUNCT
ejpam-6640	47	14	,	,	PUNCT
ejpam-6640	47	15	6640	6640	NUM
ejpam-6640	47	16	3	3	NUM
ejpam-6640	47	17	of	of	ADP
ejpam-6640	47	18	28	28	NUM
ejpam-6640	47	19	is	be	AUX
ejpam-6640	47	20	additive	additive	ADJ
ejpam-6640	47	21	,	,	PUNCT
ejpam-6640	47	22	left	left	ADJ
ejpam-6640	47	23	-	-	PUNCT
ejpam-6640	47	24	exact	exact	NOUN
ejpam-6640	47	25	functor	functor	NOUN
ejpam-6640	48	1	and	and	CCONJ
ejpam-6640	48	2	it	it	PRON
ejpam-6640	48	3	is	be	AUX
ejpam-6640	48	4	exact	exact	ADJ
ejpam-6640	48	5	if	if	SCONJ
ejpam-6640	49	1	and	and	CCONJ
ejpam-6640	49	2	only	only	ADV
ejpam-6640	49	3	if	if	SCONJ
ejpam-6640	49	4	x	x	PRON
ejpam-6640	49	5	is	be	AUX
ejpam-6640	49	6	an	an	DET
ejpam-6640	49	7	injective	injective	ADJ
ejpam-6640	49	8	object	object	NOUN
ejpam-6640	49	9	in	in	ADP
ejpam-6640	49	10	a	a	PRON
ejpam-6640	49	11	.	.	PUNCT
ejpam-6640	50	1	in	in	ADP
ejpam-6640	50	2	section	section	NOUN
ejpam-6640	50	3	3	3	NUM
ejpam-6640	50	4	,	,	PUNCT
ejpam-6640	50	5	titled	title	VERB
ejpam-6640	50	6	the	the	DET
ejpam-6640	50	7	exactness	exactness	NOUN
ejpam-6640	50	8	of	of	ADP
ejpam-6640	50	9	the	the	DET
ejpam-6640	50	10	functors	functors	PROPN
ejpam-6640	50	11	homcomp(a	homcomp(a	PROPN
ejpam-6640	50	12	)	)	PUNCT
ejpam-6640	50	13	(	(	PUNCT
ejpam-6640	50	14	x,−	x,−	PROPN
ejpam-6640	50	15	)	)	PUNCT
ejpam-6640	50	16	and	and	CCONJ
ejpam-6640	50	17	homcomp(a	homcomp(a	NOUN
ejpam-6640	50	18	)	)	PUNCT
ejpam-6640	50	19	(	(	PUNCT
ejpam-6640	50	20	−	−	PROPN
ejpam-6640	50	21	,	,	PUNCT
ejpam-6640	50	22	x	x	NOUN
ejpam-6640	50	23	)	)	PUNCT
ejpam-6640	50	24	where	where	SCONJ
ejpam-6640	50	25	a	a	PRON
ejpam-6640	50	26	is	be	AUX
ejpam-6640	50	27	a	a	DET
ejpam-6640	50	28	balanced	balanced	ADJ
ejpam-6640	50	29	abelian	abelian	ADJ
ejpam-6640	50	30	category	category	NOUN
ejpam-6640	50	31	and	and	CCONJ
ejpam-6640	50	32	x	x	X
ejpam-6640	50	33	is	be	AUX
ejpam-6640	50	34	an	an	DET
ejpam-6640	50	35	object	object	NOUN
ejpam-6640	50	36	in	in	ADP
ejpam-6640	50	37	a	a	PRON
ejpam-6640	50	38	.	.	PUNCT
ejpam-6640	51	1	we	we	PRON
ejpam-6640	51	2	proved	prove	VERB
ejpam-6640	51	3	the	the	DET
ejpam-6640	51	4	following	follow	VERB
ejpam-6640	51	5	results	result	NOUN
ejpam-6640	51	6	:	:	PUNCT
ejpam-6640	51	7	(	(	PUNCT
ejpam-6640	51	8	i	i	NOUN
ejpam-6640	51	9	)	)	PUNCT
ejpam-6640	51	10	let	let	VERB
ejpam-6640	51	11	a	a	PRON
ejpam-6640	51	12	be	be	AUX
ejpam-6640	51	13	a	a	DET
ejpam-6640	51	14	balanced	balanced	ADJ
ejpam-6640	51	15	abelian	abelian	ADJ
ejpam-6640	51	16	category	category	NOUN
ejpam-6640	51	17	and	and	CCONJ
ejpam-6640	51	18	x	x	ADP
ejpam-6640	51	19	an	an	DET
ejpam-6640	51	20	object	object	NOUN
ejpam-6640	51	21	of	of	ADP
ejpam-6640	51	22	a	a	PRON
ejpam-6640	51	23	.	.	PUNCT
ejpam-6640	52	1	then	then	ADV
ejpam-6640	52	2	:	:	PUNCT
ejpam-6640	52	3	(	(	PUNCT
ejpam-6640	52	4	a	a	X
ejpam-6640	52	5	)	)	PUNCT
ejpam-6640	52	6	the	the	DET
ejpam-6640	52	7	functor	functor	PROPN
ejpam-6640	52	8	homcomp(a	homcomp(a	PROPN
ejpam-6640	52	9	)	)	PUNCT
ejpam-6640	52	10	(	(	PUNCT
ejpam-6640	52	11	x,−	x,−	PROPN
ejpam-6640	52	12	)	)	PUNCT
ejpam-6640	52	13	:	:	PUNCT
ejpam-6640	52	14	comp(a	comp(a	NOUN
ejpam-6640	52	15	)	)	PUNCT
ejpam-6640	52	16	→	→	SYM
ejpam-6640	52	17	comp(ab	comp(ab	NOUN
ejpam-6640	52	18	)	)	PUNCT
ejpam-6640	52	19	is	be	AUX
ejpam-6640	52	20	a	a	DET
ejpam-6640	52	21	covariant	covariant	NOUN
ejpam-6640	52	22	,	,	PUNCT
ejpam-6640	52	23	additive	additive	NOUN
ejpam-6640	52	24	,	,	PUNCT
ejpam-6640	52	25	and	and	CCONJ
ejpam-6640	52	26	left	left	ADJ
ejpam-6640	52	27	-	-	PUNCT
ejpam-6640	52	28	exact	exact	NOUN
ejpam-6640	52	29	functor	functor	NOUN
ejpam-6640	52	30	;	;	PUNCT
ejpam-6640	52	31	(	(	PUNCT
ejpam-6640	52	32	b	b	X
ejpam-6640	52	33	)	)	PUNCT
ejpam-6640	52	34	the	the	DET
ejpam-6640	52	35	functor	functor	PROPN
ejpam-6640	52	36	homcomp(a	homcomp(a	PROPN
ejpam-6640	52	37	)	)	PUNCT
ejpam-6640	52	38	(	(	PUNCT
ejpam-6640	52	39	x,−	x,−	PROPN
ejpam-6640	52	40	)	)	PUNCT
ejpam-6640	52	41	:	:	PUNCT
ejpam-6640	52	42	comp(a	comp(a	NOUN
ejpam-6640	52	43	)	)	PUNCT
ejpam-6640	52	44	→	→	SYM
ejpam-6640	52	45	comp(ab	comp(ab	NOUN
ejpam-6640	52	46	)	)	PUNCT
ejpam-6640	52	47	is	be	AUX
ejpam-6640	52	48	exact	exact	ADJ
ejpam-6640	53	1	if	if	SCONJ
ejpam-6640	53	2	and	and	CCONJ
ejpam-6640	53	3	only	only	ADV
ejpam-6640	53	4	if	if	SCONJ
ejpam-6640	53	5	x	x	PRON
ejpam-6640	53	6	is	be	AUX
ejpam-6640	53	7	a	a	DET
ejpam-6640	53	8	projective	projective	ADJ
ejpam-6640	53	9	object	object	NOUN
ejpam-6640	53	10	in	in	ADP
ejpam-6640	53	11	a	a	PRON
ejpam-6640	53	12	.	.	PUNCT
ejpam-6640	54	1	(	(	PUNCT
ejpam-6640	54	2	ii	ii	NOUN
ejpam-6640	54	3	)	)	PUNCT
ejpam-6640	54	4	let	let	VERB
ejpam-6640	54	5	a	a	PRON
ejpam-6640	54	6	be	be	AUX
ejpam-6640	54	7	a	a	DET
ejpam-6640	54	8	balanced	balanced	ADJ
ejpam-6640	54	9	abelian	abelian	ADJ
ejpam-6640	54	10	category	category	NOUN
ejpam-6640	54	11	and	and	CCONJ
ejpam-6640	54	12	x	x	ADP
ejpam-6640	54	13	an	an	DET
ejpam-6640	54	14	object	object	NOUN
ejpam-6640	54	15	of	of	ADP
ejpam-6640	54	16	a	a	PRON
ejpam-6640	54	17	.	.	PUNCT
ejpam-6640	55	1	then	then	ADV
ejpam-6640	55	2	:	:	PUNCT
ejpam-6640	55	3	(	(	PUNCT
ejpam-6640	55	4	a	a	X
ejpam-6640	55	5	)	)	PUNCT
ejpam-6640	55	6	the	the	DET
ejpam-6640	55	7	functor	functor	PROPN
ejpam-6640	55	8	homcomp(a	homcomp(a	PROPN
ejpam-6640	55	9	)	)	PUNCT
ejpam-6640	55	10	(	(	PUNCT
ejpam-6640	55	11	−	−	PROPN
ejpam-6640	55	12	,	,	PUNCT
ejpam-6640	55	13	x	x	NOUN
ejpam-6640	55	14	)	)	PUNCT
ejpam-6640	55	15	:	:	PUNCT
ejpam-6640	55	16	comp(a	comp(a	NOUN
ejpam-6640	55	17	)	)	PUNCT
ejpam-6640	55	18	→	→	SYM
ejpam-6640	55	19	comp(ab	comp(ab	NOUN
ejpam-6640	55	20	)	)	PUNCT
ejpam-6640	55	21	is	be	AUX
ejpam-6640	55	22	a	a	DET
ejpam-6640	55	23	contravariant	contravariant	ADJ
ejpam-6640	55	24	,	,	PUNCT
ejpam-6640	55	25	additive	additive	NOUN
ejpam-6640	55	26	,	,	PUNCT
ejpam-6640	55	27	and	and	CCONJ
ejpam-6640	55	28	left	left	ADJ
ejpam-6640	55	29	-	-	PUNCT
ejpam-6640	55	30	exact	exact	NOUN
ejpam-6640	55	31	functor	functor	NOUN
ejpam-6640	55	32	;	;	PUNCT
ejpam-6640	55	33	(	(	PUNCT
ejpam-6640	55	34	b	b	X
ejpam-6640	55	35	)	)	PUNCT
ejpam-6640	55	36	the	the	DET
ejpam-6640	55	37	functor	functor	PROPN
ejpam-6640	55	38	homcomp(a	homcomp(a	PROPN
ejpam-6640	55	39	)	)	PUNCT
ejpam-6640	55	40	(	(	PUNCT
ejpam-6640	55	41	−	−	PROPN
ejpam-6640	55	42	,	,	PUNCT
ejpam-6640	55	43	x	x	NOUN
ejpam-6640	55	44	)	)	PUNCT
ejpam-6640	55	45	:	:	PUNCT
ejpam-6640	55	46	comp(a	comp(a	NOUN
ejpam-6640	55	47	)	)	PUNCT
ejpam-6640	55	48	→	→	SYM
ejpam-6640	55	49	comp(ab	comp(ab	NOUN
ejpam-6640	55	50	)	)	PUNCT
ejpam-6640	55	51	is	be	AUX
ejpam-6640	55	52	exact	exact	ADJ
ejpam-6640	56	1	if	if	SCONJ
ejpam-6640	56	2	and	and	CCONJ
ejpam-6640	56	3	only	only	ADV
ejpam-6640	56	4	if	if	SCONJ
ejpam-6640	56	5	x	x	PRON
ejpam-6640	56	6	is	be	AUX
ejpam-6640	56	7	an	an	DET
ejpam-6640	56	8	injective	injective	ADJ
ejpam-6640	56	9	object	object	NOUN
ejpam-6640	56	10	in	in	ADP
ejpam-6640	56	11	a	a	PRON
ejpam-6640	56	12	.	.	PUNCT
ejpam-6640	57	1	in	in	ADP
ejpam-6640	57	2	section	section	NOUN
ejpam-6640	57	3	4	4	NUM
ejpam-6640	57	4	,	,	PUNCT
ejpam-6640	57	5	we	we	PRON
ejpam-6640	57	6	studied	study	VERB
ejpam-6640	57	7	the	the	DET
ejpam-6640	57	8	homological	homological	ADJ
ejpam-6640	57	9	functors	functor	NOUN
ejpam-6640	57	10	of	of	ADP
ejpam-6640	57	11	degree	degree	NOUN
ejpam-6640	57	12	n	n	CCONJ
ejpam-6640	57	13	:	:	PUNCT
ejpam-6640	57	14	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	57	15	)	)	PUNCT
ejpam-6640	57	16	,	,	PUNCT
ejpam-6640	57	17	h̃n(−	h̃n(−	PROPN
ejpam-6640	57	18	,	,	PUNCT
ejpam-6640	57	19	x	x	NOUN
ejpam-6640	57	20	)	)	PUNCT
ejpam-6640	57	21	:	:	PUNCT
ejpam-6640	57	22	comp(a	comp(a	NOUN
ejpam-6640	57	23	)	)	PUNCT
ejpam-6640	57	24	→	→	SYM
ejpam-6640	57	25	ab	ab	X
ejpam-6640	57	26	where	where	SCONJ
ejpam-6640	57	27	a	a	PRON
ejpam-6640	57	28	is	be	AUX
ejpam-6640	57	29	a	a	DET
ejpam-6640	57	30	balanced	balanced	ADJ
ejpam-6640	57	31	abelian	abelian	ADJ
ejpam-6640	57	32	category	category	NOUN
ejpam-6640	57	33	and	and	CCONJ
ejpam-6640	57	34	n	n	PROPN
ejpam-6640	57	35	is	be	AUX
ejpam-6640	57	36	an	an	DET
ejpam-6640	57	37	integer	integer	NOUN
ejpam-6640	57	38	in	in	ADP
ejpam-6640	57	39	z.	z.	PROPN
ejpam-6640	58	1	we	we	PRON
ejpam-6640	58	2	proved	prove	VERB
ejpam-6640	58	3	the	the	DET
ejpam-6640	58	4	following	follow	VERB
ejpam-6640	58	5	results	result	NOUN
ejpam-6640	58	6	:	:	PUNCT
ejpam-6640	58	7	(	(	PUNCT
ejpam-6640	58	8	i	i	NOUN
ejpam-6640	58	9	)	)	PUNCT
ejpam-6640	58	10	the	the	DET
ejpam-6640	58	11	functor	functor	PROPN
ejpam-6640	58	12	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	58	13	)	)	PUNCT
ejpam-6640	58	14	is	be	AUX
ejpam-6640	58	15	a	a	DET
ejpam-6640	58	16	covariant	covariant	ADJ
ejpam-6640	58	17	additive	additive	ADJ
ejpam-6640	58	18	functor	functor	NOUN
ejpam-6640	58	19	.	.	PUNCT
ejpam-6640	59	1	(	(	PUNCT
ejpam-6640	59	2	ii	ii	NOUN
ejpam-6640	59	3	)	)	PUNCT
ejpam-6640	59	4	let	let	VERB
ejpam-6640	59	5	(	(	PUNCT
ejpam-6640	59	6	0	0	NUM
ejpam-6640	59	7	)	)	PUNCT
ejpam-6640	59	8	//	//	NOUN
ejpam-6640	60	1	(	(	PUNCT
ejpam-6640	60	2	y	y	PROPN
ejpam-6640	60	3	,	,	PUNCT
ejpam-6640	60	4	α	α	NOUN
ejpam-6640	60	5	)	)	PUNCT
ejpam-6640	60	6	f	f	PROPN
ejpam-6640	60	7	//	//	X
ejpam-6640	60	8	(	(	PUNCT
ejpam-6640	60	9	z	z	NOUN
ejpam-6640	60	10	,	,	PUNCT
ejpam-6640	60	11	β	β	NOUN
ejpam-6640	60	12	)	)	PUNCT
ejpam-6640	60	13	g	g	PROPN
ejpam-6640	60	14	//	//	SYM
ejpam-6640	60	15	(	(	PUNCT
ejpam-6640	60	16	t	t	PROPN
ejpam-6640	60	17	,	,	PUNCT
ejpam-6640	60	18	γ	γ	PROPN
ejpam-6640	60	19	)	)	PUNCT
ejpam-6640	60	20	//	//	NOUN
ejpam-6640	60	21	(	(	PUNCT
ejpam-6640	60	22	0	0	NUM
ejpam-6640	60	23	)	)	PUNCT
ejpam-6640	60	24	be	be	AUX
ejpam-6640	60	25	a	a	DET
ejpam-6640	60	26	short	short	ADJ
ejpam-6640	60	27	exact	exact	ADJ
ejpam-6640	60	28	sequence	sequence	NOUN
ejpam-6640	60	29	of	of	ADP
ejpam-6640	60	30	morphisms	morphism	NOUN
ejpam-6640	60	31	in	in	ADP
ejpam-6640	60	32	comp(a	comp(a	NOUN
ejpam-6640	60	33	)	)	PUNCT
ejpam-6640	60	34	,	,	PUNCT
ejpam-6640	60	35	where	where	SCONJ
ejpam-6640	60	36	x	x	PRON
ejpam-6640	60	37	is	be	AUX
ejpam-6640	60	38	a	a	DET
ejpam-6640	60	39	projective	projective	ADJ
ejpam-6640	60	40	object	object	NOUN
ejpam-6640	60	41	in	in	ADP
ejpam-6640	60	42	a	a	PRON
ejpam-6640	60	43	and	and	CCONJ
ejpam-6640	60	44	a	a	PRON
ejpam-6640	60	45	is	be	AUX
ejpam-6640	60	46	a	a	DET
ejpam-6640	60	47	balanced	balanced	ADJ
ejpam-6640	60	48	abelian	abelian	ADJ
ejpam-6640	60	49	category	category	NOUN
ejpam-6640	60	50	.	.	PUNCT
ejpam-6640	61	1	then	then	ADV
ejpam-6640	61	2	:	:	PUNCT
ejpam-6640	61	3	(	(	PUNCT
ejpam-6640	61	4	a	a	X
ejpam-6640	61	5	)	)	PUNCT
ejpam-6640	61	6	we	we	PRON
ejpam-6640	61	7	call	call	VERB
ejpam-6640	61	8	the	the	DET
ejpam-6640	61	9	morphism	morphism	NOUN
ejpam-6640	61	10	of	of	ADP
ejpam-6640	61	11	connection	connection	NOUN
ejpam-6640	61	12	associated	associate	VERB
ejpam-6640	61	13	to	to	ADP
ejpam-6640	61	14	the	the	DET
ejpam-6640	61	15	functor	functor	PROPN
ejpam-6640	61	16	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	61	17	)	)	PUNCT
ejpam-6640	61	18	,	,	PUNCT
ejpam-6640	61	19	denoted	denote	VERB
ejpam-6640	61	20	by	by	ADP
ejpam-6640	61	21	λn	λn	NOUN
ejpam-6640	61	22	,	,	PUNCT
ejpam-6640	61	23	the	the	DET
ejpam-6640	61	24	morphism	morphism	NOUN
ejpam-6640	61	25	defined	define	VERB
ejpam-6640	61	26	by	by	ADP
ejpam-6640	61	27	:	:	PUNCT
ejpam-6640	61	28	λn	λn	NOUN
ejpam-6640	61	29	:	:	PUNCT
ejpam-6640	61	30	h̃n(x,−)((t	h̃n(x,−)((t	PROPN
ejpam-6640	61	31	,	,	PUNCT
ejpam-6640	61	32	γ	γ	NOUN
ejpam-6640	61	33	)	)	PUNCT
ejpam-6640	61	34	)	)	PUNCT
ejpam-6640	62	1	−→	−→	NOUN
ejpam-6640	62	2	h̃n+1(x,−)((y	h̃n+1(x,−)((y	NOUN
ejpam-6640	62	3	,	,	PUNCT
ejpam-6640	62	4	α	α	NOUN
ejpam-6640	62	5	)	)	PUNCT
ejpam-6640	62	6	)	)	PUNCT
ejpam-6640	63	1	kn+1	kn+1	PROPN
ejpam-6640	63	2	7−→	7−→	PROPN
ejpam-6640	63	3	f∗−1	f∗−1	PROPN
ejpam-6640	63	4	n+2(β	n+2(β	PROPN
ejpam-6640	63	5	∗	∗	NOUN
ejpam-6640	63	6	n+1(g	n+1(g	PROPN
ejpam-6640	63	7	∗−1	∗−1	PROPN
ejpam-6640	63	8	n+1(kn+1	n+1(kn+1	PROPN
ejpam-6640	63	9	)	)	PUNCT
ejpam-6640	63	10	)	)	PUNCT
ejpam-6640	63	11	)	)	PUNCT
ejpam-6640	64	1	∀n	∀n	NUM
ejpam-6640	65	1	∈	∈	PROPN
ejpam-6640	65	2	z	z	X
ejpam-6640	65	3	(	(	PUNCT
ejpam-6640	65	4	b	b	X
ejpam-6640	65	5	)	)	PUNCT
ejpam-6640	65	6	the	the	DET
ejpam-6640	65	7	sequence	sequence	NOUN
ejpam-6640	65	8	·	·	PUNCT
ejpam-6640	65	9	·	·	PUNCT
ejpam-6640	65	10	·	·	PUNCT
ejpam-6640	65	11	//	//	PUNCT
ejpam-6640	66	1	h̃n(x,−)((y	h̃n(x,−)((y	PROPN
ejpam-6640	66	2	,	,	PUNCT
ejpam-6640	66	3	α	α	NOUN
ejpam-6640	66	4	)	)	PUNCT
ejpam-6640	66	5	)	)	PUNCT
ejpam-6640	66	6	h̃n(x,−)(f	h̃n(x,−)(f	PROPN
ejpam-6640	66	7	)	)	PUNCT
ejpam-6640	66	8	//	//	SYM
ejpam-6640	67	1	h̃n(x,−)((z	h̃n(x,−)((z	PROPN
ejpam-6640	67	2	,	,	PUNCT
ejpam-6640	67	3	β	β	NOUN
ejpam-6640	67	4	)	)	PUNCT
ejpam-6640	67	5	)	)	PUNCT
ejpam-6640	67	6	h̃n(x,−)(g	h̃n(x,−)(g	ADJ
ejpam-6640	67	7	)	)	PUNCT
ejpam-6640	67	8	//	//	NOUN
ejpam-6640	68	1	h̃n(x,−)((t	h̃n(x,−)((t	PROPN
ejpam-6640	68	2	,	,	PUNCT
ejpam-6640	68	3	γ	γ	NOUN
ejpam-6640	68	4	)	)	PUNCT
ejpam-6640	68	5	)	)	PUNCT
ejpam-6640	69	1	λn	λn	PROPN
ejpam-6640	69	2	//	//	NUM
ejpam-6640	69	3	h̃n+1(x,−)((y	h̃n+1(x,−)((y	PROPN
ejpam-6640	69	4	,	,	PUNCT
ejpam-6640	69	5	α	α	NOUN
ejpam-6640	69	6	)	)	PUNCT
ejpam-6640	69	7	)	)	PUNCT
ejpam-6640	69	8	h̃n+1(x,−)(f	h̃n+1(x,−)(f	X
ejpam-6640	69	9	)	)	PUNCT
ejpam-6640	69	10	//	//	SYM
ejpam-6640	70	1	h̃n+1(x,−)((z	h̃n+1(x,−)((z	PROPN
ejpam-6640	70	2	,	,	PUNCT
ejpam-6640	70	3	β	β	NOUN
ejpam-6640	70	4	)	)	PUNCT
ejpam-6640	70	5	)	)	PUNCT
ejpam-6640	70	6	h̃n+1(x,−)(g	h̃n+1(x,−)(g	NOUN
ejpam-6640	70	7	)	)	PUNCT
ejpam-6640	70	8	//	//	NOUN
ejpam-6640	71	1	h̃n+1(x,−)((t	h̃n+1(x,−)((t	PROPN
ejpam-6640	71	2	,	,	PUNCT
ejpam-6640	71	3	γ	γ	NOUN
ejpam-6640	71	4	)	)	PUNCT
ejpam-6640	71	5	)	)	PUNCT
ejpam-6640	71	6	λn+1	λn+1	ADP
ejpam-6640	71	7	//	//	SYM
ejpam-6640	71	8	·	·	PUNCT
ejpam-6640	71	9	·	·	PUNCT
ejpam-6640	71	10	·	·	PUNCT
ejpam-6640	71	11	is	be	AUX
ejpam-6640	71	12	a	a	DET
ejpam-6640	71	13	long	long	ADJ
ejpam-6640	71	14	exact	exact	ADJ
ejpam-6640	71	15	sequence	sequence	NOUN
ejpam-6640	71	16	of	of	ADP
ejpam-6640	71	17	abelian	abelian	ADJ
ejpam-6640	71	18	group	group	NOUN
ejpam-6640	71	19	morphisms	morphism	VERB
ejpam-6640	71	20	.	.	PUNCT
ejpam-6640	72	1	that	that	PRON
ejpam-6640	72	2	is	be	AUX
ejpam-6640	72	3	,	,	PUNCT
ejpam-6640	72	4	for	for	ADP
ejpam-6640	72	5	all	all	DET
ejpam-6640	72	6	n	n	PRON
ejpam-6640	72	7	∈	∈	PROPN
ejpam-6640	72	8	z:	z:	PROPN
ejpam-6640	72	9	im(h̃n(x,−)(f	im(h̃n(x,−)(f	NOUN
ejpam-6640	72	10	)	)	PUNCT
ejpam-6640	72	11	)	)	PUNCT
ejpam-6640	73	1	=	=	SYM
ejpam-6640	73	2	ker(h̃n(x,−)(g	ker(h̃n(x,−)(g	NOUN
ejpam-6640	73	3	)	)	PUNCT
ejpam-6640	73	4	)	)	PUNCT
ejpam-6640	74	1	im(h̃n(x,−)(g	im(h̃n(x,−)(g	ADJ
ejpam-6640	74	2	)	)	PUNCT
ejpam-6640	74	3	)	)	PUNCT
ejpam-6640	74	4	=	=	SYM
ejpam-6640	74	5	ker(λn	ker(λn	X
ejpam-6640	74	6	)	)	PUNCT
ejpam-6640	74	7	im(λn	im(λn	NOUN
ejpam-6640	74	8	)	)	PUNCT
ejpam-6640	74	9	=	=	SYM
ejpam-6640	75	1	ker(h̃n+1(x,−)(f	ker(h̃n+1(x,−)(f	PROPN
ejpam-6640	75	2	)	)	PUNCT
ejpam-6640	75	3	)	)	PUNCT
ejpam-6640	76	1	a.	a.	PROPN
ejpam-6640	76	2	diallo	diallo	PROPN
ejpam-6640	76	3	,	,	PUNCT
ejpam-6640	76	4	m.	m.	PROPN
ejpam-6640	76	5	b.	b.	PROPN
ejpam-6640	76	6	f.	f.	PROPN
ejpam-6640	76	7	b.	b.	PROPN
ejpam-6640	76	8	maaouia	maaouia	PROPN
ejpam-6640	76	9	,	,	PUNCT
ejpam-6640	76	10	m.	m.	NOUN
ejpam-6640	76	11	sanghare	sanghare	PROPN
ejpam-6640	76	12	/	/	SYM
ejpam-6640	76	13	eur	eur	PROPN
ejpam-6640	76	14	.	.	PUNCT
ejpam-6640	77	1	j.	j.	PROPN
ejpam-6640	77	2	pure	pure	PROPN
ejpam-6640	77	3	appl	appl	PROPN
ejpam-6640	77	4	.	.	PROPN
ejpam-6640	77	5	math	math	PROPN
ejpam-6640	77	6	,	,	PUNCT
ejpam-6640	77	7	18	18	NUM
ejpam-6640	77	8	(	(	PUNCT
ejpam-6640	77	9	4	4	NUM
ejpam-6640	77	10	)	)	PUNCT
ejpam-6640	77	11	(	(	PUNCT
ejpam-6640	77	12	2025	2025	NUM
ejpam-6640	77	13	)	)	PUNCT
ejpam-6640	77	14	,	,	PUNCT
ejpam-6640	77	15	6640	6640	NUM
ejpam-6640	77	16	4	4	NUM
ejpam-6640	77	17	of	of	ADP
ejpam-6640	77	18	28	28	NUM
ejpam-6640	77	19	(	(	PUNCT
ejpam-6640	77	20	iii	iii	NOUN
ejpam-6640	77	21	)	)	PUNCT
ejpam-6640	77	22	the	the	DET
ejpam-6640	77	23	functor	functor	PROPN
ejpam-6640	77	24	h̃n(−	h̃n(−	PROPN
ejpam-6640	77	25	,	,	PUNCT
ejpam-6640	77	26	x	x	X
ejpam-6640	77	27	)	)	PUNCT
ejpam-6640	77	28	is	be	AUX
ejpam-6640	77	29	a	a	DET
ejpam-6640	77	30	contravariant	contravariant	ADJ
ejpam-6640	77	31	additive	additive	ADJ
ejpam-6640	77	32	functor	functor	NOUN
ejpam-6640	77	33	.	.	PUNCT
ejpam-6640	78	1	(	(	PUNCT
ejpam-6640	78	2	iv	iv	X
ejpam-6640	78	3	)	)	PUNCT
ejpam-6640	78	4	let	let	VERB
ejpam-6640	78	5	(	(	PUNCT
ejpam-6640	78	6	0	0	NUM
ejpam-6640	78	7	)	)	PUNCT
ejpam-6640	78	8	//	//	NOUN
ejpam-6640	79	1	(	(	PUNCT
ejpam-6640	79	2	y	y	PROPN
ejpam-6640	79	3	,	,	PUNCT
ejpam-6640	79	4	α	α	NOUN
ejpam-6640	79	5	)	)	PUNCT
ejpam-6640	79	6	f	f	PROPN
ejpam-6640	79	7	//	//	X
ejpam-6640	79	8	(	(	PUNCT
ejpam-6640	79	9	z	z	NOUN
ejpam-6640	79	10	,	,	PUNCT
ejpam-6640	79	11	β	β	NOUN
ejpam-6640	79	12	)	)	PUNCT
ejpam-6640	79	13	g	g	PROPN
ejpam-6640	79	14	//	//	SYM
ejpam-6640	79	15	(	(	PUNCT
ejpam-6640	79	16	t	t	PROPN
ejpam-6640	79	17	,	,	PUNCT
ejpam-6640	79	18	γ	γ	PROPN
ejpam-6640	79	19	)	)	PUNCT
ejpam-6640	79	20	//	//	NOUN
ejpam-6640	79	21	(	(	PUNCT
ejpam-6640	79	22	0	0	NUM
ejpam-6640	79	23	)	)	PUNCT
ejpam-6640	79	24	be	be	AUX
ejpam-6640	79	25	a	a	DET
ejpam-6640	79	26	short	short	ADJ
ejpam-6640	79	27	exact	exact	ADJ
ejpam-6640	79	28	sequence	sequence	NOUN
ejpam-6640	79	29	in	in	ADP
ejpam-6640	79	30	comp(a	comp(a	NOUN
ejpam-6640	79	31	)	)	PUNCT
ejpam-6640	79	32	,	,	PUNCT
ejpam-6640	79	33	where	where	SCONJ
ejpam-6640	79	34	a	a	PRON
ejpam-6640	79	35	is	be	AUX
ejpam-6640	79	36	a	a	DET
ejpam-6640	79	37	balanced	balanced	ADJ
ejpam-6640	79	38	abelian	abelian	ADJ
ejpam-6640	79	39	category	category	NOUN
ejpam-6640	79	40	and	and	CCONJ
ejpam-6640	79	41	x	x	X
ejpam-6640	79	42	is	be	AUX
ejpam-6640	79	43	an	an	DET
ejpam-6640	79	44	injective	injective	ADJ
ejpam-6640	79	45	object	object	NOUN
ejpam-6640	79	46	in	in	ADP
ejpam-6640	79	47	a	a	PRON
ejpam-6640	79	48	.	.	PUNCT
ejpam-6640	80	1	then	then	ADV
ejpam-6640	80	2	:	:	PUNCT
ejpam-6640	80	3	(	(	PUNCT
ejpam-6640	80	4	a	a	X
ejpam-6640	80	5	)	)	PUNCT
ejpam-6640	80	6	we	we	PRON
ejpam-6640	80	7	call	call	VERB
ejpam-6640	80	8	the	the	DET
ejpam-6640	80	9	morphism	morphism	NOUN
ejpam-6640	80	10	of	of	ADP
ejpam-6640	80	11	connection	connection	NOUN
ejpam-6640	80	12	associated	associate	VERB
ejpam-6640	80	13	to	to	ADP
ejpam-6640	80	14	the	the	DET
ejpam-6640	80	15	functor	functor	PROPN
ejpam-6640	80	16	h̃n(−	h̃n(−	PROPN
ejpam-6640	80	17	,	,	PUNCT
ejpam-6640	80	18	x	x	NOUN
ejpam-6640	80	19	)	)	PUNCT
ejpam-6640	80	20	,	,	PUNCT
ejpam-6640	80	21	denoted	denote	VERB
ejpam-6640	80	22	by	by	ADP
ejpam-6640	80	23	λn	λn	NOUN
ejpam-6640	80	24	,	,	PUNCT
ejpam-6640	80	25	the	the	DET
ejpam-6640	80	26	morphism	morphism	NOUN
ejpam-6640	80	27	defined	define	VERB
ejpam-6640	80	28	by	by	ADP
ejpam-6640	80	29	:	:	PUNCT
ejpam-6640	80	30	δn	δn	NOUN
ejpam-6640	80	31	:	:	PUNCT
ejpam-6640	80	32	h̃n(−	h̃n(−	PROPN
ejpam-6640	80	33	,	,	PUNCT
ejpam-6640	80	34	x)((y	x)((y	PROPN
ejpam-6640	80	35	,	,	PUNCT
ejpam-6640	80	36	α	α	NOUN
ejpam-6640	80	37	)	)	PUNCT
ejpam-6640	80	38	)	)	PUNCT
ejpam-6640	80	39	−→	−→	NOUN
ejpam-6640	80	40	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	80	41	,	,	PUNCT
ejpam-6640	80	42	x)((t	x)((t	PROPN
ejpam-6640	80	43	,	,	PUNCT
ejpam-6640	80	44	γ	γ	NOUN
ejpam-6640	80	45	)	)	PUNCT
ejpam-6640	80	46	)	)	PUNCT
ejpam-6640	81	1	kn+1	kn+1	PROPN
ejpam-6640	81	2	7−→	7−→	PROPN
ejpam-6640	81	3	g∗−1	g∗−1	PROPN
ejpam-6640	81	4	n+2(β	n+2(β	PROPN
ejpam-6640	81	5	∗	∗	NOUN
ejpam-6640	81	6	n+1(f	n+1(f	ADJ
ejpam-6640	81	7	∗−1	∗−1	NOUN
ejpam-6640	81	8	n+1(kn+1	n+1(kn+1	PROPN
ejpam-6640	81	9	)	)	PUNCT
ejpam-6640	81	10	)	)	PUNCT
ejpam-6640	81	11	)	)	PUNCT
ejpam-6640	81	12	,	,	PUNCT
ejpam-6640	81	13	∀n	∀n	NUM
ejpam-6640	81	14	∈	∈	PROPN
ejpam-6640	81	15	z	z	X
ejpam-6640	81	16	(	(	PUNCT
ejpam-6640	81	17	b	b	X
ejpam-6640	81	18	)	)	PUNCT
ejpam-6640	81	19	the	the	DET
ejpam-6640	81	20	sequence	sequence	NOUN
ejpam-6640	81	21	·	·	PUNCT
ejpam-6640	81	22	·	·	PUNCT
ejpam-6640	81	23	·	·	PUNCT
ejpam-6640	82	1	//	//	PUNCT
ejpam-6640	82	2	h̃n(−	h̃n(−	PROPN
ejpam-6640	82	3	,	,	PUNCT
ejpam-6640	82	4	x)((t	x)((t	PROPN
ejpam-6640	82	5	,	,	PUNCT
ejpam-6640	82	6	γ	γ	NOUN
ejpam-6640	82	7	)	)	PUNCT
ejpam-6640	82	8	)	)	PUNCT
ejpam-6640	82	9	h̃n(−,x)(g	h̃n(−,x)(g	PROPN
ejpam-6640	82	10	)	)	PUNCT
ejpam-6640	82	11	//	//	X
ejpam-6640	83	1	h̃n(−	h̃n(−	PROPN
ejpam-6640	83	2	,	,	PUNCT
ejpam-6640	83	3	x)((z	x)((z	PROPN
ejpam-6640	83	4	,	,	PUNCT
ejpam-6640	83	5	β	β	NOUN
ejpam-6640	83	6	)	)	PUNCT
ejpam-6640	83	7	)	)	PUNCT
ejpam-6640	83	8	h̃n(−,x)(f	h̃n(−,x)(f	PROPN
ejpam-6640	83	9	)	)	PUNCT
ejpam-6640	83	10	//	//	PUNCT
ejpam-6640	84	1	h̃n(−	h̃n(−	PROPN
ejpam-6640	84	2	,	,	PUNCT
ejpam-6640	84	3	x)((y	x)((y	PROPN
ejpam-6640	84	4	,	,	PUNCT
ejpam-6640	84	5	α	α	NOUN
ejpam-6640	84	6	)	)	PUNCT
ejpam-6640	84	7	)	)	PUNCT
ejpam-6640	84	8	δn	δn	PROPN
ejpam-6640	84	9	//	//	NUM
ejpam-6640	84	10	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	84	11	,	,	PUNCT
ejpam-6640	84	12	x)((t	x)((t	PROPN
ejpam-6640	84	13	,	,	PUNCT
ejpam-6640	84	14	γ	γ	NOUN
ejpam-6640	84	15	)	)	PUNCT
ejpam-6640	84	16	)	)	PUNCT
ejpam-6640	84	17	h̃n+1(−,x)(g	h̃n+1(−,x)(g	NOUN
ejpam-6640	84	18	)	)	PUNCT
ejpam-6640	84	19	//	//	SYM
ejpam-6640	84	20	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	84	21	,	,	PUNCT
ejpam-6640	84	22	x)((z	x)((z	PROPN
ejpam-6640	84	23	,	,	PUNCT
ejpam-6640	84	24	β	β	NOUN
ejpam-6640	84	25	)	)	PUNCT
ejpam-6640	84	26	)	)	PUNCT
ejpam-6640	85	1	h̃n+1(−,x)(f	h̃n+1(−,x)(f	PROPN
ejpam-6640	85	2	)	)	PUNCT
ejpam-6640	85	3	//	//	SYM
ejpam-6640	85	4	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	85	5	,	,	PUNCT
ejpam-6640	85	6	x)((y	x)((y	PROPN
ejpam-6640	85	7	,	,	PUNCT
ejpam-6640	85	8	α	α	NOUN
ejpam-6640	85	9	)	)	PUNCT
ejpam-6640	85	10	)	)	PUNCT
ejpam-6640	85	11	δn+1	δn+1	PROPN
ejpam-6640	85	12	//	//	X
ejpam-6640	85	13	·	·	PUNCT
ejpam-6640	85	14	·	·	PUNCT
ejpam-6640	85	15	·	·	PUNCT
ejpam-6640	85	16	is	be	AUX
ejpam-6640	85	17	a	a	DET
ejpam-6640	85	18	long	long	ADJ
ejpam-6640	85	19	exact	exact	ADJ
ejpam-6640	85	20	sequence	sequence	NOUN
ejpam-6640	85	21	in	in	ADP
ejpam-6640	85	22	ab	ab	PROPN
ejpam-6640	85	23	.	.	PUNCT
ejpam-6640	86	1	that	that	PRON
ejpam-6640	86	2	is	be	AUX
ejpam-6640	86	3	(	(	PUNCT
ejpam-6640	86	4	for	for	ADP
ejpam-6640	86	5	all	all	DET
ejpam-6640	86	6	n	n	PRON
ejpam-6640	86	7	∈	∈	PROPN
ejpam-6640	86	8	z):	z):	NOUN
ejpam-6640	86	9	im(h̃n(−	im(h̃n(−	NOUN
ejpam-6640	86	10	,	,	PUNCT
ejpam-6640	86	11	x)(g	x)(g	NUM
ejpam-6640	86	12	)	)	PUNCT
ejpam-6640	86	13	)	)	PUNCT
ejpam-6640	87	1	=	=	PUNCT
ejpam-6640	87	2	ker(h̃n(−	ker(h̃n(−	PROPN
ejpam-6640	87	3	,	,	PUNCT
ejpam-6640	87	4	x)(f	x)(f	PROPN
ejpam-6640	87	5	)	)	PUNCT
ejpam-6640	87	6	)	)	PUNCT
ejpam-6640	88	1	im(h̃n(−	im(h̃n(−	NOUN
ejpam-6640	88	2	,	,	PUNCT
ejpam-6640	88	3	x)(f	x)(f	PROPN
ejpam-6640	88	4	)	)	PUNCT
ejpam-6640	88	5	)	)	PUNCT
ejpam-6640	89	1	=	=	SYM
ejpam-6640	89	2	ker(δn	ker(δn	X
ejpam-6640	89	3	)	)	PUNCT
ejpam-6640	89	4	im(δn	im(δn	PROPN
ejpam-6640	89	5	)	)	PUNCT
ejpam-6640	89	6	=	=	SYM
ejpam-6640	89	7	ker(h̃n+1(−	ker(h̃n+1(−	PROPN
ejpam-6640	89	8	,	,	PUNCT
ejpam-6640	89	9	x)(g	x)(g	NUM
ejpam-6640	89	10	)	)	PUNCT
ejpam-6640	89	11	)	)	PUNCT
ejpam-6640	89	12	.	.	PUNCT
ejpam-6640	90	1	1	1	X
ejpam-6640	90	2	.	.	X
ejpam-6640	90	3	preliminary	preliminary	ADJ
ejpam-6640	90	4	results	result	NOUN
ejpam-6640	90	5	[	[	X
ejpam-6640	90	6	abelian	abelian	ADJ
ejpam-6640	90	7	category	category	NOUN
ejpam-6640	90	8	]	]	PUNCT
ejpam-6640	90	9	an	an	DET
ejpam-6640	90	10	abelian	abelian	ADJ
ejpam-6640	90	11	category	category	NOUN
ejpam-6640	90	12	is	be	AUX
ejpam-6640	90	13	a	a	DET
ejpam-6640	90	14	category	category	NOUN
ejpam-6640	90	15	a	a	PRON
ejpam-6640	90	16	that	that	PRON
ejpam-6640	90	17	satisfies	satisfy	VERB
ejpam-6640	90	18	the	the	DET
ejpam-6640	90	19	following	follow	VERB
ejpam-6640	90	20	conditions	condition	NOUN
ejpam-6640	90	21	:	:	PUNCT
ejpam-6640	90	22	(	(	PUNCT
ejpam-6640	90	23	i	i	NOUN
ejpam-6640	90	24	)	)	PUNCT
ejpam-6640	90	25	the	the	DET
ejpam-6640	90	26	category	category	NOUN
ejpam-6640	90	27	a	a	PRON
ejpam-6640	90	28	has	have	VERB
ejpam-6640	90	29	a	a	DET
ejpam-6640	90	30	zero	zero	NUM
ejpam-6640	90	31	object	object	NOUN
ejpam-6640	90	32	;	;	PUNCT
ejpam-6640	90	33	(	(	PUNCT
ejpam-6640	90	34	ii	ii	NOUN
ejpam-6640	90	35	)	)	PUNCT
ejpam-6640	90	36	for	for	ADP
ejpam-6640	90	37	all	all	DET
ejpam-6640	90	38	objects	object	NOUN
ejpam-6640	90	39	x	x	PUNCT
ejpam-6640	90	40	and	and	CCONJ
ejpam-6640	90	41	y	y	PROPN
ejpam-6640	90	42	in	in	ADP
ejpam-6640	90	43	a	a	PRON
ejpam-6640	90	44	,	,	PUNCT
ejpam-6640	90	45	the	the	DET
ejpam-6640	90	46	set	set	ADJ
ejpam-6640	90	47	homa	homa	NOUN
ejpam-6640	90	48	(	(	PUNCT
ejpam-6640	90	49	x	x	X
ejpam-6640	90	50	,	,	PUNCT
ejpam-6640	90	51	y	y	PROPN
ejpam-6640	90	52	)	)	PUNCT
ejpam-6640	90	53	is	be	AUX
ejpam-6640	90	54	endowed	endow	VERB
ejpam-6640	90	55	with	with	ADP
ejpam-6640	90	56	an	an	DET
ejpam-6640	90	57	abelian	abelian	ADJ
ejpam-6640	90	58	group	group	NOUN
ejpam-6640	90	59	structure	structure	NOUN
ejpam-6640	90	60	whose	whose	DET
ejpam-6640	90	61	composition	composition	NOUN
ejpam-6640	90	62	law	law	NOUN
ejpam-6640	90	63	is	be	AUX
ejpam-6640	90	64	denoted	denote	VERB
ejpam-6640	90	65	additively	additively	ADV
ejpam-6640	90	66	;	;	PUNCT
ejpam-6640	90	67	(	(	PUNCT
ejpam-6640	90	68	iii	iii	X
ejpam-6640	90	69	)	)	PUNCT
ejpam-6640	90	70	the	the	DET
ejpam-6640	90	71	composition	composition	NOUN
ejpam-6640	90	72	in	in	ADP
ejpam-6640	90	73	a	a	PRON
ejpam-6640	90	74	is	be	AUX
ejpam-6640	90	75	bilinear	bilinear	ADJ
ejpam-6640	90	76	with	with	ADP
ejpam-6640	90	77	respect	respect	NOUN
ejpam-6640	90	78	to	to	ADP
ejpam-6640	90	79	the	the	DET
ejpam-6640	90	80	additions	addition	NOUN
ejpam-6640	90	81	;	;	PUNCT
ejpam-6640	90	82	(	(	PUNCT
ejpam-6640	90	83	iv	iv	X
ejpam-6640	90	84	)	)	PUNCT
ejpam-6640	90	85	every	every	DET
ejpam-6640	90	86	finite	finite	ADJ
ejpam-6640	90	87	family	family	NOUN
ejpam-6640	90	88	of	of	ADP
ejpam-6640	90	89	objects	object	NOUN
ejpam-6640	90	90	in	in	ADP
ejpam-6640	90	91	a	a	DET
ejpam-6640	90	92	has	have	AUX
ejpam-6640	90	93	a	a	DET
ejpam-6640	90	94	coproduct	coproduct	NOUN
ejpam-6640	90	95	;	;	PUNCT
ejpam-6640	90	96	(	(	PUNCT
ejpam-6640	90	97	v	v	NOUN
ejpam-6640	90	98	)	)	PUNCT
ejpam-6640	90	99	every	every	DET
ejpam-6640	90	100	morphism	morphism	NOUN
ejpam-6640	90	101	in	in	ADP
ejpam-6640	90	102	a	a	DET
ejpam-6640	90	103	has	have	AUX
ejpam-6640	90	104	a	a	DET
ejpam-6640	90	105	kernel	kernel	NOUN
ejpam-6640	90	106	and	and	CCONJ
ejpam-6640	90	107	a	a	DET
ejpam-6640	90	108	cokernel	cokernel	NOUN
ejpam-6640	90	109	;	;	PUNCT
ejpam-6640	90	110	(	(	PUNCT
ejpam-6640	90	111	vi	vi	X
ejpam-6640	90	112	)	)	PUNCT
ejpam-6640	90	113	every	every	DET
ejpam-6640	90	114	monomorphism	monomorphism	NOUN
ejpam-6640	90	115	in	in	ADP
ejpam-6640	90	116	a	a	PRON
ejpam-6640	90	117	is	be	AUX
ejpam-6640	90	118	the	the	DET
ejpam-6640	90	119	kernel	kernel	NOUN
ejpam-6640	90	120	of	of	ADP
ejpam-6640	90	121	its	its	PRON
ejpam-6640	90	122	cokernel	cokernel	NOUN
ejpam-6640	90	123	;	;	PUNCT
ejpam-6640	90	124	(	(	PUNCT
ejpam-6640	90	125	vii	vii	PROPN
ejpam-6640	90	126	)	)	PUNCT
ejpam-6640	90	127	every	every	DET
ejpam-6640	90	128	epimorphism	epimorphism	NOUN
ejpam-6640	90	129	in	in	ADP
ejpam-6640	90	130	a	a	PRON
ejpam-6640	90	131	is	be	AUX
ejpam-6640	90	132	the	the	DET
ejpam-6640	90	133	cokernel	cokernel	NOUN
ejpam-6640	90	134	of	of	ADP
ejpam-6640	90	135	its	its	PRON
ejpam-6640	90	136	kernel	kernel	NOUN
ejpam-6640	90	137	.	.	PUNCT
ejpam-6640	91	1	[	[	X
ejpam-6640	91	2	balanced	balanced	ADJ
ejpam-6640	91	3	category	category	NOUN
ejpam-6640	91	4	]	]	PUNCT
ejpam-6640	91	5	a	a	DET
ejpam-6640	91	6	category	category	NOUN
ejpam-6640	91	7	c	c	NOUN
ejpam-6640	91	8	is	be	AUX
ejpam-6640	91	9	balanced	balanced	ADJ
ejpam-6640	91	10	if	if	SCONJ
ejpam-6640	91	11	:	:	PUNCT
ejpam-6640	91	12	a.	a.	PROPN
ejpam-6640	91	13	diallo	diallo	PROPN
ejpam-6640	91	14	,	,	PUNCT
ejpam-6640	91	15	m.	m.	PROPN
ejpam-6640	91	16	b.	b.	PROPN
ejpam-6640	91	17	f.	f.	PROPN
ejpam-6640	91	18	b.	b.	PROPN
ejpam-6640	91	19	maaouia	maaouia	PROPN
ejpam-6640	91	20	,	,	PUNCT
ejpam-6640	91	21	m.	m.	NOUN
ejpam-6640	91	22	sanghare	sanghare	PROPN
ejpam-6640	91	23	/	/	SYM
ejpam-6640	91	24	eur	eur	PROPN
ejpam-6640	91	25	.	.	PUNCT
ejpam-6640	92	1	j.	j.	PROPN
ejpam-6640	92	2	pure	pure	PROPN
ejpam-6640	92	3	appl	appl	PROPN
ejpam-6640	92	4	.	.	PROPN
ejpam-6640	92	5	math	math	PROPN
ejpam-6640	92	6	,	,	PUNCT
ejpam-6640	92	7	18	18	NUM
ejpam-6640	92	8	(	(	PUNCT
ejpam-6640	92	9	4	4	NUM
ejpam-6640	92	10	)	)	PUNCT
ejpam-6640	92	11	(	(	PUNCT
ejpam-6640	92	12	2025	2025	NUM
ejpam-6640	92	13	)	)	PUNCT
ejpam-6640	92	14	,	,	PUNCT
ejpam-6640	92	15	6640	6640	NUM
ejpam-6640	92	16	5	5	NUM
ejpam-6640	92	17	of	of	ADP
ejpam-6640	92	18	28	28	NUM
ejpam-6640	92	19	(	(	PUNCT
ejpam-6640	92	20	i	i	NOUN
ejpam-6640	92	21	)	)	PUNCT
ejpam-6640	92	22	every	every	DET
ejpam-6640	92	23	monomorphism	monomorphism	NOUN
ejpam-6640	92	24	of	of	ADP
ejpam-6640	92	25	c	c	PROPN
ejpam-6640	92	26	is	be	AUX
ejpam-6640	92	27	retractable	retractable	ADJ
ejpam-6640	92	28	;	;	PUNCT
ejpam-6640	92	29	(	(	PUNCT
ejpam-6640	92	30	ii	ii	NOUN
ejpam-6640	92	31	)	)	PUNCT
ejpam-6640	92	32	and	and	CCONJ
ejpam-6640	92	33	every	every	DET
ejpam-6640	92	34	epimorphism	epimorphism	NOUN
ejpam-6640	92	35	of	of	ADP
ejpam-6640	92	36	c	c	PROPN
ejpam-6640	92	37	is	be	AUX
ejpam-6640	92	38	splittable	splittable	ADJ
ejpam-6640	92	39	.	.	PUNCT
ejpam-6640	93	1	[	[	X
ejpam-6640	93	2	left	left	ADJ
ejpam-6640	93	3	exact	exact	ADJ
ejpam-6640	93	4	sequence	sequence	NOUN
ejpam-6640	93	5	in	in	ADP
ejpam-6640	93	6	a	a	DET
ejpam-6640	93	7	]	]	X
ejpam-6640	93	8	let	let	VERB
ejpam-6640	93	9	(	(	PUNCT
ejpam-6640	93	10	s	s	X
ejpam-6640	93	11	):	):	PUNCT
ejpam-6640	93	12	0	0	PUNCT
ejpam-6640	93	13	→	→	SYM
ejpam-6640	93	14	x	x	SYM
ejpam-6640	93	15	f−→	f−→	NOUN
ejpam-6640	93	16	y	y	PROPN
ejpam-6640	93	17	g−→	g−→	NOUN
ejpam-6640	93	18	z	z	AUX
ejpam-6640	93	19	be	be	VERB
ejpam-6640	93	20	a	a	DET
ejpam-6640	93	21	short	short	ADJ
ejpam-6640	93	22	sequence	sequence	NOUN
ejpam-6640	93	23	of	of	ADP
ejpam-6640	93	24	morphisms	morphism	NOUN
ejpam-6640	93	25	in	in	ADP
ejpam-6640	93	26	a	a	PRON
ejpam-6640	93	27	.	.	PUNCT
ejpam-6640	94	1	then	then	ADV
ejpam-6640	94	2	(	(	PUNCT
ejpam-6640	94	3	s	s	X
ejpam-6640	94	4	)	)	PUNCT
ejpam-6640	94	5	is	be	AUX
ejpam-6640	94	6	called	call	VERB
ejpam-6640	94	7	left	left	ADJ
ejpam-6640	94	8	exact	exact	ADJ
ejpam-6640	94	9	if:	if:	PROPN
ejpam-6640	94	10	g	g	ADP
ejpam-6640	94	11	◦	◦	NOUN
ejpam-6640	94	12	f	f	X
ejpam-6640	95	1	=	=	SYM
ejpam-6640	95	2	ex	ex	X
ejpam-6640	95	3	,	,	PUNCT
ejpam-6640	95	4	z	z	NOUN
ejpam-6640	95	5	,	,	PUNCT
ejpam-6640	95	6	where	where	SCONJ
ejpam-6640	95	7	ex	ex	X
ejpam-6640	95	8	,	,	PUNCT
ejpam-6640	95	9	z	z	PROPN
ejpam-6640	95	10	is	be	AUX
ejpam-6640	95	11	the	the	DET
ejpam-6640	95	12	zero	zero	NUM
ejpam-6640	95	13	morphism	morphism	NOUN
ejpam-6640	95	14	of	of	ADP
ejpam-6640	95	15	the	the	DET
ejpam-6640	95	16	abelian	abelian	PROPN
ejpam-6640	95	17	group	group	PROPN
ejpam-6640	95	18	homa	homa	PROPN
ejpam-6640	95	19	(	(	PUNCT
ejpam-6640	95	20	x	x	X
ejpam-6640	95	21	,	,	PUNCT
ejpam-6640	95	22	z	z	NOUN
ejpam-6640	95	23	)	)	PUNCT
ejpam-6640	95	24	n(f	n(f	PROPN
ejpam-6640	95	25	)	)	PUNCT
ejpam-6640	96	1	=	=	PUNCT
ejpam-6640	96	2	(	(	PUNCT
ejpam-6640	96	3	0	0	NUM
ejpam-6640	96	4	,	,	PUNCT
ejpam-6640	96	5	e0,x	e0,x	PROPN
ejpam-6640	96	6	)	)	PUNCT
ejpam-6640	97	1	where	where	SCONJ
ejpam-6640	97	2	e0,x	e0,x	PROPN
ejpam-6640	97	3	:	:	PUNCT
ejpam-6640	97	4	0	0	NUM
ejpam-6640	97	5	→	→	SYM
ejpam-6640	97	6	x	x	X
ejpam-6640	97	7	is	be	AUX
ejpam-6640	97	8	the	the	DET
ejpam-6640	97	9	zero	zero	NUM
ejpam-6640	97	10	morphism	morphism	NOUN
ejpam-6640	97	11	of	of	ADP
ejpam-6640	97	12	the	the	DET
ejpam-6640	97	13	abelian	abelian	PROPN
ejpam-6640	97	14	group	group	PROPN
ejpam-6640	97	15	homa	homa	PROPN
ejpam-6640	97	16	(	(	PUNCT
ejpam-6640	97	17	0	0	NUM
ejpam-6640	97	18	,	,	PUNCT
ejpam-6640	97	19	x	x	X
ejpam-6640	97	20	)	)	PUNCT
ejpam-6640	97	21	con(h	con(h	PROPN
ejpam-6640	97	22	)	)	PUNCT
ejpam-6640	97	23	=	=	SYM
ejpam-6640	97	24	(	(	PUNCT
ejpam-6640	97	25	0	0	NUM
ejpam-6640	97	26	,	,	PUNCT
ejpam-6640	97	27	ek,0	ek,0	PROPN
ejpam-6640	97	28	)	)	PUNCT
ejpam-6640	97	29	where	where	SCONJ
ejpam-6640	97	30	ek,0	ek,0	PROPN
ejpam-6640	97	31	:	:	PUNCT
ejpam-6640	97	32	k	k	X
ejpam-6640	97	33	→	→	SYM
ejpam-6640	97	34	0	0	NUM
ejpam-6640	97	35	is	be	AUX
ejpam-6640	97	36	the	the	DET
ejpam-6640	97	37	zero	zero	NUM
ejpam-6640	97	38	morphism	morphism	NOUN
ejpam-6640	97	39	of	of	ADP
ejpam-6640	97	40	the	the	DET
ejpam-6640	97	41	abelian	abelian	PROPN
ejpam-6640	97	42	group	group	PROPN
ejpam-6640	97	43	homa	homa	PROPN
ejpam-6640	97	44	(	(	PUNCT
ejpam-6640	97	45	k	k	NOUN
ejpam-6640	97	46	,	,	PUNCT
ejpam-6640	97	47	0	0	NUM
ejpam-6640	97	48	)	)	PUNCT
ejpam-6640	97	49	with	with	ADP
ejpam-6640	97	50	h	h	NOUN
ejpam-6640	97	51	the	the	DET
ejpam-6640	97	52	morphism	morphism	NOUN
ejpam-6640	97	53	satisfying	satisfy	VERB
ejpam-6640	97	54	i	i	PRON
ejpam-6640	97	55	◦	◦	VERB
ejpam-6640	97	56	h	h	NOUN
ejpam-6640	97	57	=	=	SYM
ejpam-6640	97	58	f	f	PROPN
ejpam-6640	97	59	and	and	CCONJ
ejpam-6640	97	60	ker	ker	NOUN
ejpam-6640	97	61	g	g	PROPN
ejpam-6640	97	62	=	=	SYM
ejpam-6640	97	63	(	(	PUNCT
ejpam-6640	97	64	k	k	X
ejpam-6640	97	65	,	,	PUNCT
ejpam-6640	97	66	i	i	PROPN
ejpam-6640	97	67	)	)	PUNCT
ejpam-6640	97	68	.	.	PUNCT
ejpam-6640	98	1	k	k	X
ejpam-6640	98	2	>	>	X
ejpam-6640	98	3	>	>	X
ejpam-6640	98	4	h	h	PROPN
ejpam-6640	99	1	i	i	PRON
ejpam-6640	99	2	�	�	VERB
ejpam-6640	99	3	�	�	PROPN
ejpam-6640	99	4	0	0	NUM
ejpam-6640	99	5	//	//	PUNCT
ejpam-6640	100	1	x	x	X
ejpam-6640	100	2	f	f	PROPN
ejpam-6640	100	3	//	//	PUNCT
ejpam-6640	100	4	y	y	PROPN
ejpam-6640	100	5	g	g	PROPN
ejpam-6640	100	6	//	//	PROPN
ejpam-6640	100	7	z	z	PROPN
ejpam-6640	101	1	[	[	X
ejpam-6640	101	2	right	right	ADJ
ejpam-6640	101	3	exact	exact	ADJ
ejpam-6640	101	4	sequence	sequence	NOUN
ejpam-6640	101	5	in	in	ADP
ejpam-6640	101	6	a	a	PRON
ejpam-6640	101	7	]	]	X
ejpam-6640	101	8	let	let	VERB
ejpam-6640	101	9	(	(	PUNCT
ejpam-6640	101	10	s	s	X
ejpam-6640	101	11	):	):	PUNCT
ejpam-6640	101	12	x	x	SYM
ejpam-6640	101	13	f−→	f−→	PROPN
ejpam-6640	101	14	y	y	PROPN
ejpam-6640	101	15	g−→	g−→	NOUN
ejpam-6640	101	16	z	z	PROPN
ejpam-6640	101	17	→	→	SYM
ejpam-6640	101	18	0	0	NUM
ejpam-6640	101	19	be	be	AUX
ejpam-6640	101	20	a	a	DET
ejpam-6640	101	21	short	short	ADJ
ejpam-6640	101	22	sequence	sequence	NOUN
ejpam-6640	101	23	of	of	ADP
ejpam-6640	101	24	morphisms	morphism	NOUN
ejpam-6640	101	25	in	in	ADP
ejpam-6640	101	26	a	a	PRON
ejpam-6640	101	27	.	.	PUNCT
ejpam-6640	102	1	then	then	ADV
ejpam-6640	102	2	(	(	PUNCT
ejpam-6640	102	3	s	s	X
ejpam-6640	102	4	)	)	PUNCT
ejpam-6640	102	5	is	be	AUX
ejpam-6640	102	6	called	call	VERB
ejpam-6640	102	7	right	right	ADJ
ejpam-6640	102	8	exact	exact	ADJ
ejpam-6640	102	9	if:	if:	NUM
ejpam-6640	102	10	g	g	NOUN
ejpam-6640	102	11	◦	◦	NOUN
ejpam-6640	102	12	f	f	X
ejpam-6640	103	1	=	=	SYM
ejpam-6640	103	2	ex	ex	X
ejpam-6640	103	3	,	,	PUNCT
ejpam-6640	103	4	z	z	NOUN
ejpam-6640	103	5	,	,	PUNCT
ejpam-6640	103	6	where	where	SCONJ
ejpam-6640	103	7	ex	ex	X
ejpam-6640	103	8	,	,	PUNCT
ejpam-6640	103	9	z	z	PROPN
ejpam-6640	103	10	is	be	AUX
ejpam-6640	103	11	the	the	DET
ejpam-6640	103	12	zero	zero	NUM
ejpam-6640	103	13	morphism	morphism	NOUN
ejpam-6640	103	14	of	of	ADP
ejpam-6640	103	15	the	the	DET
ejpam-6640	103	16	abelian	abelian	PROPN
ejpam-6640	103	17	group	group	PROPN
ejpam-6640	103	18	homa	homa	PROPN
ejpam-6640	103	19	(	(	PUNCT
ejpam-6640	103	20	x	x	X
ejpam-6640	103	21	,	,	PUNCT
ejpam-6640	103	22	z	z	NOUN
ejpam-6640	103	23	)	)	PUNCT
ejpam-6640	103	24	con	con	NOUN
ejpam-6640	103	25	(	(	PUNCT
ejpam-6640	103	26	g	g	NOUN
ejpam-6640	103	27	)	)	PUNCT
ejpam-6640	103	28	=	=	SYM
ejpam-6640	103	29	(	(	PUNCT
ejpam-6640	103	30	0	0	NUM
ejpam-6640	103	31	,	,	PUNCT
ejpam-6640	103	32	ez,0	ez,0	PROPN
ejpam-6640	103	33	)	)	PUNCT
ejpam-6640	103	34	where	where	SCONJ
ejpam-6640	103	35	ez,0	ez,0	PROPN
ejpam-6640	103	36	:	:	PUNCT
ejpam-6640	103	37	z	z	X
ejpam-6640	103	38	→	→	SYM
ejpam-6640	103	39	0	0	NUM
ejpam-6640	103	40	is	be	AUX
ejpam-6640	103	41	the	the	DET
ejpam-6640	103	42	zero	zero	NUM
ejpam-6640	103	43	morphism	morphism	NOUN
ejpam-6640	103	44	of	of	ADP
ejpam-6640	103	45	the	the	DET
ejpam-6640	103	46	abelian	abelian	PROPN
ejpam-6640	103	47	group	group	PROPN
ejpam-6640	103	48	homa	homa	PROPN
ejpam-6640	103	49	(	(	PUNCT
ejpam-6640	103	50	z	z	NOUN
ejpam-6640	103	51	,	,	PUNCT
ejpam-6640	103	52	0	0	NUM
ejpam-6640	103	53	)	)	PUNCT
ejpam-6640	103	54	con(h	con(h	PROPN
ejpam-6640	103	55	)	)	PUNCT
ejpam-6640	103	56	=	=	SYM
ejpam-6640	103	57	(	(	PUNCT
ejpam-6640	103	58	0	0	NUM
ejpam-6640	103	59	,	,	PUNCT
ejpam-6640	103	60	ek,0	ek,0	PROPN
ejpam-6640	103	61	)	)	PUNCT
ejpam-6640	103	62	where	where	SCONJ
ejpam-6640	103	63	ek,0	ek,0	PROPN
ejpam-6640	103	64	:	:	PUNCT
ejpam-6640	103	65	k	k	X
ejpam-6640	103	66	→	→	SYM
ejpam-6640	103	67	0	0	NUM
ejpam-6640	103	68	is	be	AUX
ejpam-6640	103	69	the	the	DET
ejpam-6640	103	70	zero	zero	NUM
ejpam-6640	103	71	morphism	morphism	NOUN
ejpam-6640	103	72	of	of	ADP
ejpam-6640	103	73	the	the	DET
ejpam-6640	103	74	abelian	abelian	PROPN
ejpam-6640	103	75	group	group	PROPN
ejpam-6640	103	76	homa	homa	PROPN
ejpam-6640	103	77	(	(	PUNCT
ejpam-6640	103	78	k	k	NOUN
ejpam-6640	103	79	,	,	PUNCT
ejpam-6640	103	80	0	0	NUM
ejpam-6640	103	81	)	)	PUNCT
ejpam-6640	103	82	with	with	ADP
ejpam-6640	103	83	h	h	NOUN
ejpam-6640	103	84	the	the	DET
ejpam-6640	103	85	morphism	morphism	NOUN
ejpam-6640	103	86	satisfying	satisfy	VERB
ejpam-6640	103	87	i	i	PRON
ejpam-6640	103	88	◦	◦	VERB
ejpam-6640	103	89	h	h	NOUN
ejpam-6640	104	1	=	=	SYM
ejpam-6640	104	2	f	f	PROPN
ejpam-6640	104	3	and	and	CCONJ
ejpam-6640	104	4	ker	ker	NOUN
ejpam-6640	104	5	g	g	PROPN
ejpam-6640	104	6	=	=	SYM
ejpam-6640	104	7	(	(	PUNCT
ejpam-6640	104	8	k	k	X
ejpam-6640	104	9	,	,	PUNCT
ejpam-6640	104	10	i	i	PROPN
ejpam-6640	104	11	)	)	PUNCT
ejpam-6640	104	12	.	.	PUNCT
ejpam-6640	105	1	k	k	X
ejpam-6640	105	2	>	>	X
ejpam-6640	105	3	>	>	X
ejpam-6640	105	4	h	h	NOUN
ejpam-6640	106	1	i	i	PRON
ejpam-6640	106	2	�	�	VERB
ejpam-6640	106	3	�	�	PROPN
ejpam-6640	106	4	x	x	SYM
ejpam-6640	106	5	f	f	PROPN
ejpam-6640	106	6	//	//	PUNCT
ejpam-6640	106	7	y	y	PROPN
ejpam-6640	106	8	g	g	PROPN
ejpam-6640	106	9	//	//	PROPN
ejpam-6640	106	10	z	z	PROPN
ejpam-6640	106	11	//	//	NOUN
ejpam-6640	106	12	0	0	PUNCT
ejpam-6640	107	1	[	[	X
ejpam-6640	107	2	exact	exact	ADJ
ejpam-6640	107	3	sequence	sequence	NOUN
ejpam-6640	107	4	in	in	ADP
ejpam-6640	107	5	a	a	PRON
ejpam-6640	107	6	]	]	X
ejpam-6640	107	7	let	let	VERB
ejpam-6640	107	8	(	(	PUNCT
ejpam-6640	107	9	s	s	X
ejpam-6640	107	10	):	):	PUNCT
ejpam-6640	107	11	0	0	PUNCT
ejpam-6640	107	12	→	→	SYM
ejpam-6640	107	13	x	x	SYM
ejpam-6640	107	14	f−→	f−→	NOUN
ejpam-6640	107	15	y	y	PROPN
ejpam-6640	107	16	g−→	g−→	NOUN
ejpam-6640	107	17	z	z	PROPN
ejpam-6640	107	18	→	→	SYM
ejpam-6640	107	19	0	0	NUM
ejpam-6640	107	20	be	be	AUX
ejpam-6640	107	21	a	a	DET
ejpam-6640	107	22	short	short	ADJ
ejpam-6640	107	23	sequence	sequence	NOUN
ejpam-6640	107	24	of	of	ADP
ejpam-6640	107	25	morphisms	morphism	NOUN
ejpam-6640	107	26	in	in	ADP
ejpam-6640	107	27	a	a	PRON
ejpam-6640	107	28	.	.	PUNCT
ejpam-6640	108	1	then	then	ADV
ejpam-6640	108	2	(	(	PUNCT
ejpam-6640	108	3	s	s	X
ejpam-6640	108	4	)	)	PUNCT
ejpam-6640	108	5	is	be	AUX
ejpam-6640	108	6	called	call	VERB
ejpam-6640	108	7	exact	exact	ADJ
ejpam-6640	108	8	if	if	SCONJ
ejpam-6640	108	9	it	it	PRON
ejpam-6640	108	10	is	be	AUX
ejpam-6640	108	11	both	both	PRON
ejpam-6640	108	12	left	leave	VERB
ejpam-6640	108	13	exact	exact	ADJ
ejpam-6640	108	14	and	and	CCONJ
ejpam-6640	108	15	right	right	ADJ
ejpam-6640	108	16	exact	exact	ADJ
ejpam-6640	108	17	.	.	PUNCT
ejpam-6640	109	1	that	that	PRON
ejpam-6640	109	2	is:	is:	PROPN
ejpam-6640	109	3	g	g	PROPN
ejpam-6640	109	4	◦	◦	NOUN
ejpam-6640	109	5	f	f	X
ejpam-6640	109	6	=	=	SYM
ejpam-6640	109	7	ex	ex	X
ejpam-6640	109	8	,	,	PUNCT
ejpam-6640	109	9	z	z	NOUN
ejpam-6640	109	10	,	,	PUNCT
ejpam-6640	109	11	where	where	SCONJ
ejpam-6640	109	12	ex	ex	X
ejpam-6640	109	13	,	,	PUNCT
ejpam-6640	109	14	z	z	PROPN
ejpam-6640	109	15	is	be	AUX
ejpam-6640	109	16	the	the	DET
ejpam-6640	109	17	zero	zero	NUM
ejpam-6640	109	18	morphism	morphism	NOUN
ejpam-6640	109	19	of	of	ADP
ejpam-6640	109	20	the	the	DET
ejpam-6640	109	21	abelian	abelian	PROPN
ejpam-6640	109	22	group	group	PROPN
ejpam-6640	109	23	homa	homa	PROPN
ejpam-6640	109	24	(	(	PUNCT
ejpam-6640	109	25	x	x	X
ejpam-6640	109	26	,	,	PUNCT
ejpam-6640	109	27	z	z	NOUN
ejpam-6640	109	28	)	)	PUNCT
ejpam-6640	109	29	n(f	n(f	PROPN
ejpam-6640	109	30	)	)	PUNCT
ejpam-6640	109	31	=	=	PUNCT
ejpam-6640	109	32	(	(	PUNCT
ejpam-6640	109	33	0	0	NUM
ejpam-6640	109	34	,	,	PUNCT
ejpam-6640	109	35	e0,x	e0,x	PROPN
ejpam-6640	109	36	)	)	PUNCT
ejpam-6640	110	1	where	where	SCONJ
ejpam-6640	110	2	e0,x	e0,x	PROPN
ejpam-6640	110	3	:	:	PUNCT
ejpam-6640	110	4	0	0	NUM
ejpam-6640	110	5	→	→	SYM
ejpam-6640	110	6	x	x	X
ejpam-6640	110	7	is	be	AUX
ejpam-6640	110	8	the	the	DET
ejpam-6640	110	9	zero	zero	NUM
ejpam-6640	110	10	morphism	morphism	NOUN
ejpam-6640	110	11	of	of	ADP
ejpam-6640	110	12	the	the	DET
ejpam-6640	110	13	abelian	abelian	PROPN
ejpam-6640	110	14	group	group	PROPN
ejpam-6640	110	15	homa	homa	PROPN
ejpam-6640	110	16	(	(	PUNCT
ejpam-6640	110	17	0	0	NUM
ejpam-6640	110	18	,	,	PUNCT
ejpam-6640	110	19	x	x	NOUN
ejpam-6640	110	20	)	)	PUNCT
ejpam-6640	110	21	con	con	NOUN
ejpam-6640	110	22	(	(	PUNCT
ejpam-6640	110	23	g	g	NOUN
ejpam-6640	110	24	)	)	PUNCT
ejpam-6640	110	25	=	=	SYM
ejpam-6640	110	26	(	(	PUNCT
ejpam-6640	110	27	0	0	NUM
ejpam-6640	110	28	,	,	PUNCT
ejpam-6640	110	29	ez,0	ez,0	PROPN
ejpam-6640	110	30	)	)	PUNCT
ejpam-6640	110	31	where	where	SCONJ
ejpam-6640	110	32	ez,0	ez,0	PROPN
ejpam-6640	110	33	:	:	PUNCT
ejpam-6640	110	34	z	z	X
ejpam-6640	110	35	→	→	SYM
ejpam-6640	110	36	0	0	NUM
ejpam-6640	110	37	is	be	AUX
ejpam-6640	110	38	the	the	DET
ejpam-6640	110	39	zero	zero	NUM
ejpam-6640	110	40	morphism	morphism	NOUN
ejpam-6640	110	41	of	of	ADP
ejpam-6640	110	42	the	the	DET
ejpam-6640	110	43	abelian	abelian	PROPN
ejpam-6640	110	44	group	group	PROPN
ejpam-6640	110	45	homa	homa	PROPN
ejpam-6640	110	46	(	(	PUNCT
ejpam-6640	110	47	z	z	NOUN
ejpam-6640	110	48	,	,	PUNCT
ejpam-6640	110	49	0	0	NUM
ejpam-6640	110	50	)	)	PUNCT
ejpam-6640	110	51	con(h	con(h	PROPN
ejpam-6640	110	52	)	)	PUNCT
ejpam-6640	110	53	=	=	SYM
ejpam-6640	110	54	(	(	PUNCT
ejpam-6640	110	55	0	0	NUM
ejpam-6640	110	56	,	,	PUNCT
ejpam-6640	110	57	ek,0	ek,0	PROPN
ejpam-6640	110	58	)	)	PUNCT
ejpam-6640	110	59	where	where	SCONJ
ejpam-6640	110	60	ek,0	ek,0	PROPN
ejpam-6640	110	61	:	:	PUNCT
ejpam-6640	110	62	k	k	X
ejpam-6640	110	63	→	→	SYM
ejpam-6640	110	64	0	0	NUM
ejpam-6640	110	65	is	be	AUX
ejpam-6640	110	66	the	the	DET
ejpam-6640	110	67	zero	zero	NUM
ejpam-6640	110	68	morphism	morphism	NOUN
ejpam-6640	110	69	of	of	ADP
ejpam-6640	110	70	the	the	DET
ejpam-6640	110	71	abelian	abelian	PROPN
ejpam-6640	110	72	group	group	PROPN
ejpam-6640	110	73	homa	homa	PROPN
ejpam-6640	110	74	(	(	PUNCT
ejpam-6640	110	75	k	k	NOUN
ejpam-6640	110	76	,	,	PUNCT
ejpam-6640	110	77	0	0	NUM
ejpam-6640	110	78	)	)	PUNCT
ejpam-6640	110	79	with	with	ADP
ejpam-6640	110	80	h	h	NOUN
ejpam-6640	110	81	the	the	DET
ejpam-6640	110	82	morphism	morphism	NOUN
ejpam-6640	110	83	satisfying	satisfy	VERB
ejpam-6640	110	84	i	i	PRON
ejpam-6640	110	85	◦	◦	VERB
ejpam-6640	110	86	h	h	NOUN
ejpam-6640	110	87	=	=	SYM
ejpam-6640	110	88	f	f	PROPN
ejpam-6640	110	89	and	and	CCONJ
ejpam-6640	110	90	ker	ker	NOUN
ejpam-6640	110	91	g	g	PROPN
ejpam-6640	110	92	=	=	SYM
ejpam-6640	110	93	(	(	PUNCT
ejpam-6640	110	94	k	k	X
ejpam-6640	110	95	,	,	PUNCT
ejpam-6640	110	96	i	i	PROPN
ejpam-6640	110	97	)	)	PUNCT
ejpam-6640	110	98	.	.	PUNCT
ejpam-6640	111	1	k	k	X
ejpam-6640	111	2	>	>	X
ejpam-6640	111	3	>	>	X
ejpam-6640	111	4	h	h	PROPN
ejpam-6640	112	1	i	i	PRON
ejpam-6640	112	2	�	�	VERB
ejpam-6640	112	3	�	�	PROPN
ejpam-6640	112	4	0	0	NUM
ejpam-6640	112	5	//	//	PUNCT
ejpam-6640	113	1	x	x	X
ejpam-6640	113	2	f	f	PROPN
ejpam-6640	113	3	//	//	PUNCT
ejpam-6640	113	4	y	y	PROPN
ejpam-6640	113	5	g	g	PROPN
ejpam-6640	113	6	//	//	PROPN
ejpam-6640	113	7	z	z	PROPN
ejpam-6640	113	8	//	//	PROPN
ejpam-6640	113	9	0	0	NUM
ejpam-6640	113	10	a.	a.	PROPN
ejpam-6640	113	11	diallo	diallo	PROPN
ejpam-6640	113	12	,	,	PUNCT
ejpam-6640	113	13	m.	m.	PROPN
ejpam-6640	113	14	b.	b.	PROPN
ejpam-6640	113	15	f.	f.	PROPN
ejpam-6640	113	16	b.	b.	PROPN
ejpam-6640	113	17	maaouia	maaouia	PROPN
ejpam-6640	113	18	,	,	PUNCT
ejpam-6640	113	19	m.	m.	NOUN
ejpam-6640	113	20	sanghare	sanghare	PROPN
ejpam-6640	113	21	/	/	SYM
ejpam-6640	113	22	eur	eur	PROPN
ejpam-6640	113	23	.	.	PUNCT
ejpam-6640	114	1	j.	j.	PROPN
ejpam-6640	114	2	pure	pure	PROPN
ejpam-6640	114	3	appl	appl	PROPN
ejpam-6640	114	4	.	.	PROPN
ejpam-6640	114	5	math	math	PROPN
ejpam-6640	114	6	,	,	PUNCT
ejpam-6640	114	7	18	18	NUM
ejpam-6640	114	8	(	(	PUNCT
ejpam-6640	114	9	4	4	NUM
ejpam-6640	114	10	)	)	PUNCT
ejpam-6640	114	11	(	(	PUNCT
ejpam-6640	114	12	2025	2025	NUM
ejpam-6640	114	13	)	)	PUNCT
ejpam-6640	114	14	,	,	PUNCT
ejpam-6640	114	15	6640	6640	NUM
ejpam-6640	114	16	6	6	NUM
ejpam-6640	114	17	of	of	ADP
ejpam-6640	114	18	28	28	NUM
ejpam-6640	114	19	remark	remark	NOUN
ejpam-6640	114	20	1	1	NUM
ejpam-6640	114	21	.	.	NOUN
ejpam-6640	114	22	0	0	NUM
ejpam-6640	114	23	denotes	denote	VERB
ejpam-6640	114	24	the	the	DET
ejpam-6640	114	25	zero	zero	NUM
ejpam-6640	114	26	object	object	NOUN
ejpam-6640	114	27	of	of	ADP
ejpam-6640	114	28	the	the	DET
ejpam-6640	114	29	category	category	NOUN
ejpam-6640	114	30	a	a	NOUN
ejpam-6640	114	31	.	.	PUNCT
ejpam-6640	115	1	[	[	X
ejpam-6640	115	2	comp(a	comp(a	NOUN
ejpam-6640	115	3	)	)	PUNCT
ejpam-6640	115	4	]	]	PUNCT
ejpam-6640	116	1	the	the	DET
ejpam-6640	116	2	category	category	NOUN
ejpam-6640	116	3	of	of	ADP
ejpam-6640	116	4	complexes	complex	NOUN
ejpam-6640	116	5	of	of	ADP
ejpam-6640	116	6	an	an	DET
ejpam-6640	116	7	abelian	abelian	ADJ
ejpam-6640	116	8	category	category	NOUN
ejpam-6640	116	9	a	a	NOUN
ejpam-6640	116	10	,	,	PUNCT
ejpam-6640	116	11	denoted	denote	VERB
ejpam-6640	116	12	comp(a	comp(a	NOUN
ejpam-6640	116	13	)	)	PUNCT
ejpam-6640	116	14	,	,	PUNCT
ejpam-6640	116	15	is	be	AUX
ejpam-6640	116	16	defined	define	VERB
ejpam-6640	116	17	by	by	ADP
ejpam-6640	116	18	:	:	PUNCT
ejpam-6640	116	19	(	(	PUNCT
ejpam-6640	116	20	i	i	NOUN
ejpam-6640	116	21	)	)	PUNCT
ejpam-6640	116	22	the	the	DET
ejpam-6640	116	23	objects	object	NOUN
ejpam-6640	116	24	are	be	AUX
ejpam-6640	116	25	complex	complex	ADJ
ejpam-6640	116	26	sequence	sequence	NOUN
ejpam-6640	116	27	in	in	ADP
ejpam-6640	116	28	a	a	PRON
ejpam-6640	116	29	.	.	PUNCT
ejpam-6640	117	1	a	a	DET
ejpam-6640	117	2	complex	complex	ADJ
ejpam-6640	117	3	sequence	sequence	NOUN
ejpam-6640	117	4	in	in	ADP
ejpam-6640	117	5	a	a	PRON
ejpam-6640	117	6	is	be	AUX
ejpam-6640	117	7	a	a	DET
ejpam-6640	117	8	sequence	sequence	NOUN
ejpam-6640	117	9	of	of	ADP
ejpam-6640	117	10	morphisms	morphism	NOUN
ejpam-6640	117	11	in	in	ADP
ejpam-6640	117	12	a	a	DET
ejpam-6640	117	13	(	(	PUNCT
ejpam-6640	117	14	αn	αn	NOUN
ejpam-6640	117	15	:	:	PUNCT
ejpam-6640	117	16	xn	xn	PROPN
ejpam-6640	117	17	→	→	SYM
ejpam-6640	117	18	xn+1)n∈z	xn+1)n∈z	PROPN
ejpam-6640	117	19	,	,	PUNCT
ejpam-6640	117	20	denoted	denote	VERB
ejpam-6640	117	21	(	(	PUNCT
ejpam-6640	117	22	x	x	X
ejpam-6640	117	23	,	,	PUNCT
ejpam-6640	117	24	α	α	NOUN
ejpam-6640	117	25	)	)	PUNCT
ejpam-6640	117	26	,	,	PUNCT
ejpam-6640	117	27	such	such	ADJ
ejpam-6640	117	28	that	that	DET
ejpam-6640	117	29	αn+1	αn+1	NUM
ejpam-6640	117	30	◦	◦	NOUN
ejpam-6640	117	31	αn	αn	NOUN
ejpam-6640	117	32	=	=	SYM
ejpam-6640	117	33	exn	exn	PROPN
ejpam-6640	117	34	,	,	PUNCT
ejpam-6640	117	35	xn+2	xn+2	PROPN
ejpam-6640	117	36	∀n	∀n	NUM
ejpam-6640	118	1	∈	∈	PROPN
ejpam-6640	119	1	z	z	NOUN
ejpam-6640	119	2	,	,	PUNCT
ejpam-6640	119	3	where	where	SCONJ
ejpam-6640	119	4	exn	exn	PROPN
ejpam-6640	119	5	,	,	PUNCT
ejpam-6640	119	6	xn+2	xn+2	PROPN
ejpam-6640	119	7	is	be	AUX
ejpam-6640	119	8	the	the	DET
ejpam-6640	119	9	zero	zero	NUM
ejpam-6640	119	10	morphism	morphism	NOUN
ejpam-6640	119	11	of	of	ADP
ejpam-6640	119	12	the	the	DET
ejpam-6640	119	13	abelian	abelian	PROPN
ejpam-6640	119	14	group	group	PROPN
ejpam-6640	119	15	homa	homa	PROPN
ejpam-6640	119	16	(	(	PUNCT
ejpam-6640	119	17	xn	xn	PROPN
ejpam-6640	119	18	,	,	PUNCT
ejpam-6640	119	19	xn+2	xn+2	NUM
ejpam-6640	119	20	)	)	PUNCT
ejpam-6640	119	21	.	.	PUNCT
ejpam-6640	120	1	(	(	PUNCT
ejpam-6640	120	2	ii	ii	X
ejpam-6640	120	3	)	)	PUNCT
ejpam-6640	120	4	the	the	DET
ejpam-6640	120	5	morphisms	morphism	NOUN
ejpam-6640	120	6	(	(	PUNCT
ejpam-6640	120	7	arrows	arrow	NOUN
ejpam-6640	120	8	)	)	PUNCT
ejpam-6640	120	9	are	be	AUX
ejpam-6640	120	10	complex	complex	ADJ
ejpam-6640	120	11	chains	chain	NOUN
ejpam-6640	120	12	in	in	ADP
ejpam-6640	120	13	a	a	PRON
ejpam-6640	120	14	.	.	PUNCT
ejpam-6640	121	1	let	let	VERB
ejpam-6640	121	2	(	(	PUNCT
ejpam-6640	121	3	x	x	NOUN
ejpam-6640	121	4	,	,	PUNCT
ejpam-6640	121	5	α	α	NOUN
ejpam-6640	121	6	)	)	PUNCT
ejpam-6640	121	7	=	=	SYM
ejpam-6640	122	1	(	(	PUNCT
ejpam-6640	122	2	αn	αn	NOUN
ejpam-6640	122	3	:	:	PUNCT
ejpam-6640	122	4	xn	xn	PROPN
ejpam-6640	122	5	→	→	SYM
ejpam-6640	122	6	xn+1)n∈z	xn+1)n∈z	PROPN
ejpam-6640	122	7	and	and	CCONJ
ejpam-6640	122	8	(	(	PUNCT
ejpam-6640	122	9	y	y	PROPN
ejpam-6640	122	10	,	,	PUNCT
ejpam-6640	122	11	β	β	NOUN
ejpam-6640	122	12	)	)	PUNCT
ejpam-6640	122	13	=	=	SYM
ejpam-6640	123	1	(	(	PUNCT
ejpam-6640	123	2	βn	βn	NOUN
ejpam-6640	123	3	:	:	PUNCT
ejpam-6640	123	4	yn	yn	PROPN
ejpam-6640	123	5	→	→	SYM
ejpam-6640	123	6	yn+1)n∈z	yn+1)n∈z	NUM
ejpam-6640	123	7	be	be	AUX
ejpam-6640	123	8	two	two	NUM
ejpam-6640	123	9	complex	complex	ADJ
ejpam-6640	123	10	sequences	sequence	NOUN
ejpam-6640	123	11	in	in	ADP
ejpam-6640	123	12	a	a	PRON
ejpam-6640	123	13	.	.	PUNCT
ejpam-6640	124	1	a	a	DET
ejpam-6640	124	2	complex	complex	ADJ
ejpam-6640	124	3	chain	chain	NOUN
ejpam-6640	124	4	(	(	PUNCT
ejpam-6640	124	5	fn	fn	NOUN
ejpam-6640	124	6	:	:	PUNCT
ejpam-6640	124	7	xn	xn	PROPN
ejpam-6640	124	8	−→	−→	NOUN
ejpam-6640	124	9	yn)n∈z	yn)n∈z	NUM
ejpam-6640	124	10	,	,	PUNCT
ejpam-6640	124	11	denoted	denote	VERB
ejpam-6640	124	12	f	f	X
ejpam-6640	124	13	:	:	PUNCT
ejpam-6640	124	14	(	(	PUNCT
ejpam-6640	124	15	x	x	X
ejpam-6640	124	16	,	,	PUNCT
ejpam-6640	124	17	α	α	NOUN
ejpam-6640	124	18	)	)	PUNCT
ejpam-6640	124	19	→	→	SYM
ejpam-6640	124	20	(	(	PUNCT
ejpam-6640	124	21	y	y	PROPN
ejpam-6640	124	22	,	,	PUNCT
ejpam-6640	124	23	β	β	NOUN
ejpam-6640	124	24	)	)	PUNCT
ejpam-6640	124	25	,	,	PUNCT
ejpam-6640	124	26	is	be	AUX
ejpam-6640	124	27	a	a	DET
ejpam-6640	124	28	sequence	sequence	NOUN
ejpam-6640	124	29	of	of	ADP
ejpam-6640	124	30	morphisms	morphism	NOUN
ejpam-6640	124	31	in	in	ADP
ejpam-6640	124	32	a	a	DET
ejpam-6640	124	33	such	such	ADJ
ejpam-6640	124	34	that	that	SCONJ
ejpam-6640	124	35	:	:	PUNCT
ejpam-6640	124	36	fn+1	fn+1	VERB
ejpam-6640	124	37	◦	◦	NOUN
ejpam-6640	124	38	αn	αn	NOUN
ejpam-6640	124	39	=	=	SYM
ejpam-6640	125	1	βn	βn	PROPN
ejpam-6640	125	2	◦	◦	NOUN
ejpam-6640	125	3	fn	fn	NOUN
ejpam-6640	125	4	∀n	∀n	NUM
ejpam-6640	125	5	∈	∈	PROPN
ejpam-6640	125	6	z.	z.	X
ejpam-6640	126	1	[	[	X
ejpam-6640	126	2	right	right	ADJ
ejpam-6640	126	3	exact	exact	ADJ
ejpam-6640	126	4	sequence	sequence	NOUN
ejpam-6640	126	5	in	in	ADP
ejpam-6640	126	6	comp(a	comp(a	NOUN
ejpam-6640	126	7	)	)	PUNCT
ejpam-6640	126	8	]	]	PUNCT
ejpam-6640	127	1	let	let	VERB
ejpam-6640	127	2	(	(	PUNCT
ejpam-6640	127	3	s	s	X
ejpam-6640	127	4	)	)	PUNCT
ejpam-6640	127	5	:	:	PUNCT
ejpam-6640	127	6	(	(	PUNCT
ejpam-6640	127	7	y	y	PROPN
ejpam-6640	127	8	,	,	PUNCT
ejpam-6640	127	9	α	α	NOUN
ejpam-6640	127	10	)	)	PUNCT
ejpam-6640	127	11	f	f	PROPN
ejpam-6640	127	12	//	//	X
ejpam-6640	128	1	(	(	PUNCT
ejpam-6640	128	2	z	z	NOUN
ejpam-6640	128	3	,	,	PUNCT
ejpam-6640	128	4	β	β	NOUN
ejpam-6640	128	5	)	)	PUNCT
ejpam-6640	128	6	g	g	PROPN
ejpam-6640	128	7	//	//	SYM
ejpam-6640	128	8	(	(	PUNCT
ejpam-6640	128	9	t	t	PROPN
ejpam-6640	128	10	,	,	PUNCT
ejpam-6640	128	11	γ	γ	PROPN
ejpam-6640	128	12	)	)	PUNCT
ejpam-6640	128	13	//	//	NOUN
ejpam-6640	128	14	(	(	PUNCT
ejpam-6640	128	15	0	0	NUM
ejpam-6640	128	16	)	)	PUNCT
ejpam-6640	128	17	be	be	AUX
ejpam-6640	128	18	a	a	DET
ejpam-6640	128	19	short	short	ADJ
ejpam-6640	128	20	sequence	sequence	NOUN
ejpam-6640	128	21	of	of	ADP
ejpam-6640	128	22	morphisms	morphism	NOUN
ejpam-6640	128	23	in	in	ADP
ejpam-6640	128	24	comp(a	comp(a	NOUN
ejpam-6640	128	25	)	)	PUNCT
ejpam-6640	128	26	where	where	SCONJ
ejpam-6640	128	27	a	a	PRON
ejpam-6640	128	28	is	be	AUX
ejpam-6640	128	29	an	an	DET
ejpam-6640	128	30	abelian	abelian	ADJ
ejpam-6640	128	31	category	category	NOUN
ejpam-6640	128	32	.	.	PUNCT
ejpam-6640	129	1	then	then	ADV
ejpam-6640	129	2	we	we	PRON
ejpam-6640	129	3	say	say	VERB
ejpam-6640	129	4	that	that	SCONJ
ejpam-6640	129	5	(	(	PUNCT
ejpam-6640	129	6	s	s	X
ejpam-6640	129	7	)	)	PUNCT
ejpam-6640	129	8	is	be	AUX
ejpam-6640	129	9	right	right	ADV
ejpam-6640	129	10	exact	exact	ADJ
ejpam-6640	129	11	if	if	SCONJ
ejpam-6640	129	12	for	for	ADP
ejpam-6640	129	13	every	every	DET
ejpam-6640	129	14	integer	integer	NOUN
ejpam-6640	129	15	n	n	CCONJ
ejpam-6640	129	16	in	in	ADP
ejpam-6640	129	17	z	z	PROPN
ejpam-6640	129	18	the	the	DET
ejpam-6640	129	19	sequence	sequence	NOUN
ejpam-6640	130	1	yn	yn	INTJ
ejpam-6640	130	2	fn	fn	PROPN
ejpam-6640	130	3	//	//	PROPN
ejpam-6640	130	4	zn	zn	PROPN
ejpam-6640	130	5	gn	gn	PROPN
ejpam-6640	130	6	//	//	PROPN
ejpam-6640	130	7	tn	tn	PROPN
ejpam-6640	130	8	//	//	PROPN
ejpam-6640	130	9	0	0	NUM
ejpam-6640	130	10	is	be	AUX
ejpam-6640	130	11	a	a	DET
ejpam-6640	130	12	right	right	ADJ
ejpam-6640	130	13	exact	exact	ADJ
ejpam-6640	130	14	short	short	ADJ
ejpam-6640	130	15	sequence	sequence	NOUN
ejpam-6640	130	16	of	of	ADP
ejpam-6640	130	17	morphisms	morphism	NOUN
ejpam-6640	130	18	in	in	ADP
ejpam-6640	130	19	a	a	PRON
ejpam-6640	130	20	.	.	PUNCT
ejpam-6640	131	1	[	[	X
ejpam-6640	131	2	left	left	ADJ
ejpam-6640	131	3	exact	exact	ADJ
ejpam-6640	131	4	sequence	sequence	NOUN
ejpam-6640	131	5	in	in	ADP
ejpam-6640	131	6	comp(a	comp(a	NOUN
ejpam-6640	131	7	)	)	PUNCT
ejpam-6640	131	8	]	]	PUNCT
ejpam-6640	132	1	let	let	VERB
ejpam-6640	132	2	(	(	PUNCT
ejpam-6640	132	3	s	s	X
ejpam-6640	132	4	)	)	PUNCT
ejpam-6640	132	5	:	:	PUNCT
ejpam-6640	132	6	(	(	PUNCT
ejpam-6640	132	7	0	0	X
ejpam-6640	132	8	)	)	PUNCT
ejpam-6640	132	9	//	//	NOUN
ejpam-6640	133	1	(	(	PUNCT
ejpam-6640	133	2	y	y	PROPN
ejpam-6640	133	3	,	,	PUNCT
ejpam-6640	133	4	α	α	NOUN
ejpam-6640	133	5	)	)	PUNCT
ejpam-6640	133	6	f	f	PROPN
ejpam-6640	133	7	//	//	X
ejpam-6640	133	8	(	(	PUNCT
ejpam-6640	133	9	z	z	NOUN
ejpam-6640	133	10	,	,	PUNCT
ejpam-6640	133	11	β	β	NOUN
ejpam-6640	133	12	)	)	PUNCT
ejpam-6640	133	13	g	g	PROPN
ejpam-6640	133	14	//	//	SYM
ejpam-6640	133	15	(	(	PUNCT
ejpam-6640	133	16	t	t	PROPN
ejpam-6640	133	17	,	,	PUNCT
ejpam-6640	133	18	γ	γ	NOUN
ejpam-6640	133	19	)	)	PUNCT
ejpam-6640	133	20	be	be	VERB
ejpam-6640	133	21	a	a	DET
ejpam-6640	133	22	short	short	ADJ
ejpam-6640	133	23	sequence	sequence	NOUN
ejpam-6640	133	24	of	of	ADP
ejpam-6640	133	25	morphisms	morphism	NOUN
ejpam-6640	133	26	in	in	ADP
ejpam-6640	133	27	comp(a	comp(a	NOUN
ejpam-6640	133	28	)	)	PUNCT
ejpam-6640	133	29	where	where	SCONJ
ejpam-6640	133	30	a	a	PRON
ejpam-6640	133	31	is	be	AUX
ejpam-6640	133	32	an	an	DET
ejpam-6640	133	33	abelian	abelian	ADJ
ejpam-6640	133	34	category	category	NOUN
ejpam-6640	133	35	.	.	PUNCT
ejpam-6640	134	1	then	then	ADV
ejpam-6640	134	2	we	we	PRON
ejpam-6640	134	3	say	say	VERB
ejpam-6640	134	4	that	that	SCONJ
ejpam-6640	134	5	(	(	PUNCT
ejpam-6640	134	6	s	s	X
ejpam-6640	134	7	)	)	PUNCT
ejpam-6640	134	8	is	be	AUX
ejpam-6640	134	9	left	leave	VERB
ejpam-6640	134	10	exact	exact	ADJ
ejpam-6640	134	11	if	if	SCONJ
ejpam-6640	134	12	for	for	ADP
ejpam-6640	134	13	every	every	DET
ejpam-6640	134	14	integer	integer	NOUN
ejpam-6640	134	15	n	n	CCONJ
ejpam-6640	134	16	in	in	ADP
ejpam-6640	134	17	z	z	PROPN
ejpam-6640	134	18	the	the	DET
ejpam-6640	134	19	sequence	sequence	NOUN
ejpam-6640	134	20	0	0	NUM
ejpam-6640	134	21	//	//	PUNCT
ejpam-6640	135	1	yn	yn	PROPN
ejpam-6640	135	2	fn	fn	PROPN
ejpam-6640	135	3	//	//	PROPN
ejpam-6640	135	4	zn	zn	PROPN
ejpam-6640	135	5	gn	gn	PROPN
ejpam-6640	135	6	//	//	PROPN
ejpam-6640	135	7	tn	tn	PROPN
ejpam-6640	135	8	is	be	AUX
ejpam-6640	135	9	a	a	DET
ejpam-6640	135	10	left	left	ADJ
ejpam-6640	135	11	exact	exact	ADJ
ejpam-6640	135	12	short	short	ADJ
ejpam-6640	135	13	sequence	sequence	NOUN
ejpam-6640	135	14	of	of	ADP
ejpam-6640	135	15	morphisms	morphism	NOUN
ejpam-6640	135	16	in	in	ADP
ejpam-6640	135	17	a	a	PRON
ejpam-6640	135	18	.	.	PUNCT
ejpam-6640	136	1	[	[	X
ejpam-6640	136	2	exact	exact	ADJ
ejpam-6640	136	3	sequence	sequence	NOUN
ejpam-6640	136	4	in	in	ADP
ejpam-6640	136	5	comp(a	comp(a	NOUN
ejpam-6640	136	6	)	)	PUNCT
ejpam-6640	136	7	]	]	PUNCT
ejpam-6640	137	1	let	let	VERB
ejpam-6640	137	2	(	(	PUNCT
ejpam-6640	137	3	s	s	X
ejpam-6640	137	4	)	)	PUNCT
ejpam-6640	137	5	:	:	PUNCT
ejpam-6640	137	6	(	(	PUNCT
ejpam-6640	137	7	0	0	X
ejpam-6640	137	8	)	)	PUNCT
ejpam-6640	137	9	//	//	NOUN
ejpam-6640	138	1	(	(	PUNCT
ejpam-6640	138	2	y	y	PROPN
ejpam-6640	138	3	,	,	PUNCT
ejpam-6640	138	4	α	α	NOUN
ejpam-6640	138	5	)	)	PUNCT
ejpam-6640	138	6	f	f	PROPN
ejpam-6640	138	7	//	//	X
ejpam-6640	138	8	(	(	PUNCT
ejpam-6640	138	9	z	z	NOUN
ejpam-6640	138	10	,	,	PUNCT
ejpam-6640	138	11	β	β	NOUN
ejpam-6640	138	12	)	)	PUNCT
ejpam-6640	138	13	g	g	PROPN
ejpam-6640	138	14	//	//	SYM
ejpam-6640	138	15	(	(	PUNCT
ejpam-6640	138	16	t	t	PROPN
ejpam-6640	138	17	,	,	PUNCT
ejpam-6640	138	18	γ	γ	PROPN
ejpam-6640	138	19	)	)	PUNCT
ejpam-6640	138	20	//	//	NOUN
ejpam-6640	138	21	(	(	PUNCT
ejpam-6640	138	22	0	0	NUM
ejpam-6640	138	23	)	)	PUNCT
ejpam-6640	138	24	be	be	AUX
ejpam-6640	138	25	a	a	DET
ejpam-6640	138	26	short	short	ADJ
ejpam-6640	138	27	sequence	sequence	NOUN
ejpam-6640	138	28	of	of	ADP
ejpam-6640	138	29	morphisms	morphism	NOUN
ejpam-6640	138	30	in	in	ADP
ejpam-6640	138	31	comp(a	comp(a	NOUN
ejpam-6640	138	32	)	)	PUNCT
ejpam-6640	138	33	where	where	SCONJ
ejpam-6640	138	34	a	a	PRON
ejpam-6640	138	35	is	be	AUX
ejpam-6640	138	36	an	an	DET
ejpam-6640	138	37	abelian	abelian	ADJ
ejpam-6640	138	38	category	category	NOUN
ejpam-6640	138	39	.	.	PUNCT
ejpam-6640	139	1	then	then	ADV
ejpam-6640	139	2	we	we	PRON
ejpam-6640	139	3	say	say	VERB
ejpam-6640	139	4	that	that	SCONJ
ejpam-6640	139	5	(	(	PUNCT
ejpam-6640	139	6	s	s	X
ejpam-6640	139	7	)	)	PUNCT
ejpam-6640	139	8	is	be	AUX
ejpam-6640	139	9	exact	exact	ADJ
ejpam-6640	139	10	if	if	SCONJ
ejpam-6640	139	11	for	for	ADP
ejpam-6640	139	12	every	every	DET
ejpam-6640	139	13	integer	integer	NOUN
ejpam-6640	139	14	n	n	CCONJ
ejpam-6640	139	15	in	in	ADP
ejpam-6640	139	16	z	z	PROPN
ejpam-6640	139	17	the	the	DET
ejpam-6640	139	18	sequence	sequence	NOUN
ejpam-6640	139	19	0	0	NUM
ejpam-6640	139	20	//	//	PUNCT
ejpam-6640	140	1	yn	yn	PROPN
ejpam-6640	140	2	fn	fn	PROPN
ejpam-6640	140	3	//	//	PROPN
ejpam-6640	140	4	zn	zn	PROPN
ejpam-6640	140	5	gn	gn	PROPN
ejpam-6640	140	6	//	//	PROPN
ejpam-6640	140	7	tn	tn	PROPN
ejpam-6640	140	8	//	//	PROPN
ejpam-6640	140	9	0	0	NUM
ejpam-6640	140	10	is	be	AUX
ejpam-6640	140	11	a	a	DET
ejpam-6640	140	12	short	short	ADJ
ejpam-6640	140	13	exact	exact	ADJ
ejpam-6640	140	14	sequence	sequence	NOUN
ejpam-6640	140	15	of	of	ADP
ejpam-6640	140	16	morphisms	morphism	NOUN
ejpam-6640	140	17	in	in	ADP
ejpam-6640	140	18	a	a	PRON
ejpam-6640	140	19	.	.	PUNCT
ejpam-6640	141	1	let	let	VERB
ejpam-6640	141	2	a	a	PRON
ejpam-6640	141	3	be	be	AUX
ejpam-6640	141	4	an	an	DET
ejpam-6640	141	5	abelian	abelian	ADJ
ejpam-6640	141	6	category	category	NOUN
ejpam-6640	141	7	.	.	PUNCT
ejpam-6640	142	1	then	then	ADV
ejpam-6640	142	2	comp(a	comp(a	VERB
ejpam-6640	142	3	)	)	PUNCT
ejpam-6640	142	4	is	be	AUX
ejpam-6640	142	5	an	an	DET
ejpam-6640	142	6	abelian	abelian	ADJ
ejpam-6640	142	7	category	category	NOUN
ejpam-6640	142	8	.	.	PUNCT
ejpam-6640	143	1	proof	proof	NOUN
ejpam-6640	143	2	.	.	PUNCT
ejpam-6640	144	1	see	see	VERB
ejpam-6640	144	2	page	page	NOUN
ejpam-6640	144	3	319	319	NUM
ejpam-6640	145	1	[	[	X
ejpam-6640	145	2	9	9	NUM
ejpam-6640	145	3	]	]	PUNCT
ejpam-6640	145	4	.	.	PUNCT
ejpam-6640	146	1	let	let	VERB
ejpam-6640	146	2	a	a	PRON
ejpam-6640	146	3	be	be	AUX
ejpam-6640	146	4	a	a	DET
ejpam-6640	146	5	balanced	balanced	ADJ
ejpam-6640	146	6	abelian	abelian	ADJ
ejpam-6640	146	7	category	category	NOUN
ejpam-6640	146	8	.	.	PUNCT
ejpam-6640	147	1	then	then	ADV
ejpam-6640	147	2	comp(a	comp(a	VERB
ejpam-6640	147	3	)	)	PUNCT
ejpam-6640	147	4	is	be	AUX
ejpam-6640	147	5	a	a	DET
ejpam-6640	147	6	balanced	balanced	ADJ
ejpam-6640	147	7	abelian	abelian	ADJ
ejpam-6640	147	8	category	category	NOUN
ejpam-6640	147	9	.	.	PUNCT
ejpam-6640	148	1	proof	proof	NOUN
ejpam-6640	148	2	.	.	PUNCT
ejpam-6640	149	1	let	let	VERB
ejpam-6640	149	2	a	a	PRON
ejpam-6640	149	3	be	be	AUX
ejpam-6640	149	4	a	a	DET
ejpam-6640	149	5	balanced	balanced	ADJ
ejpam-6640	149	6	abelian	abelian	ADJ
ejpam-6640	149	7	category	category	NOUN
ejpam-6640	149	8	,	,	PUNCT
ejpam-6640	149	9	which	which	PRON
ejpam-6640	149	10	means	mean	VERB
ejpam-6640	149	11	:	:	PUNCT
ejpam-6640	149	12	every	every	DET
ejpam-6640	149	13	monomorphism	monomorphism	NOUN
ejpam-6640	149	14	in	in	ADP
ejpam-6640	149	15	a	a	PRON
ejpam-6640	149	16	is	be	AUX
ejpam-6640	149	17	a	a	DET
ejpam-6640	149	18	retraction	retraction	NOUN
ejpam-6640	149	19	and	and	CCONJ
ejpam-6640	149	20	every	every	DET
ejpam-6640	149	21	epimorphism	epimorphism	NOUN
ejpam-6640	149	22	in	in	ADP
ejpam-6640	149	23	a	a	PRON
ejpam-6640	149	24	is	be	AUX
ejpam-6640	149	25	a	a	DET
ejpam-6640	149	26	section	section	NOUN
ejpam-6640	149	27	.	.	PUNCT
ejpam-6640	150	1	•	•	INTJ
ejpam-6640	150	2	let	let	VERB
ejpam-6640	150	3	f	f	NOUN
ejpam-6640	150	4	:	:	PUNCT
ejpam-6640	150	5	(	(	PUNCT
ejpam-6640	150	6	x	x	X
ejpam-6640	150	7	,	,	PUNCT
ejpam-6640	150	8	α	α	NOUN
ejpam-6640	150	9	)	)	PUNCT
ejpam-6640	150	10	→	→	SYM
ejpam-6640	150	11	(	(	PUNCT
ejpam-6640	150	12	y	y	PROPN
ejpam-6640	150	13	,	,	PUNCT
ejpam-6640	150	14	β	β	NOUN
ejpam-6640	150	15	)	)	PUNCT
ejpam-6640	150	16	be	be	VERB
ejpam-6640	150	17	a	a	DET
ejpam-6640	150	18	monomorphism	monomorphism	NOUN
ejpam-6640	150	19	in	in	ADP
ejpam-6640	150	20	comp(a	comp(a	NOUN
ejpam-6640	150	21	)	)	PUNCT
ejpam-6640	150	22	.	.	PUNCT
ejpam-6640	151	1	since	since	SCONJ
ejpam-6640	151	2	f	f	PROPN
ejpam-6640	151	3	is	be	AUX
ejpam-6640	151	4	a	a	DET
ejpam-6640	151	5	monomorphism	monomorphism	NOUN
ejpam-6640	151	6	,	,	PUNCT
ejpam-6640	151	7	it	it	PRON
ejpam-6640	151	8	follows	follow	VERB
ejpam-6640	151	9	that	that	SCONJ
ejpam-6640	151	10	for	for	SCONJ
ejpam-6640	151	11	every	every	DET
ejpam-6640	151	12	n	n	NOUN
ejpam-6640	151	13	∈	∈	PROPN
ejpam-6640	151	14	z	z	PROPN
ejpam-6640	151	15	,	,	PUNCT
ejpam-6640	151	16	fn	fn	VERB
ejpam-6640	151	17	:	:	PUNCT
ejpam-6640	151	18	xn	xn	PUNCT
ejpam-6640	151	19	−→	−→	NOUN
ejpam-6640	151	20	yn	yn	PROPN
ejpam-6640	151	21	is	be	AUX
ejpam-6640	151	22	a	a	DET
ejpam-6640	151	23	monomorphism	monomorphism	NOUN
ejpam-6640	151	24	in	in	ADP
ejpam-6640	151	25	a	a	PRON
ejpam-6640	151	26	.	.	PUNCT
ejpam-6640	152	1	and	and	CCONJ
ejpam-6640	152	2	since	since	SCONJ
ejpam-6640	152	3	a	a	PRON
ejpam-6640	152	4	is	be	AUX
ejpam-6640	152	5	balanced	balanced	ADJ
ejpam-6640	152	6	,	,	PUNCT
ejpam-6640	152	7	for	for	ADP
ejpam-6640	152	8	every	every	DET
ejpam-6640	152	9	n	n	NOUN
ejpam-6640	152	10	∈	∈	PROPN
ejpam-6640	152	11	z	z	PROPN
ejpam-6640	152	12	,	,	PUNCT
ejpam-6640	152	13	fn	fn	VERB
ejpam-6640	152	14	:	:	PUNCT
ejpam-6640	152	15	xn	xn	PUNCT
ejpam-6640	153	1	−→	−→	NOUN
ejpam-6640	153	2	yn	yn	PROPN
ejpam-6640	153	3	is	be	AUX
ejpam-6640	153	4	a	a	DET
ejpam-6640	153	5	retraction	retraction	NOUN
ejpam-6640	153	6	.	.	PUNCT
ejpam-6640	154	1	therefore	therefore	ADV
ejpam-6640	154	2	,	,	PUNCT
ejpam-6640	154	3	f	f	PROPN
ejpam-6640	154	4	is	be	AUX
ejpam-6640	154	5	a	a	DET
ejpam-6640	154	6	retraction	retraction	NOUN
ejpam-6640	154	7	.	.	PUNCT
ejpam-6640	155	1	a.	a.	PROPN
ejpam-6640	155	2	diallo	diallo	PROPN
ejpam-6640	155	3	,	,	PUNCT
ejpam-6640	155	4	m.	m.	PROPN
ejpam-6640	155	5	b.	b.	PROPN
ejpam-6640	155	6	f.	f.	PROPN
ejpam-6640	155	7	b.	b.	PROPN
ejpam-6640	155	8	maaouia	maaouia	PROPN
ejpam-6640	155	9	,	,	PUNCT
ejpam-6640	155	10	m.	m.	NOUN
ejpam-6640	155	11	sanghare	sanghare	PROPN
ejpam-6640	155	12	/	/	SYM
ejpam-6640	155	13	eur	eur	PROPN
ejpam-6640	155	14	.	.	PUNCT
ejpam-6640	156	1	j.	j.	PROPN
ejpam-6640	156	2	pure	pure	PROPN
ejpam-6640	156	3	appl	appl	PROPN
ejpam-6640	156	4	.	.	PROPN
ejpam-6640	156	5	math	math	PROPN
ejpam-6640	156	6	,	,	PUNCT
ejpam-6640	156	7	18	18	NUM
ejpam-6640	156	8	(	(	PUNCT
ejpam-6640	156	9	4	4	NUM
ejpam-6640	156	10	)	)	PUNCT
ejpam-6640	156	11	(	(	PUNCT
ejpam-6640	156	12	2025	2025	NUM
ejpam-6640	156	13	)	)	PUNCT
ejpam-6640	156	14	,	,	PUNCT
ejpam-6640	156	15	6640	6640	NUM
ejpam-6640	156	16	7	7	NUM
ejpam-6640	156	17	of	of	ADP
ejpam-6640	156	18	28	28	NUM
ejpam-6640	156	19	•	•	NOUN
ejpam-6640	156	20	let	let	VERB
ejpam-6640	156	21	f	f	NOUN
ejpam-6640	156	22	:	:	PUNCT
ejpam-6640	156	23	(	(	PUNCT
ejpam-6640	156	24	x	x	X
ejpam-6640	156	25	,	,	PUNCT
ejpam-6640	156	26	α	α	NOUN
ejpam-6640	156	27	)	)	PUNCT
ejpam-6640	156	28	→	→	SYM
ejpam-6640	156	29	(	(	PUNCT
ejpam-6640	156	30	y	y	PROPN
ejpam-6640	156	31	,	,	PUNCT
ejpam-6640	156	32	β	β	NOUN
ejpam-6640	156	33	)	)	PUNCT
ejpam-6640	156	34	be	be	VERB
ejpam-6640	156	35	an	an	DET
ejpam-6640	156	36	epimorphism	epimorphism	NOUN
ejpam-6640	156	37	in	in	ADP
ejpam-6640	156	38	comp(a	comp(a	NOUN
ejpam-6640	156	39	)	)	PUNCT
ejpam-6640	156	40	.	.	PUNCT
ejpam-6640	157	1	since	since	SCONJ
ejpam-6640	157	2	f	f	PROPN
ejpam-6640	157	3	is	be	AUX
ejpam-6640	157	4	an	an	DET
ejpam-6640	157	5	epimorphism	epimorphism	NOUN
ejpam-6640	157	6	,	,	PUNCT
ejpam-6640	157	7	it	it	PRON
ejpam-6640	157	8	follows	follow	VERB
ejpam-6640	157	9	that	that	SCONJ
ejpam-6640	157	10	for	for	SCONJ
ejpam-6640	157	11	every	every	DET
ejpam-6640	157	12	n	n	NOUN
ejpam-6640	157	13	∈	∈	PROPN
ejpam-6640	157	14	z	z	PROPN
ejpam-6640	157	15	,	,	PUNCT
ejpam-6640	157	16	fn	fn	VERB
ejpam-6640	157	17	:	:	PUNCT
ejpam-6640	157	18	xn	xn	PUNCT
ejpam-6640	157	19	−→	−→	NOUN
ejpam-6640	157	20	yn	yn	PROPN
ejpam-6640	157	21	is	be	AUX
ejpam-6640	157	22	an	an	DET
ejpam-6640	157	23	epimorphism	epimorphism	NOUN
ejpam-6640	157	24	in	in	ADP
ejpam-6640	157	25	a	a	PRON
ejpam-6640	157	26	.	.	PUNCT
ejpam-6640	158	1	and	and	CCONJ
ejpam-6640	158	2	since	since	SCONJ
ejpam-6640	158	3	a	a	PRON
ejpam-6640	158	4	is	be	AUX
ejpam-6640	158	5	balanced	balanced	ADJ
ejpam-6640	158	6	,	,	PUNCT
ejpam-6640	158	7	for	for	ADP
ejpam-6640	158	8	every	every	DET
ejpam-6640	158	9	n	n	NOUN
ejpam-6640	158	10	∈	∈	PROPN
ejpam-6640	158	11	z	z	PROPN
ejpam-6640	158	12	,	,	PUNCT
ejpam-6640	158	13	fn	fn	VERB
ejpam-6640	158	14	:	:	PUNCT
ejpam-6640	158	15	xn	xn	PUNCT
ejpam-6640	159	1	−→	−→	NOUN
ejpam-6640	159	2	yn	yn	PROPN
ejpam-6640	159	3	is	be	AUX
ejpam-6640	159	4	a	a	DET
ejpam-6640	159	5	section	section	NOUN
ejpam-6640	159	6	.	.	PUNCT
ejpam-6640	160	1	therefore	therefore	ADV
ejpam-6640	160	2	,	,	PUNCT
ejpam-6640	160	3	f	f	PROPN
ejpam-6640	160	4	is	be	AUX
ejpam-6640	160	5	a	a	DET
ejpam-6640	160	6	section	section	NOUN
ejpam-6640	160	7	.	.	PUNCT
ejpam-6640	161	1	hence	hence	ADV
ejpam-6640	161	2	,	,	PUNCT
ejpam-6640	161	3	every	every	DET
ejpam-6640	161	4	monomorphism	monomorphism	NOUN
ejpam-6640	161	5	in	in	ADP
ejpam-6640	161	6	comp(a	comp(a	NOUN
ejpam-6640	161	7	)	)	PUNCT
ejpam-6640	161	8	is	be	AUX
ejpam-6640	161	9	a	a	DET
ejpam-6640	161	10	retraction	retraction	NOUN
ejpam-6640	161	11	and	and	CCONJ
ejpam-6640	161	12	every	every	DET
ejpam-6640	161	13	epimorphism	epimorphism	NOUN
ejpam-6640	161	14	of	of	ADP
ejpam-6640	161	15	comp(a	comp(a	NOUN
ejpam-6640	161	16	)	)	PUNCT
ejpam-6640	161	17	is	be	AUX
ejpam-6640	161	18	a	a	DET
ejpam-6640	161	19	section	section	NOUN
ejpam-6640	161	20	.	.	PUNCT
ejpam-6640	162	1	thus	thus	ADV
ejpam-6640	162	2	,	,	PUNCT
ejpam-6640	162	3	comp(a	comp(a	NOUN
ejpam-6640	162	4	)	)	PUNCT
ejpam-6640	162	5	is	be	AUX
ejpam-6640	162	6	balanced	balance	VERB
ejpam-6640	162	7	.	.	PUNCT
ejpam-6640	163	1	according	accord	VERB
ejpam-6640	163	2	to	to	ADP
ejpam-6640	163	3	the	the	DET
ejpam-6640	163	4	proposition	proposition	NOUN
ejpam-6640	163	5	1	1	NUM
ejpam-6640	163	6	,	,	PUNCT
ejpam-6640	163	7	comp(a	comp(a	NOUN
ejpam-6640	163	8	)	)	PUNCT
ejpam-6640	163	9	is	be	AUX
ejpam-6640	163	10	balanced	balanced	ADJ
ejpam-6640	163	11	abelian	abelian	ADJ
ejpam-6640	163	12	category	category	NOUN
ejpam-6640	163	13	.	.	PUNCT
ejpam-6640	164	1	2	2	X
ejpam-6640	164	2	.	.	X
ejpam-6640	164	3	exactness	exactness	NOUN
ejpam-6640	164	4	of	of	ADP
ejpam-6640	164	5	the	the	DET
ejpam-6640	164	6	functors	functors	PROPN
ejpam-6640	164	7	homa	homa	PROPN
ejpam-6640	164	8	(	(	PUNCT
ejpam-6640	164	9	x,−	x,−	PROPN
ejpam-6640	164	10	)	)	PUNCT
ejpam-6640	164	11	and	and	CCONJ
ejpam-6640	164	12	homa	homa	NOUN
ejpam-6640	164	13	(	(	PUNCT
ejpam-6640	164	14	−	−	PROPN
ejpam-6640	164	15	,	,	PUNCT
ejpam-6640	164	16	x	x	X
ejpam-6640	164	17	)	)	PUNCT
ejpam-6640	164	18	let	let	VERB
ejpam-6640	164	19	a	a	PRON
ejpam-6640	164	20	be	be	AUX
ejpam-6640	164	21	an	an	DET
ejpam-6640	164	22	abelian	abelian	ADJ
ejpam-6640	164	23	category	category	NOUN
ejpam-6640	164	24	,	,	PUNCT
ejpam-6640	164	25	x	x	PRON
ejpam-6640	164	26	,	,	PUNCT
ejpam-6640	164	27	y	y	PROPN
ejpam-6640	164	28	∈	∈	PROPN
ejpam-6640	164	29	ob(a	ob(a	NUM
ejpam-6640	164	30	)	)	PUNCT
ejpam-6640	164	31	,	,	PUNCT
ejpam-6640	164	32	and	and	CCONJ
ejpam-6640	164	33	f	f	X
ejpam-6640	164	34	:	:	PUNCT
ejpam-6640	164	35	x	x	X
ejpam-6640	164	36	→	→	SYM
ejpam-6640	164	37	y	y	PROPN
ejpam-6640	164	38	a	a	DET
ejpam-6640	164	39	morphism	morphism	NOUN
ejpam-6640	164	40	of	of	ADP
ejpam-6640	164	41	a	a	PRON
ejpam-6640	164	42	.	.	PUNCT
ejpam-6640	165	1	then	then	ADV
ejpam-6640	165	2	:	:	PUNCT
ejpam-6640	165	3	(	(	PUNCT
ejpam-6640	165	4	i	i	NOUN
ejpam-6640	165	5	)	)	PUNCT
ejpam-6640	165	6	the	the	DET
ejpam-6640	165	7	kernel	kernel	NOUN
ejpam-6640	165	8	of	of	ADP
ejpam-6640	165	9	f	f	PROPN
ejpam-6640	165	10	,	,	PUNCT
ejpam-6640	165	11	n(f	n(f	PROPN
ejpam-6640	165	12	)	)	PUNCT
ejpam-6640	165	13	is	be	AUX
ejpam-6640	165	14	zero	zero	NUM
ejpam-6640	165	15	if	if	SCONJ
ejpam-6640	165	16	and	and	CCONJ
ejpam-6640	165	17	only	only	ADV
ejpam-6640	165	18	if	if	SCONJ
ejpam-6640	165	19	f	f	PROPN
ejpam-6640	165	20	is	be	AUX
ejpam-6640	165	21	a	a	DET
ejpam-6640	165	22	monomorphism	monomorphism	NOUN
ejpam-6640	165	23	.	.	PUNCT
ejpam-6640	166	1	(	(	PUNCT
ejpam-6640	166	2	ii	ii	NOUN
ejpam-6640	166	3	)	)	PUNCT
ejpam-6640	166	4	the	the	DET
ejpam-6640	166	5	cokernel	cokernel	NOUN
ejpam-6640	166	6	of	of	ADP
ejpam-6640	166	7	f	f	PROPN
ejpam-6640	166	8	,	,	PUNCT
ejpam-6640	166	9	con(f	con(f	PROPN
ejpam-6640	166	10	)	)	PUNCT
ejpam-6640	166	11	is	be	AUX
ejpam-6640	166	12	zero	zero	NUM
ejpam-6640	166	13	if	if	SCONJ
ejpam-6640	166	14	and	and	CCONJ
ejpam-6640	166	15	only	only	ADV
ejpam-6640	166	16	if	if	SCONJ
ejpam-6640	166	17	f	f	PROPN
ejpam-6640	166	18	is	be	AUX
ejpam-6640	166	19	an	an	DET
ejpam-6640	166	20	epimorphism	epimorphism	NOUN
ejpam-6640	166	21	.	.	PUNCT
ejpam-6640	167	1	proof	proof	NOUN
ejpam-6640	167	2	.	.	PUNCT
ejpam-6640	168	1	[	[	X
ejpam-6640	168	2	label=)](⇒	label=)](⇒	NOUN
ejpam-6640	168	3	)	)	PUNCT
ejpam-6640	168	4	suppose	suppose	VERB
ejpam-6640	168	5	that	that	SCONJ
ejpam-6640	168	6	n(f	n(f	PROPN
ejpam-6640	168	7	)	)	PUNCT
ejpam-6640	168	8	is	be	AUX
ejpam-6640	168	9	zero	zero	NUM
ejpam-6640	168	10	and	and	CCONJ
ejpam-6640	168	11	let	let	VERB
ejpam-6640	168	12	us	we	PRON
ejpam-6640	168	13	show	show	VERB
ejpam-6640	168	14	that	that	SCONJ
ejpam-6640	168	15	f	f	PROPN
ejpam-6640	168	16	is	be	AUX
ejpam-6640	168	17	a	a	DET
ejpam-6640	168	18	monomorphism	monomorphism	NOUN
ejpam-6640	168	19	.	.	PUNCT
ejpam-6640	169	1	let	let	VERB
ejpam-6640	169	2	u	u	NOUN
ejpam-6640	169	3	,	,	PUNCT
ejpam-6640	169	4	v	v	INTJ
ejpam-6640	169	5	:	:	PUNCT
ejpam-6640	169	6	z	z	NOUN
ejpam-6640	169	7	→	→	PUNCT
ejpam-6640	169	8	x	x	X
ejpam-6640	169	9	be	be	AUX
ejpam-6640	169	10	two	two	NUM
ejpam-6640	169	11	morphisms	morphism	NOUN
ejpam-6640	169	12	in	in	ADP
ejpam-6640	169	13	a	a	DET
ejpam-6640	169	14	such	such	ADJ
ejpam-6640	169	15	that	that	DET
ejpam-6640	169	16	f	f	PROPN
ejpam-6640	169	17	◦	◦	NOUN
ejpam-6640	169	18	u	u	NOUN
ejpam-6640	170	1	=	=	PUNCT
ejpam-6640	170	2	f	f	PROPN
ejpam-6640	170	3	◦	◦	NOUN
ejpam-6640	170	4	v.	v.	CCONJ
ejpam-6640	170	5	we	we	PRON
ejpam-6640	170	6	have	have	VERB
ejpam-6640	170	7	:	:	PUNCT
ejpam-6640	170	8	f	f	X
ejpam-6640	170	9	◦	◦	NOUN
ejpam-6640	170	10	u	u	NOUN
ejpam-6640	171	1	=	=	PUNCT
ejpam-6640	171	2	f	f	PROPN
ejpam-6640	171	3	◦	◦	NOUN
ejpam-6640	171	4	v	v	ADP
ejpam-6640	171	5	⇒	⇒	NOUN
ejpam-6640	171	6	f	f	X
ejpam-6640	171	7	◦	◦	NOUN
ejpam-6640	171	8	(	(	PUNCT
ejpam-6640	171	9	u−	u−	PROPN
ejpam-6640	171	10	v	v	NOUN
ejpam-6640	171	11	)	)	PUNCT
ejpam-6640	171	12	=	=	SYM
ejpam-6640	171	13	ez	ez	PROPN
ejpam-6640	171	14	,	,	PUNCT
ejpam-6640	171	15	y	y	PROPN
ejpam-6640	171	16	.	.	PUNCT
ejpam-6640	172	1	by	by	ADP
ejpam-6640	172	2	the	the	DET
ejpam-6640	172	3	definition	definition	NOUN
ejpam-6640	172	4	of	of	ADP
ejpam-6640	172	5	the	the	DET
ejpam-6640	172	6	kernel	kernel	NOUN
ejpam-6640	172	7	of	of	ADP
ejpam-6640	172	8	f	f	PROPN
ejpam-6640	172	9	,	,	PUNCT
ejpam-6640	172	10	we	we	PRON
ejpam-6640	172	11	have	have	VERB
ejpam-6640	172	12	:	:	PUNCT
ejpam-6640	172	13	n(f	n(f	ADJ
ejpam-6640	172	14	)	)	PUNCT
ejpam-6640	172	15	=	=	PUNCT
ejpam-6640	173	1	(	(	PUNCT
ejpam-6640	173	2	k	k	X
ejpam-6640	173	3	,	,	PUNCT
ejpam-6640	173	4	i	i	NOUN
ejpam-6640	173	5	)	)	PUNCT
ejpam-6640	173	6	implies	imply	VERB
ejpam-6640	173	7	that	that	SCONJ
ejpam-6640	173	8	f	f	PROPN
ejpam-6640	173	9	◦	◦	NOUN
ejpam-6640	173	10	i	i	PRON
ejpam-6640	173	11	=	=	SYM
ejpam-6640	173	12	ek	ek	PROPN
ejpam-6640	173	13	,	,	PUNCT
ejpam-6640	173	14	y	y	PROPN
ejpam-6640	173	15	.	.	PUNCT
ejpam-6640	174	1	if	if	SCONJ
ejpam-6640	174	2	n(f	n(f	PROPN
ejpam-6640	174	3	)	)	PUNCT
ejpam-6640	174	4	=	=	SYM
ejpam-6640	175	1	(	(	PUNCT
ejpam-6640	175	2	k	k	X
ejpam-6640	175	3	,	,	PUNCT
ejpam-6640	175	4	i	i	NOUN
ejpam-6640	175	5	)	)	PUNCT
ejpam-6640	175	6	is	be	AUX
ejpam-6640	175	7	zero	zero	NUM
ejpam-6640	175	8	,	,	PUNCT
ejpam-6640	175	9	then	then	ADV
ejpam-6640	175	10	i	i	PRON
ejpam-6640	175	11	=	=	PUNCT
ejpam-6640	175	12	ek	ek	PROPN
ejpam-6640	175	13	,	,	PUNCT
ejpam-6640	175	14	x	x	X
ejpam-6640	175	15	and	and	CCONJ
ejpam-6640	176	1	thus	thus	ADV
ejpam-6640	176	2	f	f	X
ejpam-6640	176	3	◦	◦	NOUN
ejpam-6640	176	4	i	i	PRON
ejpam-6640	176	5	=	=	PUNCT
ejpam-6640	176	6	ek	ek	PROPN
ejpam-6640	176	7	,	,	PUNCT
ejpam-6640	176	8	y	y	PROPN
ejpam-6640	176	9	⇒	⇒	NOUN
ejpam-6640	176	10	f	f	AUX
ejpam-6640	176	11	◦	◦	VERB
ejpam-6640	176	12	ek	ek	NOUN
ejpam-6640	176	13	,	,	PUNCT
ejpam-6640	176	14	x	x	X
ejpam-6640	176	15	=	=	SYM
ejpam-6640	176	16	ek	ek	PROPN
ejpam-6640	176	17	,	,	PUNCT
ejpam-6640	176	18	y	y	PROPN
ejpam-6640	176	19	.	.	PUNCT
ejpam-6640	177	1	there	there	PRON
ejpam-6640	177	2	exists	exist	VERB
ejpam-6640	177	3	a	a	DET
ejpam-6640	177	4	unique	unique	ADJ
ejpam-6640	177	5	h	h	NOUN
ejpam-6640	177	6	:	:	PUNCT
ejpam-6640	177	7	z	z	X
ejpam-6640	177	8	→	→	PUNCT
ejpam-6640	177	9	k	k	X
ejpam-6640	177	10	such	such	ADJ
ejpam-6640	177	11	that	that	SCONJ
ejpam-6640	177	12	ek	ek	PROPN
ejpam-6640	177	13	,	,	PUNCT
ejpam-6640	177	14	x	x	PUNCT
ejpam-6640	177	15	◦	◦	NOUN
ejpam-6640	177	16	h	h	NOUN
ejpam-6640	177	17	=	=	SYM
ejpam-6640	177	18	u−	u−	PROPN
ejpam-6640	178	1	v.	v.	CCONJ
ejpam-6640	178	2	hence	hence	ADV
ejpam-6640	178	3	,	,	PUNCT
ejpam-6640	178	4	∀i	∀i	X
ejpam-6640	178	5	∈	∈	NOUN
ejpam-6640	178	6	homa	homa	NOUN
ejpam-6640	178	7	(	(	PUNCT
ejpam-6640	178	8	k	k	NOUN
ejpam-6640	178	9	,	,	PUNCT
ejpam-6640	178	10	x	x	NOUN
ejpam-6640	178	11	)	)	PUNCT
ejpam-6640	178	12	,	,	PUNCT
ejpam-6640	178	13	with	with	ADP
ejpam-6640	178	14	ek	ek	PROPN
ejpam-6640	178	15	,	,	PUNCT
ejpam-6640	178	16	x	x	PUNCT
ejpam-6640	178	17	being	be	AUX
ejpam-6640	178	18	the	the	DET
ejpam-6640	178	19	neutral	neutral	ADJ
ejpam-6640	178	20	element	element	NOUN
ejpam-6640	178	21	of	of	ADP
ejpam-6640	178	22	the	the	DET
ejpam-6640	178	23	abelian	abelian	PROPN
ejpam-6640	178	24	group	group	PROPN
ejpam-6640	178	25	homa	homa	PROPN
ejpam-6640	178	26	(	(	PUNCT
ejpam-6640	178	27	k	k	NOUN
ejpam-6640	178	28	,	,	PUNCT
ejpam-6640	178	29	x	x	NOUN
ejpam-6640	178	30	)	)	PUNCT
ejpam-6640	178	31	,	,	PUNCT
ejpam-6640	178	32	we	we	PRON
ejpam-6640	178	33	have	have	VERB
ejpam-6640	178	34	:	:	PUNCT
ejpam-6640	178	35	(	(	PUNCT
ejpam-6640	178	36	i+	i+	X
ejpam-6640	178	37	ek	ek	PROPN
ejpam-6640	178	38	,	,	PUNCT
ejpam-6640	178	39	x	x	NOUN
ejpam-6640	178	40	)	)	PUNCT
ejpam-6640	178	41	◦	◦	NOUN
ejpam-6640	178	42	h	h	NOUN
ejpam-6640	179	1	=	=	SYM
ejpam-6640	179	2	(	(	PUNCT
ejpam-6640	179	3	ek	ek	X
ejpam-6640	179	4	,	,	PUNCT
ejpam-6640	179	5	x	x	PROPN
ejpam-6640	180	1	+	+	NUM
ejpam-6640	180	2	i	i	NOUN
ejpam-6640	180	3	)	)	PUNCT
ejpam-6640	180	4	◦	◦	NOUN
ejpam-6640	180	5	h	h	NOUN
ejpam-6640	181	1	=	=	VERB
ejpam-6640	181	2	i	i	PRON
ejpam-6640	181	3	◦	◦	VERB
ejpam-6640	181	4	h⇒	h⇒	ADP
ejpam-6640	181	5	i	i	PRON
ejpam-6640	181	6	◦	◦	VERB
ejpam-6640	181	7	h+	h+	PUNCT
ejpam-6640	181	8	ek	ek	X
ejpam-6640	181	9	,	,	PUNCT
ejpam-6640	181	10	x	x	PUNCT
ejpam-6640	182	1	◦	◦	NOUN
ejpam-6640	182	2	h	h	NOUN
ejpam-6640	182	3	=	=	SYM
ejpam-6640	182	4	ek	ek	PROPN
ejpam-6640	182	5	,	,	PUNCT
ejpam-6640	182	6	x	x	PART
ejpam-6640	182	7	◦	◦	NOUN
ejpam-6640	182	8	h+	h+	PUNCT
ejpam-6640	182	9	i	i	PRON
ejpam-6640	182	10	◦	◦	VERB
ejpam-6640	182	11	h	h	NOUN
ejpam-6640	183	1	=	=	VERB
ejpam-6640	183	2	i	i	PRON
ejpam-6640	183	3	◦	◦	VERB
ejpam-6640	183	4	h	h	NOUN
ejpam-6640	183	5	⇒	⇒	NOUN
ejpam-6640	183	6	{	{	PUNCT
ejpam-6640	184	1	i	i	PRON
ejpam-6640	184	2	◦	◦	VERB
ejpam-6640	184	3	h+	h+	PUNCT
ejpam-6640	184	4	ek	ek	X
ejpam-6640	184	5	,	,	PUNCT
ejpam-6640	184	6	x	x	PUNCT
ejpam-6640	184	7	◦	◦	NOUN
ejpam-6640	184	8	h	h	NOUN
ejpam-6640	185	1	=	=	VERB
ejpam-6640	185	2	i	i	PRON
ejpam-6640	185	3	◦	◦	VERB
ejpam-6640	185	4	h+	h+	PUNCT
ejpam-6640	185	5	ez	ez	PROPN
ejpam-6640	185	6	,	,	PUNCT
ejpam-6640	185	7	x	x	X
ejpam-6640	186	1	=	=	VERB
ejpam-6640	186	2	i	i	PRON
ejpam-6640	186	3	◦	◦	VERB
ejpam-6640	186	4	h	h	NOUN
ejpam-6640	186	5	ek	ek	NOUN
ejpam-6640	186	6	,	,	PUNCT
ejpam-6640	186	7	x	x	VERB
ejpam-6640	186	8	◦	◦	NOUN
ejpam-6640	186	9	h+	h+	PUNCT
ejpam-6640	186	10	i	i	PRON
ejpam-6640	186	11	◦	◦	VERB
ejpam-6640	186	12	h	h	NOUN
ejpam-6640	186	13	=	=	SYM
ejpam-6640	186	14	ez	ez	PROPN
ejpam-6640	186	15	,	,	PUNCT
ejpam-6640	186	16	x	x	PROPN
ejpam-6640	187	1	+	+	CCONJ
ejpam-6640	187	2	i	i	PRON
ejpam-6640	187	3	◦	◦	VERB
ejpam-6640	187	4	h	h	NOUN
ejpam-6640	188	1	=	=	VERB
ejpam-6640	188	2	i	i	PRON
ejpam-6640	188	3	◦	◦	VERB
ejpam-6640	188	4	h	h	NOUN
ejpam-6640	188	5	⇒	⇒	VERB
ejpam-6640	188	6	ek	ek	PROPN
ejpam-6640	188	7	,	,	PUNCT
ejpam-6640	188	8	x	x	PUNCT
ejpam-6640	188	9	◦	◦	NOUN
ejpam-6640	188	10	h	h	NOUN
ejpam-6640	188	11	=	=	SYM
ejpam-6640	188	12	ez	ez	PROPN
ejpam-6640	188	13	,	,	PUNCT
ejpam-6640	188	14	x	x	PUNCT
ejpam-6640	188	15	thus	thus	ADV
ejpam-6640	188	16	,	,	PUNCT
ejpam-6640	188	17	we	we	PRON
ejpam-6640	188	18	have	have	VERB
ejpam-6640	188	19	:	:	PUNCT
ejpam-6640	188	20	ek	ek	ADJ
ejpam-6640	188	21	,	,	PUNCT
ejpam-6640	188	22	x	x	PUNCT
ejpam-6640	188	23	◦	◦	NOUN
ejpam-6640	188	24	h	h	NOUN
ejpam-6640	188	25	=	=	SYM
ejpam-6640	188	26	u−	u−	PROPN
ejpam-6640	188	27	v	v	X
ejpam-6640	188	28	=	=	SYM
ejpam-6640	188	29	ez	ez	PROPN
ejpam-6640	188	30	,	,	PUNCT
ejpam-6640	188	31	x	x	SYM
ejpam-6640	188	32	⇒	⇒	PROPN
ejpam-6640	188	33	u−	u−	PROPN
ejpam-6640	188	34	v	v	X
ejpam-6640	188	35	=	=	SYM
ejpam-6640	188	36	ez	ez	PROPN
ejpam-6640	188	37	,	,	PUNCT
ejpam-6640	188	38	x	x	SYM
ejpam-6640	188	39	⇒	⇒	PROPN
ejpam-6640	188	40	u−	u−	PROPN
ejpam-6640	188	41	v	v	NOUN
ejpam-6640	188	42	+	+	CCONJ
ejpam-6640	188	43	v	v	NOUN
ejpam-6640	188	44	=	=	SYM
ejpam-6640	188	45	ez	ez	PROPN
ejpam-6640	188	46	,	,	PUNCT
ejpam-6640	188	47	x	x	PROPN
ejpam-6640	189	1	+	+	X
ejpam-6640	189	2	v	v	ADJ
ejpam-6640	189	3	⇒	⇒	PROPN
ejpam-6640	189	4	u+	u+	NUM
ejpam-6640	189	5	ez	ez	PROPN
ejpam-6640	189	6	,	,	PUNCT
ejpam-6640	189	7	x	x	X
ejpam-6640	189	8	=	=	SYM
ejpam-6640	189	9	v	v	ADJ
ejpam-6640	189	10	⇒	⇒	X
ejpam-6640	189	11	u	u	NOUN
ejpam-6640	189	12	=	=	PROPN
ejpam-6640	189	13	v.	v.	ADP
ejpam-6640	189	14	thus	thus	ADV
ejpam-6640	189	15	,	,	PUNCT
ejpam-6640	189	16	f	f	PROPN
ejpam-6640	189	17	is	be	AUX
ejpam-6640	189	18	a	a	DET
ejpam-6640	189	19	monomorphism	monomorphism	NOUN
ejpam-6640	189	20	.	.	PUNCT
ejpam-6640	190	1	(	(	PUNCT
ejpam-6640	190	2	⇐	⇐	NOUN
ejpam-6640	190	3	)	)	PUNCT
ejpam-6640	190	4	suppose	suppose	VERB
ejpam-6640	190	5	that	that	SCONJ
ejpam-6640	190	6	f	f	PROPN
ejpam-6640	190	7	is	be	AUX
ejpam-6640	190	8	a	a	DET
ejpam-6640	190	9	monomorphism	monomorphism	NOUN
ejpam-6640	190	10	and	and	CCONJ
ejpam-6640	190	11	let	let	VERB
ejpam-6640	190	12	us	we	PRON
ejpam-6640	190	13	show	show	VERB
ejpam-6640	190	14	that	that	SCONJ
ejpam-6640	190	15	n(f	n(f	PROPN
ejpam-6640	190	16	)	)	PUNCT
ejpam-6640	190	17	is	be	AUX
ejpam-6640	190	18	zero	zero	NUM
ejpam-6640	190	19	.	.	PUNCT
ejpam-6640	191	1	a.	a.	PROPN
ejpam-6640	191	2	diallo	diallo	PROPN
ejpam-6640	191	3	,	,	PUNCT
ejpam-6640	191	4	m.	m.	PROPN
ejpam-6640	191	5	b.	b.	PROPN
ejpam-6640	191	6	f.	f.	PROPN
ejpam-6640	191	7	b.	b.	PROPN
ejpam-6640	191	8	maaouia	maaouia	PROPN
ejpam-6640	191	9	,	,	PUNCT
ejpam-6640	191	10	m.	m.	NOUN
ejpam-6640	191	11	sanghare	sanghare	PROPN
ejpam-6640	191	12	/	/	SYM
ejpam-6640	191	13	eur	eur	PROPN
ejpam-6640	191	14	.	.	PUNCT
ejpam-6640	192	1	j.	j.	PROPN
ejpam-6640	192	2	pure	pure	PROPN
ejpam-6640	192	3	appl	appl	PROPN
ejpam-6640	192	4	.	.	PROPN
ejpam-6640	192	5	math	math	PROPN
ejpam-6640	192	6	,	,	PUNCT
ejpam-6640	192	7	18	18	NUM
ejpam-6640	192	8	(	(	PUNCT
ejpam-6640	192	9	4	4	NUM
ejpam-6640	192	10	)	)	PUNCT
ejpam-6640	192	11	(	(	PUNCT
ejpam-6640	192	12	2025	2025	NUM
ejpam-6640	192	13	)	)	PUNCT
ejpam-6640	192	14	,	,	PUNCT
ejpam-6640	192	15	6640	6640	NUM
ejpam-6640	192	16	8	8	NUM
ejpam-6640	192	17	of	of	ADP
ejpam-6640	192	18	28	28	NUM
ejpam-6640	192	19	let	let	VERB
ejpam-6640	192	20	i	i	PRON
ejpam-6640	192	21	:	:	PUNCT
ejpam-6640	192	22	k	k	X
ejpam-6640	192	23	→	→	PUNCT
ejpam-6640	192	24	x	x	PUNCT
ejpam-6640	192	25	be	be	AUX
ejpam-6640	192	26	a	a	DET
ejpam-6640	192	27	morphism	morphism	NOUN
ejpam-6640	192	28	such	such	ADJ
ejpam-6640	192	29	that	that	SCONJ
ejpam-6640	192	30	f	f	PROPN
ejpam-6640	192	31	◦	◦	NOUN
ejpam-6640	193	1	i	i	PRON
ejpam-6640	193	2	=	=	PUNCT
ejpam-6640	193	3	ek	ek	PROPN
ejpam-6640	193	4	,	,	PUNCT
ejpam-6640	193	5	x	x	PROPN
ejpam-6640	193	6	.	.	PUNCT
ejpam-6640	194	1	but	but	CCONJ
ejpam-6640	194	2	ek	ek	INTJ
ejpam-6640	194	3	,	,	PUNCT
ejpam-6640	194	4	y	y	PROPN
ejpam-6640	194	5	=	=	SYM
ejpam-6640	194	6	f	f	PROPN
ejpam-6640	194	7	◦	◦	NOUN
ejpam-6640	194	8	ek	ek	NOUN
ejpam-6640	194	9	,	,	PUNCT
ejpam-6640	194	10	x	x	INTJ
ejpam-6640	194	11	.	.	PUNCT
ejpam-6640	195	1	indeed	indeed	ADV
ejpam-6640	195	2	:	:	PUNCT
ejpam-6640	195	3	∀i	∀i	X
ejpam-6640	195	4	∈	∈	PROPN
ejpam-6640	195	5	homa	homa	NOUN
ejpam-6640	195	6	(	(	PUNCT
ejpam-6640	195	7	k	k	NOUN
ejpam-6640	195	8	,	,	PUNCT
ejpam-6640	195	9	x	x	NOUN
ejpam-6640	195	10	)	)	PUNCT
ejpam-6640	195	11	,	,	PUNCT
ejpam-6640	195	12	with	with	ADP
ejpam-6640	195	13	ek	ek	PROPN
ejpam-6640	195	14	,	,	PUNCT
ejpam-6640	195	15	x	x	PUNCT
ejpam-6640	195	16	being	be	AUX
ejpam-6640	195	17	the	the	DET
ejpam-6640	195	18	neutral	neutral	ADJ
ejpam-6640	195	19	element	element	NOUN
ejpam-6640	195	20	of	of	ADP
ejpam-6640	195	21	the	the	DET
ejpam-6640	195	22	abelian	abelian	PROPN
ejpam-6640	195	23	group	group	PROPN
ejpam-6640	195	24	homa	homa	PROPN
ejpam-6640	195	25	(	(	PUNCT
ejpam-6640	195	26	k	k	NOUN
ejpam-6640	195	27	,	,	PUNCT
ejpam-6640	195	28	x	x	NOUN
ejpam-6640	195	29	)	)	PUNCT
ejpam-6640	195	30	,	,	PUNCT
ejpam-6640	195	31	we	we	PRON
ejpam-6640	195	32	have	have	VERB
ejpam-6640	195	33	:	:	PUNCT
ejpam-6640	196	1	f	f	X
ejpam-6640	196	2	◦	◦	NOUN
ejpam-6640	196	3	(	(	PUNCT
ejpam-6640	196	4	i+	i+	X
ejpam-6640	196	5	ek	ek	PROPN
ejpam-6640	196	6	,	,	PUNCT
ejpam-6640	196	7	x	x	NOUN
ejpam-6640	196	8	)	)	PUNCT
ejpam-6640	196	9	=	=	SYM
ejpam-6640	196	10	f	f	X
ejpam-6640	196	11	◦	◦	NOUN
ejpam-6640	196	12	(	(	PUNCT
ejpam-6640	196	13	ek	ek	INTJ
ejpam-6640	196	14	,	,	PUNCT
ejpam-6640	196	15	x	x	PROPN
ejpam-6640	196	16	+	+	PUNCT
ejpam-6640	196	17	i	i	NOUN
ejpam-6640	196	18	)	)	PUNCT
ejpam-6640	197	1	=	=	PUNCT
ejpam-6640	197	2	f	f	X
ejpam-6640	198	1	◦	◦	NOUN
ejpam-6640	198	2	i⇒	i⇒	PROPN
ejpam-6640	198	3	f	f	X
ejpam-6640	198	4	◦	◦	VERB
ejpam-6640	198	5	i+	i+	PUNCT
ejpam-6640	198	6	f	f	AUX
ejpam-6640	198	7	◦	◦	NOUN
ejpam-6640	198	8	ek	ek	NOUN
ejpam-6640	198	9	,	,	PUNCT
ejpam-6640	198	10	x	x	PUNCT
ejpam-6640	198	11	=	=	SYM
ejpam-6640	198	12	f	f	X
ejpam-6640	198	13	◦	◦	NOUN
ejpam-6640	198	14	ek	ek	NOUN
ejpam-6640	198	15	,	,	PUNCT
ejpam-6640	198	16	x	x	PROPN
ejpam-6640	199	1	+	+	NUM
ejpam-6640	199	2	f	f	X
ejpam-6640	199	3	◦	◦	NOUN
ejpam-6640	200	1	i	i	PRON
ejpam-6640	200	2	=	=	SYM
ejpam-6640	200	3	f	f	X
ejpam-6640	201	1	◦	◦	NOUN
ejpam-6640	201	2	i	i	PRON
ejpam-6640	201	3	⇒	⇒	VERB
ejpam-6640	201	4	f	f	AUX
ejpam-6640	201	5	◦	◦	VERB
ejpam-6640	201	6	ek	ek	NOUN
ejpam-6640	201	7	,	,	PUNCT
ejpam-6640	201	8	x	x	X
ejpam-6640	201	9	=	=	SYM
ejpam-6640	201	10	ek	ek	PROPN
ejpam-6640	201	11	,	,	PUNCT
ejpam-6640	201	12	y	y	PROPN
ejpam-6640	201	13	since	since	SCONJ
ejpam-6640	201	14	f	f	PROPN
ejpam-6640	201	15	is	be	AUX
ejpam-6640	201	16	a	a	DET
ejpam-6640	201	17	monomorphism	monomorphism	NOUN
ejpam-6640	201	18	,	,	PUNCT
ejpam-6640	201	19	i	i	PRON
ejpam-6640	201	20	=	=	PUNCT
ejpam-6640	201	21	ek	ek	PROPN
ejpam-6640	201	22	,	,	PUNCT
ejpam-6640	201	23	x	x	X
ejpam-6640	201	24	.	.	PUNCT
ejpam-6640	202	1	thus	thus	ADV
ejpam-6640	202	2	,	,	PUNCT
ejpam-6640	202	3	the	the	DET
ejpam-6640	202	4	kernel	kernel	NOUN
ejpam-6640	202	5	of	of	ADP
ejpam-6640	202	6	f	f	PROPN
ejpam-6640	202	7	,	,	PUNCT
ejpam-6640	202	8	n(f	n(f	PROPN
ejpam-6640	202	9	)	)	PUNCT
ejpam-6640	202	10	,	,	PUNCT
ejpam-6640	202	11	is	be	AUX
ejpam-6640	202	12	zero	zero	NUM
ejpam-6640	202	13	.	.	PUNCT
ejpam-6640	203	1	(	(	PUNCT
ejpam-6640	203	2	⇒	⇒	PROPN
ejpam-6640	203	3	)	)	PUNCT
ejpam-6640	203	4	suppose	suppose	VERB
ejpam-6640	203	5	that	that	SCONJ
ejpam-6640	203	6	con(f	con(f	NOUN
ejpam-6640	203	7	)	)	PUNCT
ejpam-6640	203	8	is	be	AUX
ejpam-6640	203	9	zero	zero	NUM
ejpam-6640	203	10	and	and	CCONJ
ejpam-6640	203	11	let	let	VERB
ejpam-6640	203	12	us	we	PRON
ejpam-6640	203	13	show	show	VERB
ejpam-6640	203	14	that	that	SCONJ
ejpam-6640	203	15	f	f	PROPN
ejpam-6640	203	16	is	be	AUX
ejpam-6640	203	17	an	an	DET
ejpam-6640	203	18	epimorphism	epimorphism	NOUN
ejpam-6640	203	19	.	.	PUNCT
ejpam-6640	204	1	let	let	VERB
ejpam-6640	204	2	g	g	NOUN
ejpam-6640	204	3	,	,	PUNCT
ejpam-6640	204	4	h	h	NOUN
ejpam-6640	204	5	:	:	PUNCT
ejpam-6640	204	6	y	y	PROPN
ejpam-6640	204	7	→	→	SYM
ejpam-6640	204	8	z	z	X
ejpam-6640	204	9	be	be	AUX
ejpam-6640	204	10	two	two	NUM
ejpam-6640	204	11	morphisms	morphism	NOUN
ejpam-6640	204	12	such	such	ADJ
ejpam-6640	204	13	that	that	SCONJ
ejpam-6640	204	14	g	g	PROPN
ejpam-6640	204	15	◦	◦	NOUN
ejpam-6640	204	16	f	f	X
ejpam-6640	205	1	=	=	SYM
ejpam-6640	205	2	h	h	PROPN
ejpam-6640	205	3	◦	◦	NOUN
ejpam-6640	205	4	f	f	X
ejpam-6640	205	5	.	.	PUNCT
ejpam-6640	206	1	we	we	PRON
ejpam-6640	206	2	have	have	VERB
ejpam-6640	206	3	:	:	PUNCT
ejpam-6640	206	4	g	g	PROPN
ejpam-6640	206	5	◦	◦	NOUN
ejpam-6640	206	6	f	f	X
ejpam-6640	207	1	=	=	SYM
ejpam-6640	207	2	h	h	PROPN
ejpam-6640	207	3	◦	◦	NOUN
ejpam-6640	207	4	f	f	X
ejpam-6640	207	5	⇒	⇒	NOUN
ejpam-6640	207	6	(	(	PUNCT
ejpam-6640	207	7	g	g	NOUN
ejpam-6640	207	8	−	−	PROPN
ejpam-6640	207	9	h	h	NOUN
ejpam-6640	207	10	)	)	PUNCT
ejpam-6640	207	11	◦	◦	NOUN
ejpam-6640	207	12	f	f	X
ejpam-6640	208	1	=	=	SYM
ejpam-6640	208	2	ex	ex	X
ejpam-6640	208	3	,	,	PUNCT
ejpam-6640	208	4	z	z	NOUN
ejpam-6640	208	5	.	.	PUNCT
ejpam-6640	209	1	since	since	SCONJ
ejpam-6640	209	2	con(f	con(f	NUM
ejpam-6640	209	3	)	)	PUNCT
ejpam-6640	209	4	=	=	SYM
ejpam-6640	209	5	(	(	PUNCT
ejpam-6640	209	6	y	y	PROPN
ejpam-6640	209	7	,	,	PUNCT
ejpam-6640	209	8	p	p	NOUN
ejpam-6640	209	9	)	)	PUNCT
ejpam-6640	209	10	implies	imply	VERB
ejpam-6640	209	11	p	p	X
ejpam-6640	209	12	◦	◦	NOUN
ejpam-6640	209	13	f	f	X
ejpam-6640	210	1	=	=	SYM
ejpam-6640	210	2	ex	ex	PROPN
ejpam-6640	210	3	,	,	PUNCT
ejpam-6640	210	4	t	t	NOUN
ejpam-6640	210	5	,	,	PUNCT
ejpam-6640	210	6	and	and	CCONJ
ejpam-6640	210	7	since	since	SCONJ
ejpam-6640	210	8	con(f	con(f	PROPN
ejpam-6640	210	9	)	)	PUNCT
ejpam-6640	210	10	is	be	AUX
ejpam-6640	210	11	zero	zero	NUM
ejpam-6640	210	12	,	,	PUNCT
ejpam-6640	210	13	we	we	PRON
ejpam-6640	210	14	have	have	VERB
ejpam-6640	210	15	p	p	NOUN
ejpam-6640	210	16	=	=	SYM
ejpam-6640	210	17	ey	ey	PROPN
ejpam-6640	210	18	,	,	PUNCT
ejpam-6640	210	19	t	t	NOUN
ejpam-6640	210	20	,	,	PUNCT
ejpam-6640	210	21	and	and	CCONJ
ejpam-6640	210	22	thus	thus	ADV
ejpam-6640	210	23	:	:	PUNCT
ejpam-6640	210	24	k	k	X
ejpam-6640	210	25	◦	◦	VERB
ejpam-6640	210	26	ey	ey	NOUN
ejpam-6640	210	27	,	,	PUNCT
ejpam-6640	210	28	t	t	NOUN
ejpam-6640	210	29	=	=	SYM
ejpam-6640	210	30	g	g	PROPN
ejpam-6640	210	31	−	−	PROPN
ejpam-6640	210	32	h	h	NOUN
ejpam-6640	210	33	=	=	SYM
ejpam-6640	210	34	ey	ey	PROPN
ejpam-6640	210	35	,	,	PUNCT
ejpam-6640	210	36	z	z	PROPN
ejpam-6640	210	37	thus	thus	ADV
ejpam-6640	210	38	,	,	PUNCT
ejpam-6640	210	39	we	we	PRON
ejpam-6640	210	40	have	have	VERB
ejpam-6640	210	41	:	:	PUNCT
ejpam-6640	210	42	k	k	X
ejpam-6640	210	43	◦	◦	VERB
ejpam-6640	210	44	ey	ey	NOUN
ejpam-6640	210	45	,	,	PUNCT
ejpam-6640	210	46	t	t	NOUN
ejpam-6640	211	1	=	=	SYM
ejpam-6640	211	2	g	g	PROPN
ejpam-6640	211	3	−	−	PROPN
ejpam-6640	211	4	h	h	NOUN
ejpam-6640	211	5	=	=	SYM
ejpam-6640	211	6	ey	ey	PROPN
ejpam-6640	211	7	,	,	PUNCT
ejpam-6640	211	8	z	z	NOUN
ejpam-6640	211	9	⇒	⇒	NOUN
ejpam-6640	211	10	g	g	PROPN
ejpam-6640	211	11	−	−	PROPN
ejpam-6640	211	12	h	h	PROPN
ejpam-6640	211	13	=	=	SYM
ejpam-6640	211	14	ez	ez	PROPN
ejpam-6640	211	15	,	,	PUNCT
ejpam-6640	211	16	x	x	X
ejpam-6640	211	17	⇒	⇒	NOUN
ejpam-6640	211	18	g	g	PROPN
ejpam-6640	211	19	−	−	PROPN
ejpam-6640	211	20	h+	h+	PUNCT
ejpam-6640	211	21	h	h	NOUN
ejpam-6640	211	22	=	=	SYM
ejpam-6640	211	23	ey	ey	PROPN
ejpam-6640	211	24	,	,	PUNCT
ejpam-6640	211	25	z	z	NOUN
ejpam-6640	211	26	+	+	NOUN
ejpam-6640	211	27	h	h	NOUN
ejpam-6640	211	28	⇒	⇒	NOUN
ejpam-6640	211	29	g	g	PROPN
ejpam-6640	211	30	+	+	CCONJ
ejpam-6640	211	31	ey	ey	PROPN
ejpam-6640	211	32	,	,	PUNCT
ejpam-6640	211	33	z	z	NOUN
ejpam-6640	211	34	=	=	SYM
ejpam-6640	211	35	h	h	NOUN
ejpam-6640	211	36	⇒	⇒	NOUN
ejpam-6640	211	37	g	g	PROPN
ejpam-6640	211	38	=	=	PUNCT
ejpam-6640	211	39	h.	h.	PROPN
ejpam-6640	212	1	thus	thus	ADV
ejpam-6640	212	2	,	,	PUNCT
ejpam-6640	212	3	f	f	PROPN
ejpam-6640	212	4	is	be	AUX
ejpam-6640	212	5	an	an	DET
ejpam-6640	212	6	epimorphism	epimorphism	NOUN
ejpam-6640	212	7	.	.	PUNCT
ejpam-6640	213	1	(	(	PUNCT
ejpam-6640	213	2	⇐	⇐	NOUN
ejpam-6640	213	3	)	)	PUNCT
ejpam-6640	213	4	suppose	suppose	VERB
ejpam-6640	213	5	that	that	SCONJ
ejpam-6640	213	6	f	f	PROPN
ejpam-6640	213	7	is	be	AUX
ejpam-6640	213	8	an	an	DET
ejpam-6640	213	9	epimorphism	epimorphism	NOUN
ejpam-6640	213	10	and	and	CCONJ
ejpam-6640	213	11	let	let	VERB
ejpam-6640	213	12	us	we	PRON
ejpam-6640	213	13	show	show	VERB
ejpam-6640	213	14	that	that	SCONJ
ejpam-6640	213	15	con(f	con(f	NOUN
ejpam-6640	213	16	)	)	PUNCT
ejpam-6640	213	17	is	be	AUX
ejpam-6640	213	18	zero	zero	NUM
ejpam-6640	213	19	.	.	PUNCT
ejpam-6640	214	1	let	let	VERB
ejpam-6640	214	2	p	p	NOUN
ejpam-6640	214	3	:	:	PUNCT
ejpam-6640	214	4	y	y	PROPN
ejpam-6640	214	5	→	→	SYM
ejpam-6640	214	6	t	t	PROPN
ejpam-6640	214	7	be	be	AUX
ejpam-6640	214	8	a	a	DET
ejpam-6640	214	9	morphism	morphism	NOUN
ejpam-6640	215	1	such	such	ADJ
ejpam-6640	215	2	that	that	SCONJ
ejpam-6640	215	3	p	p	PROPN
ejpam-6640	215	4	◦	◦	NOUN
ejpam-6640	215	5	f	f	X
ejpam-6640	215	6	=	=	SYM
ejpam-6640	215	7	ex	ex	PROPN
ejpam-6640	215	8	,	,	PUNCT
ejpam-6640	215	9	t	t	PROPN
ejpam-6640	215	10	.	.	PUNCT
ejpam-6640	216	1	now	now	ADV
ejpam-6640	216	2	,	,	PUNCT
ejpam-6640	216	3	ex	ex	PROPN
ejpam-6640	216	4	,	,	PUNCT
ejpam-6640	216	5	t	t	NOUN
ejpam-6640	216	6	=	=	SYM
ejpam-6640	216	7	ex	ex	X
ejpam-6640	216	8	,	,	PUNCT
ejpam-6640	216	9	t	t	PROPN
ejpam-6640	216	10	◦	◦	NOUN
ejpam-6640	216	11	f.	f.	PROPN
ejpam-6640	216	12	indeed	indeed	ADV
ejpam-6640	216	13	:	:	PUNCT
ejpam-6640	216	14	∀p	∀p	NOUN
ejpam-6640	216	15	∈	∈	PROPN
ejpam-6640	216	16	homa	homa	NOUN
ejpam-6640	216	17	(	(	PUNCT
ejpam-6640	216	18	y	y	PROPN
ejpam-6640	216	19	,	,	PUNCT
ejpam-6640	216	20	t	t	PROPN
ejpam-6640	216	21	)	)	PUNCT
ejpam-6640	216	22	,	,	PUNCT
ejpam-6640	216	23	where	where	SCONJ
ejpam-6640	216	24	ey	ey	NOUN
ejpam-6640	216	25	,	,	PUNCT
ejpam-6640	216	26	t	t	PROPN
ejpam-6640	216	27	is	be	AUX
ejpam-6640	216	28	the	the	DET
ejpam-6640	216	29	neutral	neutral	ADJ
ejpam-6640	216	30	element	element	NOUN
ejpam-6640	216	31	of	of	ADP
ejpam-6640	216	32	the	the	DET
ejpam-6640	216	33	abelian	abelian	PROPN
ejpam-6640	216	34	group	group	PROPN
ejpam-6640	216	35	homa	homa	PROPN
ejpam-6640	216	36	(	(	PUNCT
ejpam-6640	216	37	y	y	PROPN
ejpam-6640	216	38	,	,	PUNCT
ejpam-6640	216	39	t	t	PROPN
ejpam-6640	216	40	)	)	PUNCT
ejpam-6640	216	41	,	,	PUNCT
ejpam-6640	216	42	we	we	PRON
ejpam-6640	216	43	have	have	AUX
ejpam-6640	216	44	:	:	PUNCT
ejpam-6640	216	45	(	(	PUNCT
ejpam-6640	216	46	p+	p+	NOUN
ejpam-6640	216	47	ey	ey	PROPN
ejpam-6640	216	48	,	,	PUNCT
ejpam-6640	216	49	t	t	NOUN
ejpam-6640	216	50	)	)	PUNCT
ejpam-6640	217	1	◦	◦	NOUN
ejpam-6640	217	2	f	f	X
ejpam-6640	218	1	=	=	SYM
ejpam-6640	219	1	(	(	PUNCT
ejpam-6640	219	2	ey	ey	PROPN
ejpam-6640	219	3	,	,	PUNCT
ejpam-6640	219	4	t	t	NOUN
ejpam-6640	219	5	+	+	CCONJ
ejpam-6640	219	6	p	p	X
ejpam-6640	219	7	)	)	PUNCT
ejpam-6640	219	8	◦	◦	NOUN
ejpam-6640	219	9	f	f	NOUN
ejpam-6640	220	1	=	=	SYM
ejpam-6640	220	2	p	p	PROPN
ejpam-6640	220	3	◦	◦	NOUN
ejpam-6640	220	4	f	f	X
ejpam-6640	220	5	⇒	⇒	VERB
ejpam-6640	220	6	p	p	PROPN
ejpam-6640	220	7	◦	◦	NOUN
ejpam-6640	220	8	f	f	X
ejpam-6640	220	9	+	+	CCONJ
ejpam-6640	220	10	ey	ey	PROPN
ejpam-6640	220	11	,	,	PUNCT
ejpam-6640	220	12	t	t	NOUN
ejpam-6640	220	13	◦	◦	NOUN
ejpam-6640	220	14	f	f	X
ejpam-6640	220	15	=	=	SYM
ejpam-6640	220	16	ey	ey	PROPN
ejpam-6640	220	17	,	,	PUNCT
ejpam-6640	220	18	t	t	NOUN
ejpam-6640	220	19	◦	◦	NOUN
ejpam-6640	220	20	f	f	PROPN
ejpam-6640	221	1	+	+	CCONJ
ejpam-6640	221	2	p	p	PROPN
ejpam-6640	221	3	◦	◦	NOUN
ejpam-6640	221	4	f	f	X
ejpam-6640	222	1	=	=	SYM
ejpam-6640	222	2	p	p	PROPN
ejpam-6640	222	3	◦	◦	NOUN
ejpam-6640	222	4	f	f	X
ejpam-6640	222	5	⇒	⇒	NOUN
ejpam-6640	222	6	{	{	PUNCT
ejpam-6640	222	7	p	p	NOUN
ejpam-6640	222	8	◦	◦	NOUN
ejpam-6640	222	9	f	f	X
ejpam-6640	222	10	+	+	CCONJ
ejpam-6640	222	11	ey	ey	PROPN
ejpam-6640	222	12	,	,	PUNCT
ejpam-6640	222	13	t	t	NOUN
ejpam-6640	222	14	◦	◦	NOUN
ejpam-6640	222	15	f	f	X
ejpam-6640	223	1	=	=	SYM
ejpam-6640	223	2	p	p	PROPN
ejpam-6640	223	3	◦	◦	NOUN
ejpam-6640	223	4	f	f	X
ejpam-6640	224	1	+	+	CCONJ
ejpam-6640	224	2	ex	ex	X
ejpam-6640	224	3	,	,	PUNCT
ejpam-6640	224	4	t	t	NOUN
ejpam-6640	224	5	=	=	SYM
ejpam-6640	224	6	p	p	PROPN
ejpam-6640	224	7	◦	◦	NOUN
ejpam-6640	224	8	f	f	X
ejpam-6640	224	9	ey	ey	PROPN
ejpam-6640	224	10	,	,	PUNCT
ejpam-6640	224	11	t	t	NOUN
ejpam-6640	224	12	◦	◦	NOUN
ejpam-6640	224	13	f	f	PROPN
ejpam-6640	225	1	+	+	CCONJ
ejpam-6640	225	2	p	p	PROPN
ejpam-6640	225	3	◦	◦	NOUN
ejpam-6640	225	4	f	f	X
ejpam-6640	225	5	=	=	SYM
ejpam-6640	225	6	ex	ex	PROPN
ejpam-6640	225	7	,	,	PUNCT
ejpam-6640	225	8	t	t	PROPN
ejpam-6640	225	9	+	+	CCONJ
ejpam-6640	225	10	p	p	PROPN
ejpam-6640	225	11	◦	◦	NOUN
ejpam-6640	225	12	f	f	X
ejpam-6640	226	1	=	=	SYM
ejpam-6640	226	2	p	p	PROPN
ejpam-6640	226	3	◦	◦	NOUN
ejpam-6640	226	4	f	f	X
ejpam-6640	226	5	⇒	⇒	PROPN
ejpam-6640	226	6	ey	ey	PROPN
ejpam-6640	226	7	,	,	PUNCT
ejpam-6640	226	8	t	t	NOUN
ejpam-6640	226	9	◦	◦	NOUN
ejpam-6640	226	10	f	f	X
ejpam-6640	226	11	=	=	SYM
ejpam-6640	226	12	ex	ex	PROPN
ejpam-6640	226	13	,	,	PUNCT
ejpam-6640	226	14	t	t	PROPN
ejpam-6640	226	15	we	we	PRON
ejpam-6640	226	16	have	have	VERB
ejpam-6640	226	17	:	:	PUNCT
ejpam-6640	226	18	p	p	X
ejpam-6640	226	19	◦	◦	NOUN
ejpam-6640	226	20	f	f	X
ejpam-6640	226	21	=	=	SYM
ejpam-6640	226	22	ey	ey	PROPN
ejpam-6640	226	23	,	,	PUNCT
ejpam-6640	226	24	t	t	NOUN
ejpam-6640	226	25	◦	◦	NOUN
ejpam-6640	226	26	f	f	X
ejpam-6640	227	1	=	=	SYM
ejpam-6640	227	2	ex	ex	PROPN
ejpam-6640	227	3	,	,	PUNCT
ejpam-6640	227	4	t	t	PROPN
ejpam-6640	227	5	.	.	PUNCT
ejpam-6640	228	1	since	since	SCONJ
ejpam-6640	228	2	f	f	PROPN
ejpam-6640	228	3	is	be	AUX
ejpam-6640	228	4	an	an	DET
ejpam-6640	228	5	epimorphism	epimorphism	NOUN
ejpam-6640	228	6	,	,	PUNCT
ejpam-6640	228	7	p	p	X
ejpam-6640	228	8	=	=	SYM
ejpam-6640	228	9	ey	ey	PROPN
ejpam-6640	228	10	,	,	PUNCT
ejpam-6640	228	11	t	t	PROPN
ejpam-6640	228	12	.	.	PUNCT
ejpam-6640	229	1	therefore	therefore	ADV
ejpam-6640	229	2	,	,	PUNCT
ejpam-6640	229	3	the	the	DET
ejpam-6640	229	4	cokernel	cokernel	NOUN
ejpam-6640	229	5	of	of	ADP
ejpam-6640	229	6	f	f	PROPN
ejpam-6640	229	7	,	,	PUNCT
ejpam-6640	229	8	con(f	con(f	PROPN
ejpam-6640	229	9	)	)	PUNCT
ejpam-6640	229	10	,	,	PUNCT
ejpam-6640	229	11	is	be	AUX
ejpam-6640	229	12	zero	zero	NUM
ejpam-6640	229	13	.	.	PUNCT
ejpam-6640	230	1	let	let	VERB
ejpam-6640	230	2	a	a	PRON
ejpam-6640	230	3	be	be	AUX
ejpam-6640	230	4	a	a	DET
ejpam-6640	230	5	balanced	balanced	ADJ
ejpam-6640	230	6	abelian	abelian	ADJ
ejpam-6640	230	7	category	category	NOUN
ejpam-6640	230	8	and	and	CCONJ
ejpam-6640	230	9	x	x	SYM
ejpam-6640	230	10	an	an	DET
ejpam-6640	230	11	object	object	NOUN
ejpam-6640	230	12	in	in	ADP
ejpam-6640	230	13	a	a	PRON
ejpam-6640	230	14	.	.	PUNCT
ejpam-6640	231	1	then	then	ADV
ejpam-6640	231	2	the	the	DET
ejpam-6640	231	3	functor	functor	NOUN
ejpam-6640	231	4	denoted	denote	VERB
ejpam-6640	231	5	by	by	ADP
ejpam-6640	231	6	homa	homa	PROPN
ejpam-6640	231	7	(	(	PUNCT
ejpam-6640	231	8	x,−	x,−	PROPN
ejpam-6640	231	9	)	)	PUNCT
ejpam-6640	231	10	:	:	PUNCT
ejpam-6640	231	11	a	a	DET
ejpam-6640	231	12	−→	−→	NOUN
ejpam-6640	231	13	ab	ab	PROPN
ejpam-6640	231	14	defined	define	VERB
ejpam-6640	231	15	by	by	ADP
ejpam-6640	231	16	:	:	PUNCT
ejpam-6640	231	17	a.	a.	PROPN
ejpam-6640	231	18	diallo	diallo	PROPN
ejpam-6640	231	19	,	,	PUNCT
ejpam-6640	231	20	m.	m.	PROPN
ejpam-6640	231	21	b.	b.	PROPN
ejpam-6640	231	22	f.	f.	PROPN
ejpam-6640	231	23	b.	b.	PROPN
ejpam-6640	231	24	maaouia	maaouia	PROPN
ejpam-6640	231	25	,	,	PUNCT
ejpam-6640	231	26	m.	m.	NOUN
ejpam-6640	231	27	sanghare	sanghare	PROPN
ejpam-6640	231	28	/	/	SYM
ejpam-6640	231	29	eur	eur	PROPN
ejpam-6640	231	30	.	.	PUNCT
ejpam-6640	232	1	j.	j.	PROPN
ejpam-6640	232	2	pure	pure	PROPN
ejpam-6640	232	3	appl	appl	PROPN
ejpam-6640	232	4	.	.	PROPN
ejpam-6640	232	5	math	math	PROPN
ejpam-6640	232	6	,	,	PUNCT
ejpam-6640	232	7	18	18	NUM
ejpam-6640	232	8	(	(	PUNCT
ejpam-6640	232	9	4	4	NUM
ejpam-6640	232	10	)	)	PUNCT
ejpam-6640	232	11	(	(	PUNCT
ejpam-6640	232	12	2025	2025	NUM
ejpam-6640	232	13	)	)	PUNCT
ejpam-6640	232	14	,	,	PUNCT
ejpam-6640	232	15	6640	6640	NUM
ejpam-6640	232	16	9	9	NUM
ejpam-6640	232	17	of	of	ADP
ejpam-6640	232	18	28	28	NUM
ejpam-6640	232	19	(	(	PUNCT
ejpam-6640	232	20	i)(ii)(i	i)(ii)(i	NOUN
ejpam-6640	232	21	)	)	PUNCT
ejpam-6640	232	22	∀y	∀y	PROPN
ejpam-6640	232	23	∈	∈	PROPN
ejpam-6640	232	24	ob(a	ob(a	NUM
ejpam-6640	232	25	)	)	PUNCT
ejpam-6640	232	26	,	,	PUNCT
ejpam-6640	232	27	homa	homa	NOUN
ejpam-6640	232	28	(	(	PUNCT
ejpam-6640	232	29	x,−)(y	x,−)(y	PROPN
ejpam-6640	232	30	)	)	PUNCT
ejpam-6640	233	1	=	=	SYM
ejpam-6640	233	2	homa	homa	NOUN
ejpam-6640	233	3	(	(	PUNCT
ejpam-6640	233	4	x	x	X
ejpam-6640	233	5	,	,	PUNCT
ejpam-6640	233	6	y	y	PROPN
ejpam-6640	233	7	)	)	PUNCT
ejpam-6640	233	8	∈	∈	PROPN
ejpam-6640	233	9	ob(ab	ob(ab	PROPN
ejpam-6640	233	10	)	)	PUNCT
ejpam-6640	233	11	;	;	PUNCT
ejpam-6640	233	12	(	(	PUNCT
ejpam-6640	233	13	ii	ii	NOUN
ejpam-6640	233	14	)	)	PUNCT
ejpam-6640	233	15	∀f	∀f	PROPN
ejpam-6640	233	16	∈	∈	PROPN
ejpam-6640	233	17	homa	homa	NOUN
ejpam-6640	233	18	(	(	PUNCT
ejpam-6640	233	19	y	y	PROPN
ejpam-6640	233	20	,	,	PUNCT
ejpam-6640	233	21	z	z	NOUN
ejpam-6640	233	22	)	)	PUNCT
ejpam-6640	233	23	,	,	PUNCT
ejpam-6640	233	24	homa	homa	NOUN
ejpam-6640	233	25	(	(	PUNCT
ejpam-6640	233	26	x,−)(f	x,−)(f	PROPN
ejpam-6640	233	27	)	)	PUNCT
ejpam-6640	233	28	=	=	SYM
ejpam-6640	233	29	homa	homa	NOUN
ejpam-6640	233	30	(	(	PUNCT
ejpam-6640	233	31	x	x	X
ejpam-6640	233	32	,	,	PUNCT
ejpam-6640	233	33	f	f	X
ejpam-6640	233	34	)	)	PUNCT
ejpam-6640	233	35	=	=	NOUN
ejpam-6640	233	36	f∗	f∗	NOUN
ejpam-6640	233	37	:	:	PUNCT
ejpam-6640	233	38	homa	homa	NOUN
ejpam-6640	233	39	(	(	PUNCT
ejpam-6640	233	40	x	x	X
ejpam-6640	233	41	,	,	PUNCT
ejpam-6640	233	42	y	y	PROPN
ejpam-6640	233	43	)	)	PUNCT
ejpam-6640	233	44	−→	−→	PROPN
ejpam-6640	233	45	homa	homa	NOUN
ejpam-6640	233	46	(	(	PUNCT
ejpam-6640	233	47	x	x	X
ejpam-6640	233	48	,	,	PUNCT
ejpam-6640	233	49	z	z	NOUN
ejpam-6640	233	50	)	)	PUNCT
ejpam-6640	233	51	ϕ	ϕ	PROPN
ejpam-6640	234	1	7−→	7−→	PROPN
ejpam-6640	234	2	f	f	NOUN
ejpam-6640	234	3	◦	◦	NOUN
ejpam-6640	234	4	ϕ	ϕ	NOUN
ejpam-6640	234	5	is	be	AUX
ejpam-6640	234	6	covariant	covariant	ADJ
ejpam-6640	234	7	,	,	PUNCT
ejpam-6640	234	8	additive	additive	NOUN
ejpam-6640	234	9	,	,	PUNCT
ejpam-6640	234	10	left	leave	VERB
ejpam-6640	234	11	exact	exact	ADJ
ejpam-6640	234	12	functor	functor	NOUN
ejpam-6640	234	13	,	,	PUNCT
ejpam-6640	234	14	and	and	CCONJ
ejpam-6640	234	15	it	it	PRON
ejpam-6640	234	16	is	be	AUX
ejpam-6640	234	17	exact	exact	ADJ
ejpam-6640	235	1	if	if	SCONJ
ejpam-6640	235	2	and	and	CCONJ
ejpam-6640	235	3	only	only	ADV
ejpam-6640	235	4	if	if	SCONJ
ejpam-6640	235	5	x	x	PRON
ejpam-6640	235	6	is	be	AUX
ejpam-6640	235	7	a	a	DET
ejpam-6640	235	8	projective	projective	ADJ
ejpam-6640	235	9	object	object	NOUN
ejpam-6640	235	10	in	in	ADP
ejpam-6640	235	11	a	a	PRON
ejpam-6640	235	12	.	.	PUNCT
ejpam-6640	236	1	proof	proof	NOUN
ejpam-6640	236	2	.	.	PUNCT
ejpam-6640	237	1	•	•	INTJ
ejpam-6640	237	2	it	it	PRON
ejpam-6640	237	3	’s	’	VERB
ejpam-6640	237	4	evident	evident	ADJ
ejpam-6640	237	5	that	that	SCONJ
ejpam-6640	237	6	homa	homa	NOUN
ejpam-6640	237	7	(	(	PUNCT
ejpam-6640	237	8	x,−	x,−	PROPN
ejpam-6640	237	9	)	)	PUNCT
ejpam-6640	237	10	:	:	PUNCT
ejpam-6640	237	11	a	a	DET
ejpam-6640	237	12	−→	−→	NOUN
ejpam-6640	237	13	ab	ab	PROPN
ejpam-6640	237	14	is	be	AUX
ejpam-6640	237	15	an	an	DET
ejpam-6640	237	16	additive	additive	ADJ
ejpam-6640	237	17	covariant	covariant	ADJ
ejpam-6640	237	18	functor	functor	PROPN
ejpam-6640	237	19	.	.	PROPN
ejpam-6640	237	20	•	•	NUM
ejpam-6640	237	21	let	let	VERB
ejpam-6640	237	22	us	we	PRON
ejpam-6640	237	23	show	show	VERB
ejpam-6640	237	24	that	that	SCONJ
ejpam-6640	237	25	homa	homa	NOUN
ejpam-6640	237	26	(	(	PUNCT
ejpam-6640	237	27	x,−	x,−	PROPN
ejpam-6640	237	28	)	)	PUNCT
ejpam-6640	237	29	:	:	PUNCT
ejpam-6640	237	30	a	a	DET
ejpam-6640	237	31	−→	−→	NOUN
ejpam-6640	237	32	ab	ab	PROPN
ejpam-6640	237	33	is	be	AUX
ejpam-6640	237	34	a	a	DET
ejpam-6640	237	35	left	left	ADJ
ejpam-6640	237	36	-	-	PUNCT
ejpam-6640	237	37	exact	exact	NOUN
ejpam-6640	237	38	functor	functor	NOUN
ejpam-6640	237	39	.	.	PUNCT
ejpam-6640	238	1	consider	consider	VERB
ejpam-6640	238	2	the	the	DET
ejpam-6640	238	3	following	follow	VERB
ejpam-6640	238	4	short	short	ADJ
ejpam-6640	238	5	left	left	ADJ
ejpam-6640	238	6	-	-	PUNCT
ejpam-6640	238	7	exact	exact	NOUN
ejpam-6640	238	8	sequence	sequence	NOUN
ejpam-6640	238	9	of	of	ADP
ejpam-6640	238	10	morphisms	morphism	NOUN
ejpam-6640	238	11	in	in	ADP
ejpam-6640	238	12	a	a	DET
ejpam-6640	238	13	:	:	SYM
ejpam-6640	238	14	0	0	NUM
ejpam-6640	238	15	//	//	PUNCT
ejpam-6640	238	16	y	y	PROPN
ejpam-6640	238	17	f	f	PROPN
ejpam-6640	238	18	//	//	PROPN
ejpam-6640	238	19	z	z	PROPN
ejpam-6640	238	20	g	g	PROPN
ejpam-6640	238	21	//	//	PROPN
ejpam-6640	238	22	t	t	PROPN
ejpam-6640	238	23	we	we	PRON
ejpam-6640	238	24	will	will	AUX
ejpam-6640	238	25	show	show	VERB
ejpam-6640	238	26	that	that	SCONJ
ejpam-6640	238	27	{	{	PUNCT
ejpam-6640	238	28	ex,0	ex,0	PROPN
ejpam-6640	238	29	}	}	PUNCT
ejpam-6640	238	30	//	//	SYM
ejpam-6640	238	31	homa	homa	NOUN
ejpam-6640	238	32	(	(	PUNCT
ejpam-6640	238	33	x	x	X
ejpam-6640	238	34	,	,	PUNCT
ejpam-6640	238	35	y	y	PROPN
ejpam-6640	238	36	)	)	PUNCT
ejpam-6640	238	37	homa	homa	NOUN
ejpam-6640	238	38	(	(	PUNCT
ejpam-6640	238	39	x	x	X
ejpam-6640	238	40	,	,	PUNCT
ejpam-6640	238	41	f)=f∗	f)=f∗	PROPN
ejpam-6640	238	42	//	//	X
ejpam-6640	238	43	homa	homa	PROPN
ejpam-6640	238	44	(	(	PUNCT
ejpam-6640	238	45	x	x	X
ejpam-6640	238	46	,	,	PUNCT
ejpam-6640	238	47	z	z	NOUN
ejpam-6640	238	48	)	)	PUNCT
ejpam-6640	238	49	homa	homa	NOUN
ejpam-6640	238	50	(	(	PUNCT
ejpam-6640	238	51	x	x	NOUN
ejpam-6640	238	52	,	,	PUNCT
ejpam-6640	238	53	g)=g∗	g)=g∗	PROPN
ejpam-6640	238	54	//	//	SYM
ejpam-6640	238	55	homa	homa	PROPN
ejpam-6640	238	56	(	(	PUNCT
ejpam-6640	238	57	x	x	PROPN
ejpam-6640	238	58	,	,	PUNCT
ejpam-6640	238	59	t	t	PROPN
ejpam-6640	238	60	)	)	PUNCT
ejpam-6640	238	61	is	be	AUX
ejpam-6640	238	62	a	a	DET
ejpam-6640	238	63	left	left	ADJ
ejpam-6640	238	64	-	-	PUNCT
ejpam-6640	238	65	exact	exact	NOUN
ejpam-6640	238	66	sequence	sequence	NOUN
ejpam-6640	238	67	.	.	PUNCT
ejpam-6640	239	1	it	it	PRON
ejpam-6640	239	2	suffices	suffice	VERB
ejpam-6640	239	3	to	to	PART
ejpam-6640	239	4	show	show	VERB
ejpam-6640	239	5	that	that	SCONJ
ejpam-6640	239	6	ker(f∗	ker(f∗	PROPN
ejpam-6640	239	7	)	)	PUNCT
ejpam-6640	240	1	=	=	PRON
ejpam-6640	240	2	{	{	PUNCT
ejpam-6640	240	3	ex	ex	X
ejpam-6640	240	4	,	,	PUNCT
ejpam-6640	240	5	y	y	PROPN
ejpam-6640	240	6	}	}	PUNCT
ejpam-6640	240	7	,	,	PUNCT
ejpam-6640	240	8	where	where	SCONJ
ejpam-6640	240	9	ex	ex	X
ejpam-6640	240	10	,	,	PUNCT
ejpam-6640	240	11	y	y	PROPN
ejpam-6640	240	12	is	be	AUX
ejpam-6640	240	13	the	the	DET
ejpam-6640	240	14	neutral	neutral	ADJ
ejpam-6640	240	15	element	element	NOUN
ejpam-6640	240	16	(	(	PUNCT
ejpam-6640	240	17	the	the	DET
ejpam-6640	240	18	zero	zero	NUM
ejpam-6640	240	19	morphism	morphism	NOUN
ejpam-6640	240	20	)	)	PUNCT
ejpam-6640	240	21	of	of	ADP
ejpam-6640	240	22	homa	homa	PROPN
ejpam-6640	240	23	(	(	PUNCT
ejpam-6640	240	24	x	x	X
ejpam-6640	240	25	,	,	PUNCT
ejpam-6640	240	26	y	y	PROPN
ejpam-6640	240	27	)	)	PUNCT
ejpam-6640	240	28	,	,	PUNCT
ejpam-6640	240	29	and	and	CCONJ
ejpam-6640	240	30	that	that	DET
ejpam-6640	240	31	im(f∗	im(f∗	NOUN
ejpam-6640	240	32	)	)	PUNCT
ejpam-6640	240	33	=	=	PUNCT
ejpam-6640	241	1	ker(g∗	ker(g∗	NOUN
ejpam-6640	241	2	)	)	PUNCT
ejpam-6640	241	3	.	.	PUNCT
ejpam-6640	242	1	•	•	NUM
ejpam-6640	242	2	show	show	VERB
ejpam-6640	242	3	that	that	SCONJ
ejpam-6640	242	4	ker(f∗	ker(f∗	NUM
ejpam-6640	242	5	)	)	PUNCT
ejpam-6640	242	6	=	=	PRON
ejpam-6640	242	7	{	{	PUNCT
ejpam-6640	242	8	ex	ex	X
ejpam-6640	242	9	,	,	PUNCT
ejpam-6640	242	10	y	y	PROPN
ejpam-6640	242	11	}	}	PUNCT
ejpam-6640	242	12	.	.	PUNCT
ejpam-6640	243	1	since	since	SCONJ
ejpam-6640	243	2	f∗	f∗	NOUN
ejpam-6640	243	3	is	be	AUX
ejpam-6640	243	4	a	a	DET
ejpam-6640	243	5	morphism	morphism	NOUN
ejpam-6640	243	6	of	of	ADP
ejpam-6640	243	7	abelian	abelian	ADJ
ejpam-6640	243	8	groups	group	NOUN
ejpam-6640	243	9	,	,	PUNCT
ejpam-6640	243	10	the	the	DET
ejpam-6640	243	11	kernel	kernel	NOUN
ejpam-6640	243	12	of	of	ADP
ejpam-6640	243	13	f∗	f∗	PROPN
ejpam-6640	243	14	is	be	AUX
ejpam-6640	243	15	:	:	PUNCT
ejpam-6640	243	16	ker(f∗	ker(f∗	X
ejpam-6640	243	17	)	)	PUNCT
ejpam-6640	243	18	=	=	PRON
ejpam-6640	243	19	{	{	PUNCT
ejpam-6640	243	20	ϕ	ϕ	NOUN
ejpam-6640	243	21	∈	∈	PROPN
ejpam-6640	243	22	homa	homa	NOUN
ejpam-6640	243	23	(	(	PUNCT
ejpam-6640	243	24	x	x	X
ejpam-6640	243	25	,	,	PUNCT
ejpam-6640	243	26	y	y	PROPN
ejpam-6640	243	27	)	)	PUNCT
ejpam-6640	243	28	:	:	PUNCT
ejpam-6640	244	1	f∗(ϕ	f∗(ϕ	VERB
ejpam-6640	244	2	)	)	PUNCT
ejpam-6640	244	3	=	=	SYM
ejpam-6640	245	1	f	f	X
ejpam-6640	245	2	◦	◦	NOUN
ejpam-6640	245	3	ϕ	ϕ	X
ejpam-6640	245	4	=	=	PUNCT
ejpam-6640	245	5	ex	ex	X
ejpam-6640	245	6	,	,	PUNCT
ejpam-6640	245	7	z	z	NOUN
ejpam-6640	245	8	}	}	PUNCT
ejpam-6640	245	9	,	,	PUNCT
ejpam-6640	245	10	where	where	SCONJ
ejpam-6640	245	11	ex	ex	X
ejpam-6640	245	12	,	,	PUNCT
ejpam-6640	245	13	z	z	PROPN
ejpam-6640	245	14	is	be	AUX
ejpam-6640	245	15	the	the	DET
ejpam-6640	245	16	neutral	neutral	ADJ
ejpam-6640	245	17	element	element	NOUN
ejpam-6640	245	18	(	(	PUNCT
ejpam-6640	245	19	the	the	DET
ejpam-6640	245	20	zero	zero	NUM
ejpam-6640	245	21	morphism	morphism	NOUN
ejpam-6640	245	22	)	)	PUNCT
ejpam-6640	245	23	of	of	ADP
ejpam-6640	245	24	the	the	DET
ejpam-6640	245	25	abelian	abelian	PROPN
ejpam-6640	245	26	group	group	PROPN
ejpam-6640	245	27	homa	homa	PROPN
ejpam-6640	245	28	(	(	PUNCT
ejpam-6640	245	29	x	x	X
ejpam-6640	245	30	,	,	PUNCT
ejpam-6640	245	31	z	z	NOUN
ejpam-6640	245	32	)	)	PUNCT
ejpam-6640	245	33	.	.	PUNCT
ejpam-6640	246	1	let	let	VERB
ejpam-6640	246	2	ϕ	ϕ	PROPN
ejpam-6640	246	3	∈	∈	PROPN
ejpam-6640	246	4	ker(f∗	ker(f∗	PROPN
ejpam-6640	246	5	)	)	PUNCT
ejpam-6640	246	6	.	.	PUNCT
ejpam-6640	247	1	we	we	PRON
ejpam-6640	247	2	have	have	VERB
ejpam-6640	247	3	:	:	PUNCT
ejpam-6640	247	4	ϕ	ϕ	PROPN
ejpam-6640	247	5	∈	∈	PROPN
ejpam-6640	247	6	ker(f∗	ker(f∗	PROPN
ejpam-6640	247	7	)	)	PUNCT
ejpam-6640	247	8	⇒	⇒	PROPN
ejpam-6640	247	9	f∗(ϕ	f∗(ϕ	PROPN
ejpam-6640	247	10	)	)	PUNCT
ejpam-6640	247	11	=	=	SYM
ejpam-6640	248	1	f	f	X
ejpam-6640	248	2	◦	◦	NOUN
ejpam-6640	248	3	ϕ	ϕ	X
ejpam-6640	248	4	=	=	PUNCT
ejpam-6640	248	5	ex	ex	X
ejpam-6640	248	6	,	,	PUNCT
ejpam-6640	248	7	z	z	NOUN
ejpam-6640	248	8	.	.	PUNCT
ejpam-6640	249	1	now	now	ADV
ejpam-6640	249	2	,	,	PUNCT
ejpam-6640	249	3	f	f	PROPN
ejpam-6640	249	4	◦	◦	NOUN
ejpam-6640	249	5	ex	ex	PROPN
ejpam-6640	249	6	,	,	PUNCT
ejpam-6640	249	7	y	y	PROPN
ejpam-6640	249	8	=	=	SYM
ejpam-6640	249	9	ex	ex	X
ejpam-6640	249	10	,	,	PUNCT
ejpam-6640	249	11	z	z	NOUN
ejpam-6640	249	12	.	.	PUNCT
ejpam-6640	250	1	indeed	indeed	ADV
ejpam-6640	250	2	,	,	PUNCT
ejpam-6640	250	3	for	for	ADP
ejpam-6640	250	4	all	all	DET
ejpam-6640	250	5	ϕ	ϕ	PROPN
ejpam-6640	250	6	∈	∈	PROPN
ejpam-6640	250	7	homa	homa	NOUN
ejpam-6640	250	8	(	(	PUNCT
ejpam-6640	250	9	x	x	X
ejpam-6640	250	10	,	,	PUNCT
ejpam-6640	250	11	y	y	PROPN
ejpam-6640	250	12	)	)	PUNCT
ejpam-6640	250	13	,	,	PUNCT
ejpam-6640	250	14	where	where	SCONJ
ejpam-6640	250	15	ex	ex	X
ejpam-6640	250	16	,	,	PUNCT
ejpam-6640	250	17	y	y	PROPN
ejpam-6640	250	18	is	be	AUX
ejpam-6640	250	19	the	the	DET
ejpam-6640	250	20	neutral	neutral	ADJ
ejpam-6640	250	21	element	element	NOUN
ejpam-6640	250	22	of	of	ADP
ejpam-6640	250	23	the	the	DET
ejpam-6640	250	24	abelian	abelian	PROPN
ejpam-6640	250	25	group	group	PROPN
ejpam-6640	250	26	homa	homa	PROPN
ejpam-6640	250	27	(	(	PUNCT
ejpam-6640	250	28	x	x	X
ejpam-6640	250	29	,	,	PUNCT
ejpam-6640	250	30	y	y	PROPN
ejpam-6640	250	31	)	)	PUNCT
ejpam-6640	250	32	,	,	PUNCT
ejpam-6640	250	33	we	we	PRON
ejpam-6640	250	34	have	have	VERB
ejpam-6640	250	35	:	:	PUNCT
ejpam-6640	251	1	f	f	X
ejpam-6640	251	2	◦	◦	NOUN
ejpam-6640	251	3	(	(	PUNCT
ejpam-6640	251	4	ϕ+	ϕ+	X
ejpam-6640	251	5	ex	ex	X
ejpam-6640	251	6	,	,	PUNCT
ejpam-6640	251	7	y	y	PROPN
ejpam-6640	251	8	)	)	PUNCT
ejpam-6640	251	9	=	=	PUNCT
ejpam-6640	252	1	f	f	X
ejpam-6640	252	2	◦	◦	NOUN
ejpam-6640	252	3	(	(	PUNCT
ejpam-6640	252	4	ex	ex	X
ejpam-6640	252	5	,	,	PUNCT
ejpam-6640	252	6	y	y	PROPN
ejpam-6640	252	7	+	+	PROPN
ejpam-6640	252	8	ϕ	ϕ	NOUN
ejpam-6640	252	9	)	)	PUNCT
ejpam-6640	252	10	=	=	SYM
ejpam-6640	253	1	f	f	X
ejpam-6640	253	2	◦	◦	NOUN
ejpam-6640	254	1	ϕ⇒	ϕ⇒	NUM
ejpam-6640	254	2	f	f	X
ejpam-6640	255	1	◦	◦	NOUN
ejpam-6640	255	2	ϕ+	ϕ+	PUNCT
ejpam-6640	255	3	f	f	X
ejpam-6640	256	1	◦	◦	NOUN
ejpam-6640	256	2	ex	ex	PROPN
ejpam-6640	256	3	,	,	PUNCT
ejpam-6640	256	4	y	y	PROPN
ejpam-6640	256	5	=	=	SYM
ejpam-6640	256	6	f	f	PROPN
ejpam-6640	257	1	◦	◦	NOUN
ejpam-6640	257	2	ex	ex	PROPN
ejpam-6640	257	3	,	,	PUNCT
ejpam-6640	257	4	y	y	PROPN
ejpam-6640	257	5	+	+	NUM
ejpam-6640	257	6	f	f	PROPN
ejpam-6640	258	1	◦	◦	NOUN
ejpam-6640	258	2	ϕ	ϕ	X
ejpam-6640	258	3	=	=	PUNCT
ejpam-6640	258	4	f	f	PROPN
ejpam-6640	258	5	◦	◦	NOUN
ejpam-6640	258	6	ϕ	ϕ	X
ejpam-6640	258	7	⇒	⇒	NOUN
ejpam-6640	258	8	{	{	PUNCT
ejpam-6640	258	9	f	f	NOUN
ejpam-6640	258	10	◦	◦	NOUN
ejpam-6640	258	11	ϕ+	ϕ+	PUNCT
ejpam-6640	258	12	f	f	X
ejpam-6640	258	13	◦	◦	NOUN
ejpam-6640	258	14	ex	ex	PROPN
ejpam-6640	258	15	,	,	PUNCT
ejpam-6640	258	16	y	y	PROPN
ejpam-6640	258	17	=	=	SYM
ejpam-6640	258	18	f	f	PROPN
ejpam-6640	259	1	◦	◦	NOUN
ejpam-6640	259	2	ϕ+	ϕ+	PUNCT
ejpam-6640	259	3	ex	ex	X
ejpam-6640	259	4	,	,	PUNCT
ejpam-6640	259	5	z	z	NOUN
ejpam-6640	259	6	=	=	SYM
ejpam-6640	259	7	f	f	PROPN
ejpam-6640	260	1	◦	◦	NOUN
ejpam-6640	260	2	ϕ	ϕ	X
ejpam-6640	260	3	f	f	X
ejpam-6640	260	4	◦	◦	NOUN
ejpam-6640	260	5	ex	ex	PROPN
ejpam-6640	260	6	,	,	PUNCT
ejpam-6640	260	7	y	y	PROPN
ejpam-6640	261	1	+	+	NUM
ejpam-6640	261	2	f	f	PROPN
ejpam-6640	262	1	◦	◦	NOUN
ejpam-6640	262	2	ϕ	ϕ	X
ejpam-6640	262	3	=	=	PUNCT
ejpam-6640	262	4	ex	ex	X
ejpam-6640	262	5	,	,	PUNCT
ejpam-6640	262	6	z	z	PROPN
ejpam-6640	262	7	+	+	NUM
ejpam-6640	262	8	f	f	PROPN
ejpam-6640	263	1	◦	◦	NOUN
ejpam-6640	263	2	ϕ	ϕ	X
ejpam-6640	263	3	=	=	PUNCT
ejpam-6640	263	4	f	f	PROPN
ejpam-6640	263	5	◦	◦	NOUN
ejpam-6640	263	6	ϕ	ϕ	X
ejpam-6640	263	7	⇒	⇒	NOUN
ejpam-6640	263	8	f	f	PROPN
ejpam-6640	263	9	◦	◦	NOUN
ejpam-6640	263	10	ex	ex	PROPN
ejpam-6640	263	11	,	,	PUNCT
ejpam-6640	263	12	y	y	PROPN
ejpam-6640	263	13	=	=	SYM
ejpam-6640	263	14	ex	ex	X
ejpam-6640	263	15	,	,	PUNCT
ejpam-6640	263	16	z	z	NOUN
ejpam-6640	263	17	.	.	PUNCT
ejpam-6640	264	1	thus	thus	ADV
ejpam-6640	264	2	,	,	PUNCT
ejpam-6640	264	3	we	we	PRON
ejpam-6640	264	4	have	have	VERB
ejpam-6640	264	5	:	:	PUNCT
ejpam-6640	264	6	f	f	X
ejpam-6640	264	7	◦	◦	NOUN
ejpam-6640	264	8	ϕ	ϕ	X
ejpam-6640	264	9	=	=	PUNCT
ejpam-6640	264	10	f	f	PROPN
ejpam-6640	264	11	◦	◦	NOUN
ejpam-6640	264	12	ex	ex	PROPN
ejpam-6640	264	13	,	,	PUNCT
ejpam-6640	264	14	y	y	PROPN
ejpam-6640	264	15	=	=	SYM
ejpam-6640	264	16	ex	ex	X
ejpam-6640	264	17	,	,	PUNCT
ejpam-6640	264	18	z	z	NOUN
ejpam-6640	264	19	.	.	PUNCT
ejpam-6640	265	1	a.	a.	PROPN
ejpam-6640	265	2	diallo	diallo	PROPN
ejpam-6640	265	3	,	,	PUNCT
ejpam-6640	265	4	m.	m.	PROPN
ejpam-6640	265	5	b.	b.	PROPN
ejpam-6640	265	6	f.	f.	PROPN
ejpam-6640	265	7	b.	b.	PROPN
ejpam-6640	265	8	maaouia	maaouia	PROPN
ejpam-6640	265	9	,	,	PUNCT
ejpam-6640	265	10	m.	m.	NOUN
ejpam-6640	265	11	sanghare	sanghare	PROPN
ejpam-6640	265	12	/	/	SYM
ejpam-6640	265	13	eur	eur	PROPN
ejpam-6640	265	14	.	.	PUNCT
ejpam-6640	266	1	j.	j.	PROPN
ejpam-6640	266	2	pure	pure	PROPN
ejpam-6640	266	3	appl	appl	PROPN
ejpam-6640	266	4	.	.	PROPN
ejpam-6640	266	5	math	math	PROPN
ejpam-6640	266	6	,	,	PUNCT
ejpam-6640	266	7	18	18	NUM
ejpam-6640	266	8	(	(	PUNCT
ejpam-6640	266	9	4	4	NUM
ejpam-6640	266	10	)	)	PUNCT
ejpam-6640	266	11	(	(	PUNCT
ejpam-6640	266	12	2025	2025	NUM
ejpam-6640	266	13	)	)	PUNCT
ejpam-6640	266	14	,	,	PUNCT
ejpam-6640	266	15	6640	6640	NUM
ejpam-6640	266	16	10	10	NUM
ejpam-6640	266	17	of	of	ADP
ejpam-6640	266	18	28	28	NUM
ejpam-6640	266	19	or	or	CCONJ
ejpam-6640	266	20	by	by	ADP
ejpam-6640	266	21	hypothesis	hypothesis	NOUN
ejpam-6640	266	22	,	,	PUNCT
ejpam-6640	266	23	the	the	DET
ejpam-6640	266	24	kernel	kernel	NOUN
ejpam-6640	266	25	of	of	ADP
ejpam-6640	266	26	f	f	PROPN
ejpam-6640	266	27	is	be	AUX
ejpam-6640	266	28	zero	zero	NUM
ejpam-6640	266	29	n(f	n(f	PROPN
ejpam-6640	266	30	)	)	PUNCT
ejpam-6640	266	31	=	=	PUNCT
ejpam-6640	267	1	(	(	PUNCT
ejpam-6640	267	2	0	0	NUM
ejpam-6640	267	3	,	,	PUNCT
ejpam-6640	267	4	ex,0	ex,0	PROPN
ejpam-6640	267	5	)	)	PUNCT
ejpam-6640	267	6	.	.	PUNCT
ejpam-6640	268	1	bylemma	bylemma	PROPN
ejpam-6640	268	2	2	2	NUM
ejpam-6640	268	3	,	,	PUNCT
ejpam-6640	268	4	f	f	PROPN
ejpam-6640	268	5	is	be	AUX
ejpam-6640	268	6	a	a	DET
ejpam-6640	268	7	monomorphism	monomorphism	NOUN
ejpam-6640	268	8	.	.	PUNCT
ejpam-6640	269	1	hence	hence	ADV
ejpam-6640	269	2	,	,	PUNCT
ejpam-6640	269	3	f	f	PROPN
ejpam-6640	269	4	◦	◦	NOUN
ejpam-6640	269	5	ϕ	ϕ	X
ejpam-6640	269	6	=	=	PUNCT
ejpam-6640	269	7	f	f	PROPN
ejpam-6640	269	8	◦	◦	NOUN
ejpam-6640	269	9	ex	ex	NOUN
ejpam-6640	269	10	,	,	PUNCT
ejpam-6640	269	11	y	y	PROPN
ejpam-6640	269	12	⇒	⇒	VERB
ejpam-6640	269	13	ϕ	ϕ	X
ejpam-6640	270	1	=	=	PUNCT
ejpam-6640	270	2	ex	ex	X
ejpam-6640	270	3	,	,	PUNCT
ejpam-6640	270	4	y	y	PROPN
ejpam-6640	270	5	.	.	PUNCT
ejpam-6640	271	1	thus	thus	ADV
ejpam-6640	271	2	,	,	PUNCT
ejpam-6640	271	3	ker(f∗	ker(f∗	PROPN
ejpam-6640	271	4	)	)	PUNCT
ejpam-6640	271	5	=	=	PRON
ejpam-6640	271	6	{	{	PUNCT
ejpam-6640	271	7	ex	ex	X
ejpam-6640	271	8	,	,	PUNCT
ejpam-6640	271	9	y	y	PROPN
ejpam-6640	271	10	}	}	PUNCT
ejpam-6640	271	11	.	.	PUNCT
ejpam-6640	272	1	•	•	NUM
ejpam-6640	272	2	show	show	VERB
ejpam-6640	272	3	that	that	SCONJ
ejpam-6640	272	4	im(f∗	im(f∗	NOUN
ejpam-6640	272	5	)	)	PUNCT
ejpam-6640	272	6	=	=	PUNCT
ejpam-6640	272	7	ker(g∗	ker(g∗	NOUN
ejpam-6640	272	8	)	)	PUNCT
ejpam-6640	272	9	.	.	PUNCT
ejpam-6640	273	1	first	first	ADV
ejpam-6640	273	2	,	,	PUNCT
ejpam-6640	273	3	show	show	VERB
ejpam-6640	273	4	that	that	SCONJ
ejpam-6640	273	5	im(f∗	im(f∗	NOUN
ejpam-6640	273	6	)	)	PUNCT
ejpam-6640	273	7	⊂	⊂	PROPN
ejpam-6640	273	8	ker(g∗	ker(g∗	NOUN
ejpam-6640	273	9	)	)	PUNCT
ejpam-6640	273	10	.	.	PUNCT
ejpam-6640	274	1	it	it	PRON
ejpam-6640	274	2	suffices	suffice	VERB
ejpam-6640	274	3	to	to	PART
ejpam-6640	274	4	show	show	VERB
ejpam-6640	274	5	that	that	SCONJ
ejpam-6640	274	6	g∗	g∗	PROPN
ejpam-6640	274	7	◦	◦	NOUN
ejpam-6640	274	8	f∗	f∗	NOUN
ejpam-6640	274	9	=	=	SYM
ejpam-6640	274	10	ehoma	ehoma	NOUN
ejpam-6640	274	11	(	(	PUNCT
ejpam-6640	274	12	x	x	X
ejpam-6640	274	13	,	,	PUNCT
ejpam-6640	274	14	y	y	PROPN
ejpam-6640	274	15	)	)	PUNCT
ejpam-6640	274	16	,	,	PUNCT
ejpam-6640	274	17	homa	homa	NOUN
ejpam-6640	274	18	(	(	PUNCT
ejpam-6640	274	19	x	x	PROPN
ejpam-6640	274	20	,	,	PUNCT
ejpam-6640	274	21	t	t	PROPN
ejpam-6640	274	22	)	)	PUNCT
ejpam-6640	274	23	,	,	PUNCT
ejpam-6640	274	24	where	where	SCONJ
ejpam-6640	274	25	ehoma	ehoma	NOUN
ejpam-6640	274	26	(	(	PUNCT
ejpam-6640	274	27	x	x	X
ejpam-6640	274	28	,	,	PUNCT
ejpam-6640	274	29	y	y	PROPN
ejpam-6640	274	30	)	)	PUNCT
ejpam-6640	274	31	,	,	PUNCT
ejpam-6640	274	32	homa	homa	NOUN
ejpam-6640	274	33	(	(	PUNCT
ejpam-6640	274	34	x	x	X
ejpam-6640	274	35	,	,	PUNCT
ejpam-6640	274	36	t	t	PROPN
ejpam-6640	274	37	)	)	PUNCT
ejpam-6640	274	38	is	be	AUX
ejpam-6640	274	39	the	the	DET
ejpam-6640	274	40	zero	zero	NUM
ejpam-6640	274	41	morphism	morphism	NOUN
ejpam-6640	274	42	of	of	ADP
ejpam-6640	274	43	the	the	DET
ejpam-6640	274	44	abelian	abelian	ADJ
ejpam-6640	274	45	group	group	NOUN
ejpam-6640	274	46	homab(homa	homab(homa	PROPN
ejpam-6640	274	47	(	(	PUNCT
ejpam-6640	274	48	x	x	X
ejpam-6640	274	49	,	,	PUNCT
ejpam-6640	274	50	y	y	PROPN
ejpam-6640	274	51	)	)	PUNCT
ejpam-6640	274	52	,	,	PUNCT
ejpam-6640	274	53	homa	homa	NOUN
ejpam-6640	274	54	(	(	PUNCT
ejpam-6640	274	55	x	x	PROPN
ejpam-6640	274	56	,	,	PUNCT
ejpam-6640	274	57	t	t	NOUN
ejpam-6640	274	58	)	)	PUNCT
ejpam-6640	274	59	)	)	PUNCT
ejpam-6640	274	60	.	.	PUNCT
ejpam-6640	275	1	we	we	PRON
ejpam-6640	275	2	have	have	AUX
ejpam-6640	275	3	:	:	PUNCT
ejpam-6640	275	4	g∗	g∗	VERB
ejpam-6640	275	5	◦	◦	NOUN
ejpam-6640	275	6	f∗	f∗	NOUN
ejpam-6640	275	7	:	:	PUNCT
ejpam-6640	275	8	homa	homa	NOUN
ejpam-6640	275	9	(	(	PUNCT
ejpam-6640	275	10	x	x	X
ejpam-6640	275	11	,	,	PUNCT
ejpam-6640	275	12	y	y	PROPN
ejpam-6640	275	13	)	)	PUNCT
ejpam-6640	275	14	→	→	SYM
ejpam-6640	275	15	homa	homa	NOUN
ejpam-6640	275	16	(	(	PUNCT
ejpam-6640	275	17	x	x	X
ejpam-6640	275	18	,	,	PUNCT
ejpam-6640	275	19	t	t	PROPN
ejpam-6640	275	20	)	)	PUNCT
ejpam-6640	275	21	.	.	PUNCT
ejpam-6640	276	1	let	let	VERB
ejpam-6640	276	2	ϕ	ϕ	PROPN
ejpam-6640	276	3	∈	∈	PROPN
ejpam-6640	276	4	homa	homa	NOUN
ejpam-6640	276	5	(	(	PUNCT
ejpam-6640	276	6	x	x	X
ejpam-6640	276	7	,	,	PUNCT
ejpam-6640	276	8	y	y	PROPN
ejpam-6640	276	9	)	)	PUNCT
ejpam-6640	276	10	.	.	PUNCT
ejpam-6640	277	1	we	we	PRON
ejpam-6640	277	2	have	have	AUX
ejpam-6640	277	3	:	:	PUNCT
ejpam-6640	277	4	g∗	g∗	VERB
ejpam-6640	277	5	◦	◦	NOUN
ejpam-6640	277	6	f∗(ϕ	f∗(ϕ	NOUN
ejpam-6640	277	7	)	)	PUNCT
ejpam-6640	277	8	=	=	SYM
ejpam-6640	277	9	g∗(f∗(ϕ	g∗(f∗(ϕ	NOUN
ejpam-6640	277	10	)	)	PUNCT
ejpam-6640	277	11	)	)	PUNCT
ejpam-6640	278	1	=	=	SYM
ejpam-6640	278	2	g∗(f	g∗(f	NOUN
ejpam-6640	278	3	◦	◦	NOUN
ejpam-6640	278	4	ϕ	ϕ	NOUN
ejpam-6640	278	5	)	)	PUNCT
ejpam-6640	278	6	=	=	SYM
ejpam-6640	278	7	g	g	PROPN
ejpam-6640	278	8	◦	◦	NOUN
ejpam-6640	278	9	(	(	PUNCT
ejpam-6640	278	10	f	f	X
ejpam-6640	278	11	◦	◦	NOUN
ejpam-6640	278	12	ϕ	ϕ	NOUN
ejpam-6640	278	13	)	)	PUNCT
ejpam-6640	278	14	=	=	SYM
ejpam-6640	279	1	(	(	PUNCT
ejpam-6640	279	2	g	g	PROPN
ejpam-6640	279	3	◦	◦	NOUN
ejpam-6640	279	4	f	f	X
ejpam-6640	279	5	)	)	PUNCT
ejpam-6640	279	6	◦	◦	NOUN
ejpam-6640	279	7	ϕ	ϕ	NOUN
ejpam-6640	279	8	=	=	SYM
ejpam-6640	279	9	ey	ey	PROPN
ejpam-6640	279	10	,	,	PUNCT
ejpam-6640	279	11	t	t	PROPN
ejpam-6640	279	12	◦	◦	NOUN
ejpam-6640	279	13	ϕ	ϕ	X
ejpam-6640	279	14	(	(	PUNCT
ejpam-6640	279	15	since	since	SCONJ
ejpam-6640	279	16	by	by	ADP
ejpam-6640	279	17	hypothesis	hypothesis	NOUN
ejpam-6640	279	18	,	,	PUNCT
ejpam-6640	279	19	g	g	PROPN
ejpam-6640	279	20	◦	◦	NOUN
ejpam-6640	279	21	f	f	X
ejpam-6640	279	22	=	=	SYM
ejpam-6640	279	23	ey	ey	PROPN
ejpam-6640	279	24	,	,	PUNCT
ejpam-6640	279	25	t	t	NOUN
ejpam-6640	279	26	)	)	PUNCT
ejpam-6640	279	27	=	=	PUNCT
ejpam-6640	280	1	ex	ex	X
ejpam-6640	280	2	,	,	PUNCT
ejpam-6640	280	3	t	t	PROPN
ejpam-6640	280	4	because	because	SCONJ
ejpam-6640	280	5	for	for	ADP
ejpam-6640	280	6	all	all	PRON
ejpam-6640	280	7	ψ	ψ	ADP
ejpam-6640	280	8	∈	∈	PROPN
ejpam-6640	280	9	homa	homa	NOUN
ejpam-6640	280	10	(	(	PUNCT
ejpam-6640	280	11	y	y	PROPN
ejpam-6640	280	12	,	,	PUNCT
ejpam-6640	280	13	t	t	PROPN
ejpam-6640	280	14	)	)	PUNCT
ejpam-6640	280	15	,	,	PUNCT
ejpam-6640	280	16	where	where	SCONJ
ejpam-6640	280	17	ey	ey	NOUN
ejpam-6640	280	18	,	,	PUNCT
ejpam-6640	280	19	t	t	PROPN
ejpam-6640	280	20	is	be	AUX
ejpam-6640	280	21	the	the	DET
ejpam-6640	280	22	neutral	neutral	ADJ
ejpam-6640	280	23	element	element	NOUN
ejpam-6640	280	24	of	of	ADP
ejpam-6640	280	25	the	the	DET
ejpam-6640	280	26	abelian	abelian	PROPN
ejpam-6640	280	27	group	group	PROPN
ejpam-6640	280	28	homa	homa	PROPN
ejpam-6640	280	29	(	(	PUNCT
ejpam-6640	280	30	y	y	PROPN
ejpam-6640	280	31	,	,	PUNCT
ejpam-6640	280	32	t	t	PROPN
ejpam-6640	280	33	)	)	PUNCT
ejpam-6640	280	34	,	,	PUNCT
ejpam-6640	280	35	we	we	PRON
ejpam-6640	280	36	have	have	VERB
ejpam-6640	280	37	:	:	PUNCT
ejpam-6640	280	38	(	(	PUNCT
ejpam-6640	280	39	ψ	ψ	X
ejpam-6640	280	40	+	+	CCONJ
ejpam-6640	280	41	ey	ey	PROPN
ejpam-6640	280	42	,	,	PUNCT
ejpam-6640	280	43	t	t	NOUN
ejpam-6640	280	44	)	)	PUNCT
ejpam-6640	280	45	◦	◦	NOUN
ejpam-6640	280	46	ϕ	ϕ	NOUN
ejpam-6640	280	47	=	=	SYM
ejpam-6640	280	48	(	(	PUNCT
ejpam-6640	280	49	ey	ey	PROPN
ejpam-6640	280	50	,	,	PUNCT
ejpam-6640	280	51	t	t	NOUN
ejpam-6640	280	52	+	+	CCONJ
ejpam-6640	280	53	ψ	ψ	X
ejpam-6640	280	54	)	)	PUNCT
ejpam-6640	280	55	◦	◦	NOUN
ejpam-6640	280	56	ϕ	ϕ	NOUN
ejpam-6640	280	57	=	=	PUNCT
ejpam-6640	280	58	ψ	ψ	PART
ejpam-6640	280	59	◦	◦	NOUN
ejpam-6640	280	60	ϕ⇒	ϕ⇒	NOUN
ejpam-6640	280	61	ψ	ψ	X
ejpam-6640	280	62	◦	◦	NOUN
ejpam-6640	280	63	ϕ+	ϕ+	INTJ
ejpam-6640	280	64	ey	ey	NOUN
ejpam-6640	280	65	,	,	PUNCT
ejpam-6640	280	66	t	t	NOUN
ejpam-6640	280	67	◦	◦	NOUN
ejpam-6640	280	68	ϕ	ϕ	X
ejpam-6640	280	69	=	=	SYM
ejpam-6640	280	70	ey	ey	PROPN
ejpam-6640	280	71	,	,	PUNCT
ejpam-6640	280	72	t	t	NOUN
ejpam-6640	280	73	◦	◦	NOUN
ejpam-6640	280	74	ϕ+	ϕ+	ADP
ejpam-6640	280	75	ψ	ψ	X
ejpam-6640	280	76	◦	◦	NOUN
ejpam-6640	280	77	ϕ	ϕ	X
ejpam-6640	280	78	=	=	SYM
ejpam-6640	280	79	ψ	ψ	PART
ejpam-6640	280	80	◦	◦	NOUN
ejpam-6640	280	81	ϕ	ϕ	X
ejpam-6640	280	82	⇒	⇒	NOUN
ejpam-6640	280	83	{	{	PUNCT
ejpam-6640	280	84	ψ	ψ	X
ejpam-6640	280	85	◦	◦	NOUN
ejpam-6640	280	86	ϕ+	ϕ+	SYM
ejpam-6640	280	87	ey	ey	NOUN
ejpam-6640	280	88	,	,	PUNCT
ejpam-6640	280	89	t	t	NOUN
ejpam-6640	280	90	◦	◦	NOUN
ejpam-6640	280	91	ϕ	ϕ	X
ejpam-6640	280	92	=	=	PUNCT
ejpam-6640	280	93	ψ	ψ	PART
ejpam-6640	280	94	◦	◦	NOUN
ejpam-6640	280	95	ϕ+	ϕ+	PUNCT
ejpam-6640	280	96	ex	ex	X
ejpam-6640	280	97	,	,	PUNCT
ejpam-6640	280	98	t	t	NOUN
ejpam-6640	280	99	=	=	SYM
ejpam-6640	280	100	ψ	ψ	X
ejpam-6640	280	101	◦	◦	NOUN
ejpam-6640	280	102	ϕ	ϕ	SYM
ejpam-6640	280	103	ey	ey	NOUN
ejpam-6640	280	104	,	,	PUNCT
ejpam-6640	280	105	t	t	NOUN
ejpam-6640	280	106	◦	◦	NOUN
ejpam-6640	280	107	ϕ+	ϕ+	ADP
ejpam-6640	280	108	ψ	ψ	X
ejpam-6640	280	109	◦	◦	NOUN
ejpam-6640	280	110	ϕ	ϕ	X
ejpam-6640	280	111	=	=	PUNCT
ejpam-6640	280	112	ex	ex	X
ejpam-6640	280	113	,	,	PUNCT
ejpam-6640	280	114	t	t	PROPN
ejpam-6640	280	115	+	+	CCONJ
ejpam-6640	280	116	ψ	ψ	ADP
ejpam-6640	280	117	◦	◦	NOUN
ejpam-6640	280	118	ϕ	ϕ	X
ejpam-6640	280	119	=	=	SYM
ejpam-6640	280	120	ψ	ψ	PART
ejpam-6640	280	121	◦	◦	NOUN
ejpam-6640	280	122	ϕ	ϕ	X
ejpam-6640	280	123	⇒	⇒	PROPN
ejpam-6640	280	124	ey	ey	PROPN
ejpam-6640	280	125	,	,	PUNCT
ejpam-6640	280	126	t	t	PROPN
ejpam-6640	280	127	◦	◦	NOUN
ejpam-6640	280	128	ϕ	ϕ	X
ejpam-6640	280	129	=	=	PUNCT
ejpam-6640	280	130	ex	ex	X
ejpam-6640	280	131	,	,	PUNCT
ejpam-6640	280	132	t	t	PROPN
ejpam-6640	280	133	.	.	PUNCT
ejpam-6640	281	1	thus	thus	ADV
ejpam-6640	281	2	,	,	PUNCT
ejpam-6640	281	3	g∗	g∗	VERB
ejpam-6640	281	4	◦	◦	NOUN
ejpam-6640	281	5	f∗	f∗	NOUN
ejpam-6640	281	6	=	=	SYM
ejpam-6640	281	7	ehoma	ehoma	NOUN
ejpam-6640	281	8	(	(	PUNCT
ejpam-6640	281	9	x	x	X
ejpam-6640	281	10	,	,	PUNCT
ejpam-6640	281	11	y	y	PROPN
ejpam-6640	281	12	)	)	PUNCT
ejpam-6640	281	13	,	,	PUNCT
ejpam-6640	281	14	homa	homa	NOUN
ejpam-6640	281	15	(	(	PUNCT
ejpam-6640	281	16	x	x	PROPN
ejpam-6640	281	17	,	,	PUNCT
ejpam-6640	281	18	t	t	PROPN
ejpam-6640	281	19	)	)	PUNCT
ejpam-6640	281	20	,	,	PUNCT
ejpam-6640	281	21	and	and	CCONJ
ejpam-6640	281	22	therefore	therefore	ADV
ejpam-6640	281	23	im(f∗	im(f∗	NUM
ejpam-6640	281	24	)	)	PUNCT
ejpam-6640	281	25	⊂	⊂	PROPN
ejpam-6640	281	26	ker(g∗	ker(g∗	NOUN
ejpam-6640	281	27	)	)	PUNCT
ejpam-6640	281	28	.	.	PUNCT
ejpam-6640	282	1	now	now	ADV
ejpam-6640	282	2	,	,	PUNCT
ejpam-6640	282	3	show	show	VERB
ejpam-6640	282	4	that	that	SCONJ
ejpam-6640	282	5	ker(g∗	ker(g∗	VERB
ejpam-6640	282	6	)	)	PUNCT
ejpam-6640	282	7	⊂	⊂	PROPN
ejpam-6640	282	8	im(f∗	im(f∗	PROPN
ejpam-6640	282	9	)	)	PUNCT
ejpam-6640	282	10	.	.	PUNCT
ejpam-6640	283	1	we	we	PRON
ejpam-6640	283	2	have	have	VERB
ejpam-6640	283	3	:	:	PUNCT
ejpam-6640	283	4	ker(g∗	ker(g∗	NOUN
ejpam-6640	283	5	)	)	PUNCT
ejpam-6640	283	6	=	=	PRON
ejpam-6640	284	1	{	{	PUNCT
ejpam-6640	284	2	ϕ	ϕ	NOUN
ejpam-6640	284	3	∈	∈	PROPN
ejpam-6640	284	4	homa	homa	NOUN
ejpam-6640	284	5	(	(	PUNCT
ejpam-6640	284	6	x	x	X
ejpam-6640	284	7	,	,	PUNCT
ejpam-6640	284	8	z	z	NOUN
ejpam-6640	284	9	)	)	PUNCT
ejpam-6640	284	10	:	:	PUNCT
ejpam-6640	284	11	g∗(ϕ	g∗(ϕ	ADJ
ejpam-6640	284	12	)	)	PUNCT
ejpam-6640	284	13	=	=	SYM
ejpam-6640	284	14	g	g	ADP
ejpam-6640	284	15	◦	◦	NOUN
ejpam-6640	284	16	ϕ	ϕ	X
ejpam-6640	284	17	=	=	PUNCT
ejpam-6640	284	18	ex	ex	X
ejpam-6640	284	19	,	,	PUNCT
ejpam-6640	284	20	t	t	NOUN
ejpam-6640	284	21	}	}	PUNCT
ejpam-6640	284	22	.	.	PUNCT
ejpam-6640	285	1	let	let	VERB
ejpam-6640	285	2	ψ	ψ	ADP
ejpam-6640	285	3	∈	∈	NOUN
ejpam-6640	285	4	ker(g∗	ker(g∗	NOUN
ejpam-6640	285	5	)	)	PUNCT
ejpam-6640	285	6	=	=	SYM
ejpam-6640	285	7	ker(homa	ker(homa	NOUN
ejpam-6640	285	8	(	(	PUNCT
ejpam-6640	285	9	x	x	X
ejpam-6640	285	10	,	,	PUNCT
ejpam-6640	285	11	g	g	NOUN
ejpam-6640	285	12	)	)	PUNCT
ejpam-6640	285	13	)	)	PUNCT
ejpam-6640	285	14	.	.	PUNCT
ejpam-6640	286	1	show	show	VERB
ejpam-6640	286	2	that	that	SCONJ
ejpam-6640	286	3	ψ	ψ	PROPN
ejpam-6640	286	4	∈	∈	PROPN
ejpam-6640	286	5	im(f∗	im(f∗	NUM
ejpam-6640	286	6	)	)	PUNCT
ejpam-6640	286	7	.	.	PUNCT
ejpam-6640	287	1	consider	consider	VERB
ejpam-6640	287	2	the	the	DET
ejpam-6640	287	3	left	left	ADJ
ejpam-6640	287	4	-	-	PUNCT
ejpam-6640	287	5	exact	exact	ADJ
ejpam-6640	287	6	short	short	ADJ
ejpam-6640	287	7	sequence	sequence	NOUN
ejpam-6640	287	8	of	of	ADP
ejpam-6640	287	9	morphisms	morphism	NOUN
ejpam-6640	287	10	in	in	ADP
ejpam-6640	287	11	a	a	DET
ejpam-6640	287	12	:	:	SYM
ejpam-6640	287	13	0	0	NUM
ejpam-6640	287	14	→	→	SYM
ejpam-6640	287	15	y	y	PROPN
ejpam-6640	287	16	f−→	f−→	PROPN
ejpam-6640	287	17	z	z	PROPN
ejpam-6640	287	18	g−→	g−→	NOUN
ejpam-6640	287	19	t	t	PROPN
ejpam-6640	287	20	,	,	PUNCT
ejpam-6640	287	21	which	which	PRON
ejpam-6640	287	22	implies	imply	VERB
ejpam-6640	287	23	:	:	PUNCT
ejpam-6640	287	24	–	–	PUNCT
ejpam-6640	287	25	n(f	n(f	PROPN
ejpam-6640	287	26	)	)	PUNCT
ejpam-6640	287	27	=	=	PUNCT
ejpam-6640	287	28	(	(	PUNCT
ejpam-6640	287	29	0	0	NUM
ejpam-6640	287	30	,	,	PUNCT
ejpam-6640	287	31	e0,y	e0,y	PROPN
ejpam-6640	287	32	)	)	PUNCT
ejpam-6640	287	33	,	,	PUNCT
ejpam-6640	287	34	–	–	PUNCT
ejpam-6640	287	35	g	g	ADP
ejpam-6640	287	36	◦	◦	NOUN
ejpam-6640	287	37	f	f	X
ejpam-6640	287	38	=	=	SYM
ejpam-6640	287	39	ey	ey	PROPN
ejpam-6640	287	40	,	,	PUNCT
ejpam-6640	287	41	t	t	PROPN
ejpam-6640	287	42	,	,	PUNCT
ejpam-6640	287	43	a.	a.	PROPN
ejpam-6640	287	44	diallo	diallo	PROPN
ejpam-6640	287	45	,	,	PUNCT
ejpam-6640	287	46	m.	m.	PROPN
ejpam-6640	287	47	b.	b.	PROPN
ejpam-6640	287	48	f.	f.	PROPN
ejpam-6640	287	49	b.	b.	PROPN
ejpam-6640	287	50	maaouia	maaouia	PROPN
ejpam-6640	287	51	,	,	PUNCT
ejpam-6640	287	52	m.	m.	NOUN
ejpam-6640	287	53	sanghare	sanghare	PROPN
ejpam-6640	287	54	/	/	SYM
ejpam-6640	287	55	eur	eur	PROPN
ejpam-6640	287	56	.	.	PUNCT
ejpam-6640	288	1	j.	j.	PROPN
ejpam-6640	288	2	pure	pure	PROPN
ejpam-6640	288	3	appl	appl	PROPN
ejpam-6640	288	4	.	.	PROPN
ejpam-6640	288	5	math	math	PROPN
ejpam-6640	288	6	,	,	PUNCT
ejpam-6640	288	7	18	18	NUM
ejpam-6640	288	8	(	(	PUNCT
ejpam-6640	288	9	4	4	NUM
ejpam-6640	288	10	)	)	PUNCT
ejpam-6640	288	11	(	(	PUNCT
ejpam-6640	288	12	2025	2025	NUM
ejpam-6640	288	13	)	)	PUNCT
ejpam-6640	288	14	,	,	PUNCT
ejpam-6640	288	15	6640	6640	NUM
ejpam-6640	288	16	11	11	NUM
ejpam-6640	288	17	of	of	ADP
ejpam-6640	288	18	28	28	NUM
ejpam-6640	288	19	–	–	PUNCT
ejpam-6640	288	20	con(h	con(h	PROPN
ejpam-6640	288	21	)	)	PUNCT
ejpam-6640	288	22	=	=	SYM
ejpam-6640	288	23	(	(	PUNCT
ejpam-6640	288	24	0	0	NUM
ejpam-6640	288	25	,	,	PUNCT
ejpam-6640	288	26	ek,0	ek,0	PROPN
ejpam-6640	288	27	)	)	PUNCT
ejpam-6640	288	28	,	,	PUNCT
ejpam-6640	288	29	where	where	SCONJ
ejpam-6640	288	30	h	h	NOUN
ejpam-6640	288	31	:	:	PUNCT
ejpam-6640	288	32	y	y	PROPN
ejpam-6640	288	33	→	→	PUNCT
ejpam-6640	288	34	k	k	X
ejpam-6640	288	35	such	such	ADJ
ejpam-6640	288	36	that	that	SCONJ
ejpam-6640	288	37	i	i	PROPN
ejpam-6640	288	38	◦	◦	VERB
ejpam-6640	288	39	h	h	NOUN
ejpam-6640	288	40	=	=	SYM
ejpam-6640	288	41	f	f	PROPN
ejpam-6640	288	42	,	,	PUNCT
ejpam-6640	288	43	with	with	ADP
ejpam-6640	288	44	i	i	PRON
ejpam-6640	288	45	:	:	PUNCT
ejpam-6640	288	46	k	k	X
ejpam-6640	288	47	→	→	PUNCT
ejpam-6640	288	48	z	z	NOUN
ejpam-6640	288	49	being	be	AUX
ejpam-6640	288	50	the	the	DET
ejpam-6640	288	51	kernel	kernel	NOUN
ejpam-6640	288	52	of	of	ADP
ejpam-6640	288	53	g.	g.	PROPN
ejpam-6640	288	54	that	that	PRON
ejpam-6640	288	55	is	be	AUX
ejpam-6640	288	56	,	,	PUNCT
ejpam-6640	288	57	the	the	DET
ejpam-6640	288	58	following	follow	VERB
ejpam-6640	288	59	diagram	diagram	NOUN
ejpam-6640	288	60	commutes	commute	NOUN
ejpam-6640	288	61	:	:	PUNCT
ejpam-6640	288	62	k99	k99	PROPN
ejpam-6640	288	63	h	h	NOUN
ejpam-6640	289	1	i	i	PRON
ejpam-6640	289	2	�	�	VERB
ejpam-6640	289	3	�	�	PROPN
ejpam-6640	289	4	0	0	NUM
ejpam-6640	289	5	//	//	PUNCT
ejpam-6640	289	6	y	y	PROPN
ejpam-6640	289	7	f	f	PROPN
ejpam-6640	289	8	//	//	PROPN
ejpam-6640	289	9	z	z	PROPN
ejpam-6640	289	10	g	g	PROPN
ejpam-6640	289	11	//	//	PROPN
ejpam-6640	289	12	t	t	PROPN
ejpam-6640	289	13	we	we	PRON
ejpam-6640	289	14	have	have	VERB
ejpam-6640	289	15	:	:	PUNCT
ejpam-6640	289	16	ψ	ψ	X
ejpam-6640	289	17	∈	∈	PROPN
ejpam-6640	289	18	ker(g∗	ker(g∗	NOUN
ejpam-6640	289	19	)	)	PUNCT
ejpam-6640	289	20	⇒	⇒	NOUN
ejpam-6640	289	21	g∗(ψ	g∗(ψ	PROPN
ejpam-6640	289	22	)	)	PUNCT
ejpam-6640	289	23	=	=	PUNCT
ejpam-6640	290	1	ex	ex	X
ejpam-6640	290	2	,	,	PUNCT
ejpam-6640	290	3	t	t	PROPN
ejpam-6640	290	4	⇒	⇒	NOUN
ejpam-6640	290	5	g	g	PROPN
ejpam-6640	290	6	◦	◦	NOUN
ejpam-6640	290	7	ψ	ψ	X
ejpam-6640	290	8	=	=	PUNCT
ejpam-6640	290	9	ex	ex	X
ejpam-6640	290	10	,	,	PUNCT
ejpam-6640	290	11	t	t	PROPN
ejpam-6640	290	12	.	.	PUNCT
ejpam-6640	291	1	since	since	SCONJ
ejpam-6640	291	2	con(h	con(h	PROPN
ejpam-6640	291	3	)	)	PUNCT
ejpam-6640	291	4	=	=	SYM
ejpam-6640	291	5	(	(	PUNCT
ejpam-6640	291	6	0	0	NUM
ejpam-6640	291	7	,	,	PUNCT
ejpam-6640	291	8	ek,0	ek,0	PROPN
ejpam-6640	291	9	)	)	PUNCT
ejpam-6640	291	10	,	,	PUNCT
ejpam-6640	291	11	by	by	ADP
ejpam-6640	291	12	lemma	lemma	PROPN
ejpam-6640	291	13	2	2	NUM
ejpam-6640	291	14	,	,	PUNCT
ejpam-6640	291	15	h	h	NOUN
ejpam-6640	291	16	is	be	AUX
ejpam-6640	291	17	an	an	DET
ejpam-6640	291	18	epimorphism	epimorphism	NOUN
ejpam-6640	291	19	.	.	PUNCT
ejpam-6640	292	1	since	since	SCONJ
ejpam-6640	292	2	a	a	PRON
ejpam-6640	292	3	is	be	AUX
ejpam-6640	292	4	a	a	DET
ejpam-6640	292	5	balanced	balanced	ADJ
ejpam-6640	292	6	category	category	NOUN
ejpam-6640	292	7	,	,	PUNCT
ejpam-6640	292	8	every	every	DET
ejpam-6640	292	9	epimorphism	epimorphism	NOUN
ejpam-6640	292	10	is	be	AUX
ejpam-6640	292	11	split	split	VERB
ejpam-6640	292	12	.	.	PUNCT
ejpam-6640	293	1	that	that	PRON
ejpam-6640	293	2	is	be	AUX
ejpam-6640	293	3	,	,	PUNCT
ejpam-6640	293	4	there	there	PRON
ejpam-6640	293	5	exists	exist	VERB
ejpam-6640	293	6	h′	h′	PROPN
ejpam-6640	293	7	:	:	PUNCT
ejpam-6640	293	8	k	k	X
ejpam-6640	293	9	→	→	PUNCT
ejpam-6640	293	10	y	y	PROPN
ejpam-6640	293	11	such	such	ADJ
ejpam-6640	293	12	that	that	DET
ejpam-6640	293	13	h	h	NOUN
ejpam-6640	293	14	◦	◦	NOUN
ejpam-6640	293	15	h′	h′	NOUN
ejpam-6640	293	16	=	=	PUNCT
ejpam-6640	293	17	1k	1k	NUM
ejpam-6640	293	18	.	.	PUNCT
ejpam-6640	294	1	thus	thus	ADV
ejpam-6640	294	2	,	,	PUNCT
ejpam-6640	294	3	the	the	DET
ejpam-6640	294	4	following	follow	VERB
ejpam-6640	294	5	diagram	diagram	NOUN
ejpam-6640	294	6	commutes	commute	NOUN
ejpam-6640	294	7	:	:	PUNCT
ejpam-6640	294	8	k99	k99	PROPN
ejpam-6640	294	9	h	h	NOUN
ejpam-6640	295	1	i	i	PRON
ejpam-6640	295	2	�	�	VERB
ejpam-6640	295	3	�	�	PROPN
ejpam-6640	295	4	oo	oo	NOUN
ejpam-6640	295	5	ψ′	ψ′	PROPN
ejpam-6640	295	6	x	x	SYM
ejpam-6640	295	7	ψ	ψ	X
ejpam-6640	295	8	yy	yy	PROPN
ejpam-6640	295	9	0	0	PROPN
ejpam-6640	296	1	//	//	PROPN
ejpam-6640	296	2	y99	y99	PROPN
ejpam-6640	296	3	h′	h′	PROPN
ejpam-6640	296	4	f	f	PROPN
ejpam-6640	297	1	//	//	PROPN
ejpam-6640	297	2	z	z	PROPN
ejpam-6640	297	3	g	g	PROPN
ejpam-6640	297	4	//	//	PROPN
ejpam-6640	297	5	t	t	PROPN
ejpam-6640	298	1	k	k	NOUN
ejpam-6640	298	2	we	we	PRON
ejpam-6640	298	3	have	have	VERB
ejpam-6640	298	4	:	:	PUNCT
ejpam-6640	298	5	i	i	PRON
ejpam-6640	298	6	◦	◦	VERB
ejpam-6640	298	7	h	h	NOUN
ejpam-6640	299	1	=	=	SYM
ejpam-6640	299	2	f	f	PROPN
ejpam-6640	299	3	⇒	⇒	VERB
ejpam-6640	299	4	i	i	PRON
ejpam-6640	299	5	◦	◦	VERB
ejpam-6640	299	6	h	h	NOUN
ejpam-6640	299	7	◦	◦	NOUN
ejpam-6640	299	8	h′	h′	NOUN
ejpam-6640	299	9	=	=	SYM
ejpam-6640	299	10	f	f	PROPN
ejpam-6640	299	11	◦	◦	NOUN
ejpam-6640	299	12	h′	h′	PROPN
ejpam-6640	299	13	⇒	⇒	VERB
ejpam-6640	299	14	i	i	PRON
ejpam-6640	299	15	◦	◦	VERB
ejpam-6640	299	16	1k	1k	NUM
ejpam-6640	299	17	=	=	SYM
ejpam-6640	299	18	f	f	X
ejpam-6640	299	19	◦	◦	NOUN
ejpam-6640	299	20	h′	h′	PROPN
ejpam-6640	299	21	⇒	⇒	VERB
ejpam-6640	299	22	i	i	PRON
ejpam-6640	299	23	=	=	SYM
ejpam-6640	299	24	f	f	X
ejpam-6640	299	25	◦	◦	NOUN
ejpam-6640	299	26	h′	h′	PROPN
ejpam-6640	299	27	⇒	⇒	NOUN
ejpam-6640	299	28	i	i	PRON
ejpam-6640	299	29	◦	◦	VERB
ejpam-6640	299	30	ψ′	ψ′	PUNCT
ejpam-6640	299	31	=	=	SYM
ejpam-6640	299	32	f	f	X
ejpam-6640	299	33	◦	◦	PROPN
ejpam-6640	299	34	h′	h′	PROPN
ejpam-6640	299	35	◦	◦	NOUN
ejpam-6640	299	36	ψ′	ψ′	PUNCT
ejpam-6640	299	37	⇒	⇒	NOUN
ejpam-6640	299	38	ψ	ψ	X
ejpam-6640	299	39	=	=	SYM
ejpam-6640	299	40	f	f	X
ejpam-6640	299	41	◦	◦	NOUN
ejpam-6640	299	42	(	(	PUNCT
ejpam-6640	299	43	h′	h′	PROPN
ejpam-6640	299	44	◦	◦	PROPN
ejpam-6640	299	45	ψ′	ψ′	PROPN
ejpam-6640	299	46	)	)	PUNCT
ejpam-6640	299	47	⇒	⇒	NOUN
ejpam-6640	299	48	ψ	ψ	X
ejpam-6640	299	49	=	=	SYM
ejpam-6640	299	50	f∗(h′	f∗(h′	ADJ
ejpam-6640	299	51	◦	◦	NOUN
ejpam-6640	299	52	ψ′	ψ′	PROPN
ejpam-6640	299	53	)	)	PUNCT
ejpam-6640	299	54	.	.	PUNCT
ejpam-6640	300	1	thus	thus	ADV
ejpam-6640	300	2	,	,	PUNCT
ejpam-6640	300	3	ψ	ψ	PROPN
ejpam-6640	300	4	∈	∈	PROPN
ejpam-6640	300	5	im(f∗	im(f∗	NUM
ejpam-6640	300	6	)	)	PUNCT
ejpam-6640	300	7	.	.	PUNCT
ejpam-6640	301	1	hence	hence	ADV
ejpam-6640	301	2	,	,	PUNCT
ejpam-6640	301	3	ker(g∗	ker(g∗	X
ejpam-6640	301	4	)	)	PUNCT
ejpam-6640	301	5	⊂	⊂	PROPN
ejpam-6640	301	6	im(f∗	im(f∗	PROPN
ejpam-6640	301	7	)	)	PUNCT
ejpam-6640	301	8	.	.	PUNCT
ejpam-6640	302	1	therefore	therefore	ADV
ejpam-6640	302	2	,	,	PUNCT
ejpam-6640	302	3	homa	homa	PROPN
ejpam-6640	302	4	(	(	PUNCT
ejpam-6640	302	5	x,−	x,−	PROPN
ejpam-6640	302	6	)	)	PUNCT
ejpam-6640	302	7	:	:	PUNCT
ejpam-6640	302	8	a	a	DET
ejpam-6640	302	9	−→	−→	NOUN
ejpam-6640	302	10	ab	ab	PROPN
ejpam-6640	302	11	is	be	AUX
ejpam-6640	302	12	a	a	DET
ejpam-6640	302	13	covariant	covariant	NOUN
ejpam-6640	302	14	,	,	PUNCT
ejpam-6640	302	15	additive	additive	NOUN
ejpam-6640	302	16	,	,	PUNCT
ejpam-6640	302	17	and	and	CCONJ
ejpam-6640	302	18	left	left	ADJ
ejpam-6640	302	19	-	-	PUNCT
ejpam-6640	302	20	exact	exact	NOUN
ejpam-6640	302	21	functor	functor	PROPN
ejpam-6640	302	22	.	.	PROPN
ejpam-6640	302	23	•	•	NUM
ejpam-6640	302	24	show	show	VERB
ejpam-6640	302	25	that	that	SCONJ
ejpam-6640	302	26	homa	homa	NOUN
ejpam-6640	302	27	(	(	PUNCT
ejpam-6640	302	28	x,−	x,−	PROPN
ejpam-6640	302	29	)	)	PUNCT
ejpam-6640	302	30	:	:	PUNCT
ejpam-6640	302	31	a	a	DET
ejpam-6640	302	32	−→	−→	NOUN
ejpam-6640	302	33	ab	ab	PROPN
ejpam-6640	302	34	is	be	AUX
ejpam-6640	302	35	exact	exact	ADJ
ejpam-6640	303	1	if	if	SCONJ
ejpam-6640	303	2	and	and	CCONJ
ejpam-6640	303	3	only	only	ADV
ejpam-6640	303	4	if	if	SCONJ
ejpam-6640	303	5	x	x	PRON
ejpam-6640	303	6	is	be	AUX
ejpam-6640	303	7	a	a	DET
ejpam-6640	303	8	projective	projective	ADJ
ejpam-6640	303	9	object	object	NOUN
ejpam-6640	303	10	in	in	ADP
ejpam-6640	303	11	a	a	PRON
ejpam-6640	303	12	.	.	PUNCT
ejpam-6640	303	13	•	•	NOUN
ejpam-6640	303	14	suppose	suppose	VERB
ejpam-6640	303	15	x	x	PRON
ejpam-6640	303	16	is	be	AUX
ejpam-6640	303	17	a	a	DET
ejpam-6640	303	18	projective	projective	ADJ
ejpam-6640	303	19	object	object	NOUN
ejpam-6640	303	20	in	in	ADP
ejpam-6640	303	21	a	a	PRON
ejpam-6640	303	22	and	and	CCONJ
ejpam-6640	303	23	show	show	VERB
ejpam-6640	303	24	that	that	SCONJ
ejpam-6640	303	25	homa	homa	NOUN
ejpam-6640	303	26	(	(	PUNCT
ejpam-6640	303	27	x,−	x,−	PROPN
ejpam-6640	303	28	)	)	PUNCT
ejpam-6640	303	29	:	:	PUNCT
ejpam-6640	303	30	a	a	DET
ejpam-6640	303	31	−→	−→	NOUN
ejpam-6640	303	32	ab	ab	PROPN
ejpam-6640	303	33	is	be	AUX
ejpam-6640	303	34	an	an	DET
ejpam-6640	303	35	exact	exact	ADJ
ejpam-6640	303	36	functor	functor	NOUN
ejpam-6640	303	37	.	.	PUNCT
ejpam-6640	304	1	consider	consider	VERB
ejpam-6640	304	2	the	the	DET
ejpam-6640	304	3	following	follow	VERB
ejpam-6640	304	4	short	short	ADJ
ejpam-6640	304	5	exact	exact	ADJ
ejpam-6640	304	6	sequence	sequence	NOUN
ejpam-6640	304	7	of	of	ADP
ejpam-6640	304	8	morphisms	morphism	NOUN
ejpam-6640	304	9	in	in	ADP
ejpam-6640	304	10	a	a	DET
ejpam-6640	304	11	:	:	SYM
ejpam-6640	304	12	0	0	NUM
ejpam-6640	304	13	//	//	PUNCT
ejpam-6640	304	14	y	y	PROPN
ejpam-6640	304	15	f	f	PROPN
ejpam-6640	304	16	//	//	PROPN
ejpam-6640	304	17	z	z	PROPN
ejpam-6640	304	18	g	g	PROPN
ejpam-6640	304	19	//	//	PROPN
ejpam-6640	304	20	t	t	PROPN
ejpam-6640	304	21	//	//	X
ejpam-6640	304	22	0	0	NUM
ejpam-6640	304	23	a.	a.	PROPN
ejpam-6640	304	24	diallo	diallo	PROPN
ejpam-6640	304	25	,	,	PUNCT
ejpam-6640	304	26	m.	m.	PROPN
ejpam-6640	304	27	b.	b.	PROPN
ejpam-6640	304	28	f.	f.	PROPN
ejpam-6640	304	29	b.	b.	PROPN
ejpam-6640	304	30	maaouia	maaouia	PROPN
ejpam-6640	304	31	,	,	PUNCT
ejpam-6640	304	32	m.	m.	NOUN
ejpam-6640	304	33	sanghare	sanghare	PROPN
ejpam-6640	304	34	/	/	SYM
ejpam-6640	304	35	eur	eur	PROPN
ejpam-6640	304	36	.	.	PUNCT
ejpam-6640	305	1	j.	j.	PROPN
ejpam-6640	305	2	pure	pure	PROPN
ejpam-6640	305	3	appl	appl	PROPN
ejpam-6640	305	4	.	.	PROPN
ejpam-6640	305	5	math	math	PROPN
ejpam-6640	305	6	,	,	PUNCT
ejpam-6640	305	7	18	18	NUM
ejpam-6640	305	8	(	(	PUNCT
ejpam-6640	305	9	4	4	NUM
ejpam-6640	305	10	)	)	PUNCT
ejpam-6640	305	11	(	(	PUNCT
ejpam-6640	305	12	2025	2025	NUM
ejpam-6640	305	13	)	)	PUNCT
ejpam-6640	305	14	,	,	PUNCT
ejpam-6640	305	15	6640	6640	NUM
ejpam-6640	305	16	12	12	NUM
ejpam-6640	305	17	of	of	ADP
ejpam-6640	305	18	28	28	NUM
ejpam-6640	305	19	we	we	PRON
ejpam-6640	305	20	will	will	AUX
ejpam-6640	305	21	show	show	VERB
ejpam-6640	305	22	that	that	SCONJ
ejpam-6640	305	23	{	{	PUNCT
ejpam-6640	305	24	ex,0	ex,0	PROPN
ejpam-6640	305	25	}	}	PUNCT
ejpam-6640	305	26	//	//	SYM
ejpam-6640	305	27	homa	homa	NOUN
ejpam-6640	305	28	(	(	PUNCT
ejpam-6640	305	29	x	x	X
ejpam-6640	305	30	,	,	PUNCT
ejpam-6640	305	31	y	y	PROPN
ejpam-6640	305	32	)	)	PUNCT
ejpam-6640	305	33	homa	homa	NOUN
ejpam-6640	305	34	(	(	PUNCT
ejpam-6640	305	35	x	x	X
ejpam-6640	305	36	,	,	PUNCT
ejpam-6640	305	37	f)=f∗	f)=f∗	PROPN
ejpam-6640	305	38	//	//	X
ejpam-6640	305	39	homa	homa	PROPN
ejpam-6640	305	40	(	(	PUNCT
ejpam-6640	305	41	x	x	X
ejpam-6640	305	42	,	,	PUNCT
ejpam-6640	305	43	z	z	NOUN
ejpam-6640	305	44	)	)	PUNCT
ejpam-6640	305	45	homa	homa	NOUN
ejpam-6640	305	46	(	(	PUNCT
ejpam-6640	305	47	x	x	NOUN
ejpam-6640	305	48	,	,	PUNCT
ejpam-6640	305	49	g)=g∗	g)=g∗	PROPN
ejpam-6640	305	50	//	//	SYM
ejpam-6640	305	51	homa	homa	PROPN
ejpam-6640	305	52	(	(	PUNCT
ejpam-6640	305	53	x	x	PROPN
ejpam-6640	305	54	,	,	PUNCT
ejpam-6640	305	55	t	t	PROPN
ejpam-6640	305	56	)	)	PUNCT
ejpam-6640	305	57	//	//	X
ejpam-6640	305	58	{	{	PUNCT
ejpam-6640	305	59	ex,0	ex,0	PROPN
ejpam-6640	305	60	}	}	PUNCT
ejpam-6640	305	61	is	be	AUX
ejpam-6640	305	62	exact	exact	ADJ
ejpam-6640	305	63	.	.	PUNCT
ejpam-6640	306	1	by	by	ADP
ejpam-6640	306	2	part	part	NOUN
ejpam-6640	306	3	(	(	PUNCT
ejpam-6640	306	4	i	i	NOUN
ejpam-6640	306	5	)	)	PUNCT
ejpam-6640	306	6	,	,	PUNCT
ejpam-6640	306	7	we	we	PRON
ejpam-6640	306	8	know	know	VERB
ejpam-6640	306	9	that	that	SCONJ
ejpam-6640	306	10	{	{	PUNCT
ejpam-6640	306	11	ex,0	ex,0	PROPN
ejpam-6640	306	12	}	}	PUNCT
ejpam-6640	306	13	//	//	SYM
ejpam-6640	306	14	homa	homa	NOUN
ejpam-6640	306	15	(	(	PUNCT
ejpam-6640	306	16	x	x	X
ejpam-6640	306	17	,	,	PUNCT
ejpam-6640	306	18	y	y	PROPN
ejpam-6640	306	19	)	)	PUNCT
ejpam-6640	306	20	homa	homa	NOUN
ejpam-6640	306	21	(	(	PUNCT
ejpam-6640	306	22	x	x	X
ejpam-6640	306	23	,	,	PUNCT
ejpam-6640	306	24	f)=f∗	f)=f∗	PROPN
ejpam-6640	306	25	//	//	X
ejpam-6640	306	26	homa	homa	PROPN
ejpam-6640	306	27	(	(	PUNCT
ejpam-6640	306	28	x	x	X
ejpam-6640	306	29	,	,	PUNCT
ejpam-6640	306	30	z	z	NOUN
ejpam-6640	306	31	)	)	PUNCT
ejpam-6640	306	32	homa	homa	NOUN
ejpam-6640	306	33	(	(	PUNCT
ejpam-6640	306	34	x	x	NOUN
ejpam-6640	306	35	,	,	PUNCT
ejpam-6640	306	36	g)=g∗	g)=g∗	PROPN
ejpam-6640	306	37	//	//	SYM
ejpam-6640	306	38	homa	homa	PROPN
ejpam-6640	306	39	(	(	PUNCT
ejpam-6640	306	40	x	x	PROPN
ejpam-6640	306	41	,	,	PUNCT
ejpam-6640	306	42	t	t	PROPN
ejpam-6640	306	43	)	)	PUNCT
ejpam-6640	306	44	is	be	AUX
ejpam-6640	306	45	left	leave	VERB
ejpam-6640	306	46	-	-	PUNCT
ejpam-6640	306	47	exact	exact	ADJ
ejpam-6640	306	48	.	.	PUNCT
ejpam-6640	307	1	it	it	PRON
ejpam-6640	307	2	remains	remain	VERB
ejpam-6640	307	3	to	to	PART
ejpam-6640	307	4	show	show	VERB
ejpam-6640	307	5	that	that	SCONJ
ejpam-6640	307	6	homa	homa	NOUN
ejpam-6640	307	7	(	(	PUNCT
ejpam-6640	307	8	x	x	NOUN
ejpam-6640	307	9	,	,	PUNCT
ejpam-6640	307	10	g	g	NOUN
ejpam-6640	307	11	)	)	PUNCT
ejpam-6640	307	12	is	be	AUX
ejpam-6640	307	13	an	an	DET
ejpam-6640	307	14	epimorphism	epimorphism	NOUN
ejpam-6640	307	15	.	.	PUNCT
ejpam-6640	308	1	since	since	SCONJ
ejpam-6640	308	2	x	x	PRON
ejpam-6640	308	3	is	be	AUX
ejpam-6640	308	4	projective	projective	ADJ
ejpam-6640	308	5	,	,	PUNCT
ejpam-6640	308	6	for	for	ADP
ejpam-6640	308	7	every	every	DET
ejpam-6640	308	8	epimorphism	epimorphism	NOUN
ejpam-6640	308	9	g	g	NOUN
ejpam-6640	308	10	:	:	PUNCT
ejpam-6640	309	1	z	z	PROPN
ejpam-6640	309	2	↠	↠	PROPN
ejpam-6640	309	3	t	t	X
ejpam-6640	309	4	in	in	ADP
ejpam-6640	309	5	a	a	PRON
ejpam-6640	309	6	and	and	CCONJ
ejpam-6640	309	7	every	every	PRON
ejpam-6640	309	8	morphism	morphism	NOUN
ejpam-6640	309	9	f	f	PROPN
ejpam-6640	309	10	:	:	PUNCT
ejpam-6640	309	11	x	x	X
ejpam-6640	309	12	→	→	SYM
ejpam-6640	309	13	t	t	NOUN
ejpam-6640	309	14	in	in	ADP
ejpam-6640	309	15	a	a	PRON
ejpam-6640	309	16	,	,	PUNCT
ejpam-6640	309	17	there	there	PRON
ejpam-6640	309	18	exists	exist	VERB
ejpam-6640	309	19	a	a	DET
ejpam-6640	309	20	morphism	morphism	NOUN
ejpam-6640	309	21	ϕ	ϕ	NOUN
ejpam-6640	309	22	:	:	PUNCT
ejpam-6640	309	23	x	x	SYM
ejpam-6640	309	24	→	→	SYM
ejpam-6640	309	25	z	z	NOUN
ejpam-6640	309	26	in	in	ADP
ejpam-6640	309	27	a	a	DET
ejpam-6640	309	28	such	such	ADJ
ejpam-6640	309	29	that	that	DET
ejpam-6640	309	30	g	g	PROPN
ejpam-6640	309	31	◦	◦	NOUN
ejpam-6640	309	32	ϕ	ϕ	NOUN
ejpam-6640	309	33	=	=	SYM
ejpam-6640	309	34	f	f	PROPN
ejpam-6640	309	35	.	.	PUNCT
ejpam-6640	310	1	this	this	PRON
ejpam-6640	310	2	means	mean	VERB
ejpam-6640	310	3	the	the	DET
ejpam-6640	310	4	following	follow	VERB
ejpam-6640	310	5	diagram	diagram	NOUN
ejpam-6640	310	6	commutes	commute	NOUN
ejpam-6640	310	7	:	:	PUNCT
ejpam-6640	310	8	x	x	SYM
ejpam-6640	310	9	ϕ	ϕ	PROPN
ejpam-6640	310	10	~~	~~	NUM
ejpam-6640	310	11	f	f	PROPN
ejpam-6640	310	12	�	�	PROPN
ejpam-6640	310	13	�	�	PROPN
ejpam-6640	310	14	z	z	PROPN
ejpam-6640	310	15	g	g	PROPN
ejpam-6640	310	16	//	//	PROPN
ejpam-6640	310	17	//	//	PROPN
ejpam-6640	310	18	t	t	PROPN
ejpam-6640	310	19	//	//	PROPN
ejpam-6640	310	20	0	0	NUM
ejpam-6640	310	21	that	that	PRON
ejpam-6640	310	22	is	be	AUX
ejpam-6640	310	23	,	,	PUNCT
ejpam-6640	310	24	for	for	ADP
ejpam-6640	310	25	every	every	DET
ejpam-6640	310	26	f	f	PROPN
ejpam-6640	310	27	∈	∈	PROPN
ejpam-6640	310	28	homa	homa	NOUN
ejpam-6640	310	29	(	(	PUNCT
ejpam-6640	310	30	x	x	X
ejpam-6640	310	31	,	,	PUNCT
ejpam-6640	310	32	t	t	PROPN
ejpam-6640	310	33	)	)	PUNCT
ejpam-6640	310	34	,	,	PUNCT
ejpam-6640	310	35	there	there	PRON
ejpam-6640	310	36	exists	exist	VERB
ejpam-6640	310	37	ϕ	ϕ	PROPN
ejpam-6640	310	38	∈	∈	PROPN
ejpam-6640	310	39	homa	homa	NOUN
ejpam-6640	310	40	(	(	PUNCT
ejpam-6640	310	41	x	x	X
ejpam-6640	310	42	,	,	PUNCT
ejpam-6640	310	43	z	z	NOUN
ejpam-6640	310	44	)	)	PUNCT
ejpam-6640	310	45	such	such	ADJ
ejpam-6640	310	46	that	that	SCONJ
ejpam-6640	310	47	g	g	PROPN
ejpam-6640	310	48	◦	◦	NOUN
ejpam-6640	310	49	ϕ	ϕ	NOUN
ejpam-6640	310	50	=	=	X
ejpam-6640	310	51	f	f	PROPN
ejpam-6640	310	52	=	=	PUNCT
ejpam-6640	310	53	g∗(ϕ	g∗(ϕ	PROPN
ejpam-6640	310	54	)	)	PUNCT
ejpam-6640	310	55	.	.	PUNCT
ejpam-6640	311	1	hence	hence	ADV
ejpam-6640	311	2	,	,	PUNCT
ejpam-6640	311	3	homa	homa	PROPN
ejpam-6640	311	4	(	(	PUNCT
ejpam-6640	311	5	x	x	NOUN
ejpam-6640	311	6	,	,	PUNCT
ejpam-6640	311	7	g	g	NOUN
ejpam-6640	311	8	)	)	PUNCT
ejpam-6640	311	9	=	=	PUNCT
ejpam-6640	311	10	g∗	g∗	PROPN
ejpam-6640	311	11	is	be	AUX
ejpam-6640	311	12	an	an	DET
ejpam-6640	311	13	epimorphism	epimorphism	NOUN
ejpam-6640	311	14	.	.	PUNCT
ejpam-6640	312	1	•	•	NOUN
ejpam-6640	312	2	conversely	conversely	ADV
ejpam-6640	312	3	,	,	PUNCT
ejpam-6640	312	4	suppose	suppose	VERB
ejpam-6640	312	5	homa	homa	PROPN
ejpam-6640	312	6	(	(	PUNCT
ejpam-6640	312	7	x,−	x,−	PROPN
ejpam-6640	312	8	)	)	PUNCT
ejpam-6640	312	9	:	:	PUNCT
ejpam-6640	312	10	a	a	DET
ejpam-6640	312	11	−→	−→	NOUN
ejpam-6640	312	12	ab	ab	PROPN
ejpam-6640	312	13	is	be	AUX
ejpam-6640	312	14	an	an	DET
ejpam-6640	312	15	exact	exact	ADJ
ejpam-6640	312	16	functor	functor	NOUN
ejpam-6640	312	17	and	and	CCONJ
ejpam-6640	312	18	show	show	VERB
ejpam-6640	312	19	that	that	SCONJ
ejpam-6640	312	20	x	x	PRON
ejpam-6640	312	21	is	be	AUX
ejpam-6640	312	22	a	a	DET
ejpam-6640	312	23	projective	projective	ADJ
ejpam-6640	312	24	object	object	NOUN
ejpam-6640	312	25	in	in	ADP
ejpam-6640	312	26	a	a	PRON
ejpam-6640	312	27	.	.	PUNCT
ejpam-6640	313	1	we	we	PRON
ejpam-6640	313	2	have	have	VERB
ejpam-6640	313	3	:	:	PUNCT
ejpam-6640	313	4	the	the	DET
ejpam-6640	313	5	exactness	exactness	NOUN
ejpam-6640	313	6	of	of	ADP
ejpam-6640	313	7	homa	homa	PROPN
ejpam-6640	313	8	(	(	PUNCT
ejpam-6640	313	9	x,−	x,−	PROPN
ejpam-6640	313	10	)	)	PUNCT
ejpam-6640	313	11	implies	imply	VERB
ejpam-6640	313	12	that	that	SCONJ
ejpam-6640	313	13	for	for	ADP
ejpam-6640	313	14	every	every	DET
ejpam-6640	313	15	short	short	ADJ
ejpam-6640	313	16	exact	exact	ADJ
ejpam-6640	313	17	sequence	sequence	NOUN
ejpam-6640	313	18	of	of	ADP
ejpam-6640	313	19	morphisms	morphism	NOUN
ejpam-6640	313	20	in	in	ADP
ejpam-6640	313	21	a	a	DET
ejpam-6640	313	22	:	:	SYM
ejpam-6640	313	23	0	0	NUM
ejpam-6640	313	24	//	//	PUNCT
ejpam-6640	313	25	y	y	PROPN
ejpam-6640	313	26	f	f	PROPN
ejpam-6640	314	1	//	//	PROPN
ejpam-6640	314	2	z	z	PROPN
ejpam-6640	314	3	g	g	PROPN
ejpam-6640	314	4	//	//	PROPN
ejpam-6640	314	5	t	t	PROPN
ejpam-6640	314	6	//	//	PROPN
ejpam-6640	314	7	0	0	NUM
ejpam-6640	314	8	,	,	PUNCT
ejpam-6640	314	9	the	the	DET
ejpam-6640	314	10	sequence	sequence	NOUN
ejpam-6640	314	11	{	{	PUNCT
ejpam-6640	314	12	ex,0	ex,0	PROPN
ejpam-6640	314	13	}	}	PUNCT
ejpam-6640	314	14	//	//	SYM
ejpam-6640	314	15	homa	homa	NOUN
ejpam-6640	314	16	(	(	PUNCT
ejpam-6640	314	17	x	x	X
ejpam-6640	314	18	,	,	PUNCT
ejpam-6640	314	19	y	y	PROPN
ejpam-6640	314	20	)	)	PUNCT
ejpam-6640	314	21	homa	homa	NOUN
ejpam-6640	314	22	(	(	PUNCT
ejpam-6640	314	23	x	x	X
ejpam-6640	314	24	,	,	PUNCT
ejpam-6640	314	25	f)=f∗	f)=f∗	PROPN
ejpam-6640	314	26	//	//	X
ejpam-6640	314	27	homa	homa	PROPN
ejpam-6640	314	28	(	(	PUNCT
ejpam-6640	314	29	x	x	X
ejpam-6640	314	30	,	,	PUNCT
ejpam-6640	314	31	z	z	NOUN
ejpam-6640	314	32	)	)	PUNCT
ejpam-6640	314	33	homa	homa	NOUN
ejpam-6640	314	34	(	(	PUNCT
ejpam-6640	314	35	x	x	NOUN
ejpam-6640	314	36	,	,	PUNCT
ejpam-6640	314	37	g)=g∗	g)=g∗	PROPN
ejpam-6640	314	38	//	//	SYM
ejpam-6640	314	39	homa	homa	PROPN
ejpam-6640	314	40	(	(	PUNCT
ejpam-6640	314	41	x	x	PROPN
ejpam-6640	314	42	,	,	PUNCT
ejpam-6640	314	43	t	t	PROPN
ejpam-6640	314	44	)	)	PUNCT
ejpam-6640	314	45	//	//	X
ejpam-6640	314	46	{	{	PUNCT
ejpam-6640	314	47	ex,0	ex,0	PROPN
ejpam-6640	314	48	}	}	PUNCT
ejpam-6640	314	49	is	be	AUX
ejpam-6640	314	50	exact	exact	ADJ
ejpam-6640	314	51	.	.	PUNCT
ejpam-6640	315	1	this	this	PRON
ejpam-6640	315	2	means	mean	VERB
ejpam-6640	315	3	g∗	g∗	PROPN
ejpam-6640	315	4	is	be	AUX
ejpam-6640	315	5	an	an	DET
ejpam-6640	315	6	epimorphism	epimorphism	NOUN
ejpam-6640	315	7	.	.	PUNCT
ejpam-6640	316	1	therefore	therefore	ADV
ejpam-6640	316	2	,	,	PUNCT
ejpam-6640	316	3	for	for	ADP
ejpam-6640	316	4	every	every	DET
ejpam-6640	316	5	epimorphism	epimorphism	NOUN
ejpam-6640	316	6	g	g	NOUN
ejpam-6640	316	7	:	:	PUNCT
ejpam-6640	316	8	z	z	PROPN
ejpam-6640	316	9	↠	↠	PROPN
ejpam-6640	316	10	t	t	X
ejpam-6640	316	11	in	in	ADP
ejpam-6640	316	12	a	a	PRON
ejpam-6640	316	13	and	and	CCONJ
ejpam-6640	316	14	every	every	PRON
ejpam-6640	316	15	morphism	morphism	NOUN
ejpam-6640	316	16	f	f	PROPN
ejpam-6640	316	17	:	:	PUNCT
ejpam-6640	316	18	x	x	X
ejpam-6640	316	19	→	→	SYM
ejpam-6640	316	20	t	t	NOUN
ejpam-6640	316	21	in	in	ADP
ejpam-6640	316	22	a	a	PRON
ejpam-6640	316	23	,	,	PUNCT
ejpam-6640	316	24	there	there	PRON
ejpam-6640	316	25	exists	exist	VERB
ejpam-6640	316	26	a	a	DET
ejpam-6640	316	27	morphism	morphism	NOUN
ejpam-6640	316	28	ϕ	ϕ	NOUN
ejpam-6640	316	29	:	:	PUNCT
ejpam-6640	316	30	x	x	SYM
ejpam-6640	316	31	→	→	SYM
ejpam-6640	316	32	z	z	NOUN
ejpam-6640	316	33	in	in	ADP
ejpam-6640	316	34	a	a	DET
ejpam-6640	316	35	such	such	ADJ
ejpam-6640	316	36	that	that	DET
ejpam-6640	316	37	g	g	PROPN
ejpam-6640	316	38	◦	◦	NOUN
ejpam-6640	316	39	ϕ	ϕ	X
ejpam-6640	316	40	=	=	NOUN
ejpam-6640	316	41	g∗(ϕ	g∗(ϕ	NOUN
ejpam-6640	316	42	)	)	PUNCT
ejpam-6640	317	1	=	=	SYM
ejpam-6640	317	2	f	f	PROPN
ejpam-6640	317	3	.	.	PUNCT
ejpam-6640	318	1	this	this	PRON
ejpam-6640	318	2	means	mean	VERB
ejpam-6640	318	3	the	the	DET
ejpam-6640	318	4	following	follow	VERB
ejpam-6640	318	5	diagram	diagram	NOUN
ejpam-6640	318	6	commutes	commute	NOUN
ejpam-6640	318	7	:	:	PUNCT
ejpam-6640	318	8	x	x	SYM
ejpam-6640	318	9	ϕ	ϕ	PROPN
ejpam-6640	318	10	~~	~~	NUM
ejpam-6640	318	11	f	f	PROPN
ejpam-6640	318	12	�	�	PROPN
ejpam-6640	318	13	�	�	PROPN
ejpam-6640	318	14	z	z	PROPN
ejpam-6640	318	15	g	g	PROPN
ejpam-6640	318	16	//	//	PROPN
ejpam-6640	318	17	//	//	PROPN
ejpam-6640	318	18	t	t	PROPN
ejpam-6640	318	19	//	//	X
ejpam-6640	318	20	0	0	PUNCT
ejpam-6640	319	1	hence	hence	ADV
ejpam-6640	319	2	,	,	PUNCT
ejpam-6640	319	3	x	x	X
ejpam-6640	319	4	is	be	AUX
ejpam-6640	319	5	a	a	DET
ejpam-6640	319	6	projective	projective	ADJ
ejpam-6640	319	7	object	object	NOUN
ejpam-6640	319	8	in	in	ADP
ejpam-6640	319	9	a	a	PRON
ejpam-6640	319	10	.	.	PUNCT
ejpam-6640	320	1	let	let	VERB
ejpam-6640	320	2	a	a	PRON
ejpam-6640	320	3	be	be	AUX
ejpam-6640	320	4	a	a	DET
ejpam-6640	320	5	balanced	balanced	ADJ
ejpam-6640	320	6	abelian	abelian	ADJ
ejpam-6640	320	7	category	category	NOUN
ejpam-6640	320	8	and	and	CCONJ
ejpam-6640	320	9	x	x	SYM
ejpam-6640	320	10	an	an	DET
ejpam-6640	320	11	object	object	NOUN
ejpam-6640	320	12	in	in	ADP
ejpam-6640	320	13	a	a	PRON
ejpam-6640	320	14	.	.	PUNCT
ejpam-6640	321	1	then	then	ADV
ejpam-6640	321	2	the	the	DET
ejpam-6640	321	3	functor	functor	NOUN
ejpam-6640	321	4	denoted	denote	VERB
ejpam-6640	321	5	by	by	ADP
ejpam-6640	321	6	homa	homa	PROPN
ejpam-6640	321	7	(	(	PUNCT
ejpam-6640	321	8	x,−	x,−	PROPN
ejpam-6640	321	9	)	)	PUNCT
ejpam-6640	321	10	:	:	PUNCT
ejpam-6640	321	11	a	a	DET
ejpam-6640	321	12	−→	−→	NOUN
ejpam-6640	321	13	ab	ab	PROPN
ejpam-6640	321	14	defined	define	VERB
ejpam-6640	321	15	by	by	ADP
ejpam-6640	321	16	:	:	PUNCT
ejpam-6640	321	17	a.	a.	PROPN
ejpam-6640	321	18	diallo	diallo	PROPN
ejpam-6640	321	19	,	,	PUNCT
ejpam-6640	321	20	m.	m.	PROPN
ejpam-6640	321	21	b.	b.	PROPN
ejpam-6640	321	22	f.	f.	PROPN
ejpam-6640	321	23	b.	b.	PROPN
ejpam-6640	321	24	maaouia	maaouia	PROPN
ejpam-6640	321	25	,	,	PUNCT
ejpam-6640	321	26	m.	m.	NOUN
ejpam-6640	321	27	sanghare	sanghare	PROPN
ejpam-6640	321	28	/	/	SYM
ejpam-6640	321	29	eur	eur	PROPN
ejpam-6640	321	30	.	.	PUNCT
ejpam-6640	322	1	j.	j.	PROPN
ejpam-6640	322	2	pure	pure	PROPN
ejpam-6640	322	3	appl	appl	PROPN
ejpam-6640	322	4	.	.	PROPN
ejpam-6640	322	5	math	math	PROPN
ejpam-6640	322	6	,	,	PUNCT
ejpam-6640	322	7	18	18	NUM
ejpam-6640	322	8	(	(	PUNCT
ejpam-6640	322	9	4	4	NUM
ejpam-6640	322	10	)	)	PUNCT
ejpam-6640	322	11	(	(	PUNCT
ejpam-6640	322	12	2025	2025	NUM
ejpam-6640	322	13	)	)	PUNCT
ejpam-6640	322	14	,	,	PUNCT
ejpam-6640	322	15	6640	6640	NUM
ejpam-6640	322	16	13	13	NUM
ejpam-6640	322	17	of	of	ADP
ejpam-6640	322	18	28	28	NUM
ejpam-6640	322	19	(	(	PUNCT
ejpam-6640	322	20	i	i	NOUN
ejpam-6640	322	21	)	)	PUNCT
ejpam-6640	322	22	∀y	∀y	PROPN
ejpam-6640	322	23	∈	∈	PROPN
ejpam-6640	322	24	ob(a	ob(a	NUM
ejpam-6640	322	25	)	)	PUNCT
ejpam-6640	322	26	,	,	PUNCT
ejpam-6640	322	27	homa	homa	NOUN
ejpam-6640	322	28	(	(	PUNCT
ejpam-6640	322	29	−	−	PROPN
ejpam-6640	322	30	,	,	PUNCT
ejpam-6640	322	31	x)(y	x)(y	PUNCT
ejpam-6640	322	32	)	)	PUNCT
ejpam-6640	323	1	=	=	PUNCT
ejpam-6640	323	2	homa	homa	NOUN
ejpam-6640	323	3	(	(	PUNCT
ejpam-6640	323	4	y	y	NOUN
ejpam-6640	323	5	,	,	PUNCT
ejpam-6640	323	6	x	x	NOUN
ejpam-6640	323	7	)	)	PUNCT
ejpam-6640	323	8	∈	∈	PROPN
ejpam-6640	323	9	ob(ab	ob(ab	PROPN
ejpam-6640	323	10	)	)	PUNCT
ejpam-6640	323	11	(	(	PUNCT
ejpam-6640	323	12	ii	ii	NOUN
ejpam-6640	323	13	)	)	PUNCT
ejpam-6640	323	14	∀f	∀f	PROPN
ejpam-6640	323	15	∈	∈	PROPN
ejpam-6640	323	16	homa	homa	NOUN
ejpam-6640	323	17	(	(	PUNCT
ejpam-6640	323	18	y	y	PROPN
ejpam-6640	323	19	,	,	PUNCT
ejpam-6640	323	20	z	z	NOUN
ejpam-6640	323	21	)	)	PUNCT
ejpam-6640	323	22	,	,	PUNCT
ejpam-6640	323	23	homa	homa	NOUN
ejpam-6640	323	24	(	(	PUNCT
ejpam-6640	323	25	−	−	PROPN
ejpam-6640	323	26	,	,	PUNCT
ejpam-6640	323	27	x)(f	x)(f	PROPN
ejpam-6640	323	28	)	)	PUNCT
ejpam-6640	324	1	=	=	SYM
ejpam-6640	324	2	homa	homa	NOUN
ejpam-6640	324	3	(	(	PUNCT
ejpam-6640	324	4	f	f	NOUN
ejpam-6640	324	5	,	,	PUNCT
ejpam-6640	324	6	x	x	NOUN
ejpam-6640	324	7	)	)	PUNCT
ejpam-6640	324	8	=	=	SYM
ejpam-6640	324	9	f∗	f∗	NOUN
ejpam-6640	324	10	:	:	PUNCT
ejpam-6640	324	11	homa	homa	NOUN
ejpam-6640	324	12	(	(	PUNCT
ejpam-6640	324	13	x	x	X
ejpam-6640	324	14	,	,	PUNCT
ejpam-6640	324	15	y	y	PROPN
ejpam-6640	324	16	)	)	PUNCT
ejpam-6640	324	17	−→	−→	PROPN
ejpam-6640	324	18	homa	homa	NOUN
ejpam-6640	324	19	(	(	PUNCT
ejpam-6640	324	20	x	x	X
ejpam-6640	324	21	,	,	PUNCT
ejpam-6640	324	22	z	z	NOUN
ejpam-6640	324	23	)	)	PUNCT
ejpam-6640	324	24	ϕ	ϕ	PROPN
ejpam-6640	324	25	7−→	7−→	PROPN
ejpam-6640	324	26	ϕ	ϕ	PROPN
ejpam-6640	324	27	◦	◦	NOUN
ejpam-6640	324	28	f	f	PROPN
ejpam-6640	324	29	is	be	AUX
ejpam-6640	324	30	a	a	DET
ejpam-6640	324	31	contravariant	contravariant	ADJ
ejpam-6640	324	32	,	,	PUNCT
ejpam-6640	324	33	additive	additive	NOUN
ejpam-6640	324	34	,	,	PUNCT
ejpam-6640	324	35	left	leave	VERB
ejpam-6640	324	36	exact	exact	ADJ
ejpam-6640	324	37	functor	functor	NOUN
ejpam-6640	324	38	,	,	PUNCT
ejpam-6640	324	39	and	and	CCONJ
ejpam-6640	324	40	it	it	PRON
ejpam-6640	324	41	is	be	AUX
ejpam-6640	324	42	exact	exact	ADJ
ejpam-6640	324	43	if	if	SCONJ
ejpam-6640	324	44	and	and	CCONJ
ejpam-6640	324	45	only	only	ADV
ejpam-6640	324	46	if	if	SCONJ
ejpam-6640	324	47	x	x	PRON
ejpam-6640	324	48	is	be	AUX
ejpam-6640	324	49	a	a	DET
ejpam-6640	324	50	injective	injective	ADJ
ejpam-6640	324	51	object	object	NOUN
ejpam-6640	324	52	in	in	ADP
ejpam-6640	324	53	a	a	PRON
ejpam-6640	324	54	.	.	PUNCT
ejpam-6640	325	1	proof	proof	NOUN
ejpam-6640	325	2	.	.	PUNCT
ejpam-6640	326	1	•	•	INTJ
ejpam-6640	326	2	it	it	PRON
ejpam-6640	326	3	is	be	AUX
ejpam-6640	326	4	evident	evident	ADJ
ejpam-6640	326	5	that	that	SCONJ
ejpam-6640	326	6	homa	homa	NOUN
ejpam-6640	326	7	(	(	PUNCT
ejpam-6640	326	8	−	−	PROPN
ejpam-6640	326	9	,	,	PUNCT
ejpam-6640	326	10	x	x	NOUN
ejpam-6640	326	11	)	)	PUNCT
ejpam-6640	326	12	:	:	PUNCT
ejpam-6640	326	13	a	a	DET
ejpam-6640	326	14	−→	−→	NOUN
ejpam-6640	326	15	ab	ab	PROPN
ejpam-6640	326	16	is	be	AUX
ejpam-6640	326	17	a	a	DET
ejpam-6640	326	18	contravariant	contravariant	ADJ
ejpam-6640	326	19	additive	additive	ADJ
ejpam-6640	326	20	functor	functor	PROPN
ejpam-6640	326	21	.	.	PROPN
ejpam-6640	327	1	•	•	NUM
ejpam-6640	327	2	let	let	VERB
ejpam-6640	327	3	us	we	PRON
ejpam-6640	327	4	show	show	VERB
ejpam-6640	327	5	that	that	SCONJ
ejpam-6640	327	6	homa	homa	NOUN
ejpam-6640	327	7	(	(	PUNCT
ejpam-6640	327	8	−	−	PROPN
ejpam-6640	327	9	,	,	PUNCT
ejpam-6640	327	10	x	x	NOUN
ejpam-6640	327	11	)	)	PUNCT
ejpam-6640	327	12	:	:	PUNCT
ejpam-6640	327	13	a	a	DET
ejpam-6640	327	14	−→	−→	NOUN
ejpam-6640	327	15	ab	ab	PROPN
ejpam-6640	327	16	is	be	AUX
ejpam-6640	327	17	a	a	DET
ejpam-6640	327	18	left	left	ADJ
ejpam-6640	327	19	-	-	PUNCT
ejpam-6640	327	20	exact	exact	NOUN
ejpam-6640	327	21	functor	functor	NOUN
ejpam-6640	327	22	.	.	PUNCT
ejpam-6640	327	23	consider	consider	VERB
ejpam-6640	327	24	the	the	DET
ejpam-6640	327	25	right	right	ADJ
ejpam-6640	327	26	short	short	ADJ
ejpam-6640	327	27	exact	exact	ADJ
ejpam-6640	327	28	sequence	sequence	NOUN
ejpam-6640	327	29	of	of	ADP
ejpam-6640	327	30	morphisms	morphism	NOUN
ejpam-6640	327	31	in	in	ADP
ejpam-6640	327	32	a	a	PRON
ejpam-6640	327	33	:	:	PUNCT
ejpam-6640	328	1	y	y	PROPN
ejpam-6640	328	2	f	f	PROPN
ejpam-6640	328	3	//	//	PROPN
ejpam-6640	328	4	z	z	PROPN
ejpam-6640	328	5	g	g	PROPN
ejpam-6640	328	6	//	//	PROPN
ejpam-6640	328	7	t	t	PROPN
ejpam-6640	328	8	//	//	X
ejpam-6640	328	9	0	0	NUM
ejpam-6640	329	1	we	we	PRON
ejpam-6640	329	2	must	must	AUX
ejpam-6640	329	3	show	show	VERB
ejpam-6640	329	4	that	that	SCONJ
ejpam-6640	329	5	the	the	DET
ejpam-6640	329	6	sequence	sequence	NOUN
ejpam-6640	329	7	:	:	PUNCT
ejpam-6640	329	8	{	{	PUNCT
ejpam-6640	329	9	e0,x	e0,x	PROPN
ejpam-6640	329	10	}	}	PUNCT
ejpam-6640	329	11	//	//	SYM
ejpam-6640	329	12	homa	homa	PROPN
ejpam-6640	329	13	(	(	PUNCT
ejpam-6640	329	14	t	t	PROPN
ejpam-6640	329	15	,	,	PUNCT
ejpam-6640	329	16	x	x	NOUN
ejpam-6640	329	17	)	)	PUNCT
ejpam-6640	329	18	homa	homa	NOUN
ejpam-6640	329	19	(	(	PUNCT
ejpam-6640	329	20	g	g	PROPN
ejpam-6640	329	21	,	,	PUNCT
ejpam-6640	329	22	x)=g∗	x)=g∗	PROPN
ejpam-6640	329	23	//	//	SYM
ejpam-6640	329	24	homa	homa	PROPN
ejpam-6640	329	25	(	(	PUNCT
ejpam-6640	329	26	z	z	NOUN
ejpam-6640	329	27	,	,	PUNCT
ejpam-6640	329	28	x	x	NOUN
ejpam-6640	329	29	)	)	PUNCT
ejpam-6640	329	30	homa	homa	NOUN
ejpam-6640	329	31	(	(	PUNCT
ejpam-6640	329	32	f	f	X
ejpam-6640	329	33	,	,	PUNCT
ejpam-6640	329	34	x)=f∗	x)=f∗	PROPN
ejpam-6640	329	35	//	//	SYM
ejpam-6640	329	36	homa	homa	PROPN
ejpam-6640	329	37	(	(	PUNCT
ejpam-6640	329	38	y	y	PROPN
ejpam-6640	329	39	,	,	PUNCT
ejpam-6640	329	40	x	x	NOUN
ejpam-6640	329	41	)	)	PUNCT
ejpam-6640	329	42	is	be	AUX
ejpam-6640	329	43	left	leave	VERB
ejpam-6640	329	44	-	-	PUNCT
ejpam-6640	329	45	exact	exact	ADJ
ejpam-6640	329	46	.	.	PUNCT
ejpam-6640	330	1	it	it	PRON
ejpam-6640	330	2	suffices	suffice	VERB
ejpam-6640	330	3	to	to	PART
ejpam-6640	330	4	show	show	VERB
ejpam-6640	330	5	that	that	SCONJ
ejpam-6640	330	6	the	the	DET
ejpam-6640	330	7	kernel	kernel	NOUN
ejpam-6640	330	8	of	of	ADP
ejpam-6640	330	9	g∗	g∗	PROPN
ejpam-6640	330	10	,	,	PUNCT
ejpam-6640	330	11	ker	ker	PROPN
ejpam-6640	330	12	g∗	g∗	PROPN
ejpam-6640	330	13	,	,	PUNCT
ejpam-6640	330	14	is	be	AUX
ejpam-6640	330	15	zero	zero	NUM
ejpam-6640	330	16	and	and	CCONJ
ejpam-6640	330	17	that	that	SCONJ
ejpam-6640	330	18	i	i	PRON
ejpam-6640	330	19	m	m	VERB
ejpam-6640	330	20	g∗	g∗	VERB
ejpam-6640	330	21	=	=	PUNCT
ejpam-6640	330	22	ker	ker	NOUN
ejpam-6640	330	23	f∗.	f∗.	NOUN
ejpam-6640	330	24	•	•	NUM
ejpam-6640	330	25	let	let	VERB
ejpam-6640	330	26	us	we	PRON
ejpam-6640	330	27	show	show	VERB
ejpam-6640	330	28	that	that	SCONJ
ejpam-6640	330	29	the	the	DET
ejpam-6640	330	30	kernel	kernel	NOUN
ejpam-6640	330	31	of	of	ADP
ejpam-6640	330	32	g∗	g∗	PROPN
ejpam-6640	330	33	,	,	PUNCT
ejpam-6640	330	34	ker(homa	ker(homa	ADJ
ejpam-6640	330	35	(	(	PUNCT
ejpam-6640	330	36	g	g	NOUN
ejpam-6640	330	37	,	,	PUNCT
ejpam-6640	330	38	x	x	NOUN
ejpam-6640	330	39	)	)	PUNCT
ejpam-6640	330	40	)	)	PUNCT
ejpam-6640	331	1	=	=	SYM
ejpam-6640	331	2	ker	ker	PROPN
ejpam-6640	331	3	g∗	g∗	PROPN
ejpam-6640	331	4	,	,	PUNCT
ejpam-6640	331	5	is	be	AUX
ejpam-6640	331	6	zero	zero	NUM
ejpam-6640	331	7	.	.	PUNCT
ejpam-6640	332	1	by	by	ADP
ejpam-6640	332	2	lemma	lemma	PROPN
ejpam-6640	332	3	2	2	NUM
ejpam-6640	332	4	,	,	PUNCT
ejpam-6640	332	5	it	it	PRON
ejpam-6640	332	6	suffices	suffice	VERB
ejpam-6640	332	7	to	to	PART
ejpam-6640	332	8	show	show	VERB
ejpam-6640	332	9	that	that	SCONJ
ejpam-6640	332	10	homa	homa	NOUN
ejpam-6640	332	11	(	(	PUNCT
ejpam-6640	332	12	g	g	NOUN
ejpam-6640	332	13	,	,	PUNCT
ejpam-6640	332	14	x	x	NOUN
ejpam-6640	332	15	)	)	PUNCT
ejpam-6640	332	16	=	=	PUNCT
ejpam-6640	332	17	g∗	g∗	PROPN
ejpam-6640	332	18	is	be	AUX
ejpam-6640	332	19	a	a	DET
ejpam-6640	332	20	monomorphism	monomorphism	NOUN
ejpam-6640	332	21	.	.	PUNCT
ejpam-6640	333	1	by	by	ADP
ejpam-6640	333	2	definition	definition	NOUN
ejpam-6640	333	3	of	of	ADP
ejpam-6640	333	4	homa	homa	NOUN
ejpam-6640	333	5	(	(	PUNCT
ejpam-6640	333	6	g	g	NOUN
ejpam-6640	333	7	,	,	PUNCT
ejpam-6640	333	8	x	x	NOUN
ejpam-6640	333	9	)	)	PUNCT
ejpam-6640	333	10	=	=	SYM
ejpam-6640	333	11	g∗	g∗	PROPN
ejpam-6640	333	12	,	,	PUNCT
ejpam-6640	333	13	we	we	PRON
ejpam-6640	333	14	have	have	VERB
ejpam-6640	333	15	:	:	PUNCT
ejpam-6640	333	16	homa	homa	NOUN
ejpam-6640	333	17	(	(	PUNCT
ejpam-6640	333	18	g	g	NOUN
ejpam-6640	333	19	,	,	PUNCT
ejpam-6640	333	20	x	x	NOUN
ejpam-6640	333	21	)	)	PUNCT
ejpam-6640	333	22	=	=	PUNCT
ejpam-6640	334	1	g∗	g∗	NOUN
ejpam-6640	334	2	:	:	PUNCT
ejpam-6640	334	3	homa	homa	NOUN
ejpam-6640	334	4	(	(	PUNCT
ejpam-6640	334	5	t	t	PROPN
ejpam-6640	334	6	,	,	PUNCT
ejpam-6640	334	7	x	x	NOUN
ejpam-6640	334	8	)	)	PUNCT
ejpam-6640	334	9	−→	−→	ADJ
ejpam-6640	334	10	homa	homa	NOUN
ejpam-6640	334	11	(	(	PUNCT
ejpam-6640	334	12	z	z	NOUN
ejpam-6640	334	13	,	,	PUNCT
ejpam-6640	334	14	x	x	NOUN
ejpam-6640	334	15	)	)	PUNCT
ejpam-6640	334	16	ϕ	ϕ	PROPN
ejpam-6640	334	17	7−→	7−→	PROPN
ejpam-6640	334	18	ϕ	ϕ	PROPN
ejpam-6640	334	19	◦	◦	NOUN
ejpam-6640	334	20	g	g	NOUN
ejpam-6640	334	21	let	let	VERB
ejpam-6640	334	22	ϕ1	ϕ1	NOUN
ejpam-6640	334	23	,	,	PUNCT
ejpam-6640	334	24	ϕ2	ϕ2	ADV
ejpam-6640	334	25	∈	∈	PROPN
ejpam-6640	334	26	homa	homa	NOUN
ejpam-6640	334	27	(	(	PUNCT
ejpam-6640	334	28	t	t	PROPN
ejpam-6640	334	29	,	,	PUNCT
ejpam-6640	334	30	x	x	NOUN
ejpam-6640	334	31	)	)	PUNCT
ejpam-6640	334	32	such	such	ADJ
ejpam-6640	334	33	that	that	SCONJ
ejpam-6640	334	34	g∗(ϕ1	g∗(ϕ1	PROPN
ejpam-6640	334	35	)	)	PUNCT
ejpam-6640	334	36	=	=	SYM
ejpam-6640	335	1	g∗(ϕ2	g∗(ϕ2	NOUN
ejpam-6640	335	2	)	)	PUNCT
ejpam-6640	335	3	,	,	PUNCT
ejpam-6640	335	4	i.e.	i.e.	X
ejpam-6640	335	5	,	,	PUNCT
ejpam-6640	335	6	ϕ1	ϕ1	NOUN
ejpam-6640	335	7	◦	◦	NOUN
ejpam-6640	335	8	g	g	NOUN
ejpam-6640	335	9	=	=	PUNCT
ejpam-6640	335	10	ϕ2	ϕ2	ADV
ejpam-6640	335	11	◦	◦	NOUN
ejpam-6640	335	12	g.	g.	NOUN
ejpam-6640	336	1	we	we	PRON
ejpam-6640	336	2	have	have	VERB
ejpam-6640	336	3	:	:	PUNCT
ejpam-6640	336	4	ϕ1	ϕ1	VERB
ejpam-6640	336	5	◦	◦	VERB
ejpam-6640	336	6	g	g	NOUN
ejpam-6640	336	7	=	=	PUNCT
ejpam-6640	336	8	ϕ2	ϕ2	ADV
ejpam-6640	336	9	◦	◦	VERB
ejpam-6640	336	10	g	g	NOUN
ejpam-6640	336	11	=	=	NOUN
ejpam-6640	336	12	⇒	⇒	NOUN
ejpam-6640	336	13	ϕ1	ϕ1	NOUN
ejpam-6640	336	14	=	=	SYM
ejpam-6640	337	1	ϕ2	ϕ2	ADV
ejpam-6640	337	2	,	,	PUNCT
ejpam-6640	337	3	since	since	SCONJ
ejpam-6640	337	4	by	by	ADP
ejpam-6640	337	5	hypothesis	hypothesis	NOUN
ejpam-6640	337	6	,	,	PUNCT
ejpam-6640	337	7	the	the	DET
ejpam-6640	337	8	cokernel	cokernel	NOUN
ejpam-6640	337	9	of	of	ADP
ejpam-6640	337	10	g	g	PROPN
ejpam-6640	337	11	,	,	PUNCT
ejpam-6640	337	12	n(g	n(g	NUM
ejpam-6640	337	13	)	)	PUNCT
ejpam-6640	337	14	,	,	PUNCT
ejpam-6640	337	15	is	be	AUX
ejpam-6640	337	16	zero	zero	NUM
ejpam-6640	337	17	,	,	PUNCT
ejpam-6640	337	18	and	and	CCONJ
ejpam-6640	337	19	by	by	ADP
ejpam-6640	337	20	lemma	lemma	PROPN
ejpam-6640	337	21	2	2	NUM
ejpam-6640	337	22	,	,	PUNCT
ejpam-6640	337	23	g	g	PROPN
ejpam-6640	337	24	is	be	AUX
ejpam-6640	337	25	an	an	DET
ejpam-6640	337	26	epimorphism	epimorphism	NOUN
ejpam-6640	337	27	.	.	PUNCT
ejpam-6640	338	1	thus	thus	ADV
ejpam-6640	338	2	,	,	PUNCT
ejpam-6640	338	3	homa	homa	NOUN
ejpam-6640	338	4	(	(	PUNCT
ejpam-6640	338	5	g	g	NOUN
ejpam-6640	338	6	,	,	PUNCT
ejpam-6640	338	7	x	x	NOUN
ejpam-6640	338	8	)	)	PUNCT
ejpam-6640	338	9	=	=	PUNCT
ejpam-6640	338	10	g∗	g∗	PROPN
ejpam-6640	338	11	is	be	AUX
ejpam-6640	338	12	a	a	DET
ejpam-6640	338	13	monomorphism	monomorphism	NOUN
ejpam-6640	338	14	.	.	PUNCT
ejpam-6640	339	1	•	•	NUM
ejpam-6640	339	2	let	let	VERB
ejpam-6640	339	3	us	we	PRON
ejpam-6640	339	4	show	show	VERB
ejpam-6640	339	5	that	that	SCONJ
ejpam-6640	339	6	i	i	PRON
ejpam-6640	339	7	m	m	VERB
ejpam-6640	339	8	g∗	g∗	VERB
ejpam-6640	339	9	=	=	PUNCT
ejpam-6640	339	10	ker	ker	PROPN
ejpam-6640	339	11	f∗.	f∗.	PROPN
ejpam-6640	339	12	first	first	ADV
ejpam-6640	339	13	,	,	PUNCT
ejpam-6640	339	14	we	we	PRON
ejpam-6640	339	15	show	show	VERB
ejpam-6640	339	16	that	that	SCONJ
ejpam-6640	339	17	i	i	PRON
ejpam-6640	339	18	m	m	VERB
ejpam-6640	339	19	g∗	g∗	VERB
ejpam-6640	339	20	⊂	⊂	PROPN
ejpam-6640	339	21	ker	ker	PROPN
ejpam-6640	339	22	f∗.	f∗.	NOUN
ejpam-6640	339	23	it	it	PRON
ejpam-6640	339	24	suffices	suffice	VERB
ejpam-6640	339	25	to	to	PART
ejpam-6640	339	26	show	show	VERB
ejpam-6640	339	27	that	that	SCONJ
ejpam-6640	339	28	f∗	f∗	NOUN
ejpam-6640	339	29	◦	◦	NOUN
ejpam-6640	339	30	g∗	g∗	NOUN
ejpam-6640	339	31	=	=	VERB
ejpam-6640	339	32	ehoma	ehoma	NOUN
ejpam-6640	339	33	(	(	PUNCT
ejpam-6640	339	34	t	t	PROPN
ejpam-6640	339	35	,	,	PUNCT
ejpam-6640	339	36	x),homa	x),homa	PROPN
ejpam-6640	339	37	(	(	PUNCT
ejpam-6640	339	38	y	y	PROPN
ejpam-6640	339	39	,	,	PUNCT
ejpam-6640	339	40	x	x	NOUN
ejpam-6640	339	41	)	)	PUNCT
ejpam-6640	339	42	,	,	PUNCT
ejpam-6640	339	43	where	where	SCONJ
ejpam-6640	339	44	ehoma	ehoma	NOUN
ejpam-6640	339	45	(	(	PUNCT
ejpam-6640	339	46	t	t	PROPN
ejpam-6640	339	47	,	,	PUNCT
ejpam-6640	339	48	x),homa	x),homa	PROPN
ejpam-6640	339	49	(	(	PUNCT
ejpam-6640	339	50	y	y	PROPN
ejpam-6640	339	51	,	,	PUNCT
ejpam-6640	339	52	x	x	X
ejpam-6640	339	53	)	)	PUNCT
ejpam-6640	339	54	is	be	AUX
ejpam-6640	339	55	the	the	DET
ejpam-6640	339	56	neutral	neutral	ADJ
ejpam-6640	339	57	element	element	NOUN
ejpam-6640	339	58	(	(	PUNCT
ejpam-6640	339	59	zero	zero	NUM
ejpam-6640	339	60	morphism	morphism	NOUN
ejpam-6640	339	61	)	)	PUNCT
ejpam-6640	339	62	of	of	ADP
ejpam-6640	339	63	the	the	DET
ejpam-6640	339	64	abelian	abelian	ADJ
ejpam-6640	339	65	group	group	NOUN
ejpam-6640	339	66	homab(homa	homab(homa	PROPN
ejpam-6640	339	67	(	(	PUNCT
ejpam-6640	339	68	t	t	PROPN
ejpam-6640	339	69	,	,	PUNCT
ejpam-6640	339	70	x),homa	x),homa	PROPN
ejpam-6640	339	71	(	(	PUNCT
ejpam-6640	339	72	y	y	PROPN
ejpam-6640	339	73	,	,	PUNCT
ejpam-6640	339	74	x	x	NOUN
ejpam-6640	339	75	)	)	PUNCT
ejpam-6640	339	76	)	)	PUNCT
ejpam-6640	339	77	.	.	PUNCT
ejpam-6640	340	1	we	we	PRON
ejpam-6640	340	2	have	have	VERB
ejpam-6640	340	3	:	:	PUNCT
ejpam-6640	340	4	f∗	f∗	NOUN
ejpam-6640	340	5	◦	◦	NOUN
ejpam-6640	340	6	g∗	g∗	NOUN
ejpam-6640	340	7	:	:	PUNCT
ejpam-6640	341	1	homa	homa	NOUN
ejpam-6640	341	2	(	(	PUNCT
ejpam-6640	341	3	t	t	PROPN
ejpam-6640	341	4	,	,	PUNCT
ejpam-6640	341	5	x	x	NOUN
ejpam-6640	341	6	)	)	PUNCT
ejpam-6640	341	7	→	→	SYM
ejpam-6640	341	8	homa	homa	PROPN
ejpam-6640	341	9	(	(	PUNCT
ejpam-6640	341	10	y	y	PROPN
ejpam-6640	341	11	,	,	PUNCT
ejpam-6640	341	12	x	x	NOUN
ejpam-6640	341	13	)	)	PUNCT
ejpam-6640	341	14	.	.	PUNCT
ejpam-6640	342	1	a.	a.	PROPN
ejpam-6640	342	2	diallo	diallo	PROPN
ejpam-6640	342	3	,	,	PUNCT
ejpam-6640	342	4	m.	m.	PROPN
ejpam-6640	342	5	b.	b.	PROPN
ejpam-6640	342	6	f.	f.	PROPN
ejpam-6640	342	7	b.	b.	PROPN
ejpam-6640	342	8	maaouia	maaouia	PROPN
ejpam-6640	342	9	,	,	PUNCT
ejpam-6640	342	10	m.	m.	NOUN
ejpam-6640	342	11	sanghare	sanghare	PROPN
ejpam-6640	342	12	/	/	SYM
ejpam-6640	342	13	eur	eur	PROPN
ejpam-6640	342	14	.	.	PUNCT
ejpam-6640	343	1	j.	j.	PROPN
ejpam-6640	343	2	pure	pure	PROPN
ejpam-6640	343	3	appl	appl	PROPN
ejpam-6640	343	4	.	.	PROPN
ejpam-6640	343	5	math	math	PROPN
ejpam-6640	343	6	,	,	PUNCT
ejpam-6640	343	7	18	18	NUM
ejpam-6640	343	8	(	(	PUNCT
ejpam-6640	343	9	4	4	NUM
ejpam-6640	343	10	)	)	PUNCT
ejpam-6640	343	11	(	(	PUNCT
ejpam-6640	343	12	2025	2025	NUM
ejpam-6640	343	13	)	)	PUNCT
ejpam-6640	343	14	,	,	PUNCT
ejpam-6640	343	15	6640	6640	NUM
ejpam-6640	343	16	14	14	NUM
ejpam-6640	343	17	of	of	ADP
ejpam-6640	343	18	28	28	NUM
ejpam-6640	343	19	let	let	VERB
ejpam-6640	343	20	ϕ	ϕ	PROPN
ejpam-6640	343	21	∈	∈	PROPN
ejpam-6640	343	22	homa	homa	PROPN
ejpam-6640	343	23	(	(	PUNCT
ejpam-6640	343	24	t	t	PROPN
ejpam-6640	343	25	,	,	PUNCT
ejpam-6640	343	26	x	x	NOUN
ejpam-6640	343	27	)	)	PUNCT
ejpam-6640	343	28	.	.	PUNCT
ejpam-6640	344	1	then	then	ADV
ejpam-6640	344	2	:	:	PUNCT
ejpam-6640	344	3	f∗	f∗	X
ejpam-6640	344	4	◦	◦	NOUN
ejpam-6640	344	5	g∗(ϕ	g∗(ϕ	NOUN
ejpam-6640	344	6	)	)	PUNCT
ejpam-6640	344	7	=	=	SYM
ejpam-6640	344	8	f∗(g∗(ϕ	f∗(g∗(ϕ	NOUN
ejpam-6640	344	9	)	)	PUNCT
ejpam-6640	344	10	)	)	PUNCT
ejpam-6640	345	1	=	=	PUNCT
ejpam-6640	345	2	f∗(ϕ	f∗(ϕ	PROPN
ejpam-6640	345	3	◦	◦	NOUN
ejpam-6640	345	4	g	g	NOUN
ejpam-6640	345	5	)	)	PUNCT
ejpam-6640	345	6	=	=	SYM
ejpam-6640	346	1	(	(	PUNCT
ejpam-6640	346	2	ϕ	ϕ	NOUN
ejpam-6640	346	3	◦	◦	NOUN
ejpam-6640	346	4	g	g	NOUN
ejpam-6640	346	5	)	)	PUNCT
ejpam-6640	346	6	◦	◦	NOUN
ejpam-6640	346	7	f	f	NOUN
ejpam-6640	347	1	=	=	SYM
ejpam-6640	347	2	ϕ	ϕ	PROPN
ejpam-6640	347	3	◦	◦	NOUN
ejpam-6640	347	4	(	(	PUNCT
ejpam-6640	347	5	g	g	NOUN
ejpam-6640	347	6	◦	◦	NOUN
ejpam-6640	347	7	f	f	X
ejpam-6640	347	8	)	)	PUNCT
ejpam-6640	347	9	(	(	PUNCT
ejpam-6640	347	10	since	since	SCONJ
ejpam-6640	347	11	by	by	ADP
ejpam-6640	347	12	hypothesis	hypothesis	NOUN
ejpam-6640	347	13	,	,	PUNCT
ejpam-6640	347	14	g	g	PROPN
ejpam-6640	347	15	◦	◦	NOUN
ejpam-6640	347	16	f	f	X
ejpam-6640	347	17	=	=	SYM
ejpam-6640	347	18	ey	ey	PROPN
ejpam-6640	347	19	,	,	PUNCT
ejpam-6640	347	20	t	t	NOUN
ejpam-6640	347	21	)	)	PUNCT
ejpam-6640	348	1	=	=	PUNCT
ejpam-6640	348	2	ϕ	ϕ	PROPN
ejpam-6640	348	3	◦	◦	NOUN
ejpam-6640	348	4	ey	ey	NOUN
ejpam-6640	348	5	,	,	PUNCT
ejpam-6640	348	6	t	t	NOUN
ejpam-6640	348	7	=	=	SYM
ejpam-6640	348	8	ey	ey	PROPN
ejpam-6640	348	9	,	,	PUNCT
ejpam-6640	348	10	x	x	INTJ
ejpam-6640	348	11	,	,	PUNCT
ejpam-6640	348	12	because	because	SCONJ
ejpam-6640	348	13	for	for	ADP
ejpam-6640	348	14	all	all	DET
ejpam-6640	348	15	u	u	PROPN
ejpam-6640	348	16	∈	∈	PROPN
ejpam-6640	348	17	homa	homa	NOUN
ejpam-6640	348	18	(	(	PUNCT
ejpam-6640	348	19	y	y	PROPN
ejpam-6640	348	20	,	,	PUNCT
ejpam-6640	348	21	t	t	PROPN
ejpam-6640	348	22	)	)	PUNCT
ejpam-6640	348	23	,	,	PUNCT
ejpam-6640	348	24	where	where	SCONJ
ejpam-6640	348	25	ey	ey	NOUN
ejpam-6640	348	26	,	,	PUNCT
ejpam-6640	348	27	t	t	PROPN
ejpam-6640	348	28	is	be	AUX
ejpam-6640	348	29	the	the	DET
ejpam-6640	348	30	neutral	neutral	ADJ
ejpam-6640	348	31	element	element	NOUN
ejpam-6640	348	32	of	of	ADP
ejpam-6640	348	33	the	the	DET
ejpam-6640	348	34	abelian	abelian	PROPN
ejpam-6640	348	35	group	group	PROPN
ejpam-6640	348	36	homa	homa	PROPN
ejpam-6640	348	37	(	(	PUNCT
ejpam-6640	348	38	y	y	PROPN
ejpam-6640	348	39	,	,	PUNCT
ejpam-6640	348	40	t	t	PROPN
ejpam-6640	348	41	)	)	PUNCT
ejpam-6640	348	42	,	,	PUNCT
ejpam-6640	348	43	we	we	PRON
ejpam-6640	348	44	have	have	VERB
ejpam-6640	348	45	:	:	PUNCT
ejpam-6640	348	46	ϕ	ϕ	PROPN
ejpam-6640	348	47	◦	◦	NOUN
ejpam-6640	348	48	(	(	PUNCT
ejpam-6640	348	49	u+	u+	X
ejpam-6640	348	50	ey	ey	NOUN
ejpam-6640	348	51	,	,	PUNCT
ejpam-6640	348	52	t	t	NOUN
ejpam-6640	348	53	)	)	PUNCT
ejpam-6640	349	1	=	=	PUNCT
ejpam-6640	349	2	ϕ	ϕ	PROPN
ejpam-6640	349	3	◦	◦	NOUN
ejpam-6640	349	4	(	(	PUNCT
ejpam-6640	349	5	ey	ey	NOUN
ejpam-6640	349	6	,	,	PUNCT
ejpam-6640	349	7	t	t	NOUN
ejpam-6640	349	8	+	+	NUM
ejpam-6640	349	9	u	u	NOUN
ejpam-6640	349	10	)	)	PUNCT
ejpam-6640	349	11	=	=	PUNCT
ejpam-6640	349	12	ϕ	ϕ	PROPN
ejpam-6640	349	13	◦	◦	NOUN
ejpam-6640	349	14	u	u	NOUN
ejpam-6640	349	15	=	=	NOUN
ejpam-6640	349	16	⇒	⇒	X
ejpam-6640	349	17	ϕ	ϕ	PROPN
ejpam-6640	349	18	◦	◦	NOUN
ejpam-6640	349	19	u+	u+	NOUN
ejpam-6640	349	20	ϕ	ϕ	PROPN
ejpam-6640	349	21	◦	◦	NOUN
ejpam-6640	349	22	ey	ey	NOUN
ejpam-6640	349	23	,	,	PUNCT
ejpam-6640	349	24	t	t	NOUN
ejpam-6640	349	25	=	=	SYM
ejpam-6640	349	26	ϕ	ϕ	PROPN
ejpam-6640	349	27	◦	◦	NOUN
ejpam-6640	349	28	ey	ey	PROPN
ejpam-6640	349	29	,	,	PUNCT
ejpam-6640	349	30	t	t	NOUN
ejpam-6640	349	31	+	+	CCONJ
ejpam-6640	349	32	ϕ	ϕ	PROPN
ejpam-6640	349	33	◦	◦	NOUN
ejpam-6640	349	34	u	u	NOUN
ejpam-6640	349	35	=	=	PUNCT
ejpam-6640	349	36	ϕ	ϕ	PROPN
ejpam-6640	349	37	◦	◦	NOUN
ejpam-6640	349	38	u	u	NOUN
ejpam-6640	349	39	=	=	NOUN
ejpam-6640	349	40	⇒	⇒	NOUN
ejpam-6640	349	41	{	{	PUNCT
ejpam-6640	349	42	ϕ	ϕ	PROPN
ejpam-6640	349	43	◦	◦	NOUN
ejpam-6640	349	44	u+	u+	NOUN
ejpam-6640	349	45	ϕ	ϕ	PROPN
ejpam-6640	349	46	◦	◦	NOUN
ejpam-6640	349	47	ey	ey	NOUN
ejpam-6640	349	48	,	,	PUNCT
ejpam-6640	349	49	t	t	NOUN
ejpam-6640	349	50	=	=	SYM
ejpam-6640	349	51	ϕ	ϕ	PROPN
ejpam-6640	349	52	◦	◦	NOUN
ejpam-6640	349	53	u+	u+	NOUN
ejpam-6640	349	54	ey	ey	NOUN
ejpam-6640	349	55	,	,	PUNCT
ejpam-6640	349	56	x	x	X
ejpam-6640	349	57	=	=	PUNCT
ejpam-6640	349	58	ϕ	ϕ	PROPN
ejpam-6640	349	59	◦	◦	NOUN
ejpam-6640	349	60	u	u	PROPN
ejpam-6640	349	61	,	,	PUNCT
ejpam-6640	349	62	ϕ	ϕ	PROPN
ejpam-6640	349	63	◦	◦	NOUN
ejpam-6640	349	64	ey	ey	PROPN
ejpam-6640	349	65	,	,	PUNCT
ejpam-6640	349	66	t	t	NOUN
ejpam-6640	349	67	+	+	CCONJ
ejpam-6640	349	68	ϕ	ϕ	PROPN
ejpam-6640	349	69	◦	◦	NOUN
ejpam-6640	349	70	u	u	NOUN
ejpam-6640	349	71	=	=	SYM
ejpam-6640	349	72	ey	ey	PROPN
ejpam-6640	349	73	,	,	PUNCT
ejpam-6640	349	74	x	x	PUNCT
ejpam-6640	349	75	+	+	SYM
ejpam-6640	349	76	ϕ	ϕ	PROPN
ejpam-6640	349	77	◦	◦	NOUN
ejpam-6640	349	78	u	u	NOUN
ejpam-6640	349	79	=	=	PUNCT
ejpam-6640	349	80	ϕ	ϕ	PROPN
ejpam-6640	349	81	◦	◦	NOUN
ejpam-6640	349	82	u	u	NOUN
ejpam-6640	349	83	,	,	PUNCT
ejpam-6640	349	84	=	=	PRON
ejpam-6640	349	85	⇒	⇒	NOUN
ejpam-6640	349	86	ϕ	ϕ	PROPN
ejpam-6640	349	87	◦	◦	NOUN
ejpam-6640	349	88	ey	ey	NOUN
ejpam-6640	349	89	,	,	PUNCT
ejpam-6640	349	90	t	t	NOUN
ejpam-6640	349	91	=	=	SYM
ejpam-6640	349	92	ey	ey	PROPN
ejpam-6640	349	93	,	,	PUNCT
ejpam-6640	349	94	x	x	X
ejpam-6640	349	95	.	.	PUNCT
ejpam-6640	350	1	thus	thus	ADV
ejpam-6640	350	2	,	,	PUNCT
ejpam-6640	350	3	f∗	f∗	X
ejpam-6640	350	4	◦	◦	NOUN
ejpam-6640	350	5	g∗	g∗	NOUN
ejpam-6640	350	6	=	=	PUNCT
ejpam-6640	350	7	ehoma	ehoma	NOUN
ejpam-6640	350	8	(	(	PUNCT
ejpam-6640	350	9	t	t	PROPN
ejpam-6640	350	10	,	,	PUNCT
ejpam-6640	350	11	x),homa	x),homa	PROPN
ejpam-6640	350	12	(	(	PUNCT
ejpam-6640	350	13	y	y	PROPN
ejpam-6640	350	14	,	,	PUNCT
ejpam-6640	350	15	x	x	NOUN
ejpam-6640	350	16	)	)	PUNCT
ejpam-6640	350	17	,	,	PUNCT
ejpam-6640	350	18	and	and	CCONJ
ejpam-6640	351	1	therefore	therefore	ADV
ejpam-6640	351	2	i	i	PRON
ejpam-6640	351	3	m	m	VERB
ejpam-6640	351	4	g∗	g∗	VERB
ejpam-6640	351	5	⊂	⊂	PROPN
ejpam-6640	351	6	ker	ker	PROPN
ejpam-6640	351	7	f∗.	f∗.	PROPN
ejpam-6640	351	8	now	now	ADV
ejpam-6640	351	9	,	,	PUNCT
ejpam-6640	351	10	we	we	PRON
ejpam-6640	351	11	show	show	VERB
ejpam-6640	351	12	that	that	SCONJ
ejpam-6640	351	13	ker(f∗	ker(f∗	NUM
ejpam-6640	351	14	)	)	PUNCT
ejpam-6640	352	1	⊂	⊂	PROPN
ejpam-6640	353	1	i	i	PRON
ejpam-6640	353	2	m	m	VERB
ejpam-6640	353	3	g∗.	g∗.	ADJ
ejpam-6640	353	4	we	we	PRON
ejpam-6640	353	5	have	have	VERB
ejpam-6640	353	6	:	:	PUNCT
ejpam-6640	353	7	ker(f∗	ker(f∗	X
ejpam-6640	353	8	)	)	PUNCT
ejpam-6640	353	9	=	=	PRON
ejpam-6640	354	1	{	{	PUNCT
ejpam-6640	354	2	ϕ	ϕ	NOUN
ejpam-6640	354	3	∈	∈	PROPN
ejpam-6640	354	4	homa	homa	NOUN
ejpam-6640	354	5	(	(	PUNCT
ejpam-6640	354	6	z	z	NOUN
ejpam-6640	354	7	,	,	PUNCT
ejpam-6640	354	8	x	x	NOUN
ejpam-6640	354	9	)	)	PUNCT
ejpam-6640	354	10	:	:	PUNCT
ejpam-6640	354	11	f∗(ϕ	f∗(ϕ	VERB
ejpam-6640	354	12	)	)	PUNCT
ejpam-6640	354	13	=	=	PUNCT
ejpam-6640	354	14	ϕ	ϕ	PROPN
ejpam-6640	354	15	◦	◦	NOUN
ejpam-6640	354	16	f	f	X
ejpam-6640	354	17	=	=	SYM
ejpam-6640	354	18	ey	ey	PROPN
ejpam-6640	354	19	,	,	PUNCT
ejpam-6640	354	20	x	x	NOUN
ejpam-6640	354	21	}	}	PUNCT
ejpam-6640	354	22	.	.	PUNCT
ejpam-6640	355	1	let	let	VERB
ejpam-6640	355	2	ϕ	ϕ	PROPN
ejpam-6640	355	3	∈	∈	PROPN
ejpam-6640	355	4	ker(f∗	ker(f∗	PROPN
ejpam-6640	355	5	)	)	PUNCT
ejpam-6640	355	6	=	=	SYM
ejpam-6640	355	7	kerhoma	kerhoma	ADJ
ejpam-6640	355	8	(	(	PUNCT
ejpam-6640	355	9	f	f	X
ejpam-6640	355	10	,	,	PUNCT
ejpam-6640	355	11	x	x	NOUN
ejpam-6640	355	12	)	)	PUNCT
ejpam-6640	355	13	.	.	PUNCT
ejpam-6640	356	1	we	we	PRON
ejpam-6640	356	2	show	show	VERB
ejpam-6640	356	3	that	that	SCONJ
ejpam-6640	356	4	ϕ	ϕ	PROPN
ejpam-6640	356	5	∈	∈	PROPN
ejpam-6640	356	6	i	i	PRON
ejpam-6640	356	7	m	m	VERB
ejpam-6640	356	8	g∗.	g∗.	ADJ
ejpam-6640	356	9	since	since	SCONJ
ejpam-6640	356	10	ϕ	ϕ	PROPN
ejpam-6640	356	11	∈	∈	PROPN
ejpam-6640	356	12	ker(f∗	ker(f∗	PROPN
ejpam-6640	356	13	)	)	PUNCT
ejpam-6640	356	14	,	,	PUNCT
ejpam-6640	356	15	we	we	PRON
ejpam-6640	356	16	have	have	VERB
ejpam-6640	356	17	:	:	PUNCT
ejpam-6640	356	18	ϕ	ϕ	PROPN
ejpam-6640	356	19	∈	∈	PROPN
ejpam-6640	356	20	ker(f∗	ker(f∗	PROPN
ejpam-6640	356	21	)	)	PUNCT
ejpam-6640	356	22	=	=	NOUN
ejpam-6640	356	23	⇒	⇒	NOUN
ejpam-6640	356	24	f∗(ϕ	f∗(ϕ	PROPN
ejpam-6640	356	25	)	)	PUNCT
ejpam-6640	356	26	=	=	SYM
ejpam-6640	357	1	ey	ey	NOUN
ejpam-6640	357	2	,	,	PUNCT
ejpam-6640	357	3	x	x	PUNCT
ejpam-6640	357	4	=	=	VERB
ejpam-6640	357	5	⇒	⇒	X
ejpam-6640	357	6	ϕ	ϕ	PROPN
ejpam-6640	357	7	◦	◦	NOUN
ejpam-6640	357	8	f	f	X
ejpam-6640	358	1	=	=	SYM
ejpam-6640	358	2	ey	ey	PROPN
ejpam-6640	358	3	,	,	PUNCT
ejpam-6640	358	4	x	x	INTJ
ejpam-6640	358	5	.	.	PUNCT
ejpam-6640	359	1	since	since	SCONJ
ejpam-6640	359	2	the	the	DET
ejpam-6640	359	3	sequence	sequence	NOUN
ejpam-6640	359	4	:	:	PUNCT
ejpam-6640	359	5	y	y	PROPN
ejpam-6640	359	6	f	f	PROPN
ejpam-6640	359	7	//	//	PROPN
ejpam-6640	359	8	z	z	PROPN
ejpam-6640	359	9	g	g	PROPN
ejpam-6640	359	10	//	//	PROPN
ejpam-6640	359	11	t	t	PROPN
ejpam-6640	359	12	//	//	X
ejpam-6640	359	13	0	0	NUM
ejpam-6640	359	14	is	be	AUX
ejpam-6640	359	15	right	right	ADJ
ejpam-6640	359	16	short	short	ADJ
ejpam-6640	359	17	exact	exact	NOUN
ejpam-6640	359	18	,	,	PUNCT
ejpam-6640	359	19	we	we	PRON
ejpam-6640	359	20	have	have	VERB
ejpam-6640	359	21	g	g	NOUN
ejpam-6640	359	22	◦	◦	NOUN
ejpam-6640	359	23	f	f	X
ejpam-6640	359	24	=	=	SYM
ejpam-6640	359	25	ey	ey	PROPN
ejpam-6640	359	26	,	,	PUNCT
ejpam-6640	359	27	t	t	PROPN
ejpam-6640	359	28	.	.	PUNCT
ejpam-6640	360	1	let	let	VERB
ejpam-6640	360	2	con(f	con(f	VERB
ejpam-6640	360	3	)	)	PUNCT
ejpam-6640	360	4	=	=	SYM
ejpam-6640	360	5	(	(	PUNCT
ejpam-6640	360	6	j	j	PROPN
ejpam-6640	360	7	,	,	PUNCT
ejpam-6640	360	8	p	p	NOUN
ejpam-6640	360	9	)	)	PUNCT
ejpam-6640	360	10	,	,	PUNCT
ejpam-6640	360	11	and	and	CCONJ
ejpam-6640	360	12	by	by	ADP
ejpam-6640	360	13	definition	definition	NOUN
ejpam-6640	360	14	of	of	ADP
ejpam-6640	360	15	the	the	DET
ejpam-6640	360	16	cokernel	cokernel	NOUN
ejpam-6640	360	17	of	of	ADP
ejpam-6640	360	18	f	f	PROPN
ejpam-6640	360	19	,	,	PUNCT
ejpam-6640	360	20	we	we	PRON
ejpam-6640	360	21	have	have	VERB
ejpam-6640	360	22	j	j	PROPN
ejpam-6640	360	23	◦	◦	NOUN
ejpam-6640	360	24	f	f	NOUN
ejpam-6640	360	25	=	=	SYM
ejpam-6640	360	26	ey	ey	PROPN
ejpam-6640	360	27	,	,	PUNCT
ejpam-6640	360	28	p	p	NOUN
ejpam-6640	360	29	and	and	CCONJ
ejpam-6640	360	30	there	there	PRON
ejpam-6640	360	31	exists	exist	VERB
ejpam-6640	360	32	a	a	DET
ejpam-6640	360	33	unique	unique	ADJ
ejpam-6640	360	34	morphism	morphism	NOUN
ejpam-6640	360	35	h1	h1	NOUN
ejpam-6640	360	36	:	:	PUNCT
ejpam-6640	360	37	p	p	X
ejpam-6640	360	38	→	→	SYM
ejpam-6640	360	39	t	t	NOUN
ejpam-6640	361	1	such	such	ADJ
ejpam-6640	361	2	that	that	PRON
ejpam-6640	361	3	h1	h1	PROPN
ejpam-6640	361	4	◦	◦	NOUN
ejpam-6640	361	5	j	j	PROPN
ejpam-6640	361	6	=	=	SYM
ejpam-6640	361	7	g.	g.	PROPN
ejpam-6640	362	1	thus	thus	ADV
ejpam-6640	362	2	,	,	PUNCT
ejpam-6640	362	3	h1	h1	PROPN
ejpam-6640	362	4	is	be	AUX
ejpam-6640	362	5	an	an	DET
ejpam-6640	362	6	epimorphism	epimorphism	NOUN
ejpam-6640	362	7	.	.	PUNCT
ejpam-6640	363	1	indeed	indeed	ADV
ejpam-6640	363	2	,	,	PUNCT
ejpam-6640	363	3	let	let	VERB
ejpam-6640	363	4	u	u	NOUN
ejpam-6640	363	5	,	,	PUNCT
ejpam-6640	363	6	v	v	INTJ
ejpam-6640	363	7	:	:	PUNCT
ejpam-6640	363	8	r	r	NOUN
ejpam-6640	363	9	→	→	SYM
ejpam-6640	363	10	p	p	X
ejpam-6640	363	11	such	such	ADJ
ejpam-6640	363	12	that	that	DET
ejpam-6640	363	13	u	u	NOUN
ejpam-6640	363	14	◦	◦	NOUN
ejpam-6640	363	15	h1	h1	PROPN
ejpam-6640	363	16	=	=	SYM
ejpam-6640	363	17	v	v	ADJ
ejpam-6640	363	18	◦	◦	NOUN
ejpam-6640	363	19	h1	h1	NOUN
ejpam-6640	363	20	.	.	PUNCT
ejpam-6640	364	1	then	then	ADV
ejpam-6640	364	2	:	:	PUNCT
ejpam-6640	364	3	u	u	NOUN
ejpam-6640	364	4	◦	◦	NOUN
ejpam-6640	364	5	h1	h1	PROPN
ejpam-6640	364	6	=	=	SYM
ejpam-6640	364	7	v	v	ADP
ejpam-6640	364	8	◦	◦	NOUN
ejpam-6640	364	9	h1	h1	NOUN
ejpam-6640	364	10	=	=	NOUN
ejpam-6640	364	11	⇒	⇒	NOUN
ejpam-6640	364	12	(	(	PUNCT
ejpam-6640	364	13	u	u	NOUN
ejpam-6640	364	14	◦	◦	NOUN
ejpam-6640	364	15	h1	h1	NOUN
ejpam-6640	364	16	)	)	PUNCT
ejpam-6640	364	17	◦	◦	NOUN
ejpam-6640	364	18	j	j	NOUN
ejpam-6640	364	19	=	=	SYM
ejpam-6640	364	20	(	(	PUNCT
ejpam-6640	364	21	v	v	NUM
ejpam-6640	364	22	◦	◦	NOUN
ejpam-6640	364	23	h1	h1	PROPN
ejpam-6640	364	24	)	)	PUNCT
ejpam-6640	364	25	◦	◦	NOUN
ejpam-6640	364	26	j	j	NOUN
ejpam-6640	365	1	=	=	VERB
ejpam-6640	365	2	⇒	⇒	VERB
ejpam-6640	365	3	u	u	PROPN
ejpam-6640	365	4	◦	◦	NOUN
ejpam-6640	365	5	(	(	PUNCT
ejpam-6640	365	6	h1	h1	VERB
ejpam-6640	365	7	◦	◦	NOUN
ejpam-6640	365	8	j	j	NOUN
ejpam-6640	365	9	)	)	PUNCT
ejpam-6640	365	10	=	=	SYM
ejpam-6640	365	11	v	v	ADP
ejpam-6640	365	12	◦	◦	NOUN
ejpam-6640	365	13	(	(	PUNCT
ejpam-6640	365	14	h1	h1	VERB
ejpam-6640	365	15	◦	◦	NOUN
ejpam-6640	365	16	j	j	NOUN
ejpam-6640	365	17	)	)	PUNCT
ejpam-6640	366	1	=	=	VERB
ejpam-6640	366	2	⇒	⇒	VERB
ejpam-6640	366	3	u	u	NOUN
ejpam-6640	366	4	◦	◦	NOUN
ejpam-6640	366	5	g	g	NOUN
ejpam-6640	366	6	=	=	SYM
ejpam-6640	366	7	v	v	ADP
ejpam-6640	366	8	◦	◦	NOUN
ejpam-6640	366	9	g	g	NOUN
ejpam-6640	366	10	=	=	NOUN
ejpam-6640	366	11	⇒	⇒	NOUN
ejpam-6640	366	12	u	u	NOUN
ejpam-6640	366	13	=	=	PROPN
ejpam-6640	366	14	v	v	X
ejpam-6640	366	15	(	(	PUNCT
ejpam-6640	366	16	since	since	SCONJ
ejpam-6640	366	17	g	g	PROPN
ejpam-6640	366	18	is	be	AUX
ejpam-6640	366	19	an	an	DET
ejpam-6640	366	20	epimorphism	epimorphism	NOUN
ejpam-6640	366	21	)	)	PUNCT
ejpam-6640	366	22	.	.	PUNCT
ejpam-6640	367	1	thus	thus	ADV
ejpam-6640	367	2	,	,	PUNCT
ejpam-6640	367	3	h1	h1	PROPN
ejpam-6640	367	4	is	be	AUX
ejpam-6640	367	5	an	an	DET
ejpam-6640	367	6	epimorphism	epimorphism	NOUN
ejpam-6640	367	7	.	.	PUNCT
ejpam-6640	368	1	since	since	SCONJ
ejpam-6640	368	2	a	a	PRON
ejpam-6640	368	3	is	be	AUX
ejpam-6640	368	4	a	a	DET
ejpam-6640	368	5	balanced	balanced	ADJ
ejpam-6640	368	6	category	category	NOUN
ejpam-6640	368	7	,	,	PUNCT
ejpam-6640	368	8	h1	h1	PROPN
ejpam-6640	368	9	is	be	AUX
ejpam-6640	368	10	a	a	DET
ejpam-6640	368	11	split	split	ADJ
ejpam-6640	368	12	epimorphism	epimorphism	NOUN
ejpam-6640	368	13	,	,	PUNCT
ejpam-6640	368	14	i.e.	i.e.	X
ejpam-6640	368	15	,	,	PUNCT
ejpam-6640	368	16	there	there	PRON
ejpam-6640	368	17	exists	exist	VERB
ejpam-6640	368	18	a	a	DET
ejpam-6640	368	19	unique	unique	ADJ
ejpam-6640	368	20	h′1	h′1	NOUN
ejpam-6640	368	21	:	:	PUNCT
ejpam-6640	368	22	t	t	PROPN
ejpam-6640	368	23	→	→	SYM
ejpam-6640	368	24	p	p	X
ejpam-6640	368	25	such	such	ADJ
ejpam-6640	368	26	that	that	PRON
ejpam-6640	368	27	:	:	PUNCT
ejpam-6640	368	28	h1	h1	AUX
ejpam-6640	368	29	◦	◦	NOUN
ejpam-6640	368	30	h′1	h′1	X
ejpam-6640	368	31	=	=	PUNCT
ejpam-6640	368	32	1	1	NUM
ejpam-6640	368	33	t	t	NOUN
ejpam-6640	368	34	.	.	PUNCT
ejpam-6640	369	1	moreover	moreover	ADV
ejpam-6640	369	2	,	,	PUNCT
ejpam-6640	369	3	h′1	h′1	ADJ
ejpam-6640	369	4	◦	◦	NOUN
ejpam-6640	369	5	g	g	NOUN
ejpam-6640	369	6	=	=	PUNCT
ejpam-6640	369	7	j.	j.	PROPN
ejpam-6640	369	8	a.	a.	PROPN
ejpam-6640	369	9	diallo	diallo	PROPN
ejpam-6640	369	10	,	,	PUNCT
ejpam-6640	369	11	m.	m.	PROPN
ejpam-6640	369	12	b.	b.	PROPN
ejpam-6640	369	13	f.	f.	PROPN
ejpam-6640	369	14	b.	b.	PROPN
ejpam-6640	369	15	maaouia	maaouia	PROPN
ejpam-6640	369	16	,	,	PUNCT
ejpam-6640	369	17	m.	m.	NOUN
ejpam-6640	369	18	sanghare	sanghare	PROPN
ejpam-6640	369	19	/	/	SYM
ejpam-6640	369	20	eur	eur	PROPN
ejpam-6640	369	21	.	.	PUNCT
ejpam-6640	370	1	j.	j.	PROPN
ejpam-6640	370	2	pure	pure	PROPN
ejpam-6640	370	3	appl	appl	PROPN
ejpam-6640	370	4	.	.	PROPN
ejpam-6640	370	5	math	math	PROPN
ejpam-6640	370	6	,	,	PUNCT
ejpam-6640	370	7	18	18	NUM
ejpam-6640	370	8	(	(	PUNCT
ejpam-6640	370	9	4	4	NUM
ejpam-6640	370	10	)	)	PUNCT
ejpam-6640	370	11	(	(	PUNCT
ejpam-6640	370	12	2025	2025	NUM
ejpam-6640	370	13	)	)	PUNCT
ejpam-6640	370	14	,	,	PUNCT
ejpam-6640	370	15	6640	6640	NUM
ejpam-6640	370	16	15	15	NUM
ejpam-6640	370	17	of	of	ADP
ejpam-6640	370	18	28	28	NUM
ejpam-6640	370	19	since	since	SCONJ
ejpam-6640	370	20	ϕ	ϕ	NOUN
ejpam-6640	370	21	◦	◦	NOUN
ejpam-6640	370	22	f	f	X
ejpam-6640	370	23	=	=	SYM
ejpam-6640	370	24	ey	ey	PROPN
ejpam-6640	370	25	,	,	PUNCT
ejpam-6640	370	26	x	x	INTJ
ejpam-6640	370	27	,	,	PUNCT
ejpam-6640	370	28	by	by	ADP
ejpam-6640	370	29	the	the	DET
ejpam-6640	370	30	definition	definition	NOUN
ejpam-6640	370	31	of	of	ADP
ejpam-6640	370	32	con(f	con(f	PROPN
ejpam-6640	370	33	)	)	PUNCT
ejpam-6640	371	1	,	,	PUNCT
ejpam-6640	371	2	we	we	PRON
ejpam-6640	371	3	have	have	VERB
ejpam-6640	371	4	j	j	PROPN
ejpam-6640	371	5	◦	◦	NOUN
ejpam-6640	371	6	f	f	PROPN
ejpam-6640	371	7	=	=	SYM
ejpam-6640	371	8	ey	ey	PROPN
ejpam-6640	371	9	,	,	PUNCT
ejpam-6640	371	10	p	p	NOUN
ejpam-6640	371	11	,	,	PUNCT
ejpam-6640	371	12	and	and	CCONJ
ejpam-6640	371	13	there	there	PRON
ejpam-6640	371	14	exists	exist	VERB
ejpam-6640	371	15	a	a	DET
ejpam-6640	371	16	unique	unique	ADJ
ejpam-6640	371	17	h2	h2	NOUN
ejpam-6640	371	18	:	:	PUNCT
ejpam-6640	371	19	p	p	X
ejpam-6640	371	20	→	→	X
ejpam-6640	371	21	x	x	SYM
ejpam-6640	371	22	such	such	ADJ
ejpam-6640	371	23	that	that	DET
ejpam-6640	371	24	h2	h2	PROPN
ejpam-6640	371	25	◦	◦	PROPN
ejpam-6640	371	26	j	j	PROPN
ejpam-6640	371	27	=	=	PUNCT
ejpam-6640	371	28	ϕ.	ϕ.	PROPN
ejpam-6640	371	29	that	that	PRON
ejpam-6640	371	30	is	be	AUX
ejpam-6640	371	31	,	,	PUNCT
ejpam-6640	371	32	the	the	DET
ejpam-6640	371	33	following	follow	VERB
ejpam-6640	371	34	diagram	diagram	NOUN
ejpam-6640	371	35	commutes	commute	NOUN
ejpam-6640	371	36	:	:	PUNCT
ejpam-6640	371	37	t	t	PROPN
ejpam-6640	371	38	h′1	h′1	PROPN
ejpam-6640	371	39	�	�	PROPN
ejpam-6640	371	40	�	�	PROPN
ejpam-6640	371	41	y	y	PROPN
ejpam-6640	371	42	f	f	PROPN
ejpam-6640	372	1	//	//	PROPN
ejpam-6640	372	2	z	z	PROPN
ejpam-6640	372	3	g	g	PROPN
ejpam-6640	372	4	99	99	NUM
ejpam-6640	372	5	j	j	PROPN
ejpam-6640	372	6	//	//	PROPN
ejpam-6640	372	7	ϕ	ϕ	PROPN
ejpam-6640	372	8	�	�	PROPN
ejpam-6640	372	9	�	�	PROPN
ejpam-6640	372	10	p	p	PROPN
ejpam-6640	372	11	h1	h1	PROPN
ejpam-6640	372	12	oo	oo	INTJ
ejpam-6640	372	13	h2	h2	PROPN
ejpam-6640	372	14	yy	yy	NOUN
ejpam-6640	372	15	x	x	PUNCT
ejpam-6640	372	16	thus	thus	ADV
ejpam-6640	372	17	,	,	PUNCT
ejpam-6640	372	18	we	we	PRON
ejpam-6640	372	19	have	have	VERB
ejpam-6640	372	20	:	:	PUNCT
ejpam-6640	372	21	ϕ	ϕ	NOUN
ejpam-6640	373	1	=	=	PUNCT
ejpam-6640	373	2	h2	h2	PROPN
ejpam-6640	373	3	◦	◦	NOUN
ejpam-6640	373	4	j	j	PROPN
ejpam-6640	373	5	=	=	SYM
ejpam-6640	373	6	h2	h2	PROPN
ejpam-6640	373	7	◦	◦	NOUN
ejpam-6640	373	8	(	(	PUNCT
ejpam-6640	373	9	h′1	h′1	ADJ
ejpam-6640	373	10	◦	◦	NOUN
ejpam-6640	373	11	g	g	NOUN
ejpam-6640	373	12	)	)	PUNCT
ejpam-6640	373	13	(	(	PUNCT
ejpam-6640	373	14	since	since	SCONJ
ejpam-6640	373	15	h′1	h′1	VERB
ejpam-6640	373	16	◦	◦	NOUN
ejpam-6640	373	17	g	g	PROPN
ejpam-6640	373	18	=	=	SYM
ejpam-6640	373	19	j	j	PROPN
ejpam-6640	373	20	)	)	PUNCT
ejpam-6640	373	21	=	=	PUNCT
ejpam-6640	373	22	(	(	PUNCT
ejpam-6640	373	23	h2	h2	NOUN
ejpam-6640	373	24	◦	◦	NOUN
ejpam-6640	373	25	h′1	h′1	NOUN
ejpam-6640	373	26	)	)	PUNCT
ejpam-6640	373	27	◦	◦	NOUN
ejpam-6640	373	28	g	g	NOUN
ejpam-6640	373	29	ϕ	ϕ	NOUN
ejpam-6640	373	30	=	=	SYM
ejpam-6640	373	31	g∗(h2	g∗(h2	PROPN
ejpam-6640	373	32	◦	◦	NOUN
ejpam-6640	373	33	h′1	h′1	NOUN
ejpam-6640	373	34	)	)	PUNCT
ejpam-6640	373	35	.	.	PUNCT
ejpam-6640	374	1	hence	hence	ADV
ejpam-6640	374	2	,	,	PUNCT
ejpam-6640	374	3	ϕ	ϕ	PROPN
ejpam-6640	374	4	∈	∈	PROPN
ejpam-6640	374	5	im(g∗	im(g∗	NOUN
ejpam-6640	374	6	)	)	PUNCT
ejpam-6640	374	7	.	.	PUNCT
ejpam-6640	375	1	therefore	therefore	ADV
ejpam-6640	375	2	,	,	PUNCT
ejpam-6640	375	3	ker(f∗	ker(f∗	PROPN
ejpam-6640	375	4	)	)	PUNCT
ejpam-6640	375	5	⊂	⊂	PROPN
ejpam-6640	376	1	i	i	PRON
ejpam-6640	376	2	m	m	VERB
ejpam-6640	376	3	g∗.	g∗.	VERB
ejpam-6640	376	4	thus	thus	ADV
ejpam-6640	376	5	,	,	PUNCT
ejpam-6640	376	6	homa	homa	NOUN
ejpam-6640	376	7	(	(	PUNCT
ejpam-6640	376	8	−	−	PROPN
ejpam-6640	376	9	,	,	PUNCT
ejpam-6640	376	10	x	x	NOUN
ejpam-6640	376	11	)	)	PUNCT
ejpam-6640	376	12	:	:	PUNCT
ejpam-6640	376	13	a	a	DET
ejpam-6640	376	14	−→	−→	NOUN
ejpam-6640	376	15	ab	ab	PROPN
ejpam-6640	376	16	is	be	AUX
ejpam-6640	376	17	a	a	DET
ejpam-6640	376	18	contravariant	contravariant	ADJ
ejpam-6640	376	19	,	,	PUNCT
ejpam-6640	376	20	additive	additive	NOUN
ejpam-6640	376	21	,	,	PUNCT
ejpam-6640	376	22	and	and	CCONJ
ejpam-6640	376	23	left	left	ADJ
ejpam-6640	376	24	-	-	PUNCT
ejpam-6640	376	25	exact	exact	NOUN
ejpam-6640	376	26	functor	functor	NOUN
ejpam-6640	376	27	.	.	PROPN
ejpam-6640	377	1	•	•	NUM
ejpam-6640	377	2	we	we	PRON
ejpam-6640	377	3	now	now	ADV
ejpam-6640	377	4	show	show	VERB
ejpam-6640	377	5	that	that	SCONJ
ejpam-6640	377	6	homa	homa	NOUN
ejpam-6640	377	7	(	(	PUNCT
ejpam-6640	377	8	−	−	PROPN
ejpam-6640	377	9	,	,	PUNCT
ejpam-6640	377	10	x	x	NOUN
ejpam-6640	377	11	)	)	PUNCT
ejpam-6640	377	12	:	:	PUNCT
ejpam-6640	377	13	a	a	DET
ejpam-6640	377	14	−→	−→	NOUN
ejpam-6640	377	15	ab	ab	PROPN
ejpam-6640	377	16	is	be	AUX
ejpam-6640	377	17	an	an	DET
ejpam-6640	377	18	exact	exact	ADJ
ejpam-6640	377	19	functor	functor	NOUN
ejpam-6640	377	20	if	if	SCONJ
ejpam-6640	378	1	and	and	CCONJ
ejpam-6640	378	2	only	only	ADV
ejpam-6640	378	3	if	if	SCONJ
ejpam-6640	378	4	x	x	PRON
ejpam-6640	378	5	is	be	AUX
ejpam-6640	378	6	an	an	DET
ejpam-6640	378	7	injective	injective	ADJ
ejpam-6640	378	8	object	object	NOUN
ejpam-6640	378	9	in	in	ADP
ejpam-6640	378	10	a	a	PRON
ejpam-6640	378	11	.	.	PUNCT
ejpam-6640	378	12	•	•	NOUN
ejpam-6640	378	13	suppose	suppose	VERB
ejpam-6640	378	14	x	x	PRON
ejpam-6640	378	15	is	be	AUX
ejpam-6640	378	16	an	an	DET
ejpam-6640	378	17	injective	injective	ADJ
ejpam-6640	378	18	object	object	NOUN
ejpam-6640	378	19	in	in	ADP
ejpam-6640	378	20	a	a	PRON
ejpam-6640	378	21	and	and	CCONJ
ejpam-6640	378	22	show	show	VERB
ejpam-6640	378	23	that	that	SCONJ
ejpam-6640	378	24	homa	homa	NOUN
ejpam-6640	378	25	(	(	PUNCT
ejpam-6640	378	26	−	−	PROPN
ejpam-6640	378	27	,	,	PUNCT
ejpam-6640	378	28	x	x	NOUN
ejpam-6640	378	29	)	)	PUNCT
ejpam-6640	378	30	:	:	PUNCT
ejpam-6640	378	31	a	a	DET
ejpam-6640	378	32	−→	−→	NOUN
ejpam-6640	378	33	ab	ab	PROPN
ejpam-6640	378	34	is	be	AUX
ejpam-6640	378	35	exact	exact	ADJ
ejpam-6640	378	36	.	.	PUNCT
ejpam-6640	379	1	consider	consider	VERB
ejpam-6640	379	2	the	the	DET
ejpam-6640	379	3	short	short	ADJ
ejpam-6640	379	4	exact	exact	ADJ
ejpam-6640	379	5	sequence	sequence	NOUN
ejpam-6640	379	6	of	of	ADP
ejpam-6640	379	7	morphisms	morphism	NOUN
ejpam-6640	379	8	in	in	ADP
ejpam-6640	379	9	a	a	DET
ejpam-6640	379	10	:	:	SYM
ejpam-6640	379	11	0	0	NUM
ejpam-6640	379	12	//	//	PUNCT
ejpam-6640	379	13	y	y	PROPN
ejpam-6640	379	14	f	f	PROPN
ejpam-6640	379	15	//	//	PROPN
ejpam-6640	379	16	z	z	PROPN
ejpam-6640	379	17	g	g	PROPN
ejpam-6640	379	18	//	//	PROPN
ejpam-6640	379	19	t	t	PROPN
ejpam-6640	379	20	//	//	X
ejpam-6640	379	21	0	0	NUM
ejpam-6640	380	1	we	we	PRON
ejpam-6640	380	2	must	must	AUX
ejpam-6640	380	3	show	show	VERB
ejpam-6640	380	4	that	that	SCONJ
ejpam-6640	380	5	the	the	DET
ejpam-6640	380	6	sequence	sequence	NOUN
ejpam-6640	380	7	:	:	PUNCT
ejpam-6640	380	8	{	{	PUNCT
ejpam-6640	380	9	e0,x	e0,x	PROPN
ejpam-6640	380	10	}	}	PUNCT
ejpam-6640	380	11	//	//	SYM
ejpam-6640	380	12	homa	homa	PROPN
ejpam-6640	380	13	(	(	PUNCT
ejpam-6640	380	14	t	t	PROPN
ejpam-6640	380	15	,	,	PUNCT
ejpam-6640	380	16	x	x	NOUN
ejpam-6640	380	17	)	)	PUNCT
ejpam-6640	380	18	homa	homa	NOUN
ejpam-6640	380	19	(	(	PUNCT
ejpam-6640	380	20	g	g	PROPN
ejpam-6640	380	21	,	,	PUNCT
ejpam-6640	380	22	x)=g∗	x)=g∗	PROPN
ejpam-6640	380	23	//	//	SYM
ejpam-6640	380	24	homa	homa	PROPN
ejpam-6640	380	25	(	(	PUNCT
ejpam-6640	380	26	z	z	NOUN
ejpam-6640	380	27	,	,	PUNCT
ejpam-6640	380	28	x	x	NOUN
ejpam-6640	380	29	)	)	PUNCT
ejpam-6640	380	30	homa	homa	NOUN
ejpam-6640	380	31	(	(	PUNCT
ejpam-6640	380	32	f	f	X
ejpam-6640	380	33	,	,	PUNCT
ejpam-6640	380	34	x)=f∗	x)=f∗	PROPN
ejpam-6640	380	35	//	//	SYM
ejpam-6640	380	36	homa	homa	PROPN
ejpam-6640	380	37	(	(	PUNCT
ejpam-6640	380	38	y	y	PROPN
ejpam-6640	380	39	,	,	PUNCT
ejpam-6640	380	40	x	x	NOUN
ejpam-6640	380	41	)	)	PUNCT
ejpam-6640	380	42	//	//	X
ejpam-6640	380	43	{	{	PUNCT
ejpam-6640	380	44	e0,x	e0,x	NOUN
ejpam-6640	380	45	}	}	PUNCT
ejpam-6640	380	46	is	be	AUX
ejpam-6640	380	47	exact	exact	ADJ
ejpam-6640	380	48	.	.	PUNCT
ejpam-6640	381	1	by	by	ADP
ejpam-6640	381	2	part	part	NOUN
ejpam-6640	381	3	1	1	NUM
ejpam-6640	381	4	,	,	PUNCT
ejpam-6640	381	5	the	the	DET
ejpam-6640	381	6	sequence	sequence	NOUN
ejpam-6640	381	7	:	:	PUNCT
ejpam-6640	381	8	{	{	PUNCT
ejpam-6640	381	9	e0,x	e0,x	PROPN
ejpam-6640	381	10	}	}	PUNCT
ejpam-6640	381	11	//	//	SYM
ejpam-6640	381	12	homa	homa	PROPN
ejpam-6640	381	13	(	(	PUNCT
ejpam-6640	381	14	t	t	PROPN
ejpam-6640	381	15	,	,	PUNCT
ejpam-6640	381	16	x	x	NOUN
ejpam-6640	381	17	)	)	PUNCT
ejpam-6640	381	18	homa	homa	NOUN
ejpam-6640	381	19	(	(	PUNCT
ejpam-6640	381	20	g	g	PROPN
ejpam-6640	381	21	,	,	PUNCT
ejpam-6640	381	22	x)=g∗	x)=g∗	PROPN
ejpam-6640	381	23	//	//	SYM
ejpam-6640	381	24	homa	homa	PROPN
ejpam-6640	381	25	(	(	PUNCT
ejpam-6640	381	26	z	z	NOUN
ejpam-6640	381	27	,	,	PUNCT
ejpam-6640	381	28	x	x	NOUN
ejpam-6640	381	29	)	)	PUNCT
ejpam-6640	381	30	homa	homa	NOUN
ejpam-6640	381	31	(	(	PUNCT
ejpam-6640	381	32	f	f	X
ejpam-6640	381	33	,	,	PUNCT
ejpam-6640	381	34	x)=f∗	x)=f∗	PROPN
ejpam-6640	381	35	//	//	SYM
ejpam-6640	381	36	homa	homa	PROPN
ejpam-6640	381	37	(	(	PUNCT
ejpam-6640	381	38	y	y	PROPN
ejpam-6640	381	39	,	,	PUNCT
ejpam-6640	381	40	x	x	NOUN
ejpam-6640	381	41	)	)	PUNCT
ejpam-6640	381	42	is	be	AUX
ejpam-6640	381	43	left	leave	VERB
ejpam-6640	381	44	-	-	PUNCT
ejpam-6640	381	45	exact	exact	ADJ
ejpam-6640	381	46	.	.	PUNCT
ejpam-6640	382	1	it	it	PRON
ejpam-6640	382	2	remains	remain	VERB
ejpam-6640	382	3	to	to	PART
ejpam-6640	382	4	show	show	VERB
ejpam-6640	382	5	that	that	SCONJ
ejpam-6640	382	6	homa	homa	NOUN
ejpam-6640	382	7	(	(	PUNCT
ejpam-6640	382	8	f	f	PROPN
ejpam-6640	382	9	,	,	PUNCT
ejpam-6640	382	10	x	x	NOUN
ejpam-6640	382	11	)	)	PUNCT
ejpam-6640	382	12	=	=	SYM
ejpam-6640	382	13	f∗	f∗	NOUN
ejpam-6640	382	14	is	be	AUX
ejpam-6640	382	15	an	an	DET
ejpam-6640	382	16	epimorphism	epimorphism	NOUN
ejpam-6640	382	17	.	.	PUNCT
ejpam-6640	383	1	since	since	SCONJ
ejpam-6640	383	2	x	x	PRON
ejpam-6640	383	3	is	be	AUX
ejpam-6640	383	4	injective	injective	ADJ
ejpam-6640	383	5	,	,	PUNCT
ejpam-6640	383	6	for	for	ADP
ejpam-6640	383	7	every	every	DET
ejpam-6640	383	8	monomorphism	monomorphism	NOUN
ejpam-6640	383	9	f	f	X
ejpam-6640	383	10	:	:	PUNCT
ejpam-6640	383	11	y	y	PROPN
ejpam-6640	383	12	↪	↪	PROPN
ejpam-6640	383	13	→	→	SYM
ejpam-6640	383	14	z	z	NOUN
ejpam-6640	383	15	in	in	ADP
ejpam-6640	383	16	a	a	PRON
ejpam-6640	383	17	and	and	CCONJ
ejpam-6640	383	18	every	every	DET
ejpam-6640	383	19	morphism	morphism	NOUN
ejpam-6640	383	20	h	h	NOUN
ejpam-6640	383	21	:	:	PUNCT
ejpam-6640	383	22	y	y	PROPN
ejpam-6640	383	23	→	→	PUNCT
ejpam-6640	383	24	x	x	X
ejpam-6640	383	25	in	in	ADP
ejpam-6640	383	26	a	a	PRON
ejpam-6640	383	27	,	,	PUNCT
ejpam-6640	383	28	there	there	PRON
ejpam-6640	383	29	exists	exist	VERB
ejpam-6640	383	30	a	a	DET
ejpam-6640	383	31	morphism	morphism	NOUN
ejpam-6640	383	32	ϕ	ϕ	NOUN
ejpam-6640	383	33	:	:	PUNCT
ejpam-6640	383	34	z	z	X
ejpam-6640	383	35	→	→	SYM
ejpam-6640	383	36	x	x	X
ejpam-6640	383	37	in	in	ADP
ejpam-6640	383	38	a	a	DET
ejpam-6640	383	39	such	such	ADJ
ejpam-6640	383	40	that	that	DET
ejpam-6640	383	41	ϕ	ϕ	NOUN
ejpam-6640	383	42	◦	◦	NOUN
ejpam-6640	383	43	f	f	PROPN
ejpam-6640	384	1	=	=	SYM
ejpam-6640	384	2	h.	h.	PROPN
ejpam-6640	384	3	this	this	PRON
ejpam-6640	384	4	means	mean	VERB
ejpam-6640	384	5	the	the	DET
ejpam-6640	384	6	following	follow	VERB
ejpam-6640	384	7	diagram	diagram	NOUN
ejpam-6640	384	8	commutes	commute	NOUN
ejpam-6640	384	9	:	:	PUNCT
ejpam-6640	384	10	x	x	SYM
ejpam-6640	384	11	0	0	PUNCT
ejpam-6640	384	12	//	//	NUM
ejpam-6640	385	1	y	y	NOUN
ejpam-6640	385	2	h	h	NOUN
ejpam-6640	386	1	oo	oo	INTJ
ejpam-6640	386	2	f	f	PROPN
ejpam-6640	387	1	//	//	PROPN
ejpam-6640	387	2	z	z	PROPN
ejpam-6640	387	3	ϕ	ϕ	PROPN
ejpam-6640	387	4	`	`	PUNCT
ejpam-6640	387	5	`	`	PUNCT
ejpam-6640	387	6	a.	a.	PROPN
ejpam-6640	387	7	diallo	diallo	PROPN
ejpam-6640	387	8	,	,	PUNCT
ejpam-6640	387	9	m.	m.	PROPN
ejpam-6640	387	10	b.	b.	PROPN
ejpam-6640	387	11	f.	f.	PROPN
ejpam-6640	387	12	b.	b.	PROPN
ejpam-6640	387	13	maaouia	maaouia	PROPN
ejpam-6640	387	14	,	,	PUNCT
ejpam-6640	387	15	m.	m.	NOUN
ejpam-6640	387	16	sanghare	sanghare	PROPN
ejpam-6640	387	17	/	/	SYM
ejpam-6640	387	18	eur	eur	PROPN
ejpam-6640	387	19	.	.	PUNCT
ejpam-6640	388	1	j.	j.	PROPN
ejpam-6640	388	2	pure	pure	PROPN
ejpam-6640	388	3	appl	appl	PROPN
ejpam-6640	388	4	.	.	PROPN
ejpam-6640	388	5	math	math	PROPN
ejpam-6640	388	6	,	,	PUNCT
ejpam-6640	388	7	18	18	NUM
ejpam-6640	388	8	(	(	PUNCT
ejpam-6640	388	9	4	4	NUM
ejpam-6640	388	10	)	)	PUNCT
ejpam-6640	388	11	(	(	PUNCT
ejpam-6640	388	12	2025	2025	NUM
ejpam-6640	388	13	)	)	PUNCT
ejpam-6640	388	14	,	,	PUNCT
ejpam-6640	388	15	6640	6640	NUM
ejpam-6640	388	16	16	16	NUM
ejpam-6640	388	17	of	of	ADP
ejpam-6640	388	18	28	28	NUM
ejpam-6640	388	19	in	in	ADP
ejpam-6640	388	20	other	other	ADJ
ejpam-6640	388	21	words	word	NOUN
ejpam-6640	388	22	,	,	PUNCT
ejpam-6640	388	23	for	for	ADP
ejpam-6640	388	24	every	every	DET
ejpam-6640	388	25	h	h	NOUN
ejpam-6640	388	26	∈	∈	PROPN
ejpam-6640	388	27	homa	homa	NOUN
ejpam-6640	388	28	(	(	PUNCT
ejpam-6640	388	29	y	y	PROPN
ejpam-6640	388	30	,	,	PUNCT
ejpam-6640	388	31	x	x	NOUN
ejpam-6640	388	32	)	)	PUNCT
ejpam-6640	388	33	,	,	PUNCT
ejpam-6640	388	34	there	there	PRON
ejpam-6640	388	35	exists	exist	VERB
ejpam-6640	388	36	ϕ	ϕ	PROPN
ejpam-6640	388	37	∈	∈	PROPN
ejpam-6640	388	38	homa	homa	NOUN
ejpam-6640	388	39	(	(	PUNCT
ejpam-6640	388	40	z	z	NOUN
ejpam-6640	388	41	,	,	PUNCT
ejpam-6640	388	42	x	x	NOUN
ejpam-6640	388	43	)	)	PUNCT
ejpam-6640	388	44	such	such	ADJ
ejpam-6640	388	45	that	that	SCONJ
ejpam-6640	388	46	ϕ	ϕ	PROPN
ejpam-6640	388	47	◦	◦	NOUN
ejpam-6640	388	48	f	f	X
ejpam-6640	388	49	=	=	SYM
ejpam-6640	388	50	f∗(ϕ	f∗(ϕ	PROPN
ejpam-6640	388	51	)	)	PUNCT
ejpam-6640	388	52	=	=	SYM
ejpam-6640	388	53	h.	h.	PROPN
ejpam-6640	388	54	hence	hence	ADV
ejpam-6640	388	55	,	,	PUNCT
ejpam-6640	388	56	homa	homa	PROPN
ejpam-6640	388	57	(	(	PUNCT
ejpam-6640	388	58	f	f	PROPN
ejpam-6640	388	59	,	,	PUNCT
ejpam-6640	388	60	x	x	X
ejpam-6640	388	61	)	)	PUNCT
ejpam-6640	388	62	is	be	AUX
ejpam-6640	388	63	an	an	DET
ejpam-6640	388	64	epimorphism	epimorphism	NOUN
ejpam-6640	388	65	.	.	PUNCT
ejpam-6640	389	1	•	•	NOUN
ejpam-6640	389	2	conversely	conversely	ADV
ejpam-6640	389	3	,	,	PUNCT
ejpam-6640	389	4	suppose	suppose	VERB
ejpam-6640	389	5	homa	homa	NOUN
ejpam-6640	389	6	(	(	PUNCT
ejpam-6640	389	7	−	−	PROPN
ejpam-6640	389	8	,	,	PUNCT
ejpam-6640	389	9	x	x	NOUN
ejpam-6640	389	10	)	)	PUNCT
ejpam-6640	389	11	:	:	PUNCT
ejpam-6640	389	12	a	a	DET
ejpam-6640	389	13	−→	−→	NOUN
ejpam-6640	389	14	ab	ab	PROPN
ejpam-6640	389	15	is	be	AUX
ejpam-6640	389	16	exact	exact	ADJ
ejpam-6640	389	17	and	and	CCONJ
ejpam-6640	389	18	show	show	VERB
ejpam-6640	389	19	that	that	SCONJ
ejpam-6640	389	20	x	x	PRON
ejpam-6640	389	21	is	be	AUX
ejpam-6640	389	22	an	an	DET
ejpam-6640	389	23	injective	injective	ADJ
ejpam-6640	389	24	object	object	NOUN
ejpam-6640	389	25	in	in	ADP
ejpam-6640	389	26	a	a	PRON
ejpam-6640	389	27	.	.	PUNCT
ejpam-6640	390	1	since	since	SCONJ
ejpam-6640	390	2	homa	homa	PROPN
ejpam-6640	390	3	(	(	PUNCT
ejpam-6640	390	4	x,−	x,−	PROPN
ejpam-6640	390	5	)	)	PUNCT
ejpam-6640	390	6	is	be	AUX
ejpam-6640	390	7	exact	exact	ADJ
ejpam-6640	390	8	,	,	PUNCT
ejpam-6640	390	9	for	for	ADP
ejpam-6640	390	10	every	every	DET
ejpam-6640	390	11	short	short	ADJ
ejpam-6640	390	12	exact	exact	ADJ
ejpam-6640	390	13	sequence	sequence	NOUN
ejpam-6640	390	14	in	in	ADP
ejpam-6640	390	15	a	a	DET
ejpam-6640	390	16	:	:	SYM
ejpam-6640	390	17	0	0	NUM
ejpam-6640	390	18	//	//	PUNCT
ejpam-6640	391	1	y	y	PROPN
ejpam-6640	391	2	f	f	PROPN
ejpam-6640	391	3	//	//	PROPN
ejpam-6640	391	4	z	z	PROPN
ejpam-6640	391	5	g	g	PROPN
ejpam-6640	391	6	//	//	PROPN
ejpam-6640	391	7	t	t	PROPN
ejpam-6640	391	8	//	//	X
ejpam-6640	391	9	0	0	NUM
ejpam-6640	392	1	the	the	DET
ejpam-6640	392	2	sequence	sequence	NOUN
ejpam-6640	392	3	:	:	PUNCT
ejpam-6640	392	4	{	{	PUNCT
ejpam-6640	392	5	e0,x	e0,x	PROPN
ejpam-6640	392	6	}	}	PUNCT
ejpam-6640	392	7	//	//	SYM
ejpam-6640	392	8	homa	homa	PROPN
ejpam-6640	392	9	(	(	PUNCT
ejpam-6640	392	10	t	t	PROPN
ejpam-6640	392	11	,	,	PUNCT
ejpam-6640	392	12	x	x	NOUN
ejpam-6640	392	13	)	)	PUNCT
ejpam-6640	392	14	homa	homa	NOUN
ejpam-6640	392	15	(	(	PUNCT
ejpam-6640	392	16	g	g	PROPN
ejpam-6640	392	17	,	,	PUNCT
ejpam-6640	392	18	x)=g∗	x)=g∗	PROPN
ejpam-6640	392	19	//	//	SYM
ejpam-6640	392	20	homa	homa	PROPN
ejpam-6640	392	21	(	(	PUNCT
ejpam-6640	392	22	z	z	NOUN
ejpam-6640	392	23	,	,	PUNCT
ejpam-6640	392	24	x	x	NOUN
ejpam-6640	392	25	)	)	PUNCT
ejpam-6640	392	26	homa	homa	NOUN
ejpam-6640	392	27	(	(	PUNCT
ejpam-6640	392	28	f	f	X
ejpam-6640	392	29	,	,	PUNCT
ejpam-6640	392	30	x)=f∗	x)=f∗	PROPN
ejpam-6640	392	31	//	//	SYM
ejpam-6640	392	32	homa	homa	PROPN
ejpam-6640	392	33	(	(	PUNCT
ejpam-6640	392	34	y	y	PROPN
ejpam-6640	392	35	,	,	PUNCT
ejpam-6640	392	36	x	x	NOUN
ejpam-6640	392	37	)	)	PUNCT
ejpam-6640	392	38	//	//	X
ejpam-6640	392	39	{	{	PUNCT
ejpam-6640	392	40	e0,x	e0,x	NOUN
ejpam-6640	392	41	}	}	PUNCT
ejpam-6640	392	42	is	be	AUX
ejpam-6640	392	43	exact	exact	ADJ
ejpam-6640	392	44	.	.	PUNCT
ejpam-6640	393	1	this	this	PRON
ejpam-6640	393	2	means	mean	VERB
ejpam-6640	393	3	f∗	f∗	NOUN
ejpam-6640	393	4	is	be	AUX
ejpam-6640	393	5	an	an	DET
ejpam-6640	393	6	epimorphism	epimorphism	NOUN
ejpam-6640	393	7	.	.	PUNCT
ejpam-6640	394	1	thus	thus	ADV
ejpam-6640	394	2	,	,	PUNCT
ejpam-6640	394	3	for	for	ADP
ejpam-6640	394	4	every	every	DET
ejpam-6640	394	5	monomorphism	monomorphism	NOUN
ejpam-6640	394	6	f	f	X
ejpam-6640	394	7	:	:	PUNCT
ejpam-6640	394	8	y	y	PROPN
ejpam-6640	394	9	↪	↪	PROPN
ejpam-6640	394	10	→	→	SYM
ejpam-6640	394	11	z	z	NOUN
ejpam-6640	394	12	in	in	ADP
ejpam-6640	394	13	a	a	PRON
ejpam-6640	394	14	and	and	CCONJ
ejpam-6640	394	15	every	every	DET
ejpam-6640	394	16	morphism	morphism	NOUN
ejpam-6640	394	17	h	h	NOUN
ejpam-6640	394	18	:	:	PUNCT
ejpam-6640	394	19	y	y	PROPN
ejpam-6640	394	20	→	→	PUNCT
ejpam-6640	394	21	x	x	X
ejpam-6640	394	22	in	in	ADP
ejpam-6640	394	23	a	a	PRON
ejpam-6640	394	24	,	,	PUNCT
ejpam-6640	394	25	there	there	PRON
ejpam-6640	394	26	exists	exist	VERB
ejpam-6640	394	27	a	a	DET
ejpam-6640	394	28	morphism	morphism	NOUN
ejpam-6640	394	29	ϕ	ϕ	NOUN
ejpam-6640	394	30	:	:	PUNCT
ejpam-6640	394	31	z	z	X
ejpam-6640	394	32	→	→	SYM
ejpam-6640	394	33	x	x	X
ejpam-6640	394	34	in	in	ADP
ejpam-6640	394	35	a	a	DET
ejpam-6640	394	36	such	such	ADJ
ejpam-6640	394	37	that	that	DET
ejpam-6640	394	38	ϕ	ϕ	NOUN
ejpam-6640	394	39	◦	◦	NOUN
ejpam-6640	394	40	f	f	X
ejpam-6640	394	41	=	=	SYM
ejpam-6640	394	42	f∗(ϕ	f∗(ϕ	PROPN
ejpam-6640	394	43	)	)	PUNCT
ejpam-6640	394	44	=	=	VERB
ejpam-6640	395	1	h.	h.	NOUN
ejpam-6640	395	2	this	this	PRON
ejpam-6640	395	3	means	mean	VERB
ejpam-6640	395	4	the	the	DET
ejpam-6640	395	5	following	follow	VERB
ejpam-6640	395	6	diagram	diagram	NOUN
ejpam-6640	395	7	commutes	commute	NOUN
ejpam-6640	395	8	:	:	PUNCT
ejpam-6640	395	9	x	x	SYM
ejpam-6640	395	10	0	0	PUNCT
ejpam-6640	395	11	//	//	NUM
ejpam-6640	396	1	y	y	NOUN
ejpam-6640	396	2	h	h	NOUN
ejpam-6640	397	1	oo	oo	INTJ
ejpam-6640	397	2	f	f	PROPN
ejpam-6640	398	1	//	//	PROPN
ejpam-6640	398	2	z	z	PROPN
ejpam-6640	398	3	ϕ	ϕ	PROPN
ejpam-6640	398	4	`	`	PUNCT
ejpam-6640	398	5	`	`	PUNCT
ejpam-6640	398	6	hence	hence	ADV
ejpam-6640	398	7	,	,	PUNCT
ejpam-6640	398	8	x	x	PRON
ejpam-6640	398	9	is	be	AUX
ejpam-6640	398	10	an	an	DET
ejpam-6640	398	11	injective	injective	ADJ
ejpam-6640	398	12	object	object	NOUN
ejpam-6640	398	13	in	in	ADP
ejpam-6640	398	14	a	a	PRON
ejpam-6640	398	15	.	.	PUNCT
ejpam-6640	399	1	thus	thus	ADV
ejpam-6640	399	2	,	,	PUNCT
ejpam-6640	399	3	homa	homa	NOUN
ejpam-6640	399	4	(	(	PUNCT
ejpam-6640	399	5	−	−	PROPN
ejpam-6640	399	6	,	,	PUNCT
ejpam-6640	399	7	x	x	NOUN
ejpam-6640	399	8	)	)	PUNCT
ejpam-6640	399	9	:	:	PUNCT
ejpam-6640	399	10	a	a	DET
ejpam-6640	399	11	−→	−→	NOUN
ejpam-6640	399	12	ab	ab	PROPN
ejpam-6640	399	13	is	be	AUX
ejpam-6640	399	14	an	an	DET
ejpam-6640	399	15	exact	exact	ADJ
ejpam-6640	399	16	functor	functor	NOUN
ejpam-6640	399	17	if	if	SCONJ
ejpam-6640	399	18	and	and	CCONJ
ejpam-6640	399	19	only	only	ADV
ejpam-6640	399	20	if	if	SCONJ
ejpam-6640	399	21	x	x	PRON
ejpam-6640	399	22	is	be	AUX
ejpam-6640	399	23	an	an	DET
ejpam-6640	399	24	injective	injective	ADJ
ejpam-6640	399	25	object	object	NOUN
ejpam-6640	399	26	in	in	ADP
ejpam-6640	399	27	a	a	PRON
ejpam-6640	399	28	.	.	NOUN
ejpam-6640	400	1	3	3	X
ejpam-6640	400	2	.	.	X
ejpam-6640	400	3	exactness	exactness	NOUN
ejpam-6640	400	4	of	of	ADP
ejpam-6640	400	5	functors	functors	PROPN
ejpam-6640	400	6	homcomp(a	homcomp(a	PROPN
ejpam-6640	400	7	)	)	PUNCT
ejpam-6640	400	8	(	(	PUNCT
ejpam-6640	400	9	x,−	x,−	PROPN
ejpam-6640	400	10	)	)	PUNCT
ejpam-6640	400	11	and	and	CCONJ
ejpam-6640	400	12	homcomp(a	homcomp(a	NOUN
ejpam-6640	400	13	)	)	PUNCT
ejpam-6640	400	14	(	(	PUNCT
ejpam-6640	400	15	−	−	PROPN
ejpam-6640	400	16	,	,	PUNCT
ejpam-6640	400	17	x	x	X
ejpam-6640	400	18	)	)	PUNCT
ejpam-6640	400	19	let	let	VERB
ejpam-6640	400	20	a	a	PRON
ejpam-6640	400	21	be	be	AUX
ejpam-6640	400	22	a	a	DET
ejpam-6640	400	23	balanced	balanced	ADJ
ejpam-6640	400	24	abelian	abelian	ADJ
ejpam-6640	400	25	category	category	NOUN
ejpam-6640	400	26	and	and	CCONJ
ejpam-6640	400	27	x	x	SYM
ejpam-6640	400	28	an	an	DET
ejpam-6640	400	29	object	object	NOUN
ejpam-6640	400	30	in	in	ADP
ejpam-6640	400	31	a	a	PRON
ejpam-6640	400	32	.	.	PUNCT
ejpam-6640	401	1	then	then	ADV
ejpam-6640	401	2	:	:	PUNCT
ejpam-6640	401	3	[	[	X
ejpam-6640	401	4	label=.]the	label=.]the	NOUN
ejpam-6640	401	5	functor	functor	PROPN
ejpam-6640	401	6	homcomp(a	homcomp(a	PROPN
ejpam-6640	401	7	)	)	PUNCT
ejpam-6640	401	8	(	(	PUNCT
ejpam-6640	401	9	x,−	x,−	PROPN
ejpam-6640	401	10	)	)	PUNCT
ejpam-6640	401	11	:	:	PUNCT
ejpam-6640	401	12	comp(a	comp(a	NOUN
ejpam-6640	401	13	)	)	PUNCT
ejpam-6640	401	14	→	→	SYM
ejpam-6640	401	15	comp(ab	comp(ab	NOUN
ejpam-6640	401	16	)	)	PUNCT
ejpam-6640	401	17	is	be	AUX
ejpam-6640	401	18	a	a	DET
ejpam-6640	401	19	covariant	covariant	NOUN
ejpam-6640	401	20	,	,	PUNCT
ejpam-6640	401	21	additive	additive	NOUN
ejpam-6640	401	22	,	,	PUNCT
ejpam-6640	401	23	and	and	CCONJ
ejpam-6640	401	24	left	left	ADJ
ejpam-6640	401	25	-	-	PUNCT
ejpam-6640	401	26	exact	exact	NOUN
ejpam-6640	401	27	functor	functor	NOUN
ejpam-6640	401	28	.	.	PUNCT
ejpam-6640	402	1	the	the	DET
ejpam-6640	402	2	functor	functor	PROPN
ejpam-6640	402	3	homcomp(a	homcomp(a	PROPN
ejpam-6640	402	4	)	)	PUNCT
ejpam-6640	402	5	(	(	PUNCT
ejpam-6640	402	6	x,−	x,−	PROPN
ejpam-6640	402	7	)	)	PUNCT
ejpam-6640	402	8	:	:	PUNCT
ejpam-6640	402	9	comp(a	comp(a	NOUN
ejpam-6640	402	10	)	)	PUNCT
ejpam-6640	402	11	→	→	SYM
ejpam-6640	402	12	comp(ab	comp(ab	NOUN
ejpam-6640	402	13	)	)	PUNCT
ejpam-6640	402	14	is	be	AUX
ejpam-6640	402	15	exact	exact	ADJ
ejpam-6640	402	16	if	if	SCONJ
ejpam-6640	403	1	and	and	CCONJ
ejpam-6640	403	2	only	only	ADV
ejpam-6640	403	3	if	if	SCONJ
ejpam-6640	403	4	x	x	PRON
ejpam-6640	403	5	is	be	AUX
ejpam-6640	403	6	a	a	DET
ejpam-6640	403	7	projective	projective	ADJ
ejpam-6640	403	8	object	object	NOUN
ejpam-6640	403	9	in	in	ADP
ejpam-6640	403	10	a	a	PRON
ejpam-6640	403	11	.	.	PUNCT
ejpam-6640	404	1	proof	proof	NOUN
ejpam-6640	404	2	.	.	PUNCT
ejpam-6640	405	1	[	[	X
ejpam-6640	405	2	label=.]let	label=.]let	NOUN
ejpam-6640	405	3	us	we	PRON
ejpam-6640	405	4	show	show	VERB
ejpam-6640	405	5	that	that	SCONJ
ejpam-6640	405	6	the	the	DET
ejpam-6640	405	7	functor	functor	PROPN
ejpam-6640	405	8	homcomp(a	homcomp(a	PROPN
ejpam-6640	405	9	)	)	PUNCT
ejpam-6640	405	10	(	(	PUNCT
ejpam-6640	405	11	x,−	x,−	PROPN
ejpam-6640	405	12	)	)	PUNCT
ejpam-6640	405	13	:	:	PUNCT
ejpam-6640	405	14	comp(a	comp(a	NOUN
ejpam-6640	405	15	)	)	PUNCT
ejpam-6640	405	16	→	→	SYM
ejpam-6640	405	17	comp(ab	comp(ab	NOUN
ejpam-6640	405	18	)	)	PUNCT
ejpam-6640	405	19	is	be	AUX
ejpam-6640	405	20	covariant	covariant	ADJ
ejpam-6640	405	21	,	,	PUNCT
ejpam-6640	405	22	additive	additive	NOUN
ejpam-6640	405	23	,	,	PUNCT
ejpam-6640	405	24	and	and	CCONJ
ejpam-6640	405	25	left	left	ADJ
ejpam-6640	405	26	-	-	PUNCT
ejpam-6640	405	27	exact	exact	ADJ
ejpam-6640	405	28	.	.	PUNCT
ejpam-6640	406	1	it	it	PRON
ejpam-6640	406	2	is	be	AUX
ejpam-6640	406	3	evident	evident	ADJ
ejpam-6640	406	4	that	that	SCONJ
ejpam-6640	406	5	homcomp(a	homcomp(a	NOUN
ejpam-6640	406	6	)	)	PUNCT
ejpam-6640	406	7	(	(	PUNCT
ejpam-6640	406	8	x,−	x,−	PROPN
ejpam-6640	406	9	)	)	PUNCT
ejpam-6640	406	10	is	be	AUX
ejpam-6640	406	11	covariant	covariant	ADJ
ejpam-6640	406	12	and	and	CCONJ
ejpam-6640	406	13	additive	additive	NOUN
ejpam-6640	406	14	.	.	PUNCT
ejpam-6640	407	1	let	let	VERB
ejpam-6640	407	2	us	we	PRON
ejpam-6640	407	3	show	show	VERB
ejpam-6640	407	4	that	that	SCONJ
ejpam-6640	407	5	the	the	DET
ejpam-6640	407	6	functor	functor	PROPN
ejpam-6640	407	7	homcomp(a	homcomp(a	PROPN
ejpam-6640	407	8	)	)	PUNCT
ejpam-6640	407	9	(	(	PUNCT
ejpam-6640	407	10	x,−	x,−	PROPN
ejpam-6640	407	11	)	)	PUNCT
ejpam-6640	407	12	:	:	PUNCT
ejpam-6640	407	13	comp(a	comp(a	NOUN
ejpam-6640	407	14	)	)	PUNCT
ejpam-6640	407	15	→	→	SYM
ejpam-6640	407	16	comp(ab	comp(ab	NOUN
ejpam-6640	407	17	)	)	PUNCT
ejpam-6640	407	18	is	be	AUX
ejpam-6640	407	19	left	leave	VERB
ejpam-6640	407	20	-	-	PUNCT
ejpam-6640	407	21	exact	exact	ADJ
ejpam-6640	407	22	.	.	PUNCT
ejpam-6640	408	1	consider	consider	VERB
ejpam-6640	408	2	the	the	DET
ejpam-6640	408	3	left	left	ADJ
ejpam-6640	408	4	short	short	ADJ
ejpam-6640	408	5	exact	exact	ADJ
ejpam-6640	408	6	sequence	sequence	NOUN
ejpam-6640	408	7	of	of	ADP
ejpam-6640	408	8	morphisms	morphism	NOUN
ejpam-6640	408	9	in	in	ADP
ejpam-6640	408	10	comp(a	comp(a	NOUN
ejpam-6640	408	11	):	):	PUNCT
ejpam-6640	408	12	(	(	PUNCT
ejpam-6640	408	13	0	0	NUM
ejpam-6640	408	14	)	)	PUNCT
ejpam-6640	408	15	//	//	NOUN
ejpam-6640	409	1	(	(	PUNCT
ejpam-6640	409	2	y	y	PROPN
ejpam-6640	409	3	,	,	PUNCT
ejpam-6640	409	4	α	α	NOUN
ejpam-6640	409	5	)	)	PUNCT
ejpam-6640	409	6	f	f	PROPN
ejpam-6640	409	7	//	//	X
ejpam-6640	409	8	(	(	PUNCT
ejpam-6640	409	9	z	z	NOUN
ejpam-6640	409	10	,	,	PUNCT
ejpam-6640	409	11	β	β	NOUN
ejpam-6640	409	12	)	)	PUNCT
ejpam-6640	409	13	g	g	PROPN
ejpam-6640	409	14	//	//	SYM
ejpam-6640	409	15	(	(	PUNCT
ejpam-6640	409	16	t	t	PROPN
ejpam-6640	409	17	,	,	PUNCT
ejpam-6640	409	18	θ	θ	PROPN
ejpam-6640	409	19	)	)	PUNCT
ejpam-6640	409	20	where	where	SCONJ
ejpam-6640	409	21	a	a	PRON
ejpam-6640	409	22	is	be	AUX
ejpam-6640	409	23	a	a	DET
ejpam-6640	409	24	balanced	balanced	ADJ
ejpam-6640	409	25	abelian	abelian	ADJ
ejpam-6640	409	26	category	category	NOUN
ejpam-6640	409	27	.	.	PUNCT
ejpam-6640	410	1	we	we	PRON
ejpam-6640	410	2	must	must	AUX
ejpam-6640	410	3	show	show	VERB
ejpam-6640	410	4	that	that	SCONJ
ejpam-6640	410	5	homcomp(a	homcomp(a	NOUN
ejpam-6640	410	6	)	)	PUNCT
ejpam-6640	410	7	(	(	PUNCT
ejpam-6640	410	8	x,−)((0	x,−)((0	PROPN
ejpam-6640	410	9	)	)	PUNCT
ejpam-6640	410	10	)	)	PUNCT
ejpam-6640	411	1	//	//	PUNCT
ejpam-6640	411	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	411	3	)	)	PUNCT
ejpam-6640	411	4	(	(	PUNCT
ejpam-6640	411	5	x,−)((y	x,−)((y	PROPN
ejpam-6640	411	6	,	,	PUNCT
ejpam-6640	411	7	α	α	NOUN
ejpam-6640	411	8	)	)	PUNCT
ejpam-6640	411	9	)	)	PUNCT
ejpam-6640	411	10	f∗	f∗	NOUN
ejpam-6640	411	11	//	//	X
ejpam-6640	411	12	homcomp(a	homcomp(a	NOUN
ejpam-6640	411	13	)	)	PUNCT
ejpam-6640	411	14	(	(	PUNCT
ejpam-6640	411	15	x,−)((z	x,−)((z	PROPN
ejpam-6640	411	16	,	,	PUNCT
ejpam-6640	411	17	β	β	NOUN
ejpam-6640	411	18	)	)	PUNCT
ejpam-6640	411	19	)	)	PUNCT
ejpam-6640	411	20	g∗	g∗	VERB
ejpam-6640	411	21	//	//	NUM
ejpam-6640	411	22	homcomp(a	homcomp(a	NOUN
ejpam-6640	411	23	)	)	PUNCT
ejpam-6640	411	24	(	(	PUNCT
ejpam-6640	411	25	x,−)((t	x,−)((t	PROPN
ejpam-6640	411	26	,	,	PUNCT
ejpam-6640	411	27	θ	θ	NOUN
ejpam-6640	411	28	)	)	PUNCT
ejpam-6640	411	29	)	)	PUNCT
ejpam-6640	411	30	a.	a.	PROPN
ejpam-6640	411	31	diallo	diallo	PROPN
ejpam-6640	411	32	,	,	PUNCT
ejpam-6640	411	33	m.	m.	PROPN
ejpam-6640	411	34	b.	b.	PROPN
ejpam-6640	411	35	f.	f.	PROPN
ejpam-6640	411	36	b.	b.	PROPN
ejpam-6640	411	37	maaouia	maaouia	PROPN
ejpam-6640	411	38	,	,	PUNCT
ejpam-6640	411	39	m.	m.	NOUN
ejpam-6640	411	40	sanghare	sanghare	PROPN
ejpam-6640	411	41	/	/	SYM
ejpam-6640	411	42	eur	eur	PROPN
ejpam-6640	411	43	.	.	PUNCT
ejpam-6640	412	1	j.	j.	PROPN
ejpam-6640	412	2	pure	pure	PROPN
ejpam-6640	412	3	appl	appl	PROPN
ejpam-6640	412	4	.	.	PROPN
ejpam-6640	412	5	math	math	PROPN
ejpam-6640	412	6	,	,	PUNCT
ejpam-6640	412	7	18	18	NUM
ejpam-6640	412	8	(	(	PUNCT
ejpam-6640	412	9	4	4	NUM
ejpam-6640	412	10	)	)	PUNCT
ejpam-6640	412	11	(	(	PUNCT
ejpam-6640	412	12	2025	2025	NUM
ejpam-6640	412	13	)	)	PUNCT
ejpam-6640	412	14	,	,	PUNCT
ejpam-6640	412	15	6640	6640	NUM
ejpam-6640	412	16	17	17	NUM
ejpam-6640	412	17	of	of	ADP
ejpam-6640	412	18	28	28	NUM
ejpam-6640	412	19	is	be	AUX
ejpam-6640	412	20	a	a	DET
ejpam-6640	412	21	left	left	ADJ
ejpam-6640	412	22	short	short	ADJ
ejpam-6640	412	23	exact	exact	ADJ
ejpam-6640	412	24	sequence	sequence	NOUN
ejpam-6640	412	25	of	of	ADP
ejpam-6640	412	26	morphisms	morphism	NOUN
ejpam-6640	412	27	in	in	ADP
ejpam-6640	412	28	comp(ab	comp(ab	NOUN
ejpam-6640	412	29	)	)	PUNCT
ejpam-6640	412	30	.	.	PUNCT
ejpam-6640	413	1	we	we	PRON
ejpam-6640	413	2	have	have	VERB
ejpam-6640	413	3	the	the	DET
ejpam-6640	413	4	following	follow	VERB
ejpam-6640	413	5	diagram	diagram	NOUN
ejpam-6640	413	6	:	:	PUNCT
ejpam-6640	413	7	homcomp(a	homcomp(a	NOUN
ejpam-6640	413	8	)	)	PUNCT
ejpam-6640	413	9	(	(	PUNCT
ejpam-6640	413	10	x,−)((0	x,−)((0	PROPN
ejpam-6640	413	11	)	)	PUNCT
ejpam-6640	413	12	)	)	PUNCT
ejpam-6640	413	13	:	:	PUNCT
ejpam-6640	413	14	...	...	PUNCT
ejpam-6640	414	1	//	//	PUNCT
ejpam-6640	414	2	�	�	PROPN
ejpam-6640	414	3	�	�	PROPN
ejpam-6640	414	4	0homcomp(a	0homcomp(a	NUM
ejpam-6640	414	5	)	)	PUNCT
ejpam-6640	414	6	(	(	PUNCT
ejpam-6640	414	7	x,0	x,0	PROPN
ejpam-6640	414	8	)	)	PUNCT
ejpam-6640	414	9	//	//	SYM
ejpam-6640	414	10	�	�	PROPN
ejpam-6640	414	11	�	�	PROPN
ejpam-6640	414	12	0homcomp(a	0homcomp(a	NUM
ejpam-6640	414	13	)	)	PUNCT
ejpam-6640	414	14	(	(	PUNCT
ejpam-6640	414	15	x,0	x,0	PROPN
ejpam-6640	414	16	)	)	PUNCT
ejpam-6640	414	17	//	//	SYM
ejpam-6640	414	18	�	�	PROPN
ejpam-6640	414	19	�	�	PROPN
ejpam-6640	414	20	0homcomp(a	0homcomp(a	NUM
ejpam-6640	414	21	)	)	PUNCT
ejpam-6640	414	22	(	(	PUNCT
ejpam-6640	414	23	x,0	x,0	PROPN
ejpam-6640	414	24	)	)	PUNCT
ejpam-6640	414	25	//	//	SYM
ejpam-6640	414	26	�	�	PROPN
ejpam-6640	414	27	�	�	PROPN
ejpam-6640	414	28	...	...	PUNCT
ejpam-6640	414	29	homcomp(a	homcomp(a	NOUN
ejpam-6640	414	30	)	)	PUNCT
ejpam-6640	414	31	(	(	PUNCT
ejpam-6640	414	32	x,−)((y	x,−)((y	PROPN
ejpam-6640	414	33	,	,	PUNCT
ejpam-6640	414	34	α	α	NOUN
ejpam-6640	414	35	)	)	PUNCT
ejpam-6640	414	36	)	)	PUNCT
ejpam-6640	414	37	:	:	PUNCT
ejpam-6640	414	38	...	...	PUNCT
ejpam-6640	415	1	//	//	NUM
ejpam-6640	415	2	f∗	f∗	X
ejpam-6640	415	3	�	�	PROPN
ejpam-6640	415	4	�	�	PROPN
ejpam-6640	415	5	homcomp(a	homcomp(a	PROPN
ejpam-6640	415	6	)	)	PUNCT
ejpam-6640	415	7	(	(	PUNCT
ejpam-6640	415	8	x	x	X
ejpam-6640	415	9	,	,	PUNCT
ejpam-6640	415	10	yn	yn	NOUN
ejpam-6640	415	11	)	)	PUNCT
ejpam-6640	415	12	α∗	α∗	VERB
ejpam-6640	415	13	n//	n//	PRON
ejpam-6640	415	14	f∗	f∗	NOUN
ejpam-6640	415	15	n	n	PROPN
ejpam-6640	415	16	�	�	PROPN
ejpam-6640	415	17	�	�	PROPN
ejpam-6640	415	18	homcomp(a	homcomp(a	PROPN
ejpam-6640	415	19	)	)	PUNCT
ejpam-6640	415	20	(	(	PUNCT
ejpam-6640	415	21	x	x	X
ejpam-6640	415	22	,	,	PUNCT
ejpam-6640	415	23	yn+1	yn+1	X
ejpam-6640	415	24	)	)	PUNCT
ejpam-6640	415	25	α∗	α∗	VERB
ejpam-6640	415	26	n+1	n+1	PROPN
ejpam-6640	415	27	//	//	NUM
ejpam-6640	415	28	f∗	f∗	PROPN
ejpam-6640	415	29	n+1	n+1	PROPN
ejpam-6640	415	30	�	�	PROPN
ejpam-6640	415	31	�	�	PROPN
ejpam-6640	415	32	homcomp(a	homcomp(a	PROPN
ejpam-6640	415	33	)	)	PUNCT
ejpam-6640	415	34	(	(	PUNCT
ejpam-6640	415	35	x	x	NOUN
ejpam-6640	415	36	,	,	PUNCT
ejpam-6640	415	37	yn+2	yn+2	NUM
ejpam-6640	415	38	)	)	PUNCT
ejpam-6640	415	39	//	//	NOUN
ejpam-6640	416	1	f∗	f∗	PROPN
ejpam-6640	416	2	n+2	n+2	NUM
ejpam-6640	416	3	�	�	PROPN
ejpam-6640	416	4	�	�	PROPN
ejpam-6640	416	5	...	...	PUNCT
ejpam-6640	416	6	homcomp(a	homcomp(a	NOUN
ejpam-6640	416	7	)	)	PUNCT
ejpam-6640	416	8	(	(	PUNCT
ejpam-6640	416	9	x,−)((z	x,−)((z	PROPN
ejpam-6640	416	10	,	,	PUNCT
ejpam-6640	416	11	β	β	NOUN
ejpam-6640	416	12	)	)	PUNCT
ejpam-6640	416	13	)	)	PUNCT
ejpam-6640	416	14	:	:	PUNCT
ejpam-6640	416	15	...	...	PUNCT
ejpam-6640	417	1	//	//	PUNCT
ejpam-6640	417	2	g∗	g∗	PROPN
ejpam-6640	417	3	�	�	PROPN
ejpam-6640	417	4	�	�	PROPN
ejpam-6640	417	5	homcomp(a	homcomp(a	PROPN
ejpam-6640	417	6	)	)	PUNCT
ejpam-6640	417	7	(	(	PUNCT
ejpam-6640	417	8	x	x	X
ejpam-6640	417	9	,	,	PUNCT
ejpam-6640	417	10	zn	zn	NOUN
ejpam-6640	417	11	)	)	PUNCT
ejpam-6640	417	12	β∗	β∗	NOUN
ejpam-6640	417	13	n//	n//	PRON
ejpam-6640	417	14	g∗	g∗	VERB
ejpam-6640	417	15	n	n	PRON
ejpam-6640	417	16	�	�	PROPN
ejpam-6640	417	17	�	�	PROPN
ejpam-6640	417	18	homcomp(a	homcomp(a	PROPN
ejpam-6640	417	19	)	)	PUNCT
ejpam-6640	417	20	(	(	PUNCT
ejpam-6640	417	21	x	x	NOUN
ejpam-6640	417	22	,	,	PUNCT
ejpam-6640	417	23	zn+1	zn+1	X
ejpam-6640	417	24	)	)	PUNCT
ejpam-6640	417	25	β∗	β∗	NOUN
ejpam-6640	417	26	n+1	n+1	PROPN
ejpam-6640	417	27	//	//	PUNCT
ejpam-6640	417	28	g∗	g∗	PROPN
ejpam-6640	417	29	n+1	n+1	PROPN
ejpam-6640	417	30	�	�	PROPN
ejpam-6640	417	31	�	�	PROPN
ejpam-6640	417	32	homcomp(a	homcomp(a	PROPN
ejpam-6640	417	33	)	)	PUNCT
ejpam-6640	417	34	(	(	PUNCT
ejpam-6640	417	35	x	x	X
ejpam-6640	417	36	,	,	PUNCT
ejpam-6640	417	37	zn+2	zn+2	NUM
ejpam-6640	417	38	)	)	PUNCT
ejpam-6640	417	39	g∗	g∗	VERB
ejpam-6640	417	40	n+2	n+2	NUM
ejpam-6640	417	41	�	�	PROPN
ejpam-6640	417	42	�	�	PROPN
ejpam-6640	417	43	//	//	NUM
ejpam-6640	417	44	...	...	PUNCT
ejpam-6640	418	1	homcomp(a	homcomp(a	NOUN
ejpam-6640	418	2	)	)	PUNCT
ejpam-6640	418	3	(	(	PUNCT
ejpam-6640	418	4	x,−)((t	x,−)((t	PROPN
ejpam-6640	418	5	,	,	PUNCT
ejpam-6640	418	6	θ	θ	NOUN
ejpam-6640	418	7	)	)	PUNCT
ejpam-6640	418	8	)	)	PUNCT
ejpam-6640	418	9	:	:	PUNCT
ejpam-6640	418	10	...	...	PUNCT
ejpam-6640	419	1	//	//	PUNCT
ejpam-6640	419	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	419	3	)	)	PUNCT
ejpam-6640	419	4	(	(	PUNCT
ejpam-6640	419	5	x	x	NOUN
ejpam-6640	419	6	,	,	PUNCT
ejpam-6640	419	7	tn	tn	PROPN
ejpam-6640	419	8	)	)	PUNCT
ejpam-6640	419	9	θ∗	θ∗	NOUN
ejpam-6640	419	10	n//	n//	PROPN
ejpam-6640	419	11	homcomp(a	homcomp(a	NOUN
ejpam-6640	419	12	)	)	PUNCT
ejpam-6640	419	13	(	(	PUNCT
ejpam-6640	419	14	x	x	NOUN
ejpam-6640	419	15	,	,	PUNCT
ejpam-6640	419	16	tn+1	tn+1	NOUN
ejpam-6640	419	17	)	)	PUNCT
ejpam-6640	419	18	θ∗	θ∗	NOUN
ejpam-6640	419	19	n+1	n+1	PROPN
ejpam-6640	419	20	//	//	NUM
ejpam-6640	419	21	homcomp(a	homcomp(a	NOUN
ejpam-6640	419	22	)	)	PUNCT
ejpam-6640	419	23	(	(	PUNCT
ejpam-6640	419	24	x	x	NOUN
ejpam-6640	419	25	,	,	PUNCT
ejpam-6640	419	26	tn+2	tn+2	NUM
ejpam-6640	419	27	)	)	PUNCT
ejpam-6640	419	28	//	//	NOUN
ejpam-6640	419	29	...	...	PUNCT
ejpam-6640	419	30	by	by	ADP
ejpam-6640	419	31	theorem	theorem	NOUN
ejpam-6640	419	32	2	2	NUM
ejpam-6640	419	33	,	,	PUNCT
ejpam-6640	419	34	for	for	ADP
ejpam-6640	419	35	every	every	DET
ejpam-6640	419	36	integer	integer	NOUN
ejpam-6640	419	37	n	n	PROPN
ejpam-6640	419	38	∈	∈	PROPN
ejpam-6640	419	39	z	z	PROPN
ejpam-6640	419	40	,	,	PUNCT
ejpam-6640	419	41	the	the	DET
ejpam-6640	419	42	sequence	sequence	NOUN
ejpam-6640	419	43	0homcomp(a	0homcomp(a	NUM
ejpam-6640	419	44	)	)	PUNCT
ejpam-6640	419	45	(	(	PUNCT
ejpam-6640	419	46	x,0	x,0	PROPN
ejpam-6640	419	47	)	)	PUNCT
ejpam-6640	420	1	//	//	PROPN
ejpam-6640	420	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	420	3	)	)	PUNCT
ejpam-6640	420	4	(	(	PUNCT
ejpam-6640	420	5	x	x	X
ejpam-6640	420	6	,	,	PUNCT
ejpam-6640	420	7	yn	yn	PROPN
ejpam-6640	420	8	)	)	PUNCT
ejpam-6640	420	9	homa	homa	NOUN
ejpam-6640	420	10	(	(	PUNCT
ejpam-6640	420	11	x	x	X
ejpam-6640	420	12	,	,	PUNCT
ejpam-6640	420	13	f)=f∗	f)=f∗	ADV
ejpam-6640	420	14	n//	n//	PROPN
ejpam-6640	420	15	homcomp(a	homcomp(a	NOUN
ejpam-6640	420	16	)	)	PUNCT
ejpam-6640	420	17	(	(	PUNCT
ejpam-6640	420	18	x	x	X
ejpam-6640	420	19	,	,	PUNCT
ejpam-6640	420	20	zn	zn	NOUN
ejpam-6640	420	21	)	)	PUNCT
ejpam-6640	420	22	homa	homa	NOUN
ejpam-6640	420	23	(	(	PUNCT
ejpam-6640	420	24	x	x	NOUN
ejpam-6640	420	25	,	,	PUNCT
ejpam-6640	420	26	g)=g∗	g)=g∗	VERB
ejpam-6640	420	27	n//	n//	PROPN
ejpam-6640	420	28	homcomp(a	homcomp(a	NOUN
ejpam-6640	420	29	)	)	PUNCT
ejpam-6640	420	30	(	(	PUNCT
ejpam-6640	420	31	x	x	X
ejpam-6640	420	32	,	,	PUNCT
ejpam-6640	420	33	tn	tn	PROPN
ejpam-6640	420	34	)	)	PUNCT
ejpam-6640	420	35	is	be	AUX
ejpam-6640	420	36	a	a	DET
ejpam-6640	420	37	left	left	ADJ
ejpam-6640	420	38	short	short	ADJ
ejpam-6640	420	39	exact	exact	ADJ
ejpam-6640	420	40	sequence	sequence	NOUN
ejpam-6640	420	41	of	of	ADP
ejpam-6640	420	42	morphisms	morphism	NOUN
ejpam-6640	420	43	in	in	ADP
ejpam-6640	420	44	comp(ab	comp(ab	NOUN
ejpam-6640	420	45	)	)	PUNCT
ejpam-6640	420	46	.	.	PUNCT
ejpam-6640	421	1	hence	hence	ADV
ejpam-6640	421	2	,	,	PUNCT
ejpam-6640	421	3	homcomp(a	homcomp(a	NOUN
ejpam-6640	421	4	)	)	PUNCT
ejpam-6640	421	5	(	(	PUNCT
ejpam-6640	421	6	x,−)((0	x,−)((0	PROPN
ejpam-6640	421	7	)	)	PUNCT
ejpam-6640	421	8	)	)	PUNCT
ejpam-6640	422	1	//	//	PUNCT
ejpam-6640	422	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	422	3	)	)	PUNCT
ejpam-6640	422	4	(	(	PUNCT
ejpam-6640	422	5	x,−)((y	x,−)((y	PROPN
ejpam-6640	422	6	,	,	PUNCT
ejpam-6640	422	7	α	α	NOUN
ejpam-6640	422	8	)	)	PUNCT
ejpam-6640	422	9	)	)	PUNCT
ejpam-6640	423	1	f	f	PROPN
ejpam-6640	423	2	//	//	NUM
ejpam-6640	423	3	homcomp(a	homcomp(a	PROPN
ejpam-6640	423	4	)	)	PUNCT
ejpam-6640	423	5	(	(	PUNCT
ejpam-6640	423	6	x,−)((z	x,−)((z	PROPN
ejpam-6640	423	7	,	,	PUNCT
ejpam-6640	423	8	β	β	NOUN
ejpam-6640	423	9	)	)	PUNCT
ejpam-6640	423	10	)	)	PUNCT
ejpam-6640	424	1	g	g	NOUN
ejpam-6640	424	2	//	//	NUM
ejpam-6640	424	3	homcomp(a	homcomp(a	NOUN
ejpam-6640	424	4	)	)	PUNCT
ejpam-6640	424	5	(	(	PUNCT
ejpam-6640	424	6	x,−)((t	x,−)((t	PROPN
ejpam-6640	424	7	,	,	PUNCT
ejpam-6640	424	8	θ	θ	NOUN
ejpam-6640	424	9	)	)	PUNCT
ejpam-6640	424	10	)	)	PUNCT
ejpam-6640	424	11	is	be	AUX
ejpam-6640	424	12	a	a	DET
ejpam-6640	424	13	left	left	ADJ
ejpam-6640	424	14	short	short	ADJ
ejpam-6640	424	15	exact	exact	ADJ
ejpam-6640	424	16	sequence	sequence	NOUN
ejpam-6640	424	17	of	of	ADP
ejpam-6640	424	18	morphisms	morphism	NOUN
ejpam-6640	424	19	in	in	ADP
ejpam-6640	424	20	comp(ab	comp(ab	NOUN
ejpam-6640	424	21	)	)	PUNCT
ejpam-6640	424	22	.	.	PUNCT
ejpam-6640	425	1	items	item	NOUN
ejpam-6640	425	2	i.a	i.a	PROPN
ejpam-6640	425	3	and	and	CCONJ
ejpam-6640	425	4	i.b	i.b	PROPN
ejpam-6640	425	5	imply	imply	VERB
ejpam-6640	425	6	that	that	SCONJ
ejpam-6640	425	7	the	the	DET
ejpam-6640	425	8	functor	functor	PROPN
ejpam-6640	425	9	homcomp(a	homcomp(a	PROPN
ejpam-6640	425	10	)	)	PUNCT
ejpam-6640	425	11	(	(	PUNCT
ejpam-6640	425	12	x,−	x,−	PROPN
ejpam-6640	425	13	)	)	PUNCT
ejpam-6640	425	14	:	:	PUNCT
ejpam-6640	425	15	comp(a	comp(a	NOUN
ejpam-6640	425	16	)	)	PUNCT
ejpam-6640	425	17	→	→	SYM
ejpam-6640	425	18	comp(ab	comp(ab	NOUN
ejpam-6640	425	19	)	)	PUNCT
ejpam-6640	425	20	is	be	AUX
ejpam-6640	425	21	covariant	covariant	ADJ
ejpam-6640	425	22	,	,	PUNCT
ejpam-6640	425	23	additive	additive	NOUN
ejpam-6640	425	24	,	,	PUNCT
ejpam-6640	425	25	and	and	CCONJ
ejpam-6640	425	26	left	left	ADJ
ejpam-6640	425	27	-	-	PUNCT
ejpam-6640	425	28	exact	exact	ADJ
ejpam-6640	425	29	.	.	PUNCT
ejpam-6640	426	1	let	let	VERB
ejpam-6640	426	2	us	we	PRON
ejpam-6640	426	3	show	show	VERB
ejpam-6640	426	4	that	that	SCONJ
ejpam-6640	426	5	the	the	DET
ejpam-6640	426	6	functor	functor	PROPN
ejpam-6640	426	7	homcomp(a	homcomp(a	PROPN
ejpam-6640	426	8	)	)	PUNCT
ejpam-6640	426	9	(	(	PUNCT
ejpam-6640	426	10	x,−	x,−	PROPN
ejpam-6640	426	11	)	)	PUNCT
ejpam-6640	426	12	:	:	PUNCT
ejpam-6640	426	13	comp(a	comp(a	NOUN
ejpam-6640	426	14	)	)	PUNCT
ejpam-6640	426	15	→	→	SYM
ejpam-6640	426	16	comp(ab	comp(ab	NOUN
ejpam-6640	426	17	)	)	PUNCT
ejpam-6640	426	18	is	be	AUX
ejpam-6640	426	19	exact	exact	ADJ
ejpam-6640	426	20	if	if	SCONJ
ejpam-6640	426	21	and	and	CCONJ
ejpam-6640	426	22	only	only	ADV
ejpam-6640	426	23	ifx	ifx	PROPN
ejpam-6640	426	24	is	be	AUX
ejpam-6640	426	25	a	a	DET
ejpam-6640	426	26	projective	projective	ADJ
ejpam-6640	426	27	object	object	NOUN
ejpam-6640	426	28	in	in	ADP
ejpam-6640	426	29	a	a	PRON
ejpam-6640	426	30	.	.	PUNCT
ejpam-6640	426	31	suppose	suppose	VERB
ejpam-6640	426	32	that	that	SCONJ
ejpam-6640	426	33	the	the	DET
ejpam-6640	426	34	functor	functor	PROPN
ejpam-6640	426	35	homcomp(a	homcomp(a	PROPN
ejpam-6640	426	36	)	)	PUNCT
ejpam-6640	426	37	(	(	PUNCT
ejpam-6640	426	38	x,−	x,−	PROPN
ejpam-6640	426	39	)	)	PUNCT
ejpam-6640	426	40	:	:	PUNCT
ejpam-6640	426	41	comp(a	comp(a	NOUN
ejpam-6640	426	42	)	)	PUNCT
ejpam-6640	426	43	→	→	SYM
ejpam-6640	426	44	comp(ab	comp(ab	NOUN
ejpam-6640	426	45	)	)	PUNCT
ejpam-6640	426	46	is	be	AUX
ejpam-6640	426	47	exact	exact	ADJ
ejpam-6640	426	48	and	and	CCONJ
ejpam-6640	426	49	show	show	VERB
ejpam-6640	426	50	that	that	SCONJ
ejpam-6640	426	51	x	x	PRON
ejpam-6640	426	52	is	be	AUX
ejpam-6640	426	53	a	a	DET
ejpam-6640	426	54	projective	projective	ADJ
ejpam-6640	426	55	object	object	NOUN
ejpam-6640	426	56	in	in	ADP
ejpam-6640	426	57	a	a	PRON
ejpam-6640	426	58	.	.	PUNCT
ejpam-6640	427	1	we	we	PRON
ejpam-6640	427	2	have	have	VERB
ejpam-6640	427	3	:	:	PUNCT
ejpam-6640	427	4	homcomp(a	homcomp(a	NOUN
ejpam-6640	427	5	)	)	PUNCT
ejpam-6640	427	6	(	(	PUNCT
ejpam-6640	427	7	x,−	x,−	PROPN
ejpam-6640	427	8	)	)	PUNCT
ejpam-6640	427	9	:	:	PUNCT
ejpam-6640	427	10	comp(a	comp(a	NOUN
ejpam-6640	427	11	)	)	PUNCT
ejpam-6640	427	12	→	→	SYM
ejpam-6640	427	13	comp(ab	comp(ab	PROPN
ejpam-6640	427	14	)	)	PUNCT
ejpam-6640	427	15	being	be	AUX
ejpam-6640	427	16	exact	exact	ADJ
ejpam-6640	427	17	implies	imply	VERB
ejpam-6640	427	18	that	that	SCONJ
ejpam-6640	427	19	for	for	ADP
ejpam-6640	427	20	every	every	DET
ejpam-6640	427	21	short	short	ADJ
ejpam-6640	427	22	exact	exact	ADJ
ejpam-6640	427	23	sequence	sequence	NOUN
ejpam-6640	427	24	of	of	ADP
ejpam-6640	427	25	morphisms	morphism	NOUN
ejpam-6640	427	26	in	in	ADP
ejpam-6640	427	27	comp(a	comp(a	NOUN
ejpam-6640	427	28	)	)	PUNCT
ejpam-6640	427	29	,	,	PUNCT
ejpam-6640	427	30	(	(	PUNCT
ejpam-6640	427	31	0	0	NUM
ejpam-6640	427	32	)	)	PUNCT
ejpam-6640	427	33	//	//	NOUN
ejpam-6640	427	34	(	(	PUNCT
ejpam-6640	427	35	y	y	PROPN
ejpam-6640	427	36	,	,	PUNCT
ejpam-6640	427	37	α	α	NOUN
ejpam-6640	427	38	)	)	PUNCT
ejpam-6640	427	39	f	f	PROPN
ejpam-6640	427	40	//	//	X
ejpam-6640	427	41	(	(	PUNCT
ejpam-6640	427	42	z	z	NOUN
ejpam-6640	427	43	,	,	PUNCT
ejpam-6640	427	44	β	β	NOUN
ejpam-6640	427	45	)	)	PUNCT
ejpam-6640	427	46	g	g	PROPN
ejpam-6640	427	47	//	//	SYM
ejpam-6640	427	48	(	(	PUNCT
ejpam-6640	427	49	t	t	PROPN
ejpam-6640	427	50	,	,	PUNCT
ejpam-6640	427	51	θ	θ	PROPN
ejpam-6640	427	52	)	)	PUNCT
ejpam-6640	427	53	//	//	NOUN
ejpam-6640	427	54	(	(	PUNCT
ejpam-6640	427	55	0	0	NUM
ejpam-6640	427	56	)	)	PUNCT
ejpam-6640	427	57	the	the	DET
ejpam-6640	427	58	sequence	sequence	NOUN
ejpam-6640	427	59	homcomp(a	homcomp(a	NOUN
ejpam-6640	427	60	)	)	PUNCT
ejpam-6640	427	61	(	(	PUNCT
ejpam-6640	427	62	x,−)((0	x,−)((0	PROPN
ejpam-6640	427	63	)	)	PUNCT
ejpam-6640	427	64	)	)	PUNCT
ejpam-6640	428	1	//	//	PUNCT
ejpam-6640	428	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	428	3	)	)	PUNCT
ejpam-6640	428	4	(	(	PUNCT
ejpam-6640	428	5	x,−)((y	x,−)((y	PROPN
ejpam-6640	428	6	,	,	PUNCT
ejpam-6640	428	7	α	α	NOUN
ejpam-6640	428	8	)	)	PUNCT
ejpam-6640	428	9	)	)	PUNCT
ejpam-6640	428	10	f∗	f∗	NOUN
ejpam-6640	428	11	//	//	X
ejpam-6640	428	12	homcomp(a	homcomp(a	NOUN
ejpam-6640	428	13	)	)	PUNCT
ejpam-6640	428	14	(	(	PUNCT
ejpam-6640	428	15	x,−)((z	x,−)((z	PROPN
ejpam-6640	428	16	,	,	PUNCT
ejpam-6640	428	17	β	β	NOUN
ejpam-6640	428	18	)	)	PUNCT
ejpam-6640	428	19	)	)	PUNCT
ejpam-6640	428	20	g∗	g∗	VERB
ejpam-6640	428	21	//	//	NUM
ejpam-6640	428	22	homcomp(a	homcomp(a	NOUN
ejpam-6640	428	23	)	)	PUNCT
ejpam-6640	428	24	(	(	PUNCT
ejpam-6640	428	25	x,−)((t	x,−)((t	PROPN
ejpam-6640	428	26	,	,	PUNCT
ejpam-6640	428	27	θ	θ	NOUN
ejpam-6640	428	28	)	)	PUNCT
ejpam-6640	428	29	)	)	PUNCT
ejpam-6640	429	1	//	//	PUNCT
ejpam-6640	429	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	429	3	)	)	PUNCT
ejpam-6640	429	4	(	(	PUNCT
ejpam-6640	429	5	x,−)((0	x,−)((0	PROPN
ejpam-6640	429	6	)	)	PUNCT
ejpam-6640	429	7	)	)	PUNCT
ejpam-6640	429	8	is	be	AUX
ejpam-6640	429	9	a	a	DET
ejpam-6640	429	10	short	short	ADJ
ejpam-6640	429	11	exact	exact	ADJ
ejpam-6640	429	12	sequence	sequence	NOUN
ejpam-6640	429	13	of	of	ADP
ejpam-6640	429	14	morphisms	morphism	NOUN
ejpam-6640	429	15	in	in	ADP
ejpam-6640	429	16	comp(ab	comp(ab	NOUN
ejpam-6640	429	17	)	)	PUNCT
ejpam-6640	429	18	.	.	PUNCT
ejpam-6640	430	1	this	this	PRON
ejpam-6640	430	2	means	mean	VERB
ejpam-6640	430	3	the	the	DET
ejpam-6640	430	4	following	follow	VERB
ejpam-6640	430	5	dia	dia	PROPN
ejpam-6640	430	6	.	.	PROPN
ejpam-6640	430	7	diallo	diallo	PROPN
ejpam-6640	430	8	,	,	PUNCT
ejpam-6640	430	9	m.	m.	PROPN
ejpam-6640	430	10	b.	b.	PROPN
ejpam-6640	430	11	f.	f.	PROPN
ejpam-6640	430	12	b.	b.	PROPN
ejpam-6640	430	13	maaouia	maaouia	PROPN
ejpam-6640	430	14	,	,	PUNCT
ejpam-6640	430	15	m.	m.	NOUN
ejpam-6640	430	16	sanghare	sanghare	PROPN
ejpam-6640	430	17	/	/	SYM
ejpam-6640	430	18	eur	eur	PROPN
ejpam-6640	430	19	.	.	PUNCT
ejpam-6640	431	1	j.	j.	PROPN
ejpam-6640	431	2	pure	pure	PROPN
ejpam-6640	431	3	appl	appl	PROPN
ejpam-6640	431	4	.	.	PROPN
ejpam-6640	431	5	math	math	PROPN
ejpam-6640	431	6	,	,	PUNCT
ejpam-6640	431	7	18	18	NUM
ejpam-6640	431	8	(	(	PUNCT
ejpam-6640	431	9	4	4	NUM
ejpam-6640	431	10	)	)	PUNCT
ejpam-6640	431	11	(	(	PUNCT
ejpam-6640	431	12	2025	2025	NUM
ejpam-6640	431	13	)	)	PUNCT
ejpam-6640	431	14	,	,	PUNCT
ejpam-6640	431	15	6640	6640	NUM
ejpam-6640	431	16	18	18	NUM
ejpam-6640	431	17	of	of	ADP
ejpam-6640	431	18	28	28	NUM
ejpam-6640	431	19	agram	agram	NOUN
ejpam-6640	431	20	commutes	commute	NOUN
ejpam-6640	431	21	:	:	PUNCT
ejpam-6640	431	22	homcomp(a	homcomp(a	NOUN
ejpam-6640	431	23	)	)	PUNCT
ejpam-6640	431	24	(	(	PUNCT
ejpam-6640	431	25	−	−	PROPN
ejpam-6640	431	26	,	,	PUNCT
ejpam-6640	431	27	x)((0	x)((0	PROPN
ejpam-6640	431	28	)	)	PUNCT
ejpam-6640	431	29	)	)	PUNCT
ejpam-6640	431	30	:	:	PUNCT
ejpam-6640	431	31	...	...	PUNCT
ejpam-6640	432	1	//	//	PUNCT
ejpam-6640	432	2	�	�	PROPN
ejpam-6640	432	3	�	�	PROPN
ejpam-6640	432	4	0homcomp(a	0homcomp(a	NUM
ejpam-6640	432	5	)	)	PUNCT
ejpam-6640	432	6	(	(	PUNCT
ejpam-6640	432	7	x,0	x,0	PROPN
ejpam-6640	432	8	)	)	PUNCT
ejpam-6640	432	9	//	//	SYM
ejpam-6640	432	10	�	�	PROPN
ejpam-6640	432	11	�	�	PROPN
ejpam-6640	432	12	0homcomp(a	0homcomp(a	NUM
ejpam-6640	432	13	)	)	PUNCT
ejpam-6640	432	14	(	(	PUNCT
ejpam-6640	432	15	x,0	x,0	PROPN
ejpam-6640	432	16	)	)	PUNCT
ejpam-6640	432	17	//	//	SYM
ejpam-6640	432	18	�	�	PROPN
ejpam-6640	432	19	�	�	PROPN
ejpam-6640	432	20	0homcomp(a	0homcomp(a	NUM
ejpam-6640	432	21	)	)	PUNCT
ejpam-6640	432	22	(	(	PUNCT
ejpam-6640	432	23	x,0	x,0	PROPN
ejpam-6640	432	24	)	)	PUNCT
ejpam-6640	432	25	//	//	SYM
ejpam-6640	432	26	�	�	PROPN
ejpam-6640	432	27	�	�	PROPN
ejpam-6640	432	28	...	...	PUNCT
ejpam-6640	432	29	homcomp(a	homcomp(a	NOUN
ejpam-6640	432	30	)	)	PUNCT
ejpam-6640	432	31	(	(	PUNCT
ejpam-6640	432	32	x,−)((y	x,−)((y	PROPN
ejpam-6640	432	33	,	,	PUNCT
ejpam-6640	432	34	α	α	NOUN
ejpam-6640	432	35	)	)	PUNCT
ejpam-6640	432	36	)	)	PUNCT
ejpam-6640	432	37	:	:	PUNCT
ejpam-6640	432	38	...	...	PUNCT
ejpam-6640	433	1	//	//	NUM
ejpam-6640	433	2	f∗	f∗	X
ejpam-6640	433	3	�	�	PROPN
ejpam-6640	433	4	�	�	PROPN
ejpam-6640	433	5	homcomp(a	homcomp(a	PROPN
ejpam-6640	433	6	)	)	PUNCT
ejpam-6640	433	7	(	(	PUNCT
ejpam-6640	433	8	x	x	X
ejpam-6640	433	9	,	,	PUNCT
ejpam-6640	433	10	yn	yn	NOUN
ejpam-6640	433	11	)	)	PUNCT
ejpam-6640	433	12	α∗	α∗	VERB
ejpam-6640	433	13	n//	n//	PRON
ejpam-6640	433	14	f∗	f∗	NOUN
ejpam-6640	433	15	n	n	PROPN
ejpam-6640	433	16	�	�	PROPN
ejpam-6640	433	17	�	�	PROPN
ejpam-6640	433	18	homcomp(a	homcomp(a	PROPN
ejpam-6640	433	19	)	)	PUNCT
ejpam-6640	433	20	(	(	PUNCT
ejpam-6640	433	21	x	x	X
ejpam-6640	433	22	,	,	PUNCT
ejpam-6640	433	23	yn+1	yn+1	X
ejpam-6640	433	24	)	)	PUNCT
ejpam-6640	433	25	α∗	α∗	VERB
ejpam-6640	433	26	n+1	n+1	PROPN
ejpam-6640	433	27	//	//	NUM
ejpam-6640	433	28	f∗	f∗	PROPN
ejpam-6640	433	29	n+1	n+1	PROPN
ejpam-6640	433	30	�	�	PROPN
ejpam-6640	433	31	�	�	PROPN
ejpam-6640	433	32	homcomp(a	homcomp(a	PROPN
ejpam-6640	433	33	)	)	PUNCT
ejpam-6640	433	34	(	(	PUNCT
ejpam-6640	433	35	x	x	NOUN
ejpam-6640	433	36	,	,	PUNCT
ejpam-6640	433	37	yn+2	yn+2	NUM
ejpam-6640	433	38	)	)	PUNCT
ejpam-6640	433	39	//	//	NOUN
ejpam-6640	434	1	f∗	f∗	PROPN
ejpam-6640	434	2	n+2	n+2	NUM
ejpam-6640	434	3	�	�	PROPN
ejpam-6640	434	4	�	�	PROPN
ejpam-6640	434	5	...	...	PUNCT
ejpam-6640	434	6	homcomp(a	homcomp(a	NOUN
ejpam-6640	434	7	)	)	PUNCT
ejpam-6640	434	8	(	(	PUNCT
ejpam-6640	434	9	x,−)((z	x,−)((z	PROPN
ejpam-6640	434	10	,	,	PUNCT
ejpam-6640	434	11	β	β	NOUN
ejpam-6640	434	12	)	)	PUNCT
ejpam-6640	434	13	)	)	PUNCT
ejpam-6640	434	14	:	:	PUNCT
ejpam-6640	434	15	...	...	PUNCT
ejpam-6640	435	1	//	//	PUNCT
ejpam-6640	435	2	g∗	g∗	PROPN
ejpam-6640	435	3	�	�	PROPN
ejpam-6640	435	4	�	�	PROPN
ejpam-6640	435	5	homcomp(a	homcomp(a	PROPN
ejpam-6640	435	6	)	)	PUNCT
ejpam-6640	435	7	(	(	PUNCT
ejpam-6640	435	8	x	x	X
ejpam-6640	435	9	,	,	PUNCT
ejpam-6640	435	10	zn	zn	NOUN
ejpam-6640	435	11	)	)	PUNCT
ejpam-6640	435	12	β∗	β∗	NOUN
ejpam-6640	435	13	n//	n//	PRON
ejpam-6640	435	14	g∗	g∗	VERB
ejpam-6640	435	15	n	n	PRON
ejpam-6640	435	16	�	�	PROPN
ejpam-6640	435	17	�	�	PROPN
ejpam-6640	435	18	homcomp(a	homcomp(a	PROPN
ejpam-6640	435	19	)	)	PUNCT
ejpam-6640	435	20	(	(	PUNCT
ejpam-6640	435	21	x	x	NOUN
ejpam-6640	435	22	,	,	PUNCT
ejpam-6640	435	23	zn+1	zn+1	X
ejpam-6640	435	24	)	)	PUNCT
ejpam-6640	435	25	β∗	β∗	NOUN
ejpam-6640	435	26	n+1	n+1	PROPN
ejpam-6640	435	27	//	//	PUNCT
ejpam-6640	435	28	g∗	g∗	PROPN
ejpam-6640	435	29	n+1	n+1	PROPN
ejpam-6640	435	30	�	�	PROPN
ejpam-6640	435	31	�	�	PROPN
ejpam-6640	435	32	homcomp(a	homcomp(a	PROPN
ejpam-6640	435	33	)	)	PUNCT
ejpam-6640	435	34	(	(	PUNCT
ejpam-6640	435	35	x	x	X
ejpam-6640	435	36	,	,	PUNCT
ejpam-6640	435	37	zn+2	zn+2	NUM
ejpam-6640	435	38	)	)	PUNCT
ejpam-6640	435	39	g∗	g∗	VERB
ejpam-6640	435	40	n+2	n+2	NUM
ejpam-6640	435	41	�	�	PROPN
ejpam-6640	435	42	�	�	PROPN
ejpam-6640	435	43	//	//	NUM
ejpam-6640	435	44	...	...	PUNCT
ejpam-6640	436	1	homcomp(a	homcomp(a	NOUN
ejpam-6640	436	2	)	)	PUNCT
ejpam-6640	436	3	(	(	PUNCT
ejpam-6640	436	4	x,−)((t	x,−)((t	PROPN
ejpam-6640	436	5	,	,	PUNCT
ejpam-6640	436	6	θ	θ	NOUN
ejpam-6640	436	7	)	)	PUNCT
ejpam-6640	436	8	)	)	PUNCT
ejpam-6640	436	9	:	:	PUNCT
ejpam-6640	436	10	...	...	PUNCT
ejpam-6640	437	1	//	//	PUNCT
ejpam-6640	437	2	�	�	PROPN
ejpam-6640	437	3	�	�	PROPN
ejpam-6640	437	4	homcomp(a	homcomp(a	PROPN
ejpam-6640	437	5	)	)	PUNCT
ejpam-6640	437	6	(	(	PUNCT
ejpam-6640	437	7	x	x	NOUN
ejpam-6640	437	8	,	,	PUNCT
ejpam-6640	437	9	tn	tn	PROPN
ejpam-6640	437	10	)	)	PUNCT
ejpam-6640	437	11	θ∗	θ∗	PROPN
ejpam-6640	437	12	n//	n//	PROPN
ejpam-6640	437	13	�	�	PROPN
ejpam-6640	437	14	�	�	PROPN
ejpam-6640	437	15	homcomp(a	homcomp(a	PROPN
ejpam-6640	437	16	)	)	PUNCT
ejpam-6640	437	17	(	(	PUNCT
ejpam-6640	437	18	x	x	NOUN
ejpam-6640	437	19	,	,	PUNCT
ejpam-6640	437	20	tn+1	tn+1	NOUN
ejpam-6640	437	21	)	)	PUNCT
ejpam-6640	437	22	θ∗	θ∗	NOUN
ejpam-6640	437	23	n+1	n+1	PROPN
ejpam-6640	437	24	//	//	SYM
ejpam-6640	437	25	�	�	PROPN
ejpam-6640	437	26	�	�	PROPN
ejpam-6640	437	27	homcomp(a	homcomp(a	PROPN
ejpam-6640	437	28	)	)	PUNCT
ejpam-6640	437	29	(	(	PUNCT
ejpam-6640	437	30	x	x	NOUN
ejpam-6640	437	31	,	,	PUNCT
ejpam-6640	437	32	tn+2	tn+2	NUM
ejpam-6640	437	33	)	)	PUNCT
ejpam-6640	437	34	//	//	SYM
ejpam-6640	437	35	�	�	PROPN
ejpam-6640	437	36	�	�	PROPN
ejpam-6640	437	37	...	...	PUNCT
ejpam-6640	437	38	homcomp(a	homcomp(a	NOUN
ejpam-6640	437	39	)	)	PUNCT
ejpam-6640	437	40	(	(	PUNCT
ejpam-6640	437	41	−	−	PROPN
ejpam-6640	437	42	,	,	PUNCT
ejpam-6640	437	43	x)((0	x)((0	PROPN
ejpam-6640	437	44	)	)	PUNCT
ejpam-6640	437	45	)	)	PUNCT
ejpam-6640	437	46	:	:	PUNCT
ejpam-6640	437	47	...	...	PUNCT
ejpam-6640	438	1	//	//	NUM
ejpam-6640	438	2	0homcomp(a	0homcomp(a	NUM
ejpam-6640	438	3	)	)	PUNCT
ejpam-6640	438	4	(	(	PUNCT
ejpam-6640	438	5	x,0	x,0	PROPN
ejpam-6640	438	6	)	)	PUNCT
ejpam-6640	438	7	//	//	PROPN
ejpam-6640	438	8	0homcomp(a	0homcomp(a	NUM
ejpam-6640	438	9	)	)	PUNCT
ejpam-6640	438	10	(	(	PUNCT
ejpam-6640	438	11	x,0	x,0	PROPN
ejpam-6640	438	12	)	)	PUNCT
ejpam-6640	438	13	//	//	PROPN
ejpam-6640	438	14	0homcomp(a	0homcomp(a	NUM
ejpam-6640	438	15	)	)	PUNCT
ejpam-6640	438	16	(	(	PUNCT
ejpam-6640	438	17	x,0	x,0	PROPN
ejpam-6640	438	18	)	)	PUNCT
ejpam-6640	439	1	//	//	NOUN
ejpam-6640	439	2	...	...	PUNCT
ejpam-6640	440	1	we	we	PRON
ejpam-6640	440	2	have	have	VERB
ejpam-6640	440	3	for	for	ADP
ejpam-6640	440	4	every	every	DET
ejpam-6640	440	5	integer	integer	NOUN
ejpam-6640	440	6	n	n	PROPN
ejpam-6640	440	7	∈	∈	PROPN
ejpam-6640	440	8	z	z	PROPN
ejpam-6640	440	9	,	,	PUNCT
ejpam-6640	440	10	g∗n	g∗n	X
ejpam-6640	440	11	is	be	AUX
ejpam-6640	440	12	an	an	DET
ejpam-6640	440	13	epimorphism	epimorphism	NOUN
ejpam-6640	440	14	.	.	PUNCT
ejpam-6640	441	1	therefore	therefore	ADV
ejpam-6640	441	2	,	,	PUNCT
ejpam-6640	441	3	for	for	SCONJ
ejpam-6640	441	4	every	every	DET
ejpam-6640	441	5	epimorphism	epimorphism	NOUN
ejpam-6640	441	6	gn	gn	PROPN
ejpam-6640	441	7	:	:	PUNCT
ejpam-6640	441	8	zn	zn	PROPN
ejpam-6640	441	9	↠	↠	PROPN
ejpam-6640	441	10	tn	tn	PROPN
ejpam-6640	441	11	in	in	ADP
ejpam-6640	441	12	a	a	PRON
ejpam-6640	441	13	and	and	CCONJ
ejpam-6640	441	14	every	every	DET
ejpam-6640	441	15	morphism	morphism	NOUN
ejpam-6640	441	16	fn	fn	NOUN
ejpam-6640	441	17	:	:	PUNCT
ejpam-6640	441	18	x	x	X
ejpam-6640	441	19	→	→	SYM
ejpam-6640	441	20	tn	tn	NOUN
ejpam-6640	441	21	in	in	ADP
ejpam-6640	441	22	a	a	PRON
ejpam-6640	441	23	,	,	PUNCT
ejpam-6640	441	24	there	there	PRON
ejpam-6640	441	25	exists	exist	VERB
ejpam-6640	441	26	a	a	DET
ejpam-6640	441	27	morphism	morphism	NOUN
ejpam-6640	441	28	ϕn	ϕn	ADP
ejpam-6640	441	29	:	:	PUNCT
ejpam-6640	441	30	x	x	X
ejpam-6640	441	31	→	→	SYM
ejpam-6640	441	32	zn	zn	PROPN
ejpam-6640	441	33	in	in	ADP
ejpam-6640	441	34	a	a	DET
ejpam-6640	441	35	such	such	ADJ
ejpam-6640	441	36	that	that	DET
ejpam-6640	441	37	gn	gn	INTJ
ejpam-6640	441	38	◦	◦	NOUN
ejpam-6640	441	39	ϕn	ϕn	X
ejpam-6640	442	1	=	=	SYM
ejpam-6640	443	1	g∗(ϕn	g∗(ϕn	PROPN
ejpam-6640	443	2	)	)	PUNCT
ejpam-6640	444	1	=	=	SYM
ejpam-6640	444	2	fn	fn	NOUN
ejpam-6640	444	3	.	.	PUNCT
ejpam-6640	445	1	this	this	PRON
ejpam-6640	445	2	means	mean	VERB
ejpam-6640	445	3	the	the	DET
ejpam-6640	445	4	following	follow	VERB
ejpam-6640	445	5	diagram	diagram	NOUN
ejpam-6640	445	6	commutes	commute	NOUN
ejpam-6640	445	7	:	:	PUNCT
ejpam-6640	445	8	x	x	X
ejpam-6640	445	9	ϕn	ϕn	X
ejpam-6640	445	10	}	}	PUNCT
ejpam-6640	445	11	}	}	PUNCT
ejpam-6640	445	12	fn	fn	PROPN
ejpam-6640	445	13	�	�	PROPN
ejpam-6640	445	14	�	�	PROPN
ejpam-6640	445	15	zn	zn	PROPN
ejpam-6640	445	16	gn	gn	PROPN
ejpam-6640	445	17	//	//	PROPN
ejpam-6640	445	18	//	//	PROPN
ejpam-6640	445	19	tn	tn	PROPN
ejpam-6640	445	20	//	//	PROPN
ejpam-6640	445	21	0	0	PUNCT
ejpam-6640	446	1	hence	hence	ADV
ejpam-6640	446	2	,	,	PUNCT
ejpam-6640	446	3	x	x	X
ejpam-6640	446	4	is	be	AUX
ejpam-6640	446	5	a	a	DET
ejpam-6640	446	6	projective	projective	ADJ
ejpam-6640	446	7	object	object	NOUN
ejpam-6640	446	8	in	in	ADP
ejpam-6640	446	9	a	a	PRON
ejpam-6640	446	10	.	.	PUNCT
ejpam-6640	447	1	suppose	suppose	VERB
ejpam-6640	447	2	that	that	SCONJ
ejpam-6640	447	3	x	x	PRON
ejpam-6640	447	4	is	be	AUX
ejpam-6640	447	5	a	a	DET
ejpam-6640	447	6	projective	projective	ADJ
ejpam-6640	447	7	object	object	NOUN
ejpam-6640	447	8	of	of	ADP
ejpam-6640	447	9	a	a	PRON
ejpam-6640	447	10	and	and	CCONJ
ejpam-6640	447	11	let	let	VERB
ejpam-6640	447	12	us	we	PRON
ejpam-6640	447	13	show	show	VERB
ejpam-6640	447	14	that	that	SCONJ
ejpam-6640	447	15	the	the	DET
ejpam-6640	447	16	functor	functor	PROPN
ejpam-6640	447	17	homcomp(a	homcomp(a	PROPN
ejpam-6640	447	18	)	)	PUNCT
ejpam-6640	447	19	(	(	PUNCT
ejpam-6640	447	20	x,−	x,−	PROPN
ejpam-6640	447	21	)	)	PUNCT
ejpam-6640	447	22	:	:	PUNCT
ejpam-6640	447	23	comp(a	comp(a	NOUN
ejpam-6640	447	24	)	)	PUNCT
ejpam-6640	447	25	→	→	SYM
ejpam-6640	447	26	comp(ab	comp(ab	NOUN
ejpam-6640	447	27	)	)	PUNCT
ejpam-6640	447	28	is	be	AUX
ejpam-6640	447	29	an	an	DET
ejpam-6640	447	30	exact	exact	ADJ
ejpam-6640	447	31	functor	functor	NOUN
ejpam-6640	447	32	.	.	PUNCT
ejpam-6640	448	1	let	let	VERB
ejpam-6640	448	2	the	the	DET
ejpam-6640	448	3	following	follow	VERB
ejpam-6640	448	4	short	short	ADJ
ejpam-6640	448	5	exact	exact	ADJ
ejpam-6640	448	6	sequence	sequence	NOUN
ejpam-6640	448	7	of	of	ADP
ejpam-6640	448	8	morphisms	morphism	NOUN
ejpam-6640	448	9	in	in	ADP
ejpam-6640	448	10	a	a	DET
ejpam-6640	448	11	:	:	PUNCT
ejpam-6640	448	12	(	(	PUNCT
ejpam-6640	448	13	0	0	NUM
ejpam-6640	448	14	)	)	PUNCT
ejpam-6640	448	15	//	//	NOUN
ejpam-6640	448	16	(	(	PUNCT
ejpam-6640	448	17	y	y	PROPN
ejpam-6640	448	18	,	,	PUNCT
ejpam-6640	448	19	α	α	NOUN
ejpam-6640	448	20	)	)	PUNCT
ejpam-6640	448	21	f	f	PROPN
ejpam-6640	449	1	//	//	X
ejpam-6640	449	2	(	(	PUNCT
ejpam-6640	449	3	z	z	NOUN
ejpam-6640	449	4	,	,	PUNCT
ejpam-6640	449	5	β	β	NOUN
ejpam-6640	449	6	)	)	PUNCT
ejpam-6640	449	7	g	g	PROPN
ejpam-6640	449	8	//	//	SYM
ejpam-6640	449	9	(	(	PUNCT
ejpam-6640	449	10	t	t	PROPN
ejpam-6640	449	11	,	,	PUNCT
ejpam-6640	449	12	θ	θ	PROPN
ejpam-6640	449	13	)	)	PUNCT
ejpam-6640	449	14	//	//	NOUN
ejpam-6640	449	15	(	(	PUNCT
ejpam-6640	449	16	0	0	NUM
ejpam-6640	449	17	)	)	PUNCT
ejpam-6640	449	18	we	we	PRON
ejpam-6640	449	19	show	show	VERB
ejpam-6640	449	20	that	that	SCONJ
ejpam-6640	449	21	homcomp(a	homcomp(a	NOUN
ejpam-6640	449	22	)	)	PUNCT
ejpam-6640	449	23	(	(	PUNCT
ejpam-6640	449	24	x,−)((0	x,−)((0	PROPN
ejpam-6640	449	25	)	)	PUNCT
ejpam-6640	449	26	)	)	PUNCT
ejpam-6640	450	1	//	//	PUNCT
ejpam-6640	450	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	450	3	)	)	PUNCT
ejpam-6640	450	4	(	(	PUNCT
ejpam-6640	450	5	x,−)((y	x,−)((y	PROPN
ejpam-6640	450	6	,	,	PUNCT
ejpam-6640	450	7	α	α	NOUN
ejpam-6640	450	8	)	)	PUNCT
ejpam-6640	450	9	)	)	PUNCT
ejpam-6640	450	10	f∗	f∗	NOUN
ejpam-6640	450	11	//	//	X
ejpam-6640	450	12	homcomp(a	homcomp(a	NOUN
ejpam-6640	450	13	)	)	PUNCT
ejpam-6640	450	14	(	(	PUNCT
ejpam-6640	450	15	x,−)((z	x,−)((z	PROPN
ejpam-6640	450	16	,	,	PUNCT
ejpam-6640	450	17	β	β	NOUN
ejpam-6640	450	18	)	)	PUNCT
ejpam-6640	450	19	)	)	PUNCT
ejpam-6640	450	20	g∗	g∗	VERB
ejpam-6640	450	21	//	//	NUM
ejpam-6640	450	22	homcomp(a	homcomp(a	NOUN
ejpam-6640	450	23	)	)	PUNCT
ejpam-6640	450	24	(	(	PUNCT
ejpam-6640	450	25	x,−)((t	x,−)((t	PROPN
ejpam-6640	450	26	,	,	PUNCT
ejpam-6640	450	27	θ	θ	NOUN
ejpam-6640	450	28	)	)	PUNCT
ejpam-6640	450	29	)	)	PUNCT
ejpam-6640	451	1	//	//	PUNCT
ejpam-6640	451	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	451	3	)	)	PUNCT
ejpam-6640	451	4	(	(	PUNCT
ejpam-6640	451	5	x,−)((0	x,−)((0	PROPN
ejpam-6640	451	6	)	)	PUNCT
ejpam-6640	451	7	)	)	PUNCT
ejpam-6640	451	8	is	be	AUX
ejpam-6640	451	9	a	a	DET
ejpam-6640	451	10	short	short	ADJ
ejpam-6640	451	11	exact	exact	ADJ
ejpam-6640	451	12	sequence	sequence	NOUN
ejpam-6640	451	13	of	of	ADP
ejpam-6640	451	14	morphisms	morphism	NOUN
ejpam-6640	451	15	in	in	ADP
ejpam-6640	451	16	comp(ab	comp(ab	NOUN
ejpam-6640	451	17	)	)	PUNCT
ejpam-6640	451	18	.	.	PUNCT
ejpam-6640	452	1	by	by	ADP
ejpam-6640	452	2	i.	i.	PROPN
ejpam-6640	452	3	,	,	PUNCT
ejpam-6640	452	4	we	we	PRON
ejpam-6640	452	5	have	have	VERB
ejpam-6640	452	6	:	:	PUNCT
ejpam-6640	452	7	homcomp(a	homcomp(a	NOUN
ejpam-6640	452	8	)	)	PUNCT
ejpam-6640	452	9	(	(	PUNCT
ejpam-6640	452	10	x,−)((0	x,−)((0	PROPN
ejpam-6640	452	11	)	)	PUNCT
ejpam-6640	452	12	)	)	PUNCT
ejpam-6640	453	1	//	//	PUNCT
ejpam-6640	453	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	453	3	)	)	PUNCT
ejpam-6640	453	4	(	(	PUNCT
ejpam-6640	453	5	x,−)((y	x,−)((y	PROPN
ejpam-6640	453	6	,	,	PUNCT
ejpam-6640	453	7	α	α	NOUN
ejpam-6640	453	8	)	)	PUNCT
ejpam-6640	453	9	)	)	PUNCT
ejpam-6640	453	10	f∗	f∗	NOUN
ejpam-6640	453	11	//	//	X
ejpam-6640	453	12	homcomp(a	homcomp(a	NOUN
ejpam-6640	453	13	)	)	PUNCT
ejpam-6640	453	14	(	(	PUNCT
ejpam-6640	453	15	x,−)((z	x,−)((z	PROPN
ejpam-6640	453	16	,	,	PUNCT
ejpam-6640	453	17	β	β	NOUN
ejpam-6640	453	18	)	)	PUNCT
ejpam-6640	453	19	)	)	PUNCT
ejpam-6640	453	20	g∗	g∗	VERB
ejpam-6640	453	21	//	//	NUM
ejpam-6640	453	22	homcomp(a	homcomp(a	NOUN
ejpam-6640	453	23	)	)	PUNCT
ejpam-6640	453	24	(	(	PUNCT
ejpam-6640	453	25	x,−)((t	x,−)((t	PROPN
ejpam-6640	453	26	,	,	PUNCT
ejpam-6640	453	27	θ	θ	NOUN
ejpam-6640	453	28	)	)	PUNCT
ejpam-6640	453	29	)	)	PUNCT
ejpam-6640	453	30	is	be	AUX
ejpam-6640	453	31	a	a	DET
ejpam-6640	453	32	left	left	ADJ
ejpam-6640	453	33	short	short	ADJ
ejpam-6640	453	34	exact	exact	ADJ
ejpam-6640	453	35	sequence	sequence	NOUN
ejpam-6640	453	36	of	of	ADP
ejpam-6640	453	37	morphisms	morphism	NOUN
ejpam-6640	453	38	in	in	ADP
ejpam-6640	453	39	comp(ab	comp(ab	NOUN
ejpam-6640	453	40	)	)	PUNCT
ejpam-6640	453	41	.	.	PUNCT
ejpam-6640	454	1	thus	thus	ADV
ejpam-6640	454	2	,	,	PUNCT
ejpam-6640	454	3	it	it	PRON
ejpam-6640	454	4	remains	remain	VERB
ejpam-6640	454	5	to	to	PART
ejpam-6640	454	6	show	show	VERB
ejpam-6640	454	7	that	that	SCONJ
ejpam-6640	454	8	for	for	ADP
ejpam-6640	454	9	every	every	DET
ejpam-6640	454	10	n	n	NOUN
ejpam-6640	454	11	,	,	PUNCT
ejpam-6640	454	12	homa	homa	NOUN
ejpam-6640	454	13	(	(	PUNCT
ejpam-6640	454	14	x	x	NOUN
ejpam-6640	454	15	,	,	PUNCT
ejpam-6640	454	16	gn	gn	PROPN
ejpam-6640	454	17	)	)	PUNCT
ejpam-6640	454	18	is	be	AUX
ejpam-6640	454	19	an	an	DET
ejpam-6640	454	20	epimorphism	epimorphism	NOUN
ejpam-6640	454	21	.	.	PUNCT
ejpam-6640	455	1	sincex	sincex	PROPN
ejpam-6640	455	2	is	be	AUX
ejpam-6640	455	3	projective	projective	ADJ
ejpam-6640	455	4	,	,	PUNCT
ejpam-6640	455	5	by	by	ADP
ejpam-6640	455	6	theorem	theorem	NOUN
ejpam-6640	455	7	2	2	NUM
ejpam-6640	455	8	,	,	PUNCT
ejpam-6640	455	9	for	for	ADP
ejpam-6640	455	10	every	every	DET
ejpam-6640	455	11	epimorphism	epimorphism	NOUN
ejpam-6640	455	12	gn	gn	PROPN
ejpam-6640	456	1	:	:	PUNCT
ejpam-6640	456	2	zn	zn	PROPN
ejpam-6640	456	3	↠	↠	PROPN
ejpam-6640	456	4	tn	tn	PROPN
ejpam-6640	456	5	in	in	ADP
ejpam-6640	456	6	a	a	PRON
ejpam-6640	456	7	and	and	CCONJ
ejpam-6640	456	8	every	every	DET
ejpam-6640	456	9	morphism	morphism	NOUN
ejpam-6640	456	10	fn	fn	NOUN
ejpam-6640	456	11	:	:	PUNCT
ejpam-6640	456	12	x	x	X
ejpam-6640	456	13	→	→	SYM
ejpam-6640	456	14	tn	tn	PROPN
ejpam-6640	456	15	in	in	ADP
ejpam-6640	456	16	a.	a.	PROPN
ejpam-6640	456	17	diallo	diallo	PROPN
ejpam-6640	456	18	,	,	PUNCT
ejpam-6640	456	19	m.	m.	PROPN
ejpam-6640	456	20	b.	b.	PROPN
ejpam-6640	456	21	f.	f.	PROPN
ejpam-6640	456	22	b.	b.	PROPN
ejpam-6640	456	23	maaouia	maaouia	PROPN
ejpam-6640	456	24	,	,	PUNCT
ejpam-6640	456	25	m.	m.	NOUN
ejpam-6640	456	26	sanghare	sanghare	PROPN
ejpam-6640	456	27	/	/	SYM
ejpam-6640	456	28	eur	eur	PROPN
ejpam-6640	456	29	.	.	PUNCT
ejpam-6640	457	1	j.	j.	PROPN
ejpam-6640	457	2	pure	pure	PROPN
ejpam-6640	457	3	appl	appl	PROPN
ejpam-6640	457	4	.	.	PROPN
ejpam-6640	457	5	math	math	PROPN
ejpam-6640	457	6	,	,	PUNCT
ejpam-6640	457	7	18	18	NUM
ejpam-6640	457	8	(	(	PUNCT
ejpam-6640	457	9	4	4	NUM
ejpam-6640	457	10	)	)	PUNCT
ejpam-6640	457	11	(	(	PUNCT
ejpam-6640	457	12	2025	2025	NUM
ejpam-6640	457	13	)	)	PUNCT
ejpam-6640	457	14	,	,	PUNCT
ejpam-6640	457	15	6640	6640	NUM
ejpam-6640	457	16	19	19	NUM
ejpam-6640	457	17	of	of	ADP
ejpam-6640	457	18	28	28	NUM
ejpam-6640	457	19	a	a	PRON
ejpam-6640	457	20	,	,	PUNCT
ejpam-6640	457	21	there	there	PRON
ejpam-6640	457	22	exists	exist	VERB
ejpam-6640	457	23	a	a	DET
ejpam-6640	457	24	morphism	morphism	NOUN
ejpam-6640	457	25	ϕn	ϕn	ADP
ejpam-6640	457	26	:	:	PUNCT
ejpam-6640	457	27	x	x	X
ejpam-6640	457	28	→	→	SYM
ejpam-6640	457	29	zn	zn	PROPN
ejpam-6640	457	30	in	in	ADP
ejpam-6640	457	31	a	a	DET
ejpam-6640	457	32	such	such	ADJ
ejpam-6640	457	33	that	that	DET
ejpam-6640	457	34	gn	gn	INTJ
ejpam-6640	457	35	◦	◦	NOUN
ejpam-6640	457	36	ϕn	ϕn	X
ejpam-6640	458	1	=	=	NOUN
ejpam-6640	459	1	fn	fn	PROPN
ejpam-6640	459	2	.	.	PUNCT
ejpam-6640	460	1	this	this	PRON
ejpam-6640	460	2	means	mean	VERB
ejpam-6640	460	3	that	that	SCONJ
ejpam-6640	460	4	the	the	DET
ejpam-6640	460	5	following	follow	VERB
ejpam-6640	460	6	diagram	diagram	NOUN
ejpam-6640	460	7	commutes	commute	NOUN
ejpam-6640	460	8	:	:	PUNCT
ejpam-6640	460	9	x	x	X
ejpam-6640	460	10	ϕn	ϕn	X
ejpam-6640	460	11	}	}	PUNCT
ejpam-6640	460	12	}	}	PUNCT
ejpam-6640	460	13	fn	fn	PROPN
ejpam-6640	460	14	�	�	PROPN
ejpam-6640	460	15	�	�	PROPN
ejpam-6640	460	16	zn	zn	PROPN
ejpam-6640	460	17	gn	gn	PROPN
ejpam-6640	460	18	//	//	PROPN
ejpam-6640	460	19	//	//	PROPN
ejpam-6640	460	20	tn	tn	PROPN
ejpam-6640	460	21	//	//	PROPN
ejpam-6640	460	22	0	0	NUM
ejpam-6640	460	23	that	that	PRON
ejpam-6640	460	24	is	be	AUX
ejpam-6640	460	25	,	,	PUNCT
ejpam-6640	460	26	for	for	ADP
ejpam-6640	460	27	every	every	DET
ejpam-6640	460	28	fn	fn	NOUN
ejpam-6640	460	29	∈	∈	PROPN
ejpam-6640	460	30	homcomp(a	homcomp(a	NOUN
ejpam-6640	460	31	)	)	PUNCT
ejpam-6640	460	32	(	(	PUNCT
ejpam-6640	460	33	x	x	NOUN
ejpam-6640	460	34	,	,	PUNCT
ejpam-6640	460	35	tn	tn	PROPN
ejpam-6640	460	36	)	)	PUNCT
ejpam-6640	460	37	,	,	PUNCT
ejpam-6640	460	38	there	there	PRON
ejpam-6640	460	39	exists	exist	VERB
ejpam-6640	460	40	ϕn	ϕn	ADP
ejpam-6640	460	41	∈	∈	PROPN
ejpam-6640	460	42	homcomp(a	homcomp(a	NOUN
ejpam-6640	460	43	)	)	PUNCT
ejpam-6640	460	44	(	(	PUNCT
ejpam-6640	460	45	x	x	X
ejpam-6640	460	46	,	,	PUNCT
ejpam-6640	460	47	zn	zn	NOUN
ejpam-6640	460	48	)	)	PUNCT
ejpam-6640	461	1	such	such	ADJ
ejpam-6640	461	2	that	that	SCONJ
ejpam-6640	461	3	gn	gn	INTJ
ejpam-6640	461	4	◦	◦	NOUN
ejpam-6640	461	5	ϕn	ϕn	ADP
ejpam-6640	461	6	=	=	X
ejpam-6640	461	7	fn	fn	NOUN
ejpam-6640	461	8	=	=	NOUN
ejpam-6640	461	9	g∗n(ϕn	g∗n(ϕn	NOUN
ejpam-6640	461	10	)	)	PUNCT
ejpam-6640	461	11	.	.	PUNCT
ejpam-6640	462	1	hence	hence	ADV
ejpam-6640	462	2	,	,	PUNCT
ejpam-6640	462	3	homcomp(a	homcomp(a	NOUN
ejpam-6640	462	4	)	)	PUNCT
ejpam-6640	462	5	(	(	PUNCT
ejpam-6640	462	6	x	x	NOUN
ejpam-6640	462	7	,	,	PUNCT
ejpam-6640	462	8	gn	gn	PROPN
ejpam-6640	462	9	)	)	PUNCT
ejpam-6640	462	10	=	=	PRON
ejpam-6640	463	1	g∗n	g∗n	X
ejpam-6640	463	2	is	be	AUX
ejpam-6640	463	3	an	an	DET
ejpam-6640	463	4	epimorphism	epimorphism	NOUN
ejpam-6640	463	5	for	for	ADP
ejpam-6640	463	6	every	every	DET
ejpam-6640	463	7	integer	integer	NOUN
ejpam-6640	463	8	n	n	PROPN
ejpam-6640	463	9	in	in	ADP
ejpam-6640	463	10	z.	z.	PROPN
ejpam-6640	463	11	therefore	therefore	ADV
ejpam-6640	463	12	,	,	PUNCT
ejpam-6640	463	13	the	the	DET
ejpam-6640	463	14	functor	functor	PROPN
ejpam-6640	463	15	homcomp(a	homcomp(a	PROPN
ejpam-6640	463	16	)	)	PUNCT
ejpam-6640	463	17	(	(	PUNCT
ejpam-6640	463	18	x,−	x,−	PROPN
ejpam-6640	463	19	)	)	PUNCT
ejpam-6640	463	20	:	:	PUNCT
ejpam-6640	463	21	comp(a	comp(a	NOUN
ejpam-6640	463	22	)	)	PUNCT
ejpam-6640	463	23	→	→	SYM
ejpam-6640	463	24	comp(ab	comp(ab	NOUN
ejpam-6640	463	25	)	)	PUNCT
ejpam-6640	463	26	is	be	AUX
ejpam-6640	463	27	exact	exact	ADJ
ejpam-6640	463	28	.	.	PUNCT
ejpam-6640	464	1	thus	thus	ADV
ejpam-6640	464	2	,	,	PUNCT
ejpam-6640	464	3	(	(	PUNCT
ejpam-6640	464	4	ii.1	ii.1	X
ejpam-6640	464	5	)	)	PUNCT
ejpam-6640	464	6	and	and	CCONJ
ejpam-6640	464	7	(	(	PUNCT
ejpam-6640	464	8	ii.2	ii.2	NOUN
ejpam-6640	464	9	)	)	PUNCT
ejpam-6640	464	10	imply	imply	VERB
ejpam-6640	464	11	that	that	SCONJ
ejpam-6640	464	12	the	the	DET
ejpam-6640	464	13	functor	functor	PROPN
ejpam-6640	464	14	homcomp(a	homcomp(a	PROPN
ejpam-6640	464	15	)	)	PUNCT
ejpam-6640	464	16	(	(	PUNCT
ejpam-6640	464	17	x,−	x,−	PROPN
ejpam-6640	464	18	)	)	PUNCT
ejpam-6640	464	19	:	:	PUNCT
ejpam-6640	464	20	comp(a	comp(a	NOUN
ejpam-6640	464	21	)	)	PUNCT
ejpam-6640	464	22	→	→	SYM
ejpam-6640	464	23	comp(ab	comp(ab	NOUN
ejpam-6640	464	24	)	)	PUNCT
ejpam-6640	464	25	is	be	AUX
ejpam-6640	464	26	exact	exact	ADJ
ejpam-6640	464	27	if	if	SCONJ
ejpam-6640	464	28	and	and	CCONJ
ejpam-6640	464	29	only	only	ADV
ejpam-6640	464	30	if	if	SCONJ
ejpam-6640	464	31	x	x	PRON
ejpam-6640	464	32	is	be	AUX
ejpam-6640	464	33	a	a	DET
ejpam-6640	464	34	projective	projective	ADJ
ejpam-6640	464	35	object	object	NOUN
ejpam-6640	464	36	in	in	ADP
ejpam-6640	464	37	a	a	PRON
ejpam-6640	464	38	.	.	PUNCT
ejpam-6640	465	1	let	let	VERB
ejpam-6640	465	2	a	a	PRON
ejpam-6640	465	3	be	be	AUX
ejpam-6640	465	4	a	a	DET
ejpam-6640	465	5	balanced	balanced	ADJ
ejpam-6640	465	6	abelian	abelian	ADJ
ejpam-6640	465	7	category	category	NOUN
ejpam-6640	465	8	and	and	CCONJ
ejpam-6640	465	9	x	x	SYM
ejpam-6640	465	10	an	an	DET
ejpam-6640	465	11	object	object	NOUN
ejpam-6640	465	12	in	in	ADP
ejpam-6640	465	13	a	a	PRON
ejpam-6640	465	14	.	.	PUNCT
ejpam-6640	466	1	then	then	ADV
ejpam-6640	466	2	:	:	PUNCT
ejpam-6640	466	3	[	[	X
ejpam-6640	466	4	label=.]the	label=.]the	NOUN
ejpam-6640	466	5	functor	functor	PROPN
ejpam-6640	466	6	homcomp(a	homcomp(a	PROPN
ejpam-6640	466	7	)	)	PUNCT
ejpam-6640	466	8	(	(	PUNCT
ejpam-6640	466	9	−	−	PROPN
ejpam-6640	466	10	,	,	PUNCT
ejpam-6640	466	11	x	x	NOUN
ejpam-6640	466	12	)	)	PUNCT
ejpam-6640	466	13	:	:	PUNCT
ejpam-6640	466	14	comp(a	comp(a	NOUN
ejpam-6640	466	15	)	)	PUNCT
ejpam-6640	466	16	→	→	SYM
ejpam-6640	466	17	comp(ab	comp(ab	NOUN
ejpam-6640	466	18	)	)	PUNCT
ejpam-6640	466	19	is	be	AUX
ejpam-6640	466	20	a	a	DET
ejpam-6640	466	21	contravariant	contravariant	ADJ
ejpam-6640	466	22	,	,	PUNCT
ejpam-6640	466	23	additive	additive	NOUN
ejpam-6640	466	24	,	,	PUNCT
ejpam-6640	466	25	and	and	CCONJ
ejpam-6640	466	26	left	left	ADJ
ejpam-6640	466	27	-	-	PUNCT
ejpam-6640	466	28	exact	exact	NOUN
ejpam-6640	466	29	functor	functor	NOUN
ejpam-6640	466	30	;	;	PUNCT
ejpam-6640	466	31	the	the	DET
ejpam-6640	466	32	functor	functor	PROPN
ejpam-6640	466	33	homcomp(a	homcomp(a	PROPN
ejpam-6640	466	34	)	)	PUNCT
ejpam-6640	466	35	(	(	PUNCT
ejpam-6640	466	36	−	−	PROPN
ejpam-6640	466	37	,	,	PUNCT
ejpam-6640	466	38	x	x	NOUN
ejpam-6640	466	39	)	)	PUNCT
ejpam-6640	466	40	:	:	PUNCT
ejpam-6640	466	41	comp(a	comp(a	NOUN
ejpam-6640	466	42	)	)	PUNCT
ejpam-6640	466	43	→	→	SYM
ejpam-6640	466	44	comp(ab	comp(ab	NOUN
ejpam-6640	466	45	)	)	PUNCT
ejpam-6640	466	46	is	be	AUX
ejpam-6640	466	47	exact	exact	ADJ
ejpam-6640	466	48	if	if	SCONJ
ejpam-6640	467	1	and	and	CCONJ
ejpam-6640	467	2	only	only	ADV
ejpam-6640	467	3	if	if	SCONJ
ejpam-6640	467	4	x	x	PRON
ejpam-6640	467	5	is	be	AUX
ejpam-6640	467	6	a	a	DET
ejpam-6640	467	7	injective	injective	ADJ
ejpam-6640	467	8	object	object	NOUN
ejpam-6640	467	9	in	in	ADP
ejpam-6640	467	10	a	a	PRON
ejpam-6640	467	11	.	.	PUNCT
ejpam-6640	468	1	proof	proof	NOUN
ejpam-6640	468	2	.	.	PUNCT
ejpam-6640	469	1	i.	i.	PROPN
ejpam-6640	469	2	let	let	VERB
ejpam-6640	469	3	us	we	PRON
ejpam-6640	469	4	show	show	VERB
ejpam-6640	469	5	that	that	SCONJ
ejpam-6640	469	6	the	the	DET
ejpam-6640	469	7	functor	functor	PROPN
ejpam-6640	469	8	homcomp(a	homcomp(a	PROPN
ejpam-6640	469	9	)	)	PUNCT
ejpam-6640	469	10	(	(	PUNCT
ejpam-6640	469	11	−	−	PROPN
ejpam-6640	469	12	,	,	PUNCT
ejpam-6640	469	13	x	x	NOUN
ejpam-6640	469	14	)	)	PUNCT
ejpam-6640	469	15	:	:	PUNCT
ejpam-6640	469	16	comp(a	comp(a	NOUN
ejpam-6640	469	17	)	)	PUNCT
ejpam-6640	469	18	→	→	SYM
ejpam-6640	469	19	comp(ab	comp(ab	NOUN
ejpam-6640	469	20	)	)	PUNCT
ejpam-6640	469	21	is	be	AUX
ejpam-6640	469	22	contravariant	contravariant	ADJ
ejpam-6640	469	23	,	,	PUNCT
ejpam-6640	469	24	additive	additive	NOUN
ejpam-6640	469	25	,	,	PUNCT
ejpam-6640	469	26	and	and	CCONJ
ejpam-6640	469	27	left	leave	VERB
ejpam-6640	469	28	exact	exact	ADJ
ejpam-6640	469	29	.	.	PUNCT
ejpam-6640	470	1	(	(	PUNCT
ejpam-6640	470	2	i)(ii)ii.ai.b(i)ii.1ii.2(i)(ii)i.1	i)(ii)ii.ai.b(i)ii.1ii.2(i)(ii)i.1	ADJ
ejpam-6640	470	3	it	it	PRON
ejpam-6640	470	4	is	be	AUX
ejpam-6640	470	5	evident	evident	ADJ
ejpam-6640	470	6	that	that	SCONJ
ejpam-6640	470	7	homcomp(a	homcomp(a	NOUN
ejpam-6640	470	8	)	)	PUNCT
ejpam-6640	470	9	(	(	PUNCT
ejpam-6640	470	10	−	−	PROPN
ejpam-6640	470	11	,	,	PUNCT
ejpam-6640	470	12	x	x	X
ejpam-6640	470	13	)	)	PUNCT
ejpam-6640	470	14	is	be	AUX
ejpam-6640	470	15	contravariant	contravariant	ADJ
ejpam-6640	470	16	and	and	CCONJ
ejpam-6640	470	17	additive	additive	NOUN
ejpam-6640	470	18	.	.	PUNCT
ejpam-6640	471	1	i.2	i.2	PROPN
ejpam-6640	471	2	let	let	VERB
ejpam-6640	471	3	us	we	PRON
ejpam-6640	471	4	show	show	VERB
ejpam-6640	471	5	that	that	SCONJ
ejpam-6640	471	6	the	the	DET
ejpam-6640	471	7	functor	functor	PROPN
ejpam-6640	471	8	homcomp(a	homcomp(a	PROPN
ejpam-6640	471	9	)	)	PUNCT
ejpam-6640	471	10	(	(	PUNCT
ejpam-6640	471	11	−	−	PROPN
ejpam-6640	471	12	,	,	PUNCT
ejpam-6640	471	13	x	x	NOUN
ejpam-6640	471	14	)	)	PUNCT
ejpam-6640	471	15	:	:	PUNCT
ejpam-6640	471	16	comp(a	comp(a	NOUN
ejpam-6640	471	17	)	)	PUNCT
ejpam-6640	471	18	→	→	SYM
ejpam-6640	471	19	comp(ab	comp(ab	NOUN
ejpam-6640	471	20	)	)	PUNCT
ejpam-6640	471	21	is	be	AUX
ejpam-6640	471	22	left	leave	VERB
ejpam-6640	471	23	exact	exact	ADJ
ejpam-6640	471	24	.	.	PUNCT
ejpam-6640	472	1	let	let	VERB
ejpam-6640	472	2	(	(	PUNCT
ejpam-6640	472	3	y	y	PROPN
ejpam-6640	472	4	,	,	PUNCT
ejpam-6640	472	5	α	α	NOUN
ejpam-6640	472	6	)	)	PUNCT
ejpam-6640	472	7	f	f	PROPN
ejpam-6640	473	1	//	//	X
ejpam-6640	474	1	(	(	PUNCT
ejpam-6640	474	2	z	z	NOUN
ejpam-6640	474	3	,	,	PUNCT
ejpam-6640	474	4	β	β	NOUN
ejpam-6640	474	5	)	)	PUNCT
ejpam-6640	475	1	g	g	PROPN
ejpam-6640	475	2	//	//	SYM
ejpam-6640	475	3	(	(	PUNCT
ejpam-6640	475	4	t	t	PROPN
ejpam-6640	475	5	,	,	PUNCT
ejpam-6640	475	6	θ	θ	PROPN
ejpam-6640	475	7	)	)	PUNCT
ejpam-6640	475	8	//	//	NOUN
ejpam-6640	475	9	(	(	PUNCT
ejpam-6640	475	10	0	0	NUM
ejpam-6640	475	11	)	)	PUNCT
ejpam-6640	475	12	be	be	AUX
ejpam-6640	475	13	a	a	DET
ejpam-6640	475	14	right	right	ADJ
ejpam-6640	475	15	short	short	ADJ
ejpam-6640	475	16	exact	exact	ADJ
ejpam-6640	475	17	sequence	sequence	NOUN
ejpam-6640	475	18	of	of	ADP
ejpam-6640	475	19	morphisms	morphism	NOUN
ejpam-6640	475	20	in	in	ADP
ejpam-6640	475	21	comp(a	comp(a	NOUN
ejpam-6640	475	22	)	)	PUNCT
ejpam-6640	475	23	,	,	PUNCT
ejpam-6640	475	24	where	where	SCONJ
ejpam-6640	475	25	a	a	PRON
ejpam-6640	475	26	is	be	AUX
ejpam-6640	475	27	a	a	DET
ejpam-6640	475	28	balanced	balanced	ADJ
ejpam-6640	475	29	abelian	abelian	ADJ
ejpam-6640	475	30	category	category	NOUN
ejpam-6640	475	31	.	.	PUNCT
ejpam-6640	476	1	we	we	PRON
ejpam-6640	476	2	show	show	VERB
ejpam-6640	476	3	that	that	SCONJ
ejpam-6640	476	4	homcomp(a	homcomp(a	NOUN
ejpam-6640	476	5	)	)	PUNCT
ejpam-6640	476	6	(	(	PUNCT
ejpam-6640	476	7	−	−	PROPN
ejpam-6640	476	8	,	,	PUNCT
ejpam-6640	476	9	x)((0	x)((0	PROPN
ejpam-6640	476	10	)	)	PUNCT
ejpam-6640	476	11	)	)	PUNCT
ejpam-6640	477	1	//	//	PUNCT
ejpam-6640	477	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	477	3	)	)	PUNCT
ejpam-6640	477	4	(	(	PUNCT
ejpam-6640	477	5	−	−	PROPN
ejpam-6640	477	6	,	,	PUNCT
ejpam-6640	477	7	x)((t	x)((t	NUM
ejpam-6640	477	8	,	,	PUNCT
ejpam-6640	477	9	θ	θ	NOUN
ejpam-6640	477	10	)	)	PUNCT
ejpam-6640	477	11	)	)	PUNCT
ejpam-6640	477	12	g∗	g∗	VERB
ejpam-6640	477	13	//	//	NUM
ejpam-6640	477	14	homcomp(a	homcomp(a	NOUN
ejpam-6640	477	15	)	)	PUNCT
ejpam-6640	477	16	(	(	PUNCT
ejpam-6640	477	17	−	−	PROPN
ejpam-6640	477	18	,	,	PUNCT
ejpam-6640	477	19	x)((z	x)((z	PROPN
ejpam-6640	477	20	,	,	PUNCT
ejpam-6640	477	21	β	β	NOUN
ejpam-6640	477	22	)	)	PUNCT
ejpam-6640	477	23	)	)	PUNCT
ejpam-6640	478	1	f∗	f∗	NOUN
ejpam-6640	478	2	//	//	X
ejpam-6640	478	3	homcomp(a	homcomp(a	NOUN
ejpam-6640	478	4	)	)	PUNCT
ejpam-6640	478	5	(	(	PUNCT
ejpam-6640	478	6	−	−	PROPN
ejpam-6640	478	7	,	,	PUNCT
ejpam-6640	478	8	x)((y	x)((y	PROPN
ejpam-6640	478	9	,	,	PUNCT
ejpam-6640	478	10	α	α	NOUN
ejpam-6640	478	11	)	)	PUNCT
ejpam-6640	478	12	)	)	PUNCT
ejpam-6640	478	13	is	be	AUX
ejpam-6640	478	14	a	a	DET
ejpam-6640	478	15	left	left	ADJ
ejpam-6640	478	16	short	short	ADJ
ejpam-6640	478	17	exact	exact	ADJ
ejpam-6640	478	18	sequence	sequence	NOUN
ejpam-6640	478	19	of	of	ADP
ejpam-6640	478	20	morphisms	morphism	NOUN
ejpam-6640	478	21	in	in	ADP
ejpam-6640	478	22	comp(ab	comp(ab	NOUN
ejpam-6640	478	23	)	)	PUNCT
ejpam-6640	478	24	.	.	PUNCT
ejpam-6640	479	1	consider	consider	VERB
ejpam-6640	479	2	the	the	DET
ejpam-6640	479	3	following	follow	VERB
ejpam-6640	479	4	a.	a.	PROPN
ejpam-6640	479	5	diallo	diallo	PROPN
ejpam-6640	479	6	,	,	PUNCT
ejpam-6640	479	7	m.	m.	PROPN
ejpam-6640	479	8	b.	b.	PROPN
ejpam-6640	479	9	f.	f.	PROPN
ejpam-6640	479	10	b.	b.	PROPN
ejpam-6640	479	11	maaouia	maaouia	PROPN
ejpam-6640	479	12	,	,	PUNCT
ejpam-6640	479	13	m.	m.	NOUN
ejpam-6640	479	14	sanghare	sanghare	PROPN
ejpam-6640	479	15	/	/	SYM
ejpam-6640	479	16	eur	eur	PROPN
ejpam-6640	479	17	.	.	PUNCT
ejpam-6640	480	1	j.	j.	PROPN
ejpam-6640	480	2	pure	pure	PROPN
ejpam-6640	480	3	appl	appl	PROPN
ejpam-6640	480	4	.	.	PROPN
ejpam-6640	480	5	math	math	PROPN
ejpam-6640	480	6	,	,	PUNCT
ejpam-6640	480	7	18	18	NUM
ejpam-6640	480	8	(	(	PUNCT
ejpam-6640	480	9	4	4	NUM
ejpam-6640	480	10	)	)	PUNCT
ejpam-6640	480	11	(	(	PUNCT
ejpam-6640	480	12	2025	2025	NUM
ejpam-6640	480	13	)	)	PUNCT
ejpam-6640	480	14	,	,	PUNCT
ejpam-6640	480	15	6640	6640	NUM
ejpam-6640	480	16	20	20	NUM
ejpam-6640	480	17	of	of	ADP
ejpam-6640	480	18	28	28	NUM
ejpam-6640	480	19	diagram	diagram	NOUN
ejpam-6640	480	20	:	:	PUNCT
ejpam-6640	480	21	homcomp(a	homcomp(a	NOUN
ejpam-6640	480	22	)	)	PUNCT
ejpam-6640	480	23	(	(	PUNCT
ejpam-6640	480	24	−	−	PROPN
ejpam-6640	480	25	,	,	PUNCT
ejpam-6640	480	26	x)((0	x)((0	PROPN
ejpam-6640	480	27	)	)	PUNCT
ejpam-6640	480	28	)	)	PUNCT
ejpam-6640	480	29	:	:	PUNCT
ejpam-6640	480	30	...	...	PUNCT
ejpam-6640	481	1	//	//	PUNCT
ejpam-6640	481	2	�	�	PROPN
ejpam-6640	481	3	�	�	PROPN
ejpam-6640	481	4	0homcomp(a	0homcomp(a	NUM
ejpam-6640	481	5	)	)	PUNCT
ejpam-6640	481	6	(	(	PUNCT
ejpam-6640	481	7	0,x	0,x	PROPN
ejpam-6640	481	8	)	)	PUNCT
ejpam-6640	481	9	//	//	SYM
ejpam-6640	481	10	�	�	PROPN
ejpam-6640	481	11	�	�	PROPN
ejpam-6640	481	12	0homcomp(a	0homcomp(a	NUM
ejpam-6640	481	13	)	)	PUNCT
ejpam-6640	481	14	(	(	PUNCT
ejpam-6640	481	15	0,x	0,x	PROPN
ejpam-6640	481	16	)	)	PUNCT
ejpam-6640	481	17	//	//	SYM
ejpam-6640	481	18	�	�	PROPN
ejpam-6640	481	19	�	�	PROPN
ejpam-6640	481	20	0homcomp(a	0homcomp(a	NUM
ejpam-6640	481	21	)	)	PUNCT
ejpam-6640	481	22	(	(	PUNCT
ejpam-6640	481	23	0,x	0,x	PROPN
ejpam-6640	481	24	)	)	PUNCT
ejpam-6640	481	25	//	//	SYM
ejpam-6640	481	26	�	�	PROPN
ejpam-6640	481	27	�	�	PROPN
ejpam-6640	481	28	...	...	PUNCT
ejpam-6640	481	29	homcomp(a	homcomp(a	NOUN
ejpam-6640	481	30	)	)	PUNCT
ejpam-6640	481	31	(	(	PUNCT
ejpam-6640	481	32	−	−	PROPN
ejpam-6640	481	33	,	,	PUNCT
ejpam-6640	481	34	x)((t	x)((t	NUM
ejpam-6640	481	35	,	,	PUNCT
ejpam-6640	481	36	θ	θ	NOUN
ejpam-6640	481	37	)	)	PUNCT
ejpam-6640	481	38	)	)	PUNCT
ejpam-6640	481	39	:	:	PUNCT
ejpam-6640	481	40	...	...	PUNCT
ejpam-6640	481	41	//	//	PUNCT
ejpam-6640	481	42	g∗	g∗	PROPN
ejpam-6640	481	43	�	�	PROPN
ejpam-6640	481	44	�	�	PROPN
ejpam-6640	481	45	homcomp(a	homcomp(a	PROPN
ejpam-6640	481	46	)	)	PUNCT
ejpam-6640	481	47	(	(	PUNCT
ejpam-6640	481	48	tn	tn	NOUN
ejpam-6640	481	49	,	,	PUNCT
ejpam-6640	481	50	x	x	NOUN
ejpam-6640	481	51	)	)	PUNCT
ejpam-6640	481	52	θ∗	θ∗	NOUN
ejpam-6640	481	53	n//	n//	PRON
ejpam-6640	481	54	g∗	g∗	VERB
ejpam-6640	481	55	n	n	NUM
ejpam-6640	481	56	�	�	PROPN
ejpam-6640	481	57	�	�	PROPN
ejpam-6640	481	58	homcomp(a	homcomp(a	PROPN
ejpam-6640	481	59	)	)	PUNCT
ejpam-6640	481	60	(	(	PUNCT
ejpam-6640	481	61	tn+1	tn+1	NOUN
ejpam-6640	481	62	,	,	PUNCT
ejpam-6640	481	63	x	x	X
ejpam-6640	481	64	)	)	PUNCT
ejpam-6640	481	65	θ∗	θ∗	NOUN
ejpam-6640	481	66	n+1	n+1	PROPN
ejpam-6640	481	67	//	//	PUNCT
ejpam-6640	481	68	g∗	g∗	PROPN
ejpam-6640	481	69	n+1	n+1	PROPN
ejpam-6640	481	70	�	�	PROPN
ejpam-6640	481	71	�	�	PROPN
ejpam-6640	481	72	homcomp(a	homcomp(a	PROPN
ejpam-6640	481	73	)	)	PUNCT
ejpam-6640	481	74	(	(	PUNCT
ejpam-6640	481	75	tn+2	tn+2	ADV
ejpam-6640	481	76	,	,	PUNCT
ejpam-6640	481	77	x	x	X
ejpam-6640	481	78	)	)	PUNCT
ejpam-6640	481	79	//	//	PUNCT
ejpam-6640	481	80	g∗	g∗	VERB
ejpam-6640	481	81	n+2	n+2	NUM
ejpam-6640	481	82	�	�	PROPN
ejpam-6640	481	83	�	�	PROPN
ejpam-6640	481	84	...	...	PUNCT
ejpam-6640	481	85	homcomp(a	homcomp(a	NOUN
ejpam-6640	481	86	)	)	PUNCT
ejpam-6640	481	87	(	(	PUNCT
ejpam-6640	481	88	−	−	PROPN
ejpam-6640	481	89	,	,	PUNCT
ejpam-6640	481	90	x)((z	x)((z	PROPN
ejpam-6640	481	91	,	,	PUNCT
ejpam-6640	481	92	β	β	NOUN
ejpam-6640	481	93	)	)	PUNCT
ejpam-6640	481	94	)	)	PUNCT
ejpam-6640	481	95	:	:	PUNCT
ejpam-6640	481	96	...	...	PUNCT
ejpam-6640	482	1	//	//	NUM
ejpam-6640	482	2	f∗	f∗	X
ejpam-6640	482	3	�	�	PROPN
ejpam-6640	482	4	�	�	PROPN
ejpam-6640	482	5	homcomp(a	homcomp(a	PROPN
ejpam-6640	482	6	)	)	PUNCT
ejpam-6640	482	7	(	(	PUNCT
ejpam-6640	482	8	zn	zn	PROPN
ejpam-6640	482	9	,	,	PUNCT
ejpam-6640	482	10	x	x	NOUN
ejpam-6640	482	11	)	)	PUNCT
ejpam-6640	482	12	β∗	β∗	NOUN
ejpam-6640	483	1	n//	n//	ADP
ejpam-6640	483	2	f∗	f∗	NOUN
ejpam-6640	483	3	n	n	PROPN
ejpam-6640	483	4	�	�	PROPN
ejpam-6640	483	5	�	�	PROPN
ejpam-6640	483	6	homcomp(a	homcomp(a	PROPN
ejpam-6640	483	7	)	)	PUNCT
ejpam-6640	483	8	(	(	PUNCT
ejpam-6640	483	9	zn+1	zn+1	PROPN
ejpam-6640	483	10	,	,	PUNCT
ejpam-6640	483	11	x	x	NOUN
ejpam-6640	483	12	)	)	PUNCT
ejpam-6640	483	13	β∗	β∗	NOUN
ejpam-6640	483	14	n+1	n+1	PROPN
ejpam-6640	483	15	//	//	NUM
ejpam-6640	483	16	f∗	f∗	PROPN
ejpam-6640	483	17	n+1	n+1	PROPN
ejpam-6640	483	18	�	�	PROPN
ejpam-6640	483	19	�	�	PROPN
ejpam-6640	483	20	homcomp(a	homcomp(a	PROPN
ejpam-6640	483	21	)	)	PUNCT
ejpam-6640	483	22	(	(	PUNCT
ejpam-6640	483	23	zn+2	zn+2	NUM
ejpam-6640	483	24	,	,	PUNCT
ejpam-6640	483	25	x	x	NOUN
ejpam-6640	483	26	)	)	PUNCT
ejpam-6640	483	27	f∗	f∗	NOUN
ejpam-6640	483	28	n+2	n+2	NUM
ejpam-6640	483	29	�	�	PROPN
ejpam-6640	483	30	�	�	PROPN
ejpam-6640	483	31	//	//	NUM
ejpam-6640	483	32	...	...	PUNCT
ejpam-6640	484	1	homcomp(a	homcomp(a	NOUN
ejpam-6640	484	2	)	)	PUNCT
ejpam-6640	484	3	(	(	PUNCT
ejpam-6640	484	4	−	−	PROPN
ejpam-6640	484	5	,	,	PUNCT
ejpam-6640	484	6	x)((y	x)((y	PROPN
ejpam-6640	484	7	,	,	PUNCT
ejpam-6640	484	8	α	α	NOUN
ejpam-6640	484	9	)	)	PUNCT
ejpam-6640	484	10	)	)	PUNCT
ejpam-6640	484	11	:	:	PUNCT
ejpam-6640	484	12	...	...	PUNCT
ejpam-6640	485	1	//	//	PUNCT
ejpam-6640	485	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	485	3	)	)	PUNCT
ejpam-6640	485	4	(	(	PUNCT
ejpam-6640	485	5	yn	yn	PROPN
ejpam-6640	485	6	,	,	PUNCT
ejpam-6640	485	7	x	x	NOUN
ejpam-6640	485	8	)	)	PUNCT
ejpam-6640	485	9	α∗	α∗	VERB
ejpam-6640	485	10	n//	n//	PROPN
ejpam-6640	485	11	homcomp(a	homcomp(a	NOUN
ejpam-6640	485	12	)	)	PUNCT
ejpam-6640	485	13	(	(	PUNCT
ejpam-6640	485	14	yn+1	yn+1	PROPN
ejpam-6640	485	15	,	,	PUNCT
ejpam-6640	485	16	x	x	X
ejpam-6640	485	17	)	)	PUNCT
ejpam-6640	485	18	α∗	α∗	VERB
ejpam-6640	485	19	n+1	n+1	PROPN
ejpam-6640	485	20	//	//	NUM
ejpam-6640	485	21	homcomp(a	homcomp(a	NOUN
ejpam-6640	485	22	)	)	PUNCT
ejpam-6640	485	23	(	(	PUNCT
ejpam-6640	485	24	yn+2	yn+2	PROPN
ejpam-6640	485	25	,	,	PUNCT
ejpam-6640	485	26	x	x	NOUN
ejpam-6640	485	27	)	)	PUNCT
ejpam-6640	485	28	//	//	NOUN
ejpam-6640	485	29	...	...	PUNCT
ejpam-6640	486	1	now	now	ADV
ejpam-6640	486	2	,	,	PUNCT
ejpam-6640	486	3	by	by	ADP
ejpam-6640	486	4	theorem	theorem	NOUN
ejpam-6640	486	5	2	2	NUM
ejpam-6640	486	6	,	,	PUNCT
ejpam-6640	486	7	for	for	ADP
ejpam-6640	486	8	every	every	DET
ejpam-6640	486	9	integer	integer	NOUN
ejpam-6640	486	10	n	n	X
ejpam-6640	486	11	in	in	ADP
ejpam-6640	486	12	z	z	PROPN
ejpam-6640	486	13	,	,	PUNCT
ejpam-6640	486	14	the	the	DET
ejpam-6640	486	15	sequence	sequence	NOUN
ejpam-6640	486	16	homcomp(a	homcomp(a	NOUN
ejpam-6640	486	17	)	)	PUNCT
ejpam-6640	486	18	(	(	PUNCT
ejpam-6640	486	19	0	0	NUM
ejpam-6640	486	20	,	,	PUNCT
ejpam-6640	486	21	x	x	X
ejpam-6640	486	22	)	)	PUNCT
ejpam-6640	486	23	//	//	NUM
ejpam-6640	486	24	homcomp(a	homcomp(a	NOUN
ejpam-6640	486	25	)	)	PUNCT
ejpam-6640	486	26	(	(	PUNCT
ejpam-6640	486	27	tn	tn	NOUN
ejpam-6640	486	28	,	,	PUNCT
ejpam-6640	486	29	x	x	NOUN
ejpam-6640	486	30	)	)	PUNCT
ejpam-6640	486	31	g∗	g∗	VERB
ejpam-6640	486	32	n	n	PRON
ejpam-6640	486	33	//	//	NUM
ejpam-6640	486	34	homcomp(a	homcomp(a	NOUN
ejpam-6640	486	35	)	)	PUNCT
ejpam-6640	486	36	(	(	PUNCT
ejpam-6640	486	37	zn	zn	PROPN
ejpam-6640	486	38	,	,	PUNCT
ejpam-6640	486	39	x	x	NOUN
ejpam-6640	486	40	)	)	PUNCT
ejpam-6640	486	41	f∗	f∗	NOUN
ejpam-6640	487	1	n	n	PROPN
ejpam-6640	487	2	//	//	NUM
ejpam-6640	487	3	homcomp(a	homcomp(a	NOUN
ejpam-6640	487	4	)	)	PUNCT
ejpam-6640	487	5	(	(	PUNCT
ejpam-6640	487	6	yn	yn	PROPN
ejpam-6640	487	7	,	,	PUNCT
ejpam-6640	487	8	x	x	X
ejpam-6640	487	9	)	)	PUNCT
ejpam-6640	487	10	is	be	AUX
ejpam-6640	487	11	a	a	DET
ejpam-6640	487	12	left	left	ADJ
ejpam-6640	487	13	short	short	ADJ
ejpam-6640	487	14	exact	exact	ADJ
ejpam-6640	487	15	sequence	sequence	NOUN
ejpam-6640	487	16	of	of	ADP
ejpam-6640	487	17	morphisms	morphism	NOUN
ejpam-6640	487	18	in	in	ADP
ejpam-6640	487	19	comp(ab	comp(ab	NOUN
ejpam-6640	487	20	)	)	PUNCT
ejpam-6640	487	21	.	.	PUNCT
ejpam-6640	488	1	hence	hence	ADV
ejpam-6640	488	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	488	3	)	)	PUNCT
ejpam-6640	488	4	(	(	PUNCT
ejpam-6640	488	5	−	−	PROPN
ejpam-6640	488	6	,	,	PUNCT
ejpam-6640	488	7	x)((0	x)((0	PROPN
ejpam-6640	488	8	)	)	PUNCT
ejpam-6640	488	9	)	)	PUNCT
ejpam-6640	489	1	//	//	PUNCT
ejpam-6640	489	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	489	3	)	)	PUNCT
ejpam-6640	489	4	(	(	PUNCT
ejpam-6640	489	5	−	−	PROPN
ejpam-6640	489	6	,	,	PUNCT
ejpam-6640	489	7	x)((t	x)((t	NUM
ejpam-6640	489	8	,	,	PUNCT
ejpam-6640	489	9	θ	θ	NOUN
ejpam-6640	489	10	)	)	PUNCT
ejpam-6640	489	11	)	)	PUNCT
ejpam-6640	489	12	g∗	g∗	VERB
ejpam-6640	489	13	//	//	NUM
ejpam-6640	489	14	homcomp(a	homcomp(a	NOUN
ejpam-6640	489	15	)	)	PUNCT
ejpam-6640	489	16	(	(	PUNCT
ejpam-6640	489	17	−	−	PROPN
ejpam-6640	489	18	,	,	PUNCT
ejpam-6640	489	19	x)((z	x)((z	PROPN
ejpam-6640	489	20	,	,	PUNCT
ejpam-6640	489	21	β	β	NOUN
ejpam-6640	489	22	)	)	PUNCT
ejpam-6640	489	23	)	)	PUNCT
ejpam-6640	490	1	f∗	f∗	NOUN
ejpam-6640	490	2	//	//	X
ejpam-6640	490	3	homcomp(a	homcomp(a	NOUN
ejpam-6640	490	4	)	)	PUNCT
ejpam-6640	490	5	(	(	PUNCT
ejpam-6640	490	6	−	−	PROPN
ejpam-6640	490	7	,	,	PUNCT
ejpam-6640	490	8	x)((y	x)((y	PROPN
ejpam-6640	490	9	,	,	PUNCT
ejpam-6640	490	10	α	α	NOUN
ejpam-6640	490	11	)	)	PUNCT
ejpam-6640	490	12	)	)	PUNCT
ejpam-6640	490	13	is	be	AUX
ejpam-6640	490	14	a	a	DET
ejpam-6640	490	15	left	left	ADJ
ejpam-6640	490	16	short	short	ADJ
ejpam-6640	490	17	exact	exact	ADJ
ejpam-6640	490	18	sequence	sequence	NOUN
ejpam-6640	490	19	of	of	ADP
ejpam-6640	490	20	morphisms	morphism	NOUN
ejpam-6640	490	21	in	in	ADP
ejpam-6640	490	22	comp(ab	comp(ab	NOUN
ejpam-6640	490	23	)	)	PUNCT
ejpam-6640	490	24	.	.	PUNCT
ejpam-6640	491	1	therefor	therefor	ADP
ejpam-6640	491	2	i.1	i.1	PROPN
ejpam-6640	491	3	and	and	CCONJ
ejpam-6640	491	4	i.2	i.2	PROPN
ejpam-6640	491	5	imply	imply	VERB
ejpam-6640	491	6	that	that	SCONJ
ejpam-6640	491	7	the	the	DET
ejpam-6640	491	8	functor	functor	PROPN
ejpam-6640	491	9	homcomp(a	homcomp(a	PROPN
ejpam-6640	491	10	)	)	PUNCT
ejpam-6640	491	11	(	(	PUNCT
ejpam-6640	491	12	−	−	PROPN
ejpam-6640	491	13	,	,	PUNCT
ejpam-6640	491	14	x	x	NOUN
ejpam-6640	491	15	)	)	PUNCT
ejpam-6640	491	16	:	:	PUNCT
ejpam-6640	491	17	comp(a	comp(a	NOUN
ejpam-6640	491	18	)	)	PUNCT
ejpam-6640	491	19	→	→	SYM
ejpam-6640	491	20	comp(ab	comp(ab	NOUN
ejpam-6640	491	21	)	)	PUNCT
ejpam-6640	491	22	is	be	AUX
ejpam-6640	491	23	contravariant	contravariant	ADJ
ejpam-6640	491	24	,	,	PUNCT
ejpam-6640	491	25	additive	additive	NOUN
ejpam-6640	491	26	,	,	PUNCT
ejpam-6640	491	27	and	and	CCONJ
ejpam-6640	491	28	left	leave	VERB
ejpam-6640	491	29	exact	exact	ADJ
ejpam-6640	491	30	.	.	PUNCT
ejpam-6640	492	1	ii	ii	PROPN
ejpam-6640	492	2	let	let	VERB
ejpam-6640	492	3	us	we	PRON
ejpam-6640	492	4	show	show	VERB
ejpam-6640	492	5	that	that	SCONJ
ejpam-6640	492	6	the	the	DET
ejpam-6640	492	7	functor	functor	PROPN
ejpam-6640	492	8	homcomp(a	homcomp(a	PROPN
ejpam-6640	492	9	)	)	PUNCT
ejpam-6640	492	10	(	(	PUNCT
ejpam-6640	492	11	−	−	PROPN
ejpam-6640	492	12	,	,	PUNCT
ejpam-6640	492	13	x	x	NOUN
ejpam-6640	492	14	)	)	PUNCT
ejpam-6640	492	15	:	:	PUNCT
ejpam-6640	492	16	comp(a	comp(a	NOUN
ejpam-6640	492	17	)	)	PUNCT
ejpam-6640	492	18	→	→	SYM
ejpam-6640	492	19	comp(ab	comp(ab	NOUN
ejpam-6640	492	20	)	)	PUNCT
ejpam-6640	492	21	is	be	AUX
ejpam-6640	492	22	exact	exact	ADJ
ejpam-6640	492	23	if	if	SCONJ
ejpam-6640	492	24	and	and	CCONJ
ejpam-6640	492	25	only	only	ADV
ejpam-6640	492	26	if	if	SCONJ
ejpam-6640	492	27	x	x	PRON
ejpam-6640	492	28	is	be	AUX
ejpam-6640	492	29	an	an	DET
ejpam-6640	492	30	injective	injective	ADJ
ejpam-6640	492	31	object	object	NOUN
ejpam-6640	492	32	in	in	ADP
ejpam-6640	492	33	a	a	PRON
ejpam-6640	492	34	.	.	PUNCT
ejpam-6640	493	1	ii.1	ii.1	PROPN
ejpam-6640	493	2	suppose	suppose	VERB
ejpam-6640	493	3	that	that	SCONJ
ejpam-6640	493	4	the	the	DET
ejpam-6640	493	5	functor	functor	PROPN
ejpam-6640	493	6	homcomp(a	homcomp(a	PROPN
ejpam-6640	493	7	)	)	PUNCT
ejpam-6640	493	8	(	(	PUNCT
ejpam-6640	493	9	−	−	PROPN
ejpam-6640	493	10	,	,	PUNCT
ejpam-6640	493	11	x	x	NOUN
ejpam-6640	493	12	)	)	PUNCT
ejpam-6640	493	13	:	:	PUNCT
ejpam-6640	493	14	comp(a	comp(a	NOUN
ejpam-6640	493	15	)	)	PUNCT
ejpam-6640	493	16	→	→	SYM
ejpam-6640	493	17	comp(ab	comp(ab	NOUN
ejpam-6640	493	18	)	)	PUNCT
ejpam-6640	493	19	is	be	AUX
ejpam-6640	493	20	exact	exact	ADJ
ejpam-6640	493	21	and	and	CCONJ
ejpam-6640	493	22	show	show	VERB
ejpam-6640	493	23	that	that	SCONJ
ejpam-6640	493	24	x	x	PRON
ejpam-6640	493	25	is	be	AUX
ejpam-6640	493	26	an	an	DET
ejpam-6640	493	27	injective	injective	ADJ
ejpam-6640	493	28	object	object	NOUN
ejpam-6640	493	29	in	in	ADP
ejpam-6640	493	30	a	a	PRON
ejpam-6640	493	31	.	.	PUNCT
ejpam-6640	494	1	we	we	PRON
ejpam-6640	494	2	have	have	VERB
ejpam-6640	494	3	:	:	PUNCT
ejpam-6640	494	4	homcomp(a	homcomp(a	NOUN
ejpam-6640	494	5	)	)	PUNCT
ejpam-6640	494	6	(	(	PUNCT
ejpam-6640	494	7	x,−	x,−	PROPN
ejpam-6640	494	8	)	)	PUNCT
ejpam-6640	494	9	:	:	PUNCT
ejpam-6640	494	10	comp(a	comp(a	NOUN
ejpam-6640	494	11	)	)	PUNCT
ejpam-6640	494	12	→	→	SYM
ejpam-6640	494	13	comp(ab	comp(ab	PROPN
ejpam-6640	494	14	)	)	PUNCT
ejpam-6640	494	15	being	be	AUX
ejpam-6640	494	16	exact	exact	ADJ
ejpam-6640	494	17	implies	imply	VERB
ejpam-6640	494	18	that	that	SCONJ
ejpam-6640	494	19	for	for	ADP
ejpam-6640	494	20	every	every	DET
ejpam-6640	494	21	short	short	ADJ
ejpam-6640	494	22	exact	exact	ADJ
ejpam-6640	494	23	sequence	sequence	NOUN
ejpam-6640	494	24	of	of	ADP
ejpam-6640	494	25	morphisms	morphism	NOUN
ejpam-6640	494	26	in	in	ADP
ejpam-6640	494	27	comp(a	comp(a	NOUN
ejpam-6640	494	28	)	)	PUNCT
ejpam-6640	494	29	,	,	PUNCT
ejpam-6640	494	30	(	(	PUNCT
ejpam-6640	494	31	0	0	NUM
ejpam-6640	494	32	)	)	PUNCT
ejpam-6640	494	33	//	//	NOUN
ejpam-6640	494	34	(	(	PUNCT
ejpam-6640	494	35	y	y	PROPN
ejpam-6640	494	36	,	,	PUNCT
ejpam-6640	494	37	α	α	NOUN
ejpam-6640	494	38	)	)	PUNCT
ejpam-6640	494	39	f	f	PROPN
ejpam-6640	494	40	//	//	X
ejpam-6640	494	41	(	(	PUNCT
ejpam-6640	494	42	z	z	NOUN
ejpam-6640	494	43	,	,	PUNCT
ejpam-6640	494	44	β	β	NOUN
ejpam-6640	494	45	)	)	PUNCT
ejpam-6640	494	46	g	g	PROPN
ejpam-6640	494	47	//	//	SYM
ejpam-6640	494	48	(	(	PUNCT
ejpam-6640	494	49	t	t	PROPN
ejpam-6640	494	50	,	,	PUNCT
ejpam-6640	494	51	θ	θ	PROPN
ejpam-6640	494	52	)	)	PUNCT
ejpam-6640	494	53	//	//	NOUN
ejpam-6640	494	54	(	(	PUNCT
ejpam-6640	494	55	0	0	NUM
ejpam-6640	494	56	)	)	PUNCT
ejpam-6640	494	57	then	then	ADV
ejpam-6640	494	58	homcomp(a	homcomp(a	NOUN
ejpam-6640	494	59	)	)	PUNCT
ejpam-6640	494	60	(	(	PUNCT
ejpam-6640	494	61	−	−	PROPN
ejpam-6640	494	62	,	,	PUNCT
ejpam-6640	494	63	x)((0	x)((0	PROPN
ejpam-6640	494	64	)	)	PUNCT
ejpam-6640	494	65	)	)	PUNCT
ejpam-6640	495	1	//	//	PUNCT
ejpam-6640	495	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	495	3	)	)	PUNCT
ejpam-6640	495	4	(	(	PUNCT
ejpam-6640	495	5	−	−	PROPN
ejpam-6640	495	6	,	,	PUNCT
ejpam-6640	495	7	x)((t	x)((t	NUM
ejpam-6640	495	8	,	,	PUNCT
ejpam-6640	495	9	θ	θ	NOUN
ejpam-6640	495	10	)	)	PUNCT
ejpam-6640	495	11	)	)	PUNCT
ejpam-6640	495	12	g∗	g∗	VERB
ejpam-6640	495	13	//	//	NUM
ejpam-6640	495	14	homcomp(a	homcomp(a	NOUN
ejpam-6640	495	15	)	)	PUNCT
ejpam-6640	495	16	(	(	PUNCT
ejpam-6640	495	17	−	−	PROPN
ejpam-6640	495	18	,	,	PUNCT
ejpam-6640	495	19	x)((z	x)((z	PROPN
ejpam-6640	495	20	,	,	PUNCT
ejpam-6640	495	21	β	β	NOUN
ejpam-6640	495	22	)	)	PUNCT
ejpam-6640	495	23	)	)	PUNCT
ejpam-6640	496	1	f∗	f∗	NOUN
ejpam-6640	496	2	//	//	X
ejpam-6640	496	3	homcomp(a	homcomp(a	NOUN
ejpam-6640	496	4	)	)	PUNCT
ejpam-6640	496	5	(	(	PUNCT
ejpam-6640	496	6	−	−	PROPN
ejpam-6640	496	7	,	,	PUNCT
ejpam-6640	496	8	x)((y	x)((y	PROPN
ejpam-6640	496	9	,	,	PUNCT
ejpam-6640	496	10	α	α	NOUN
ejpam-6640	496	11	)	)	PUNCT
ejpam-6640	496	12	)	)	PUNCT
ejpam-6640	497	1	//	//	PUNCT
ejpam-6640	497	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	497	3	)	)	PUNCT
ejpam-6640	497	4	(	(	PUNCT
ejpam-6640	497	5	−	−	PROPN
ejpam-6640	497	6	,	,	PUNCT
ejpam-6640	497	7	x)((0	x)((0	PROPN
ejpam-6640	497	8	)	)	PUNCT
ejpam-6640	497	9	)	)	PUNCT
ejpam-6640	497	10	is	be	AUX
ejpam-6640	497	11	a	a	DET
ejpam-6640	497	12	short	short	ADJ
ejpam-6640	497	13	exact	exact	ADJ
ejpam-6640	497	14	sequence	sequence	NOUN
ejpam-6640	497	15	of	of	ADP
ejpam-6640	497	16	morphisms	morphism	NOUN
ejpam-6640	497	17	in	in	ADP
ejpam-6640	497	18	comp(ab	comp(ab	NOUN
ejpam-6640	497	19	)	)	PUNCT
ejpam-6640	497	20	.	.	PUNCT
ejpam-6640	498	1	this	this	PRON
ejpam-6640	498	2	means	mean	VERB
ejpam-6640	498	3	that	that	SCONJ
ejpam-6640	498	4	the	the	DET
ejpam-6640	498	5	following	follow	VERB
ejpam-6640	498	6	a.	a.	PROPN
ejpam-6640	498	7	diallo	diallo	PROPN
ejpam-6640	498	8	,	,	PUNCT
ejpam-6640	498	9	m.	m.	PROPN
ejpam-6640	498	10	b.	b.	PROPN
ejpam-6640	498	11	f.	f.	PROPN
ejpam-6640	498	12	b.	b.	PROPN
ejpam-6640	498	13	maaouia	maaouia	PROPN
ejpam-6640	498	14	,	,	PUNCT
ejpam-6640	498	15	m.	m.	NOUN
ejpam-6640	498	16	sanghare	sanghare	PROPN
ejpam-6640	498	17	/	/	SYM
ejpam-6640	498	18	eur	eur	PROPN
ejpam-6640	498	19	.	.	PUNCT
ejpam-6640	499	1	j.	j.	PROPN
ejpam-6640	499	2	pure	pure	PROPN
ejpam-6640	499	3	appl	appl	PROPN
ejpam-6640	499	4	.	.	PROPN
ejpam-6640	499	5	math	math	PROPN
ejpam-6640	499	6	,	,	PUNCT
ejpam-6640	499	7	18	18	NUM
ejpam-6640	499	8	(	(	PUNCT
ejpam-6640	499	9	4	4	NUM
ejpam-6640	499	10	)	)	PUNCT
ejpam-6640	499	11	(	(	PUNCT
ejpam-6640	499	12	2025	2025	NUM
ejpam-6640	499	13	)	)	PUNCT
ejpam-6640	499	14	,	,	PUNCT
ejpam-6640	499	15	6640	6640	NUM
ejpam-6640	499	16	21	21	NUM
ejpam-6640	499	17	of	of	ADP
ejpam-6640	499	18	28	28	NUM
ejpam-6640	499	19	diagram	diagram	NOUN
ejpam-6640	499	20	is	be	AUX
ejpam-6640	499	21	commutative	commutative	ADJ
ejpam-6640	499	22	:	:	PUNCT
ejpam-6640	499	23	homcomp(a	homcomp(a	NOUN
ejpam-6640	499	24	)	)	PUNCT
ejpam-6640	499	25	(	(	PUNCT
ejpam-6640	499	26	−	−	PROPN
ejpam-6640	499	27	,	,	PUNCT
ejpam-6640	499	28	x)((0	x)((0	PROPN
ejpam-6640	499	29	)	)	PUNCT
ejpam-6640	499	30	)	)	PUNCT
ejpam-6640	499	31	:	:	PUNCT
ejpam-6640	499	32	...	...	PUNCT
ejpam-6640	500	1	//	//	PUNCT
ejpam-6640	500	2	�	�	PROPN
ejpam-6640	500	3	�	�	PROPN
ejpam-6640	500	4	0homcomp(a	0homcomp(a	NUM
ejpam-6640	500	5	)	)	PUNCT
ejpam-6640	500	6	(	(	PUNCT
ejpam-6640	500	7	0,x	0,x	PROPN
ejpam-6640	500	8	)	)	PUNCT
ejpam-6640	500	9	//	//	SYM
ejpam-6640	500	10	�	�	PROPN
ejpam-6640	500	11	�	�	PROPN
ejpam-6640	500	12	0homcomp(a	0homcomp(a	NUM
ejpam-6640	500	13	)	)	PUNCT
ejpam-6640	500	14	(	(	PUNCT
ejpam-6640	500	15	0,x	0,x	PROPN
ejpam-6640	500	16	)	)	PUNCT
ejpam-6640	500	17	//	//	SYM
ejpam-6640	500	18	�	�	PROPN
ejpam-6640	500	19	�	�	PROPN
ejpam-6640	500	20	0homcomp(a	0homcomp(a	NUM
ejpam-6640	500	21	)	)	PUNCT
ejpam-6640	500	22	(	(	PUNCT
ejpam-6640	500	23	0,x	0,x	PROPN
ejpam-6640	500	24	)	)	PUNCT
ejpam-6640	500	25	//	//	SYM
ejpam-6640	500	26	�	�	PROPN
ejpam-6640	500	27	�	�	PROPN
ejpam-6640	500	28	...	...	PUNCT
ejpam-6640	500	29	homcomp(a	homcomp(a	NOUN
ejpam-6640	500	30	)	)	PUNCT
ejpam-6640	500	31	(	(	PUNCT
ejpam-6640	500	32	−	−	PROPN
ejpam-6640	500	33	,	,	PUNCT
ejpam-6640	500	34	x)((t	x)((t	NUM
ejpam-6640	500	35	,	,	PUNCT
ejpam-6640	500	36	θ	θ	NOUN
ejpam-6640	500	37	)	)	PUNCT
ejpam-6640	500	38	)	)	PUNCT
ejpam-6640	500	39	:	:	PUNCT
ejpam-6640	500	40	...	...	PUNCT
ejpam-6640	500	41	//	//	PUNCT
ejpam-6640	500	42	g∗	g∗	PROPN
ejpam-6640	500	43	�	�	PROPN
ejpam-6640	500	44	�	�	PROPN
ejpam-6640	500	45	homcomp(a	homcomp(a	PROPN
ejpam-6640	500	46	)	)	PUNCT
ejpam-6640	500	47	(	(	PUNCT
ejpam-6640	500	48	tn	tn	NOUN
ejpam-6640	500	49	,	,	PUNCT
ejpam-6640	500	50	x	x	NOUN
ejpam-6640	500	51	)	)	PUNCT
ejpam-6640	500	52	θ∗	θ∗	NOUN
ejpam-6640	500	53	n//	n//	PRON
ejpam-6640	500	54	g∗	g∗	VERB
ejpam-6640	500	55	n	n	NUM
ejpam-6640	500	56	�	�	PROPN
ejpam-6640	500	57	�	�	PROPN
ejpam-6640	500	58	homcomp(a	homcomp(a	PROPN
ejpam-6640	500	59	)	)	PUNCT
ejpam-6640	500	60	(	(	PUNCT
ejpam-6640	500	61	tn+1	tn+1	NOUN
ejpam-6640	500	62	,	,	PUNCT
ejpam-6640	500	63	x	x	X
ejpam-6640	500	64	)	)	PUNCT
ejpam-6640	500	65	θ∗	θ∗	NOUN
ejpam-6640	500	66	n+1	n+1	PROPN
ejpam-6640	500	67	//	//	PUNCT
ejpam-6640	500	68	g∗	g∗	PROPN
ejpam-6640	500	69	n+1	n+1	PROPN
ejpam-6640	500	70	�	�	PROPN
ejpam-6640	500	71	�	�	PROPN
ejpam-6640	500	72	homcomp(a	homcomp(a	PROPN
ejpam-6640	500	73	)	)	PUNCT
ejpam-6640	500	74	(	(	PUNCT
ejpam-6640	500	75	tn+2	tn+2	ADV
ejpam-6640	500	76	,	,	PUNCT
ejpam-6640	500	77	x	x	X
ejpam-6640	500	78	)	)	PUNCT
ejpam-6640	500	79	//	//	PUNCT
ejpam-6640	500	80	g∗	g∗	VERB
ejpam-6640	500	81	n+2	n+2	NUM
ejpam-6640	500	82	�	�	PROPN
ejpam-6640	500	83	�	�	PROPN
ejpam-6640	500	84	...	...	PUNCT
ejpam-6640	500	85	homcomp(a	homcomp(a	NOUN
ejpam-6640	500	86	)	)	PUNCT
ejpam-6640	500	87	(	(	PUNCT
ejpam-6640	500	88	−	−	PROPN
ejpam-6640	500	89	,	,	PUNCT
ejpam-6640	500	90	x)((z	x)((z	PROPN
ejpam-6640	500	91	,	,	PUNCT
ejpam-6640	500	92	β	β	NOUN
ejpam-6640	500	93	)	)	PUNCT
ejpam-6640	500	94	)	)	PUNCT
ejpam-6640	500	95	:	:	PUNCT
ejpam-6640	500	96	...	...	PUNCT
ejpam-6640	501	1	//	//	NUM
ejpam-6640	501	2	f∗	f∗	X
ejpam-6640	501	3	�	�	PROPN
ejpam-6640	501	4	�	�	PROPN
ejpam-6640	501	5	homcomp(a	homcomp(a	PROPN
ejpam-6640	501	6	)	)	PUNCT
ejpam-6640	501	7	(	(	PUNCT
ejpam-6640	501	8	zn	zn	PROPN
ejpam-6640	501	9	,	,	PUNCT
ejpam-6640	501	10	x	x	NOUN
ejpam-6640	501	11	)	)	PUNCT
ejpam-6640	501	12	β∗	β∗	NOUN
ejpam-6640	502	1	n//	n//	ADP
ejpam-6640	502	2	f∗	f∗	NOUN
ejpam-6640	502	3	n	n	PROPN
ejpam-6640	502	4	�	�	PROPN
ejpam-6640	502	5	�	�	PROPN
ejpam-6640	502	6	homcomp(a	homcomp(a	PROPN
ejpam-6640	502	7	)	)	PUNCT
ejpam-6640	502	8	(	(	PUNCT
ejpam-6640	502	9	zn+1	zn+1	PROPN
ejpam-6640	502	10	,	,	PUNCT
ejpam-6640	502	11	x	x	NOUN
ejpam-6640	502	12	)	)	PUNCT
ejpam-6640	502	13	β∗	β∗	NOUN
ejpam-6640	502	14	n+1	n+1	PROPN
ejpam-6640	502	15	//	//	NUM
ejpam-6640	502	16	f∗	f∗	PROPN
ejpam-6640	502	17	n+1	n+1	PROPN
ejpam-6640	502	18	�	�	PROPN
ejpam-6640	502	19	�	�	PROPN
ejpam-6640	502	20	homcomp(a	homcomp(a	PROPN
ejpam-6640	502	21	)	)	PUNCT
ejpam-6640	502	22	(	(	PUNCT
ejpam-6640	502	23	zn+2	zn+2	NUM
ejpam-6640	502	24	,	,	PUNCT
ejpam-6640	502	25	x	x	NOUN
ejpam-6640	502	26	)	)	PUNCT
ejpam-6640	502	27	f∗	f∗	NOUN
ejpam-6640	502	28	n+2	n+2	NUM
ejpam-6640	502	29	�	�	PROPN
ejpam-6640	502	30	�	�	PROPN
ejpam-6640	502	31	//	//	NUM
ejpam-6640	502	32	...	...	PUNCT
ejpam-6640	503	1	homcomp(a	homcomp(a	NOUN
ejpam-6640	503	2	)	)	PUNCT
ejpam-6640	503	3	(	(	PUNCT
ejpam-6640	503	4	−	−	PROPN
ejpam-6640	503	5	,	,	PUNCT
ejpam-6640	503	6	x)((y	x)((y	PROPN
ejpam-6640	503	7	,	,	PUNCT
ejpam-6640	503	8	α	α	NOUN
ejpam-6640	503	9	)	)	PUNCT
ejpam-6640	503	10	)	)	PUNCT
ejpam-6640	503	11	:	:	PUNCT
ejpam-6640	503	12	...	...	PUNCT
ejpam-6640	504	1	//	//	PUNCT
ejpam-6640	504	2	�	�	PROPN
ejpam-6640	504	3	�	�	PROPN
ejpam-6640	504	4	homcomp(a	homcomp(a	PROPN
ejpam-6640	504	5	)	)	PUNCT
ejpam-6640	504	6	(	(	PUNCT
ejpam-6640	504	7	yn	yn	PROPN
ejpam-6640	504	8	,	,	PUNCT
ejpam-6640	504	9	x	x	NOUN
ejpam-6640	504	10	)	)	PUNCT
ejpam-6640	504	11	α∗	α∗	VERB
ejpam-6640	504	12	n//	n//	PRON
ejpam-6640	504	13	�	�	NOUN
ejpam-6640	504	14	�	�	PROPN
ejpam-6640	504	15	homcomp(a	homcomp(a	PROPN
ejpam-6640	504	16	)	)	PUNCT
ejpam-6640	504	17	(	(	PUNCT
ejpam-6640	504	18	yn+1	yn+1	PROPN
ejpam-6640	504	19	,	,	PUNCT
ejpam-6640	504	20	x	x	X
ejpam-6640	504	21	)	)	PUNCT
ejpam-6640	504	22	α∗	α∗	VERB
ejpam-6640	504	23	n+1	n+1	PROPN
ejpam-6640	504	24	//	//	SYM
ejpam-6640	504	25	�	�	PROPN
ejpam-6640	504	26	�	�	PROPN
ejpam-6640	504	27	homcomp(a	homcomp(a	PROPN
ejpam-6640	504	28	)	)	PUNCT
ejpam-6640	504	29	(	(	PUNCT
ejpam-6640	504	30	yn+2	yn+2	PROPN
ejpam-6640	504	31	,	,	PUNCT
ejpam-6640	504	32	x	x	NOUN
ejpam-6640	504	33	)	)	PUNCT
ejpam-6640	504	34	//	//	SYM
ejpam-6640	504	35	�	�	PROPN
ejpam-6640	504	36	�	�	PROPN
ejpam-6640	504	37	...	...	PUNCT
ejpam-6640	504	38	homcomp(a	homcomp(a	NOUN
ejpam-6640	504	39	)	)	PUNCT
ejpam-6640	504	40	(	(	PUNCT
ejpam-6640	504	41	−	−	PROPN
ejpam-6640	504	42	,	,	PUNCT
ejpam-6640	504	43	x)((0	x)((0	PROPN
ejpam-6640	504	44	)	)	PUNCT
ejpam-6640	504	45	)	)	PUNCT
ejpam-6640	504	46	:	:	PUNCT
ejpam-6640	504	47	...	...	PUNCT
ejpam-6640	505	1	//	//	NUM
ejpam-6640	505	2	0homcomp(a	0homcomp(a	NUM
ejpam-6640	505	3	)	)	PUNCT
ejpam-6640	505	4	(	(	PUNCT
ejpam-6640	505	5	0,x	0,x	PROPN
ejpam-6640	505	6	)	)	PUNCT
ejpam-6640	505	7	//	//	NOUN
ejpam-6640	505	8	0homcomp(a	0homcomp(a	NUM
ejpam-6640	505	9	)	)	PUNCT
ejpam-6640	505	10	(	(	PUNCT
ejpam-6640	505	11	0,x	0,x	PROPN
ejpam-6640	505	12	)	)	PUNCT
ejpam-6640	505	13	//	//	NOUN
ejpam-6640	505	14	0homcomp(a	0homcomp(a	NUM
ejpam-6640	505	15	)	)	PUNCT
ejpam-6640	505	16	(	(	PUNCT
ejpam-6640	505	17	0,x	0,x	PROPN
ejpam-6640	505	18	)	)	PUNCT
ejpam-6640	505	19	//	//	NOUN
ejpam-6640	505	20	...	...	PUNCT
ejpam-6640	506	1	we	we	PRON
ejpam-6640	506	2	have	have	VERB
ejpam-6640	506	3	for	for	ADP
ejpam-6640	506	4	every	every	DET
ejpam-6640	506	5	integer	integer	NOUN
ejpam-6640	506	6	n	n	X
ejpam-6640	506	7	in	in	ADP
ejpam-6640	506	8	z	z	PROPN
ejpam-6640	506	9	,	,	PUNCT
ejpam-6640	506	10	f∗n	f∗n	PUNCT
ejpam-6640	506	11	is	be	AUX
ejpam-6640	506	12	an	an	DET
ejpam-6640	506	13	epimorphism	epimorphism	NOUN
ejpam-6640	506	14	.	.	PUNCT
ejpam-6640	507	1	therefore	therefore	ADV
ejpam-6640	507	2	,	,	PUNCT
ejpam-6640	507	3	for	for	ADP
ejpam-6640	507	4	every	every	DET
ejpam-6640	507	5	monomorphism	monomorphism	NOUN
ejpam-6640	507	6	fn	fn	INTJ
ejpam-6640	507	7	:	:	PUNCT
ejpam-6640	507	8	yn	yn	PROPN
ejpam-6640	507	9	↪	↪	PROPN
ejpam-6640	507	10	→	→	SYM
ejpam-6640	507	11	zn	zn	PROPN
ejpam-6640	507	12	in	in	ADP
ejpam-6640	507	13	a	a	PRON
ejpam-6640	507	14	and	and	CCONJ
ejpam-6640	507	15	every	every	DET
ejpam-6640	507	16	morphism	morphism	NOUN
ejpam-6640	507	17	hn	hn	PROPN
ejpam-6640	507	18	:	:	PUNCT
ejpam-6640	507	19	yn	yn	PROPN
ejpam-6640	507	20	→	→	PUNCT
ejpam-6640	507	21	x	x	PROPN
ejpam-6640	507	22	in	in	ADP
ejpam-6640	507	23	a	a	PRON
ejpam-6640	507	24	,	,	PUNCT
ejpam-6640	507	25	there	there	PRON
ejpam-6640	507	26	exists	exist	VERB
ejpam-6640	507	27	a	a	DET
ejpam-6640	507	28	morphism	morphism	NOUN
ejpam-6640	507	29	ϕn	ϕn	X
ejpam-6640	507	30	:	:	PUNCT
ejpam-6640	507	31	zn	zn	PROPN
ejpam-6640	507	32	→	→	SYM
ejpam-6640	507	33	x	x	X
ejpam-6640	507	34	in	in	ADP
ejpam-6640	507	35	a	a	DET
ejpam-6640	507	36	such	such	ADJ
ejpam-6640	507	37	that	that	PRON
ejpam-6640	507	38	ϕn	ϕn	INTJ
ejpam-6640	507	39	◦	◦	NOUN
ejpam-6640	507	40	fn	fn	NOUN
ejpam-6640	507	41	=	=	ADJ
ejpam-6640	507	42	f∗n(ϕn	f∗n(ϕn	NOUN
ejpam-6640	507	43	)	)	PUNCT
ejpam-6640	508	1	=	=	SYM
ejpam-6640	508	2	hn	hn	PROPN
ejpam-6640	508	3	.	.	PUNCT
ejpam-6640	509	1	this	this	PRON
ejpam-6640	509	2	means	mean	VERB
ejpam-6640	509	3	that	that	SCONJ
ejpam-6640	509	4	the	the	DET
ejpam-6640	509	5	following	follow	VERB
ejpam-6640	509	6	diagram	diagram	NOUN
ejpam-6640	509	7	commutes	commute	NOUN
ejpam-6640	509	8	:	:	PUNCT
ejpam-6640	509	9	x	x	SYM
ejpam-6640	509	10	o	o	X
ejpam-6640	509	11	//	//	X
ejpam-6640	509	12	yn	yn	INTJ
ejpam-6640	509	13	hn	hn	INTJ
ejpam-6640	509	14	oo	oo	INTJ
ejpam-6640	509	15	fn	fn	PROPN
ejpam-6640	509	16	//	//	PROPN
ejpam-6640	509	17	zn	zn	INTJ
ejpam-6640	509	18	ϕn	ϕn	INTJ
ejpam-6640	509	19	aa	aa	INTJ
ejpam-6640	509	20	hence	hence	ADV
ejpam-6640	509	21	,	,	PUNCT
ejpam-6640	509	22	x	x	X
ejpam-6640	509	23	is	be	AUX
ejpam-6640	509	24	an	an	DET
ejpam-6640	509	25	injective	injective	ADJ
ejpam-6640	509	26	object	object	NOUN
ejpam-6640	509	27	of	of	ADP
ejpam-6640	509	28	a	a	PRON
ejpam-6640	509	29	.	.	PUNCT
ejpam-6640	510	1	ii.2	ii.2	PROPN
ejpam-6640	510	2	suppose	suppose	VERB
ejpam-6640	510	3	thatx	thatx	NOUN
ejpam-6640	510	4	is	be	AUX
ejpam-6640	510	5	an	an	DET
ejpam-6640	510	6	injective	injective	ADJ
ejpam-6640	510	7	object	object	NOUN
ejpam-6640	510	8	in	in	ADP
ejpam-6640	510	9	a	a	PRON
ejpam-6640	510	10	and	and	CCONJ
ejpam-6640	510	11	show	show	VERB
ejpam-6640	510	12	that	that	SCONJ
ejpam-6640	510	13	the	the	DET
ejpam-6640	510	14	functor	functor	PROPN
ejpam-6640	510	15	homcomp(a	homcomp(a	PROPN
ejpam-6640	510	16	)	)	PUNCT
ejpam-6640	510	17	(	(	PUNCT
ejpam-6640	510	18	−	−	PROPN
ejpam-6640	510	19	,	,	PUNCT
ejpam-6640	510	20	x	x	NOUN
ejpam-6640	510	21	)	)	PUNCT
ejpam-6640	510	22	:	:	PUNCT
ejpam-6640	510	23	comp(a	comp(a	NOUN
ejpam-6640	510	24	)	)	PUNCT
ejpam-6640	510	25	→	→	SYM
ejpam-6640	510	26	comp(ab	comp(ab	NOUN
ejpam-6640	510	27	)	)	PUNCT
ejpam-6640	510	28	is	be	AUX
ejpam-6640	510	29	exact	exact	ADJ
ejpam-6640	510	30	.	.	PUNCT
ejpam-6640	511	1	let	let	VERB
ejpam-6640	511	2	the	the	DET
ejpam-6640	511	3	short	short	ADJ
ejpam-6640	511	4	exact	exact	ADJ
ejpam-6640	511	5	sequence	sequence	NOUN
ejpam-6640	511	6	of	of	ADP
ejpam-6640	511	7	morphisms	morphism	NOUN
ejpam-6640	511	8	in	in	ADP
ejpam-6640	511	9	a	a	DET
ejpam-6640	511	10	(	(	PUNCT
ejpam-6640	511	11	0	0	NUM
ejpam-6640	511	12	)	)	PUNCT
ejpam-6640	511	13	//	//	NOUN
ejpam-6640	511	14	(	(	PUNCT
ejpam-6640	511	15	y	y	PROPN
ejpam-6640	511	16	,	,	PUNCT
ejpam-6640	511	17	α	α	NOUN
ejpam-6640	511	18	)	)	PUNCT
ejpam-6640	511	19	f	f	PROPN
ejpam-6640	511	20	//	//	X
ejpam-6640	512	1	(	(	PUNCT
ejpam-6640	512	2	z	z	NOUN
ejpam-6640	512	3	,	,	PUNCT
ejpam-6640	512	4	β	β	NOUN
ejpam-6640	512	5	)	)	PUNCT
ejpam-6640	513	1	g	g	PROPN
ejpam-6640	513	2	//	//	SYM
ejpam-6640	513	3	(	(	PUNCT
ejpam-6640	513	4	t	t	PROPN
ejpam-6640	513	5	,	,	PUNCT
ejpam-6640	513	6	θ	θ	PROPN
ejpam-6640	513	7	)	)	PUNCT
ejpam-6640	513	8	//	//	NOUN
ejpam-6640	513	9	(	(	PUNCT
ejpam-6640	513	10	0	0	NUM
ejpam-6640	513	11	)	)	PUNCT
ejpam-6640	514	1	and	and	CCONJ
ejpam-6640	514	2	show	show	VERB
ejpam-6640	514	3	that	that	SCONJ
ejpam-6640	514	4	homcomp(a	homcomp(a	NOUN
ejpam-6640	514	5	)	)	PUNCT
ejpam-6640	514	6	(	(	PUNCT
ejpam-6640	514	7	−	−	PROPN
ejpam-6640	514	8	,	,	PUNCT
ejpam-6640	514	9	x)((0	x)((0	PROPN
ejpam-6640	514	10	)	)	PUNCT
ejpam-6640	514	11	)	)	PUNCT
ejpam-6640	515	1	//	//	PUNCT
ejpam-6640	515	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	515	3	)	)	PUNCT
ejpam-6640	515	4	(	(	PUNCT
ejpam-6640	515	5	−	−	PROPN
ejpam-6640	515	6	,	,	PUNCT
ejpam-6640	515	7	x)((t	x)((t	NUM
ejpam-6640	515	8	,	,	PUNCT
ejpam-6640	515	9	θ	θ	NOUN
ejpam-6640	515	10	)	)	PUNCT
ejpam-6640	515	11	)	)	PUNCT
ejpam-6640	515	12	g∗	g∗	VERB
ejpam-6640	515	13	//	//	NUM
ejpam-6640	515	14	homcomp(a	homcomp(a	NOUN
ejpam-6640	515	15	)	)	PUNCT
ejpam-6640	515	16	(	(	PUNCT
ejpam-6640	515	17	−	−	PROPN
ejpam-6640	515	18	,	,	PUNCT
ejpam-6640	515	19	x)((z	x)((z	PROPN
ejpam-6640	515	20	,	,	PUNCT
ejpam-6640	515	21	β	β	NOUN
ejpam-6640	515	22	)	)	PUNCT
ejpam-6640	515	23	)	)	PUNCT
ejpam-6640	516	1	f∗	f∗	NOUN
ejpam-6640	516	2	//	//	X
ejpam-6640	516	3	homcomp(a	homcomp(a	NOUN
ejpam-6640	516	4	)	)	PUNCT
ejpam-6640	516	5	(	(	PUNCT
ejpam-6640	516	6	−	−	PROPN
ejpam-6640	516	7	,	,	PUNCT
ejpam-6640	516	8	x)((y	x)((y	PROPN
ejpam-6640	516	9	,	,	PUNCT
ejpam-6640	516	10	α	α	NOUN
ejpam-6640	516	11	)	)	PUNCT
ejpam-6640	516	12	)	)	PUNCT
ejpam-6640	517	1	//	//	PUNCT
ejpam-6640	517	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	517	3	)	)	PUNCT
ejpam-6640	517	4	(	(	PUNCT
ejpam-6640	517	5	−	−	PROPN
ejpam-6640	517	6	,	,	PUNCT
ejpam-6640	517	7	x)((0	x)((0	PROPN
ejpam-6640	517	8	)	)	PUNCT
ejpam-6640	517	9	)	)	PUNCT
ejpam-6640	517	10	is	be	AUX
ejpam-6640	517	11	a	a	DET
ejpam-6640	517	12	short	short	ADJ
ejpam-6640	517	13	exact	exact	ADJ
ejpam-6640	517	14	sequence	sequence	NOUN
ejpam-6640	517	15	of	of	ADP
ejpam-6640	517	16	morphisms	morphism	NOUN
ejpam-6640	517	17	in	in	ADP
ejpam-6640	517	18	comp(ab	comp(ab	NOUN
ejpam-6640	517	19	)	)	PUNCT
ejpam-6640	517	20	.	.	PUNCT
ejpam-6640	518	1	by	by	ADP
ejpam-6640	518	2	(	(	PUNCT
ejpam-6640	518	3	i	i	NOUN
ejpam-6640	518	4	)	)	PUNCT
ejpam-6640	518	5	,	,	PUNCT
ejpam-6640	518	6	we	we	PRON
ejpam-6640	518	7	have	have	VERB
ejpam-6640	518	8	:	:	PUNCT
ejpam-6640	518	9	homcomp(a	homcomp(a	NOUN
ejpam-6640	518	10	)	)	PUNCT
ejpam-6640	518	11	(	(	PUNCT
ejpam-6640	518	12	−	−	PROPN
ejpam-6640	518	13	,	,	PUNCT
ejpam-6640	518	14	x)((0	x)((0	PROPN
ejpam-6640	518	15	)	)	PUNCT
ejpam-6640	518	16	)	)	PUNCT
ejpam-6640	519	1	//	//	PUNCT
ejpam-6640	519	2	homcomp(a	homcomp(a	NOUN
ejpam-6640	519	3	)	)	PUNCT
ejpam-6640	519	4	(	(	PUNCT
ejpam-6640	519	5	−	−	PROPN
ejpam-6640	519	6	,	,	PUNCT
ejpam-6640	519	7	x)((t	x)((t	NUM
ejpam-6640	519	8	,	,	PUNCT
ejpam-6640	519	9	θ	θ	NOUN
ejpam-6640	519	10	)	)	PUNCT
ejpam-6640	519	11	)	)	PUNCT
ejpam-6640	519	12	g∗	g∗	VERB
ejpam-6640	519	13	//	//	NUM
ejpam-6640	519	14	homcomp(a	homcomp(a	NOUN
ejpam-6640	519	15	)	)	PUNCT
ejpam-6640	519	16	(	(	PUNCT
ejpam-6640	519	17	−	−	PROPN
ejpam-6640	519	18	,	,	PUNCT
ejpam-6640	519	19	x)((z	x)((z	PROPN
ejpam-6640	519	20	,	,	PUNCT
ejpam-6640	519	21	β	β	NOUN
ejpam-6640	519	22	)	)	PUNCT
ejpam-6640	519	23	)	)	PUNCT
ejpam-6640	520	1	f∗	f∗	NOUN
ejpam-6640	520	2	//	//	X
ejpam-6640	520	3	homcomp(a	homcomp(a	NOUN
ejpam-6640	520	4	)	)	PUNCT
ejpam-6640	520	5	(	(	PUNCT
ejpam-6640	520	6	−	−	PROPN
ejpam-6640	520	7	,	,	PUNCT
ejpam-6640	520	8	x)((y	x)((y	PROPN
ejpam-6640	520	9	,	,	PUNCT
ejpam-6640	520	10	α	α	NOUN
ejpam-6640	520	11	)	)	PUNCT
ejpam-6640	520	12	)	)	PUNCT
ejpam-6640	520	13	is	be	AUX
ejpam-6640	520	14	a	a	DET
ejpam-6640	520	15	left	left	ADJ
ejpam-6640	520	16	short	short	ADJ
ejpam-6640	520	17	exact	exact	ADJ
ejpam-6640	520	18	sequence	sequence	NOUN
ejpam-6640	520	19	of	of	ADP
ejpam-6640	520	20	morphisms	morphism	NOUN
ejpam-6640	520	21	in	in	ADP
ejpam-6640	520	22	comp(ab	comp(ab	NOUN
ejpam-6640	520	23	)	)	PUNCT
ejpam-6640	520	24	.	.	PUNCT
ejpam-6640	521	1	thus	thus	ADV
ejpam-6640	521	2	,	,	PUNCT
ejpam-6640	521	3	it	it	PRON
ejpam-6640	521	4	remains	remain	VERB
ejpam-6640	521	5	to	to	PART
ejpam-6640	521	6	show	show	VERB
ejpam-6640	521	7	that	that	SCONJ
ejpam-6640	521	8	for	for	ADP
ejpam-6640	521	9	every	every	DET
ejpam-6640	521	10	n	n	CCONJ
ejpam-6640	521	11	,	,	PUNCT
ejpam-6640	521	12	homcomp(a	homcomp(a	NOUN
ejpam-6640	521	13	)	)	PUNCT
ejpam-6640	521	14	(	(	PUNCT
ejpam-6640	521	15	f	f	X
ejpam-6640	521	16	,	,	PUNCT
ejpam-6640	521	17	x	x	NOUN
ejpam-6640	521	18	)	)	PUNCT
ejpam-6640	521	19	=	=	SYM
ejpam-6640	521	20	f∗	f∗	NOUN
ejpam-6640	521	21	is	be	AUX
ejpam-6640	521	22	an	an	DET
ejpam-6640	521	23	epimorphism	epimorphism	NOUN
ejpam-6640	521	24	.	.	PUNCT
ejpam-6640	522	1	by	by	ADP
ejpam-6640	522	2	theorem	theorem	NOUN
ejpam-6640	522	3	2	2	NUM
ejpam-6640	522	4	,	,	PUNCT
ejpam-6640	522	5	for	for	ADP
ejpam-6640	522	6	every	every	DET
ejpam-6640	522	7	integer	integer	NOUN
ejpam-6640	522	8	n	n	X
ejpam-6640	522	9	in	in	ADP
ejpam-6640	522	10	z	z	PROPN
ejpam-6640	522	11	,	,	PUNCT
ejpam-6640	522	12	since	since	SCONJ
ejpam-6640	522	13	x	x	PRON
ejpam-6640	522	14	is	be	AUX
ejpam-6640	522	15	injective	injective	ADJ
ejpam-6640	522	16	,	,	PUNCT
ejpam-6640	522	17	for	for	ADP
ejpam-6640	522	18	every	every	DET
ejpam-6640	522	19	monomorphism	monomorphism	NOUN
ejpam-6640	523	1	fn	fn	INTJ
ejpam-6640	523	2	:	:	PUNCT
ejpam-6640	523	3	yn	yn	PROPN
ejpam-6640	523	4	↪	↪	PROPN
ejpam-6640	523	5	→	→	SYM
ejpam-6640	523	6	zn	zn	PROPN
ejpam-6640	523	7	in	in	ADP
ejpam-6640	523	8	a	a	PRON
ejpam-6640	523	9	and	and	CCONJ
ejpam-6640	523	10	every	every	DET
ejpam-6640	523	11	morphism	morphism	NOUN
ejpam-6640	523	12	hn	hn	PROPN
ejpam-6640	523	13	:	:	PUNCT
ejpam-6640	523	14	yn	yn	PROPN
ejpam-6640	523	15	→	→	PUNCT
ejpam-6640	523	16	x	x	PROPN
ejpam-6640	523	17	in	in	ADP
ejpam-6640	523	18	a	a	PRON
ejpam-6640	523	19	,	,	PUNCT
ejpam-6640	523	20	there	there	PRON
ejpam-6640	523	21	exists	exist	VERB
ejpam-6640	523	22	a	a	DET
ejpam-6640	523	23	morphism	morphism	NOUN
ejpam-6640	523	24	ϕn	ϕn	X
ejpam-6640	523	25	:	:	PUNCT
ejpam-6640	523	26	zn	zn	PROPN
ejpam-6640	523	27	→	→	SYM
ejpam-6640	523	28	x	x	PUNCT
ejpam-6640	523	29	a.	a.	PROPN
ejpam-6640	523	30	diallo	diallo	PROPN
ejpam-6640	523	31	,	,	PUNCT
ejpam-6640	523	32	m.	m.	PROPN
ejpam-6640	523	33	b.	b.	PROPN
ejpam-6640	523	34	f.	f.	PROPN
ejpam-6640	523	35	b.	b.	PROPN
ejpam-6640	523	36	maaouia	maaouia	PROPN
ejpam-6640	523	37	,	,	PUNCT
ejpam-6640	523	38	m.	m.	NOUN
ejpam-6640	523	39	sanghare	sanghare	PROPN
ejpam-6640	523	40	/	/	SYM
ejpam-6640	523	41	eur	eur	PROPN
ejpam-6640	523	42	.	.	PUNCT
ejpam-6640	524	1	j.	j.	PROPN
ejpam-6640	524	2	pure	pure	PROPN
ejpam-6640	524	3	appl	appl	PROPN
ejpam-6640	524	4	.	.	PROPN
ejpam-6640	524	5	math	math	PROPN
ejpam-6640	524	6	,	,	PUNCT
ejpam-6640	524	7	18	18	NUM
ejpam-6640	524	8	(	(	PUNCT
ejpam-6640	524	9	4	4	NUM
ejpam-6640	524	10	)	)	PUNCT
ejpam-6640	524	11	(	(	PUNCT
ejpam-6640	524	12	2025	2025	NUM
ejpam-6640	524	13	)	)	PUNCT
ejpam-6640	524	14	,	,	PUNCT
ejpam-6640	524	15	6640	6640	NUM
ejpam-6640	524	16	22	22	NUM
ejpam-6640	524	17	of	of	ADP
ejpam-6640	524	18	28	28	NUM
ejpam-6640	524	19	in	in	ADP
ejpam-6640	524	20	a	a	DET
ejpam-6640	524	21	such	such	ADJ
ejpam-6640	524	22	that	that	PRON
ejpam-6640	524	23	ϕn	ϕn	INTJ
ejpam-6640	525	1	◦	◦	NOUN
ejpam-6640	525	2	fn	fn	NOUN
ejpam-6640	526	1	=	=	NOUN
ejpam-6640	526	2	hn	hn	PROPN
ejpam-6640	526	3	.	.	PUNCT
ejpam-6640	527	1	this	this	PRON
ejpam-6640	527	2	means	mean	VERB
ejpam-6640	527	3	that	that	SCONJ
ejpam-6640	527	4	the	the	DET
ejpam-6640	527	5	following	follow	VERB
ejpam-6640	527	6	diagram	diagram	NOUN
ejpam-6640	527	7	commutes	commute	NOUN
ejpam-6640	527	8	:	:	PUNCT
ejpam-6640	527	9	x	x	SYM
ejpam-6640	527	10	o	o	X
ejpam-6640	527	11	//	//	X
ejpam-6640	527	12	yn	yn	INTJ
ejpam-6640	527	13	hn	hn	INTJ
ejpam-6640	527	14	oo	oo	INTJ
ejpam-6640	527	15	fn	fn	PROPN
ejpam-6640	527	16	//	//	PROPN
ejpam-6640	527	17	zn	zn	INTJ
ejpam-6640	527	18	ϕn	ϕn	INTJ
ejpam-6640	527	19	aa	aa	INTJ
ejpam-6640	527	20	that	that	PRON
ejpam-6640	527	21	is	be	AUX
ejpam-6640	527	22	,	,	PUNCT
ejpam-6640	527	23	for	for	ADP
ejpam-6640	527	24	every	every	DET
ejpam-6640	527	25	hn	hn	PROPN
ejpam-6640	527	26	∈	∈	PROPN
ejpam-6640	527	27	homcomp(a	homcomp(a	NOUN
ejpam-6640	527	28	)	)	PUNCT
ejpam-6640	527	29	(	(	PUNCT
ejpam-6640	527	30	yn	yn	PROPN
ejpam-6640	527	31	,	,	PUNCT
ejpam-6640	527	32	x	x	NOUN
ejpam-6640	527	33	)	)	PUNCT
ejpam-6640	527	34	,	,	PUNCT
ejpam-6640	527	35	there	there	PRON
ejpam-6640	527	36	exists	exist	VERB
ejpam-6640	527	37	ϕn	ϕn	ADP
ejpam-6640	527	38	∈	∈	PROPN
ejpam-6640	527	39	homcomp(a	homcomp(a	NOUN
ejpam-6640	527	40	)	)	PUNCT
ejpam-6640	527	41	(	(	PUNCT
ejpam-6640	527	42	zn	zn	PROPN
ejpam-6640	527	43	,	,	PUNCT
ejpam-6640	527	44	x	x	NOUN
ejpam-6640	527	45	)	)	PUNCT
ejpam-6640	527	46	such	such	ADJ
ejpam-6640	527	47	that	that	PRON
ejpam-6640	527	48	ϕn	ϕn	ADP
ejpam-6640	527	49	◦	◦	NOUN
ejpam-6640	527	50	fn	fn	NOUN
ejpam-6640	527	51	=	=	SYM
ejpam-6640	527	52	f∗n(ϕn	f∗n(ϕn	NOUN
ejpam-6640	527	53	)	)	PUNCT
ejpam-6640	528	1	=	=	SYM
ejpam-6640	529	1	hn	hn	PROPN
ejpam-6640	529	2	.	.	PUNCT
ejpam-6640	530	1	hence	hence	ADV
ejpam-6640	530	2	,	,	PUNCT
ejpam-6640	530	3	homa	homa	PROPN
ejpam-6640	530	4	(	(	PUNCT
ejpam-6640	530	5	f	f	PROPN
ejpam-6640	530	6	,	,	PUNCT
ejpam-6640	530	7	x	x	X
ejpam-6640	530	8	)	)	PUNCT
ejpam-6640	530	9	is	be	AUX
ejpam-6640	530	10	an	an	DET
ejpam-6640	530	11	epimorphism	epimorphism	NOUN
ejpam-6640	530	12	.	.	PUNCT
ejpam-6640	531	1	therefore	therefore	ADV
ejpam-6640	531	2	,	,	PUNCT
ejpam-6640	531	3	the	the	DET
ejpam-6640	531	4	functor	functor	PROPN
ejpam-6640	531	5	homcomp(a	homcomp(a	PROPN
ejpam-6640	531	6	)	)	PUNCT
ejpam-6640	531	7	(	(	PUNCT
ejpam-6640	531	8	−	−	PROPN
ejpam-6640	531	9	,	,	PUNCT
ejpam-6640	531	10	x	x	NOUN
ejpam-6640	531	11	)	)	PUNCT
ejpam-6640	531	12	:	:	PUNCT
ejpam-6640	531	13	comp(a	comp(a	NOUN
ejpam-6640	531	14	)	)	PUNCT
ejpam-6640	531	15	→	→	SYM
ejpam-6640	531	16	comp(ab	comp(ab	NOUN
ejpam-6640	531	17	)	)	PUNCT
ejpam-6640	531	18	is	be	AUX
ejpam-6640	531	19	exact	exact	ADJ
ejpam-6640	531	20	.	.	PUNCT
ejpam-6640	532	1	thus	thus	ADV
ejpam-6640	532	2	,	,	PUNCT
ejpam-6640	532	3	(	(	PUNCT
ejpam-6640	532	4	ii.1	ii.1	X
ejpam-6640	532	5	)	)	PUNCT
ejpam-6640	532	6	and	and	CCONJ
ejpam-6640	532	7	(	(	PUNCT
ejpam-6640	532	8	ii.2	ii.2	NOUN
ejpam-6640	532	9	)	)	PUNCT
ejpam-6640	532	10	imply	imply	VERB
ejpam-6640	532	11	that	that	SCONJ
ejpam-6640	532	12	the	the	DET
ejpam-6640	532	13	functor	functor	PROPN
ejpam-6640	532	14	homcomp(a	homcomp(a	PROPN
ejpam-6640	532	15	)	)	PUNCT
ejpam-6640	532	16	(	(	PUNCT
ejpam-6640	532	17	−	−	PROPN
ejpam-6640	532	18	,	,	PUNCT
ejpam-6640	532	19	x	x	NOUN
ejpam-6640	532	20	)	)	PUNCT
ejpam-6640	532	21	:	:	PUNCT
ejpam-6640	532	22	comp(a	comp(a	NOUN
ejpam-6640	532	23	)	)	PUNCT
ejpam-6640	532	24	→	→	SYM
ejpam-6640	532	25	comp(ab	comp(ab	NOUN
ejpam-6640	532	26	)	)	PUNCT
ejpam-6640	532	27	is	be	AUX
ejpam-6640	532	28	exact	exact	ADJ
ejpam-6640	532	29	if	if	SCONJ
ejpam-6640	532	30	and	and	CCONJ
ejpam-6640	532	31	only	only	ADV
ejpam-6640	532	32	if	if	SCONJ
ejpam-6640	532	33	x	x	PRON
ejpam-6640	532	34	is	be	AUX
ejpam-6640	532	35	an	an	DET
ejpam-6640	532	36	injective	injective	ADJ
ejpam-6640	532	37	object	object	NOUN
ejpam-6640	532	38	in	in	ADP
ejpam-6640	532	39	a	a	PRON
ejpam-6640	532	40	.	.	NOUN
ejpam-6640	533	1	4	4	X
ejpam-6640	533	2	.	.	NOUN
ejpam-6640	533	3	exactness	exactness	NOUN
ejpam-6640	533	4	of	of	ADP
ejpam-6640	533	5	homological	homological	ADJ
ejpam-6640	533	6	functors	functor	NOUN
ejpam-6640	533	7	of	of	ADP
ejpam-6640	533	8	degree	degree	NOUN
ejpam-6640	533	9	n	n	CCONJ
ejpam-6640	533	10	:	:	PUNCT
ejpam-6640	533	11	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	533	12	)	)	PUNCT
ejpam-6640	533	13	and	and	CCONJ
ejpam-6640	533	14	h̃n(−	h̃n(−	PROPN
ejpam-6640	533	15	,	,	PUNCT
ejpam-6640	533	16	x	x	X
ejpam-6640	533	17	)	)	PUNCT
ejpam-6640	533	18	consider	consider	VERB
ejpam-6640	533	19	the	the	DET
ejpam-6640	533	20	homological	homological	ADJ
ejpam-6640	533	21	functor	functor	NOUN
ejpam-6640	533	22	hn	hn	PROPN
ejpam-6640	533	23	:	:	PUNCT
ejpam-6640	533	24	comp(ab	comp(ab	PROPN
ejpam-6640	533	25	)	)	PUNCT
ejpam-6640	533	26	=	=	SYM
ejpam-6640	533	27	comp(z	comp(z	NOUN
ejpam-6640	533	28	−mod	−mod	PRON
ejpam-6640	533	29	)	)	PUNCT
ejpam-6640	533	30	−→	−→	PROPN
ejpam-6640	533	31	ab	ab	PROPN
ejpam-6640	533	32	which	which	PRON
ejpam-6640	533	33	is	be	AUX
ejpam-6640	533	34	a	a	DET
ejpam-6640	533	35	special	special	ADJ
ejpam-6640	533	36	case	case	NOUN
ejpam-6640	533	37	of	of	ADP
ejpam-6640	533	38	the	the	DET
ejpam-6640	533	39	homological	homological	ADJ
ejpam-6640	533	40	functor	functor	NOUN
ejpam-6640	533	41	hn	hn	PROPN
ejpam-6640	533	42	:	:	PUNCT
ejpam-6640	533	43	comp(a	comp(a	NOUN
ejpam-6640	533	44	-	-	PUNCT
ejpam-6640	533	45	mod	mod	ADJ
ejpam-6640	533	46	)	)	PUNCT
ejpam-6640	533	47	−→	−→	NOUN
ejpam-6640	533	48	ab	ab	PROPN
ejpam-6640	533	49	for	for	ADP
ejpam-6640	533	50	all	all	DET
ejpam-6640	533	51	n	n	PRON
ejpam-6640	533	52	∈	∈	NOUN
ejpam-6640	533	53	z.	z.	X
ejpam-6640	533	54	that	that	PRON
ejpam-6640	533	55	is	be	AUX
ejpam-6640	533	56	,	,	PUNCT
ejpam-6640	533	57	hn	hn	PROPN
ejpam-6640	533	58	is	be	AUX
ejpam-6640	533	59	a	a	DET
ejpam-6640	533	60	covariant	covariant	ADJ
ejpam-6640	533	61	additive	additive	ADJ
ejpam-6640	533	62	functor	functor	NOUN
ejpam-6640	533	63	.	.	PUNCT
ejpam-6640	534	1	[	[	X
ejpam-6640	534	2	h̃n(x,−	h̃n(x,−	X
ejpam-6640	534	3	)	)	PUNCT
ejpam-6640	534	4	]	]	PUNCT
ejpam-6640	534	5	let	let	VERB
ejpam-6640	534	6	a	a	PRON
ejpam-6640	534	7	be	be	AUX
ejpam-6640	534	8	a	a	DET
ejpam-6640	534	9	balanced	balanced	ADJ
ejpam-6640	534	10	abelian	abelian	ADJ
ejpam-6640	534	11	category	category	NOUN
ejpam-6640	534	12	and	and	CCONJ
ejpam-6640	534	13	x	x	ADP
ejpam-6640	534	14	a	a	DET
ejpam-6640	534	15	projective	projective	ADJ
ejpam-6640	534	16	object	object	NOUN
ejpam-6640	534	17	in	in	ADP
ejpam-6640	534	18	a	a	PRON
ejpam-6640	534	19	.	.	PUNCT
ejpam-6640	535	1	then	then	ADV
ejpam-6640	535	2	homological	homological	PROPN
ejpam-6640	535	3	functor	functor	PROPN
ejpam-6640	535	4	of	of	ADP
ejpam-6640	535	5	degree	degree	NOUN
ejpam-6640	535	6	n	n	CCONJ
ejpam-6640	535	7	(	(	PUNCT
ejpam-6640	535	8	n	n	X
ejpam-6640	535	9	∈	∈	PROPN
ejpam-6640	535	10	z	z	PROPN
ejpam-6640	535	11	)	)	PUNCT
ejpam-6640	535	12	,	,	PUNCT
ejpam-6640	535	13	denoted	denote	VERB
ejpam-6640	535	14	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	535	15	)	)	PUNCT
ejpam-6640	536	1	=	=	PUNCT
ejpam-6640	536	2	hn	hn	PROPN
ejpam-6640	536	3	◦	◦	NOUN
ejpam-6640	536	4	homcomp(a	homcomp(a	NOUN
ejpam-6640	536	5	)	)	PUNCT
ejpam-6640	536	6	(	(	PUNCT
ejpam-6640	536	7	x,−	x,−	PROPN
ejpam-6640	536	8	)	)	PUNCT
ejpam-6640	536	9	where	where	SCONJ
ejpam-6640	536	10	hn	hn	PRON
ejpam-6640	536	11	:	:	PUNCT
ejpam-6640	536	12	comp(ab	comp(ab	PROPN
ejpam-6640	536	13	)	)	PUNCT
ejpam-6640	536	14	−→	−→	PROPN
ejpam-6640	536	15	ab	ab	PROPN
ejpam-6640	536	16	,	,	PUNCT
ejpam-6640	536	17	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	536	18	)	)	PUNCT
ejpam-6640	536	19	:	:	PUNCT
ejpam-6640	536	20	comp(a	comp(a	NOUN
ejpam-6640	536	21	)	)	PUNCT
ejpam-6640	536	22	−→	−→	PROPN
ejpam-6640	536	23	ab	ab	PROPN
ejpam-6640	536	24	is	be	AUX
ejpam-6640	536	25	defined	define	VERB
ejpam-6640	536	26	by	by	ADP
ejpam-6640	536	27	:	:	PUNCT
ejpam-6640	536	28	(	(	PUNCT
ejpam-6640	536	29	i	i	NOUN
ejpam-6640	536	30	)	)	PUNCT
ejpam-6640	536	31	for	for	ADP
ejpam-6640	536	32	any	any	DET
ejpam-6640	536	33	complex	complex	ADJ
ejpam-6640	536	34	sequence	sequence	NOUN
ejpam-6640	536	35	in	in	ADP
ejpam-6640	536	36	comp(a	comp(a	NOUN
ejpam-6640	536	37	)	)	PUNCT
ejpam-6640	536	38	(	(	PUNCT
ejpam-6640	536	39	βn	βn	NOUN
ejpam-6640	536	40	:	:	PUNCT
ejpam-6640	536	41	yn	yn	PROPN
ejpam-6640	536	42	→	→	SYM
ejpam-6640	536	43	yn+1)n∈z	yn+1)n∈z	NOUN
ejpam-6640	536	44	denoted	denote	VERB
ejpam-6640	536	45	(	(	PUNCT
ejpam-6640	536	46	y	y	NOUN
ejpam-6640	536	47	,	,	PUNCT
ejpam-6640	536	48	β	β	NOUN
ejpam-6640	536	49	)	)	PUNCT
ejpam-6640	536	50	,	,	PUNCT
ejpam-6640	536	51	we	we	PRON
ejpam-6640	536	52	associate	associate	VERB
ejpam-6640	536	53	h̃n(x,−)((y	h̃n(x,−)((y	PROPN
ejpam-6640	536	54	,	,	PUNCT
ejpam-6640	536	55	β	β	NOUN
ejpam-6640	536	56	)	)	PUNCT
ejpam-6640	536	57	)	)	PUNCT
ejpam-6640	537	1	=	=	PRON
ejpam-6640	537	2	(	(	PUNCT
ejpam-6640	537	3	hn	hn	PROPN
ejpam-6640	537	4	◦	◦	NOUN
ejpam-6640	537	5	homcomp(a	homcomp(a	NOUN
ejpam-6640	537	6	)	)	PUNCT
ejpam-6640	537	7	(	(	PUNCT
ejpam-6640	537	8	x,−))((y	x,−))((y	PROPN
ejpam-6640	537	9	,	,	PUNCT
ejpam-6640	537	10	β	β	NOUN
ejpam-6640	537	11	)	)	PUNCT
ejpam-6640	537	12	)	)	PUNCT
ejpam-6640	537	13	=	=	PUNCT
ejpam-6640	537	14	kerβ∗n+1	kerβ∗n+1	VERB
ejpam-6640	537	15	/	/	SYM
ejpam-6640	537	16	imβ	imβ	PRON
ejpam-6640	537	17	∗	∗	NOUN
ejpam-6640	537	18	n	n	CCONJ
ejpam-6640	537	19	∀n	∀n	NUM
ejpam-6640	537	20	∈	∈	PROPN
ejpam-6640	537	21	z	z	NOUN
ejpam-6640	537	22	;	;	PUNCT
ejpam-6640	537	23	(	(	PUNCT
ejpam-6640	537	24	ii	ii	NOUN
ejpam-6640	537	25	)	)	PUNCT
ejpam-6640	537	26	for	for	ADP
ejpam-6640	537	27	any	any	DET
ejpam-6640	537	28	complex	complex	ADJ
ejpam-6640	537	29	sequence	sequence	NOUN
ejpam-6640	537	30	(	(	PUNCT
ejpam-6640	537	31	y	y	NOUN
ejpam-6640	537	32	,	,	PUNCT
ejpam-6640	537	33	β	β	NOUN
ejpam-6640	537	34	)	)	PUNCT
ejpam-6640	537	35	=	=	SYM
ejpam-6640	537	36	(	(	PUNCT
ejpam-6640	537	37	βn	βn	NOUN
ejpam-6640	537	38	:	:	PUNCT
ejpam-6640	537	39	yn	yn	PROPN
ejpam-6640	537	40	→	→	SYM
ejpam-6640	537	41	yn+1)n∈z	yn+1)n∈z	NOUN
ejpam-6640	537	42	in	in	ADP
ejpam-6640	537	43	comp(a	comp(a	NOUN
ejpam-6640	537	44	)	)	PUNCT
ejpam-6640	537	45	,	,	PUNCT
ejpam-6640	537	46	any	any	DET
ejpam-6640	537	47	complex	complex	ADJ
ejpam-6640	537	48	sequence	sequence	NOUN
ejpam-6640	537	49	(	(	PUNCT
ejpam-6640	537	50	z	z	NOUN
ejpam-6640	537	51	,	,	PUNCT
ejpam-6640	537	52	α	α	NOUN
ejpam-6640	537	53	)	)	PUNCT
ejpam-6640	537	54	=	=	SYM
ejpam-6640	537	55	(	(	PUNCT
ejpam-6640	537	56	αn	αn	INTJ
ejpam-6640	537	57	:	:	PUNCT
ejpam-6640	537	58	zn	zn	PROPN
ejpam-6640	537	59	→	→	SYM
ejpam-6640	537	60	zn+1)n∈z	zn+1)n∈z	PROPN
ejpam-6640	537	61	in	in	ADP
ejpam-6640	537	62	comp(a	comp(a	NOUN
ejpam-6640	537	63	)	)	PUNCT
ejpam-6640	537	64	,	,	PUNCT
ejpam-6640	537	65	and	and	CCONJ
ejpam-6640	537	66	any	any	DET
ejpam-6640	537	67	complex	complex	ADJ
ejpam-6640	537	68	chain	chain	NOUN
ejpam-6640	537	69	f	f	NOUN
ejpam-6640	537	70	:	:	PUNCT
ejpam-6640	537	71	(	(	PUNCT
ejpam-6640	537	72	y	y	NOUN
ejpam-6640	537	73	,	,	PUNCT
ejpam-6640	537	74	β	β	NOUN
ejpam-6640	537	75	)	)	PUNCT
ejpam-6640	537	76	→	→	SYM
ejpam-6640	537	77	(	(	PUNCT
ejpam-6640	537	78	z	z	NOUN
ejpam-6640	537	79	,	,	PUNCT
ejpam-6640	537	80	α	α	NOUN
ejpam-6640	537	81	)	)	PUNCT
ejpam-6640	537	82	=	=	PUNCT
ejpam-6640	537	83	(	(	PUNCT
ejpam-6640	537	84	fn	fn	NOUN
ejpam-6640	537	85	:	:	PUNCT
ejpam-6640	537	86	yn	yn	PROPN
ejpam-6640	537	87	−→	−→	PROPN
ejpam-6640	537	88	zn)n∈z	zn)n∈z	NUM
ejpam-6640	537	89	in	in	ADP
ejpam-6640	537	90	comp(a	comp(a	NOUN
ejpam-6640	537	91	)	)	PUNCT
ejpam-6640	537	92	denoted	denote	VERB
ejpam-6640	537	93	f	f	X
ejpam-6640	537	94	:	:	PUNCT
ejpam-6640	538	1	(	(	PUNCT
ejpam-6640	538	2	y	y	NOUN
ejpam-6640	538	3	,	,	PUNCT
ejpam-6640	538	4	β	β	NOUN
ejpam-6640	538	5	)	)	PUNCT
ejpam-6640	538	6	−→	−→	NOUN
ejpam-6640	538	7	(	(	PUNCT
ejpam-6640	538	8	z	z	NOUN
ejpam-6640	538	9	,	,	PUNCT
ejpam-6640	538	10	α	α	NOUN
ejpam-6640	538	11	)	)	PUNCT
ejpam-6640	538	12	,	,	PUNCT
ejpam-6640	538	13	we	we	PRON
ejpam-6640	538	14	associate	associate	VERB
ejpam-6640	538	15	:	:	PUNCT
ejpam-6640	538	16	h̃n(x,−)(f	h̃n(x,−)(f	NUM
ejpam-6640	538	17	)	)	PUNCT
ejpam-6640	538	18	:	:	PUNCT
ejpam-6640	538	19	(	(	PUNCT
ejpam-6640	538	20	hn	hn	PROPN
ejpam-6640	538	21	◦	◦	NOUN
ejpam-6640	538	22	homcomp(a	homcomp(a	NOUN
ejpam-6640	538	23	)	)	PUNCT
ejpam-6640	538	24	(	(	PUNCT
ejpam-6640	538	25	x,−))((y	x,−))((y	PROPN
ejpam-6640	538	26	,	,	PUNCT
ejpam-6640	538	27	β	β	NOUN
ejpam-6640	538	28	)	)	PUNCT
ejpam-6640	538	29	)	)	PUNCT
ejpam-6640	539	1	−→	−→	NOUN
ejpam-6640	539	2	(	(	PUNCT
ejpam-6640	539	3	hn	hn	PROPN
ejpam-6640	539	4	◦	◦	NOUN
ejpam-6640	539	5	homcomp(a	homcomp(a	NOUN
ejpam-6640	539	6	)	)	PUNCT
ejpam-6640	539	7	(	(	PUNCT
ejpam-6640	539	8	x,−))((z	x,−))((z	PROPN
ejpam-6640	539	9	,	,	PUNCT
ejpam-6640	539	10	α	α	NOUN
ejpam-6640	539	11	)	)	PUNCT
ejpam-6640	539	12	)	)	PUNCT
ejpam-6640	540	1	gn	gn	PROPN
ejpam-6640	540	2	7−→	7−→	PROPN
ejpam-6640	540	3	fn(gn	fn(gn	NOUN
ejpam-6640	540	4	)	)	PUNCT
ejpam-6640	540	5	is	be	AUX
ejpam-6640	540	6	a	a	DET
ejpam-6640	540	7	covariant	covariant	ADJ
ejpam-6640	540	8	additive	additive	ADJ
ejpam-6640	540	9	functor	functor	NOUN
ejpam-6640	540	10	.	.	PUNCT
ejpam-6640	541	1	proof	proof	NOUN
ejpam-6640	541	2	.	.	PUNCT
ejpam-6640	542	1	we	we	PRON
ejpam-6640	542	2	know	know	VERB
ejpam-6640	542	3	that	that	SCONJ
ejpam-6640	542	4	the	the	DET
ejpam-6640	542	5	homology	homology	NOUN
ejpam-6640	542	6	functor	functor	PROPN
ejpam-6640	542	7	hn	hn	PROPN
ejpam-6640	542	8	:	:	PUNCT
ejpam-6640	542	9	comp(a	comp(a	NOUN
ejpam-6640	542	10	-	-	PUNCT
ejpam-6640	542	11	mod	mod	NOUN
ejpam-6640	542	12	)	)	PUNCT
ejpam-6640	542	13	−→	−→	NOUN
ejpam-6640	542	14	ab	ab	PROPN
ejpam-6640	542	15	is	be	AUX
ejpam-6640	542	16	defined	define	VERB
ejpam-6640	542	17	by	by	ADP
ejpam-6640	542	18	:	:	PUNCT
ejpam-6640	542	19	(	(	PUNCT
ejpam-6640	542	20	i	i	NOUN
ejpam-6640	542	21	)	)	PUNCT
ejpam-6640	542	22	for	for	ADP
ejpam-6640	542	23	any	any	DET
ejpam-6640	542	24	complex	complex	ADJ
ejpam-6640	542	25	sequence	sequence	NOUN
ejpam-6640	542	26	in	in	ADP
ejpam-6640	542	27	comp(a	comp(a	NOUN
ejpam-6640	542	28	-	-	PUNCT
ejpam-6640	542	29	mod	mod	NOUN
ejpam-6640	542	30	)	)	PUNCT
ejpam-6640	542	31	(	(	PUNCT
ejpam-6640	542	32	βn	βn	NOUN
ejpam-6640	542	33	:	:	PUNCT
ejpam-6640	542	34	yn	yn	PROPN
ejpam-6640	542	35	→	→	SYM
ejpam-6640	542	36	yn+1)n∈z	yn+1)n∈z	NOUN
ejpam-6640	542	37	denoted	denote	VERB
ejpam-6640	542	38	(	(	PUNCT
ejpam-6640	542	39	y	y	NOUN
ejpam-6640	542	40	,	,	PUNCT
ejpam-6640	542	41	β	β	NOUN
ejpam-6640	542	42	)	)	PUNCT
ejpam-6640	542	43	,	,	PUNCT
ejpam-6640	542	44	we	we	PRON
ejpam-6640	542	45	associate	associate	VERB
ejpam-6640	542	46	hn(y	hn(y	PROPN
ejpam-6640	542	47	,	,	PUNCT
ejpam-6640	542	48	β	β	X
ejpam-6640	542	49	)	)	PUNCT
ejpam-6640	542	50	=	=	SYM
ejpam-6640	542	51	kerβn+1	kerβn+1	PROPN
ejpam-6640	542	52	/	/	SYM
ejpam-6640	542	53	imβn	imβn	NOUN
ejpam-6640	542	54	∀n	∀n	PUNCT
ejpam-6640	543	1	∈	∈	PROPN
ejpam-6640	543	2	z	z	PROPN
ejpam-6640	543	3	;	;	PUNCT
ejpam-6640	543	4	a.	a.	PROPN
ejpam-6640	543	5	diallo	diallo	PROPN
ejpam-6640	543	6	,	,	PUNCT
ejpam-6640	543	7	m.	m.	PROPN
ejpam-6640	543	8	b.	b.	PROPN
ejpam-6640	543	9	f.	f.	PROPN
ejpam-6640	543	10	b.	b.	PROPN
ejpam-6640	543	11	maaouia	maaouia	PROPN
ejpam-6640	543	12	,	,	PUNCT
ejpam-6640	543	13	m.	m.	NOUN
ejpam-6640	543	14	sanghare	sanghare	PROPN
ejpam-6640	543	15	/	/	SYM
ejpam-6640	543	16	eur	eur	PROPN
ejpam-6640	543	17	.	.	PUNCT
ejpam-6640	544	1	j.	j.	PROPN
ejpam-6640	544	2	pure	pure	PROPN
ejpam-6640	544	3	appl	appl	PROPN
ejpam-6640	544	4	.	.	PROPN
ejpam-6640	544	5	math	math	PROPN
ejpam-6640	544	6	,	,	PUNCT
ejpam-6640	544	7	18	18	NUM
ejpam-6640	544	8	(	(	PUNCT
ejpam-6640	544	9	4	4	NUM
ejpam-6640	544	10	)	)	PUNCT
ejpam-6640	544	11	(	(	PUNCT
ejpam-6640	544	12	2025	2025	NUM
ejpam-6640	544	13	)	)	PUNCT
ejpam-6640	544	14	,	,	PUNCT
ejpam-6640	544	15	6640	6640	NUM
ejpam-6640	544	16	23	23	NUM
ejpam-6640	544	17	of	of	ADP
ejpam-6640	544	18	28	28	NUM
ejpam-6640	544	19	(	(	PUNCT
ejpam-6640	544	20	ii	ii	NOUN
ejpam-6640	544	21	)	)	PUNCT
ejpam-6640	544	22	for	for	ADP
ejpam-6640	544	23	any	any	DET
ejpam-6640	544	24	complex	complex	ADJ
ejpam-6640	544	25	sequence	sequence	NOUN
ejpam-6640	544	26	(	(	PUNCT
ejpam-6640	544	27	y	y	NOUN
ejpam-6640	544	28	,	,	PUNCT
ejpam-6640	544	29	β	β	NOUN
ejpam-6640	544	30	)	)	PUNCT
ejpam-6640	544	31	=	=	SYM
ejpam-6640	544	32	(	(	PUNCT
ejpam-6640	544	33	βn	βn	NOUN
ejpam-6640	544	34	:	:	PUNCT
ejpam-6640	544	35	yn	yn	PROPN
ejpam-6640	544	36	→	→	SYM
ejpam-6640	544	37	yn+1)n∈z	yn+1)n∈z	NOUN
ejpam-6640	544	38	in	in	ADP
ejpam-6640	544	39	comp(a	comp(a	NOUN
ejpam-6640	544	40	-	-	PUNCT
ejpam-6640	544	41	mod	mod	NOUN
ejpam-6640	544	42	)	)	PUNCT
ejpam-6640	544	43	,	,	PUNCT
ejpam-6640	544	44	any	any	DET
ejpam-6640	544	45	complex	complex	ADJ
ejpam-6640	544	46	sequence	sequence	NOUN
ejpam-6640	544	47	(	(	PUNCT
ejpam-6640	544	48	z	z	NOUN
ejpam-6640	544	49	,	,	PUNCT
ejpam-6640	544	50	α	α	NOUN
ejpam-6640	544	51	)	)	PUNCT
ejpam-6640	544	52	=	=	SYM
ejpam-6640	544	53	(	(	PUNCT
ejpam-6640	544	54	αn	αn	INTJ
ejpam-6640	544	55	:	:	PUNCT
ejpam-6640	544	56	zn	zn	PROPN
ejpam-6640	544	57	→	→	SYM
ejpam-6640	544	58	zn+1)n∈z	zn+1)n∈z	PROPN
ejpam-6640	544	59	in	in	ADP
ejpam-6640	544	60	comp(a	comp(a	NOUN
ejpam-6640	544	61	-	-	PUNCT
ejpam-6640	544	62	mod	mod	NOUN
ejpam-6640	544	63	)	)	PUNCT
ejpam-6640	544	64	,	,	PUNCT
ejpam-6640	544	65	and	and	CCONJ
ejpam-6640	544	66	any	any	DET
ejpam-6640	544	67	complex	complex	ADJ
ejpam-6640	544	68	chain	chain	NOUN
ejpam-6640	544	69	f	f	NOUN
ejpam-6640	544	70	:	:	PUNCT
ejpam-6640	544	71	(	(	PUNCT
ejpam-6640	544	72	y	y	NOUN
ejpam-6640	544	73	,	,	PUNCT
ejpam-6640	544	74	β	β	NOUN
ejpam-6640	544	75	)	)	PUNCT
ejpam-6640	544	76	→	→	SYM
ejpam-6640	544	77	(	(	PUNCT
ejpam-6640	544	78	z	z	NOUN
ejpam-6640	544	79	,	,	PUNCT
ejpam-6640	544	80	α	α	NOUN
ejpam-6640	544	81	)	)	PUNCT
ejpam-6640	544	82	=	=	PUNCT
ejpam-6640	544	83	(	(	PUNCT
ejpam-6640	544	84	fn	fn	NOUN
ejpam-6640	544	85	:	:	PUNCT
ejpam-6640	544	86	yn	yn	PROPN
ejpam-6640	544	87	−→	−→	PROPN
ejpam-6640	544	88	zn)n∈z	zn)n∈z	NUM
ejpam-6640	544	89	in	in	ADP
ejpam-6640	544	90	comp(a	comp(a	NOUN
ejpam-6640	544	91	-	-	PUNCT
ejpam-6640	544	92	mod	mod	NOUN
ejpam-6640	544	93	)	)	PUNCT
ejpam-6640	544	94	denoted	denote	VERB
ejpam-6640	544	95	f	f	X
ejpam-6640	544	96	:	:	PUNCT
ejpam-6640	544	97	(	(	PUNCT
ejpam-6640	544	98	y	y	NOUN
ejpam-6640	544	99	,	,	PUNCT
ejpam-6640	544	100	β	β	NOUN
ejpam-6640	544	101	)	)	PUNCT
ejpam-6640	544	102	−→	−→	NOUN
ejpam-6640	544	103	(	(	PUNCT
ejpam-6640	544	104	z	z	NOUN
ejpam-6640	544	105	,	,	PUNCT
ejpam-6640	544	106	α	α	NOUN
ejpam-6640	544	107	)	)	PUNCT
ejpam-6640	544	108	,	,	PUNCT
ejpam-6640	544	109	we	we	PRON
ejpam-6640	544	110	associate	associate	VERB
ejpam-6640	544	111	:	:	PUNCT
ejpam-6640	544	112	hn(f	hn(f	PUNCT
ejpam-6640	544	113	)	)	PUNCT
ejpam-6640	544	114	:	:	PUNCT
ejpam-6640	545	1	hn(y	hn(y	X
ejpam-6640	545	2	,	,	PUNCT
ejpam-6640	545	3	β	β	X
ejpam-6640	545	4	)	)	PUNCT
ejpam-6640	545	5	−→	−→	NOUN
ejpam-6640	545	6	hn(z	hn(z	NOUN
ejpam-6640	545	7	,	,	PUNCT
ejpam-6640	545	8	α	α	NOUN
ejpam-6640	545	9	)	)	PUNCT
ejpam-6640	545	10	gn	gn	PROPN
ejpam-6640	545	11	7−→	7−→	PROPN
ejpam-6640	545	12	fn(gn	fn(gn	NOUN
ejpam-6640	545	13	)	)	PUNCT
ejpam-6640	545	14	and	and	CCONJ
ejpam-6640	545	15	hn	hn	PROPN
ejpam-6640	545	16	is	be	AUX
ejpam-6640	545	17	a	a	DET
ejpam-6640	545	18	covariant	covariant	ADJ
ejpam-6640	545	19	additive	additive	ADJ
ejpam-6640	545	20	functor	functor	NOUN
ejpam-6640	545	21	.	.	PUNCT
ejpam-6640	546	1	since	since	SCONJ
ejpam-6640	546	2	comp(ab	comp(ab	NOUN
ejpam-6640	546	3	)	)	PUNCT
ejpam-6640	546	4	=	=	SYM
ejpam-6640	546	5	comp(z	comp(z	NOUN
ejpam-6640	546	6	−	−	PROPN
ejpam-6640	546	7	mod	mod	PROPN
ejpam-6640	546	8	)	)	PUNCT
ejpam-6640	546	9	is	be	AUX
ejpam-6640	546	10	a	a	DET
ejpam-6640	546	11	special	special	ADJ
ejpam-6640	546	12	case	case	NOUN
ejpam-6640	546	13	of	of	ADP
ejpam-6640	546	14	comp(a	comp(a	NOUN
ejpam-6640	546	15	-	-	PUNCT
ejpam-6640	546	16	mod	mod	NOUN
ejpam-6640	546	17	)	)	PUNCT
ejpam-6640	546	18	,	,	PUNCT
ejpam-6640	546	19	the	the	DET
ejpam-6640	546	20	functor	functor	PROPN
ejpam-6640	546	21	h̃n	h̃n	NOUN
ejpam-6640	546	22	is	be	AUX
ejpam-6640	546	23	covariant	covariant	ADJ
ejpam-6640	546	24	.	.	PUNCT
ejpam-6640	547	1	by	by	ADP
ejpam-6640	547	2	theorem	theorem	NOUN
ejpam-6640	547	3	3	3	NUM
ejpam-6640	547	4	,	,	PUNCT
ejpam-6640	547	5	homcomp(a	homcomp(a	NOUN
ejpam-6640	547	6	)	)	PUNCT
ejpam-6640	547	7	(	(	PUNCT
ejpam-6640	547	8	x,−	x,−	PROPN
ejpam-6640	547	9	)	)	PUNCT
ejpam-6640	547	10	is	be	AUX
ejpam-6640	547	11	covariant	covariant	ADJ
ejpam-6640	547	12	.	.	PUNCT
ejpam-6640	548	1	now	now	ADV
ejpam-6640	548	2	,	,	PUNCT
ejpam-6640	548	3	the	the	DET
ejpam-6640	548	4	composition	composition	NOUN
ejpam-6640	548	5	of	of	ADP
ejpam-6640	548	6	two	two	NUM
ejpam-6640	548	7	covariant	covariant	ADJ
ejpam-6640	548	8	functors	functor	NOUN
ejpam-6640	548	9	is	be	AUX
ejpam-6640	548	10	covariant	covariant	ADJ
ejpam-6640	548	11	,	,	PUNCT
ejpam-6640	548	12	so	so	ADV
ejpam-6640	548	13	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	548	14	)	)	PUNCT
ejpam-6640	548	15	:	:	PUNCT
ejpam-6640	548	16	comp(a	comp(a	NOUN
ejpam-6640	548	17	)	)	PUNCT
ejpam-6640	548	18	−→	−→	PROPN
ejpam-6640	548	19	ab	ab	PROPN
ejpam-6640	548	20	is	be	AUX
ejpam-6640	548	21	well	well	ADV
ejpam-6640	548	22	-	-	PUNCT
ejpam-6640	548	23	defined	define	VERB
ejpam-6640	548	24	and	and	CCONJ
ejpam-6640	548	25	is	be	AUX
ejpam-6640	548	26	a	a	DET
ejpam-6640	548	27	covariant	covariant	ADJ
ejpam-6640	548	28	functor	functor	NOUN
ejpam-6640	548	29	.	.	PUNCT
ejpam-6640	548	30	by	by	ADP
ejpam-6640	548	31	proposition	proposition	NOUN
ejpam-6640	548	32	1	1	NUM
ejpam-6640	548	33	and	and	CCONJ
ejpam-6640	548	34	theorem	theorem	VERB
ejpam-6640	548	35	2	2	NUM
ejpam-6640	548	36	,	,	PUNCT
ejpam-6640	548	37	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	548	38	)	)	PUNCT
ejpam-6640	548	39	is	be	AUX
ejpam-6640	548	40	an	an	DET
ejpam-6640	548	41	additive	additive	ADJ
ejpam-6640	548	42	functor	functor	NOUN
ejpam-6640	548	43	.	.	PUNCT
ejpam-6640	549	1	hence	hence	ADV
ejpam-6640	549	2	,	,	PUNCT
ejpam-6640	549	3	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	549	4	)	)	PUNCT
ejpam-6640	549	5	is	be	AUX
ejpam-6640	549	6	a	a	DET
ejpam-6640	549	7	covariant	covariant	ADJ
ejpam-6640	549	8	additive	additive	ADJ
ejpam-6640	549	9	functor	functor	NOUN
ejpam-6640	549	10	.	.	PUNCT
ejpam-6640	550	1	and	and	CCONJ
ejpam-6640	550	2	hn	hn	PROPN
ejpam-6640	550	3	is	be	AUX
ejpam-6640	550	4	a	a	DET
ejpam-6640	550	5	covariant	covariant	ADJ
ejpam-6640	550	6	additive	additive	ADJ
ejpam-6640	550	7	functor	functor	NOUN
ejpam-6640	550	8	.	.	PUNCT
ejpam-6640	551	1	since	since	SCONJ
ejpam-6640	551	2	comp(ab	comp(ab	PROPN
ejpam-6640	551	3	)	)	PUNCT
ejpam-6640	551	4	=	=	SYM
ejpam-6640	551	5	comp(z−mod	comp(z−mod	X
ejpam-6640	551	6	)	)	PUNCT
ejpam-6640	551	7	is	be	AUX
ejpam-6640	551	8	a	a	DET
ejpam-6640	551	9	special	special	ADJ
ejpam-6640	551	10	case	case	NOUN
ejpam-6640	551	11	of	of	ADP
ejpam-6640	551	12	comp(a	comp(a	NOUN
ejpam-6640	551	13	-	-	PUNCT
ejpam-6640	551	14	mod	mod	NOUN
ejpam-6640	551	15	)	)	PUNCT
ejpam-6640	551	16	,	,	PUNCT
ejpam-6640	551	17	the	the	DET
ejpam-6640	551	18	functor	functor	PROPN
ejpam-6640	551	19	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	551	20	)	)	PUNCT
ejpam-6640	551	21	is	be	AUX
ejpam-6640	551	22	well	well	ADV
ejpam-6640	551	23	-	-	PUNCT
ejpam-6640	551	24	defined	define	VERB
ejpam-6640	551	25	and	and	CCONJ
ejpam-6640	551	26	is	be	AUX
ejpam-6640	551	27	a	a	DET
ejpam-6640	551	28	covariant	covariant	ADJ
ejpam-6640	551	29	additive	additive	ADJ
ejpam-6640	551	30	functor	functor	NOUN
ejpam-6640	551	31	.	.	PUNCT
ejpam-6640	552	1	let	let	VERB
ejpam-6640	552	2	(	(	PUNCT
ejpam-6640	552	3	0	0	NUM
ejpam-6640	552	4	)	)	PUNCT
ejpam-6640	552	5	//	//	NOUN
ejpam-6640	553	1	(	(	PUNCT
ejpam-6640	553	2	y	y	PROPN
ejpam-6640	553	3	,	,	PUNCT
ejpam-6640	553	4	α	α	NOUN
ejpam-6640	553	5	)	)	PUNCT
ejpam-6640	553	6	f	f	PROPN
ejpam-6640	553	7	//	//	X
ejpam-6640	553	8	(	(	PUNCT
ejpam-6640	553	9	z	z	NOUN
ejpam-6640	553	10	,	,	PUNCT
ejpam-6640	553	11	β	β	NOUN
ejpam-6640	553	12	)	)	PUNCT
ejpam-6640	553	13	g	g	PROPN
ejpam-6640	553	14	//	//	SYM
ejpam-6640	553	15	(	(	PUNCT
ejpam-6640	553	16	t	t	PROPN
ejpam-6640	553	17	,	,	PUNCT
ejpam-6640	553	18	γ	γ	PROPN
ejpam-6640	553	19	)	)	PUNCT
ejpam-6640	553	20	//	//	NOUN
ejpam-6640	553	21	(	(	PUNCT
ejpam-6640	553	22	0	0	NUM
ejpam-6640	553	23	)	)	PUNCT
ejpam-6640	553	24	be	be	AUX
ejpam-6640	553	25	a	a	DET
ejpam-6640	553	26	short	short	ADJ
ejpam-6640	553	27	exact	exact	ADJ
ejpam-6640	553	28	sequence	sequence	NOUN
ejpam-6640	553	29	of	of	ADP
ejpam-6640	553	30	morphisms	morphism	NOUN
ejpam-6640	553	31	in	in	ADP
ejpam-6640	553	32	comp(a	comp(a	NOUN
ejpam-6640	553	33	)	)	PUNCT
ejpam-6640	553	34	,	,	PUNCT
ejpam-6640	553	35	where	where	SCONJ
ejpam-6640	553	36	x	x	PRON
ejpam-6640	553	37	is	be	AUX
ejpam-6640	553	38	a	a	DET
ejpam-6640	553	39	projective	projective	ADJ
ejpam-6640	553	40	object	object	NOUN
ejpam-6640	553	41	in	in	ADP
ejpam-6640	553	42	a	a	PRON
ejpam-6640	553	43	and	and	CCONJ
ejpam-6640	553	44	a	a	PRON
ejpam-6640	553	45	is	be	AUX
ejpam-6640	553	46	a	a	DET
ejpam-6640	553	47	balanced	balanced	ADJ
ejpam-6640	553	48	abelian	abelian	ADJ
ejpam-6640	553	49	category	category	NOUN
ejpam-6640	553	50	.	.	PUNCT
ejpam-6640	554	1	then	then	ADV
ejpam-6640	554	2	:	:	PUNCT
ejpam-6640	554	3	(	(	PUNCT
ejpam-6640	554	4	i	i	NOUN
ejpam-6640	554	5	)	)	PUNCT
ejpam-6640	554	6	the	the	DET
ejpam-6640	554	7	morphism	morphism	NOUN
ejpam-6640	554	8	of	of	ADP
ejpam-6640	554	9	connection	connection	NOUN
ejpam-6640	554	10	associated	associate	VERB
ejpam-6640	554	11	to	to	ADP
ejpam-6640	554	12	the	the	DET
ejpam-6640	554	13	covariant	covariant	ADJ
ejpam-6640	554	14	functor	functor	PROPN
ejpam-6640	554	15	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	554	16	)	)	PUNCT
ejpam-6640	554	17	is	be	AUX
ejpam-6640	554	18	defined	define	VERB
ejpam-6640	554	19	by	by	ADP
ejpam-6640	554	20	:	:	PUNCT
ejpam-6640	554	21	λn	λn	NOUN
ejpam-6640	554	22	:	:	PUNCT
ejpam-6640	554	23	h̃n(x,−)((t	h̃n(x,−)((t	PROPN
ejpam-6640	554	24	,	,	PUNCT
ejpam-6640	554	25	γ	γ	NOUN
ejpam-6640	554	26	)	)	PUNCT
ejpam-6640	554	27	)	)	PUNCT
ejpam-6640	555	1	−→	−→	NOUN
ejpam-6640	555	2	h̃n+1(x,−)((y	h̃n+1(x,−)((y	NOUN
ejpam-6640	555	3	,	,	PUNCT
ejpam-6640	555	4	α	α	NOUN
ejpam-6640	555	5	)	)	PUNCT
ejpam-6640	555	6	)	)	PUNCT
ejpam-6640	555	7	kn+1	kn+1	PROPN
ejpam-6640	555	8	7−→	7−→	PROPN
ejpam-6640	555	9	f∗−1	f∗−1	PROPN
ejpam-6640	555	10	n+2(β	n+2(β	PROPN
ejpam-6640	555	11	∗	∗	NOUN
ejpam-6640	555	12	n+1(g	n+1(g	PROPN
ejpam-6640	555	13	∗−1	∗−1	PROPN
ejpam-6640	555	14	n+1(kn+1	n+1(kn+1	PROPN
ejpam-6640	555	15	)	)	PUNCT
ejpam-6640	555	16	)	)	PUNCT
ejpam-6640	555	17	)	)	PUNCT
ejpam-6640	556	1	∀n	∀n	X
ejpam-6640	556	2	∈	∈	PROPN
ejpam-6640	557	1	z	z	NOUN
ejpam-6640	557	2	;	;	PUNCT
ejpam-6640	557	3	(	(	PUNCT
ejpam-6640	557	4	ii	ii	NOUN
ejpam-6640	557	5	)	)	PUNCT
ejpam-6640	557	6	the	the	DET
ejpam-6640	557	7	sequence	sequence	NOUN
ejpam-6640	557	8	.	.	PUNCT
ejpam-6640	557	9	.	.	PUNCT
ejpam-6640	557	10	.	.	PUNCT
ejpam-6640	558	1	//	//	PUNCT
ejpam-6640	559	1	h̃n(x,−)((y	h̃n(x,−)((y	PROPN
ejpam-6640	559	2	,	,	PUNCT
ejpam-6640	559	3	α	α	NOUN
ejpam-6640	559	4	)	)	PUNCT
ejpam-6640	559	5	)	)	PUNCT
ejpam-6640	559	6	h̃n(x,−)(f	h̃n(x,−)(f	PROPN
ejpam-6640	559	7	)	)	PUNCT
ejpam-6640	559	8	//	//	SYM
ejpam-6640	560	1	h̃n(x,−)((z	h̃n(x,−)((z	PROPN
ejpam-6640	560	2	,	,	PUNCT
ejpam-6640	560	3	β	β	NOUN
ejpam-6640	560	4	)	)	PUNCT
ejpam-6640	560	5	)	)	PUNCT
ejpam-6640	560	6	h̃n(x,−)(g	h̃n(x,−)(g	ADJ
ejpam-6640	560	7	)	)	PUNCT
ejpam-6640	560	8	//	//	X
ejpam-6640	560	9	h̃n((t	h̃n((t	NOUN
ejpam-6640	560	10	,	,	PUNCT
ejpam-6640	560	11	γ	γ	NOUN
ejpam-6640	560	12	)	)	PUNCT
ejpam-6640	560	13	)	)	PUNCT
ejpam-6640	561	1	λn	λn	PROPN
ejpam-6640	561	2	//	//	NUM
ejpam-6640	561	3	h̃n+1(x,−)((y	h̃n+1(x,−)((y	PROPN
ejpam-6640	561	4	,	,	PUNCT
ejpam-6640	561	5	α	α	NOUN
ejpam-6640	561	6	)	)	PUNCT
ejpam-6640	561	7	)	)	PUNCT
ejpam-6640	561	8	h̃n+1(x,−)(f	h̃n+1(x,−)(f	X
ejpam-6640	561	9	)	)	PUNCT
ejpam-6640	561	10	//	//	SYM
ejpam-6640	562	1	h̃n+1(x,−)((z	h̃n+1(x,−)((z	PROPN
ejpam-6640	562	2	,	,	PUNCT
ejpam-6640	562	3	β	β	NOUN
ejpam-6640	562	4	)	)	PUNCT
ejpam-6640	562	5	)	)	PUNCT
ejpam-6640	562	6	h̃n+1(x,−)(g	h̃n+1(x,−)(g	NOUN
ejpam-6640	562	7	)	)	PUNCT
ejpam-6640	562	8	//	//	NOUN
ejpam-6640	563	1	h̃n+1(x,−)((t	h̃n+1(x,−)((t	PROPN
ejpam-6640	563	2	,	,	PUNCT
ejpam-6640	563	3	γ	γ	NOUN
ejpam-6640	563	4	)	)	PUNCT
ejpam-6640	563	5	)	)	PUNCT
ejpam-6640	563	6	λn+1	λn+1	ADP
ejpam-6640	563	7	//	//	PROPN
ejpam-6640	563	8	.	.	PUNCT
ejpam-6640	563	9	.	.	PUNCT
ejpam-6640	563	10	.	.	PUNCT
ejpam-6640	564	1	is	be	AUX
ejpam-6640	564	2	a	a	DET
ejpam-6640	564	3	long	long	ADJ
ejpam-6640	564	4	exact	exact	ADJ
ejpam-6640	564	5	sequence	sequence	NOUN
ejpam-6640	564	6	of	of	ADP
ejpam-6640	564	7	abelian	abelian	ADJ
ejpam-6640	564	8	group	group	NOUN
ejpam-6640	564	9	morphisms	morphism	VERB
ejpam-6640	564	10	.	.	PUNCT
ejpam-6640	565	1	that	that	PRON
ejpam-6640	565	2	is	be	AUX
ejpam-6640	565	3	,	,	PUNCT
ejpam-6640	565	4	for	for	ADP
ejpam-6640	565	5	all	all	DET
ejpam-6640	565	6	n	n	PRON
ejpam-6640	565	7	∈	∈	PROPN
ejpam-6640	565	8	z:	z:	PROPN
ejpam-6640	565	9	im(h̃n(x,−)(f	im(h̃n(x,−)(f	NOUN
ejpam-6640	565	10	)	)	PUNCT
ejpam-6640	565	11	)	)	PUNCT
ejpam-6640	566	1	=	=	SYM
ejpam-6640	566	2	ker(h̃n(x,−)(g	ker(h̃n(x,−)(g	NOUN
ejpam-6640	566	3	)	)	PUNCT
ejpam-6640	566	4	)	)	PUNCT
ejpam-6640	567	1	im(h̃n(x,−)(g	im(h̃n(x,−)(g	ADJ
ejpam-6640	567	2	)	)	PUNCT
ejpam-6640	567	3	)	)	PUNCT
ejpam-6640	567	4	=	=	SYM
ejpam-6640	567	5	ker(λn	ker(λn	X
ejpam-6640	567	6	)	)	PUNCT
ejpam-6640	567	7	im(λn	im(λn	NOUN
ejpam-6640	567	8	)	)	PUNCT
ejpam-6640	567	9	=	=	SYM
ejpam-6640	567	10	ker(h̃n+1(x,−)(f	ker(h̃n+1(x,−)(f	PROPN
ejpam-6640	567	11	)	)	PUNCT
ejpam-6640	567	12	)	)	PUNCT
ejpam-6640	567	13	.	.	PUNCT
ejpam-6640	568	1	proof	proof	NOUN
ejpam-6640	568	2	.	.	PUNCT
ejpam-6640	569	1	(	(	PUNCT
ejpam-6640	569	2	i	i	NOUN
ejpam-6640	569	3	)	)	PUNCT
ejpam-6640	569	4	we	we	PRON
ejpam-6640	569	5	know	know	VERB
ejpam-6640	569	6	that	that	SCONJ
ejpam-6640	569	7	if	if	SCONJ
ejpam-6640	569	8	the	the	DET
ejpam-6640	569	9	homological	homological	ADJ
ejpam-6640	569	10	functor	functor	NOUN
ejpam-6640	569	11	hn	hn	PROPN
ejpam-6640	569	12	:	:	PUNCT
ejpam-6640	569	13	comp(a	comp(a	NOUN
ejpam-6640	569	14	-	-	PUNCT
ejpam-6640	569	15	mod	mod	NOUN
ejpam-6640	569	16	)	)	PUNCT
ejpam-6640	569	17	−→	−→	NOUN
ejpam-6640	569	18	ab	ab	PROPN
ejpam-6640	569	19	is	be	AUX
ejpam-6640	569	20	covariant	covariant	ADJ
ejpam-6640	569	21	,	,	PUNCT
ejpam-6640	569	22	then	then	ADV
ejpam-6640	569	23	for	for	ADP
ejpam-6640	569	24	every	every	DET
ejpam-6640	569	25	short	short	ADJ
ejpam-6640	569	26	exact	exact	ADJ
ejpam-6640	569	27	sequence	sequence	NOUN
ejpam-6640	569	28	of	of	ADP
ejpam-6640	569	29	morphisms	morphism	NOUN
ejpam-6640	569	30	in	in	ADP
ejpam-6640	569	31	comp(a	comp(a	NOUN
ejpam-6640	569	32	-	-	PUNCT
ejpam-6640	569	33	mod	mod	NOUN
ejpam-6640	569	34	)	)	PUNCT
ejpam-6640	569	35	a.	a.	NOUN
ejpam-6640	569	36	diallo	diallo	PROPN
ejpam-6640	569	37	,	,	PUNCT
ejpam-6640	569	38	m.	m.	PROPN
ejpam-6640	569	39	b.	b.	PROPN
ejpam-6640	569	40	f.	f.	PROPN
ejpam-6640	569	41	b.	b.	PROPN
ejpam-6640	569	42	maaouia	maaouia	PROPN
ejpam-6640	569	43	,	,	PUNCT
ejpam-6640	569	44	m.	m.	NOUN
ejpam-6640	569	45	sanghare	sanghare	PROPN
ejpam-6640	569	46	/	/	SYM
ejpam-6640	569	47	eur	eur	PROPN
ejpam-6640	569	48	.	.	PUNCT
ejpam-6640	570	1	j.	j.	PROPN
ejpam-6640	570	2	pure	pure	PROPN
ejpam-6640	570	3	appl	appl	PROPN
ejpam-6640	570	4	.	.	PROPN
ejpam-6640	570	5	math	math	PROPN
ejpam-6640	570	6	,	,	PUNCT
ejpam-6640	570	7	18	18	NUM
ejpam-6640	570	8	(	(	PUNCT
ejpam-6640	570	9	4	4	NUM
ejpam-6640	570	10	)	)	PUNCT
ejpam-6640	570	11	(	(	PUNCT
ejpam-6640	570	12	2025	2025	NUM
ejpam-6640	570	13	)	)	PUNCT
ejpam-6640	570	14	,	,	PUNCT
ejpam-6640	570	15	6640	6640	NUM
ejpam-6640	570	16	24	24	NUM
ejpam-6640	570	17	of	of	ADP
ejpam-6640	570	18	28	28	NUM
ejpam-6640	570	19	(	(	PUNCT
ejpam-6640	570	20	0	0	NUM
ejpam-6640	570	21	)	)	PUNCT
ejpam-6640	570	22	//	//	NOUN
ejpam-6640	571	1	(	(	PUNCT
ejpam-6640	571	2	y	y	PROPN
ejpam-6640	571	3	,	,	PUNCT
ejpam-6640	571	4	α	α	NOUN
ejpam-6640	571	5	)	)	PUNCT
ejpam-6640	571	6	f	f	PROPN
ejpam-6640	571	7	//	//	X
ejpam-6640	571	8	(	(	PUNCT
ejpam-6640	571	9	z	z	NOUN
ejpam-6640	571	10	,	,	PUNCT
ejpam-6640	571	11	β	β	NOUN
ejpam-6640	571	12	)	)	PUNCT
ejpam-6640	571	13	g	g	PROPN
ejpam-6640	571	14	//	//	SYM
ejpam-6640	571	15	(	(	PUNCT
ejpam-6640	571	16	t	t	PROPN
ejpam-6640	571	17	,	,	PUNCT
ejpam-6640	571	18	γ	γ	PROPN
ejpam-6640	571	19	)	)	PUNCT
ejpam-6640	571	20	//	//	NOUN
ejpam-6640	571	21	(	(	PUNCT
ejpam-6640	571	22	0	0	NUM
ejpam-6640	571	23	)	)	PUNCT
ejpam-6640	571	24	the	the	DET
ejpam-6640	571	25	connecting	connect	VERB
ejpam-6640	571	26	morphism	morphism	NOUN
ejpam-6640	571	27	is	be	AUX
ejpam-6640	571	28	defined	define	VERB
ejpam-6640	571	29	by	by	ADP
ejpam-6640	571	30	λn	λn	PROPN
ejpam-6640	571	31	:	:	PUNCT
ejpam-6640	571	32	hn((t	hn((t	PROPN
ejpam-6640	571	33	,	,	PUNCT
ejpam-6640	571	34	γ	γ	NOUN
ejpam-6640	571	35	)	)	PUNCT
ejpam-6640	571	36	)	)	PUNCT
ejpam-6640	572	1	−→	−→	PROPN
ejpam-6640	572	2	hn+1((y	hn+1((y	PROPN
ejpam-6640	572	3	,	,	PUNCT
ejpam-6640	572	4	α	α	NOUN
ejpam-6640	572	5	)	)	PUNCT
ejpam-6640	572	6	)	)	PUNCT
ejpam-6640	573	1	kn+1	kn+1	PROPN
ejpam-6640	573	2	7−→	7−→	PROPN
ejpam-6640	573	3	f−1	f−1	PROPN
ejpam-6640	573	4	n+2(βn+1(g	n+2(βn+1(g	NUM
ejpam-6640	573	5	−1	−1	NOUN
ejpam-6640	573	6	n+1(kn+1	n+1(kn+1	PROPN
ejpam-6640	573	7	)	)	PUNCT
ejpam-6640	573	8	)	)	PUNCT
ejpam-6640	573	9	)	)	PUNCT
ejpam-6640	574	1	∀n	∀n	PUNCT
ejpam-6640	574	2	∈	∈	PROPN
ejpam-6640	574	3	z.	z.	PROPN
ejpam-6640	574	4	since	since	SCONJ
ejpam-6640	574	5	comp(ab	comp(ab	PROPN
ejpam-6640	574	6	)	)	PUNCT
ejpam-6640	574	7	=	=	SYM
ejpam-6640	574	8	comp(z−mod	comp(z−mod	X
ejpam-6640	574	9	)	)	PUNCT
ejpam-6640	574	10	is	be	AUX
ejpam-6640	574	11	a	a	DET
ejpam-6640	574	12	special	special	ADJ
ejpam-6640	574	13	case	case	NOUN
ejpam-6640	574	14	of	of	ADP
ejpam-6640	574	15	comp(a	comp(a	NOUN
ejpam-6640	574	16	-	-	PUNCT
ejpam-6640	574	17	mod	mod	NOUN
ejpam-6640	574	18	)	)	PUNCT
ejpam-6640	574	19	,	,	PUNCT
ejpam-6640	574	20	by	by	ADP
ejpam-6640	574	21	theorem	theorem	NOUN
ejpam-6640	574	22	3	3	NUM
ejpam-6640	574	23	if	if	SCONJ
ejpam-6640	574	24	x	x	PRON
ejpam-6640	574	25	is	be	AUX
ejpam-6640	574	26	a	a	DET
ejpam-6640	574	27	projective	projective	ADJ
ejpam-6640	574	28	object	object	NOUN
ejpam-6640	574	29	in	in	ADP
ejpam-6640	574	30	a	a	DET
ejpam-6640	574	31	where	where	SCONJ
ejpam-6640	574	32	a	a	PRON
ejpam-6640	574	33	is	be	AUX
ejpam-6640	574	34	a	a	DET
ejpam-6640	574	35	balanced	balanced	ADJ
ejpam-6640	574	36	abelian	abelian	ADJ
ejpam-6640	574	37	category	category	NOUN
ejpam-6640	574	38	,	,	PUNCT
ejpam-6640	574	39	then	then	ADV
ejpam-6640	574	40	λn	λn	X
ejpam-6640	574	41	:	:	PUNCT
ejpam-6640	574	42	h̃n(x,−)((t	h̃n(x,−)((t	PROPN
ejpam-6640	574	43	,	,	PUNCT
ejpam-6640	574	44	γ	γ	NOUN
ejpam-6640	574	45	)	)	PUNCT
ejpam-6640	574	46	)	)	PUNCT
ejpam-6640	574	47	−→	−→	NOUN
ejpam-6640	574	48	˜hn+1(x,−)((y	˜hn+1(x,−)((y	NOUN
ejpam-6640	574	49	,	,	PUNCT
ejpam-6640	574	50	α	α	NOUN
ejpam-6640	574	51	)	)	PUNCT
ejpam-6640	574	52	)	)	PUNCT
ejpam-6640	575	1	kn+1	kn+1	PROPN
ejpam-6640	575	2	7−→	7−→	PROPN
ejpam-6640	575	3	f∗−1	f∗−1	PROPN
ejpam-6640	575	4	n+2(β	n+2(β	PROPN
ejpam-6640	575	5	∗	∗	NOUN
ejpam-6640	575	6	n+1(g	n+1(g	PROPN
ejpam-6640	575	7	∗−1	∗−1	PROPN
ejpam-6640	575	8	n+1(kn+1	n+1(kn+1	PROPN
ejpam-6640	575	9	)	)	PUNCT
ejpam-6640	575	10	)	)	PUNCT
ejpam-6640	575	11	)	)	PUNCT
ejpam-6640	576	1	∀n	∀n	PUNCT
ejpam-6640	577	1	∈	∈	PROPN
ejpam-6640	577	2	z	z	NOUN
ejpam-6640	577	3	is	be	AUX
ejpam-6640	577	4	well	well	ADV
ejpam-6640	577	5	-	-	PUNCT
ejpam-6640	577	6	defined	define	VERB
ejpam-6640	577	7	with	with	ADP
ejpam-6640	577	8	hn	hn	PRON
ejpam-6640	577	9	:	:	PUNCT
ejpam-6640	577	10	comp(ab	comp(ab	PROPN
ejpam-6640	577	11	)	)	PUNCT
ejpam-6640	577	12	−→	−→	PROPN
ejpam-6640	577	13	ab	ab	PROPN
ejpam-6640	577	14	.	.	PUNCT
ejpam-6640	578	1	(	(	PUNCT
ejpam-6640	578	2	ii	ii	PROPN
ejpam-6640	578	3	)	)	PUNCT
ejpam-6640	578	4	according	accord	VERB
ejpam-6640	578	5	to	to	ADP
ejpam-6640	578	6	theorem	theorem	ADJ
ejpam-6640	578	7	3	3	NUM
ejpam-6640	578	8	,	,	PUNCT
ejpam-6640	578	9	if	if	SCONJ
ejpam-6640	578	10	x	x	PRON
ejpam-6640	578	11	is	be	AUX
ejpam-6640	578	12	a	a	DET
ejpam-6640	578	13	projective	projective	ADJ
ejpam-6640	578	14	object	object	NOUN
ejpam-6640	578	15	in	in	ADP
ejpam-6640	578	16	a	a	PRON
ejpam-6640	578	17	,	,	PUNCT
ejpam-6640	578	18	where	where	SCONJ
ejpam-6640	578	19	a	a	PRON
ejpam-6640	578	20	is	be	AUX
ejpam-6640	578	21	a	a	DET
ejpam-6640	578	22	balanced	balanced	ADJ
ejpam-6640	578	23	abelian	abelian	ADJ
ejpam-6640	578	24	category	category	NOUN
ejpam-6640	578	25	,	,	PUNCT
ejpam-6640	578	26	then	then	ADV
ejpam-6640	578	27	homcomp(a	homcomp(a	NOUN
ejpam-6640	578	28	)	)	PUNCT
ejpam-6640	578	29	(	(	PUNCT
ejpam-6640	578	30	x,−	x,−	PROPN
ejpam-6640	578	31	)	)	PUNCT
ejpam-6640	578	32	transforms	transform	VERB
ejpam-6640	578	33	any	any	DET
ejpam-6640	578	34	complex	complex	ADJ
ejpam-6640	578	35	sequence	sequence	NOUN
ejpam-6640	578	36	in	in	ADP
ejpam-6640	578	37	comp(a	comp(a	NOUN
ejpam-6640	578	38	)	)	PUNCT
ejpam-6640	578	39	into	into	ADP
ejpam-6640	578	40	a	a	DET
ejpam-6640	578	41	complex	complex	ADJ
ejpam-6640	578	42	sequence	sequence	NOUN
ejpam-6640	578	43	in	in	ADP
ejpam-6640	578	44	comp(ab	comp(ab	PROPN
ejpam-6640	578	45	)	)	PUNCT
ejpam-6640	578	46	.	.	PUNCT
ejpam-6640	579	1	however	however	ADV
ejpam-6640	579	2	,	,	PUNCT
ejpam-6640	579	3	hn	hn	PROPN
ejpam-6640	579	4	transforms	transform	VERB
ejpam-6640	579	5	every	every	DET
ejpam-6640	579	6	short	short	ADJ
ejpam-6640	579	7	exact	exact	ADJ
ejpam-6640	579	8	sequence	sequence	NOUN
ejpam-6640	579	9	in	in	ADP
ejpam-6640	579	10	comp(a	comp(a	NOUN
ejpam-6640	579	11	-	-	PUNCT
ejpam-6640	579	12	mod	mod	NOUN
ejpam-6640	579	13	)	)	PUNCT
ejpam-6640	579	14	into	into	ADP
ejpam-6640	579	15	a	a	DET
ejpam-6640	579	16	long	long	ADJ
ejpam-6640	579	17	exact	exact	ADJ
ejpam-6640	579	18	sequence	sequence	NOUN
ejpam-6640	579	19	of	of	ADP
ejpam-6640	579	20	morphisms	morphism	NOUN
ejpam-6640	579	21	in	in	ADP
ejpam-6640	579	22	ab	ab	PROPN
ejpam-6640	579	23	.	.	PUNCT
ejpam-6640	580	1	in	in	ADP
ejpam-6640	580	2	particular	particular	ADJ
ejpam-6640	580	3	,	,	PUNCT
ejpam-6640	580	4	hn	hn	PROPN
ejpam-6640	580	5	transforms	transform	VERB
ejpam-6640	580	6	any	any	DET
ejpam-6640	580	7	complex	complex	ADJ
ejpam-6640	580	8	sequence	sequence	NOUN
ejpam-6640	580	9	of	of	ADP
ejpam-6640	580	10	morphisms	morphism	NOUN
ejpam-6640	580	11	in	in	ADP
ejpam-6640	580	12	comp(ab	comp(ab	NOUN
ejpam-6640	580	13	)	)	PUNCT
ejpam-6640	580	14	=	=	SYM
ejpam-6640	580	15	comp(z	comp(z	NOUN
ejpam-6640	580	16	−	−	PROPN
ejpam-6640	580	17	mod	mod	PROPN
ejpam-6640	580	18	)	)	PUNCT
ejpam-6640	580	19	into	into	ADP
ejpam-6640	580	20	a	a	DET
ejpam-6640	580	21	long	long	ADJ
ejpam-6640	580	22	exact	exact	ADJ
ejpam-6640	580	23	sequence	sequence	NOUN
ejpam-6640	580	24	of	of	ADP
ejpam-6640	580	25	morphisms	morphism	NOUN
ejpam-6640	580	26	in	in	ADP
ejpam-6640	580	27	ab	ab	PROPN
ejpam-6640	580	28	.	.	PUNCT
ejpam-6640	581	1	now	now	ADV
ejpam-6640	581	2	,	,	PUNCT
ejpam-6640	581	3	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	581	4	)	)	PUNCT
ejpam-6640	582	1	=	=	PUNCT
ejpam-6640	582	2	hn	hn	PROPN
ejpam-6640	582	3	◦	◦	NOUN
ejpam-6640	582	4	homcomp(a	homcomp(a	NOUN
ejpam-6640	582	5	)	)	PUNCT
ejpam-6640	582	6	(	(	PUNCT
ejpam-6640	582	7	x,−	x,−	PROPN
ejpam-6640	582	8	)	)	PUNCT
ejpam-6640	582	9	,	,	PUNCT
ejpam-6640	582	10	where	where	SCONJ
ejpam-6640	582	11	hn	hn	PROPN
ejpam-6640	582	12	:	:	PUNCT
ejpam-6640	582	13	comp(ab	comp(ab	PROPN
ejpam-6640	582	14	)	)	PUNCT
ejpam-6640	582	15	−→	−→	PROPN
ejpam-6640	582	16	ab	ab	PROPN
ejpam-6640	582	17	,	,	PUNCT
ejpam-6640	582	18	and	and	CCONJ
ejpam-6640	582	19	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	582	20	)	)	PUNCT
ejpam-6640	582	21	:	:	PUNCT
ejpam-6640	582	22	comp(a	comp(a	NOUN
ejpam-6640	582	23	)	)	PUNCT
ejpam-6640	582	24	−→	−→	PROPN
ejpam-6640	582	25	ab	ab	PROPN
ejpam-6640	582	26	.	.	PUNCT
ejpam-6640	583	1	thus	thus	ADV
ejpam-6640	583	2	,	,	PUNCT
ejpam-6640	583	3	the	the	DET
ejpam-6640	583	4	sequence	sequence	NOUN
ejpam-6640	583	5	.	.	PUNCT
ejpam-6640	583	6	.	.	PUNCT
ejpam-6640	583	7	.	.	PUNCT
ejpam-6640	584	1	//	//	PUNCT
ejpam-6640	585	1	h̃n(x,−)((y	h̃n(x,−)((y	PROPN
ejpam-6640	585	2	,	,	PUNCT
ejpam-6640	585	3	α	α	NOUN
ejpam-6640	585	4	)	)	PUNCT
ejpam-6640	585	5	)	)	PUNCT
ejpam-6640	585	6	h̃n(x,−)(f	h̃n(x,−)(f	PROPN
ejpam-6640	585	7	)	)	PUNCT
ejpam-6640	585	8	//	//	SYM
ejpam-6640	586	1	h̃n(x,−)((z	h̃n(x,−)((z	PROPN
ejpam-6640	586	2	,	,	PUNCT
ejpam-6640	586	3	β	β	NOUN
ejpam-6640	586	4	)	)	PUNCT
ejpam-6640	586	5	)	)	PUNCT
ejpam-6640	586	6	h̃n(x,−)(g	h̃n(x,−)(g	ADJ
ejpam-6640	586	7	)	)	PUNCT
ejpam-6640	586	8	//	//	X
ejpam-6640	586	9	h̃n((t	h̃n((t	NOUN
ejpam-6640	586	10	,	,	PUNCT
ejpam-6640	586	11	γ	γ	NOUN
ejpam-6640	586	12	)	)	PUNCT
ejpam-6640	586	13	)	)	PUNCT
ejpam-6640	587	1	λn	λn	PROPN
ejpam-6640	587	2	//	//	NUM
ejpam-6640	587	3	h̃n+1(x,−)((y	h̃n+1(x,−)((y	PROPN
ejpam-6640	587	4	,	,	PUNCT
ejpam-6640	587	5	α	α	NOUN
ejpam-6640	587	6	)	)	PUNCT
ejpam-6640	587	7	)	)	PUNCT
ejpam-6640	587	8	h̃n+1(x,−)(f	h̃n+1(x,−)(f	X
ejpam-6640	587	9	)	)	PUNCT
ejpam-6640	587	10	//	//	SYM
ejpam-6640	588	1	h̃n+1(x,−)((z	h̃n+1(x,−)((z	PROPN
ejpam-6640	588	2	,	,	PUNCT
ejpam-6640	588	3	β	β	NOUN
ejpam-6640	588	4	)	)	PUNCT
ejpam-6640	588	5	)	)	PUNCT
ejpam-6640	588	6	h̃n+1(x,−)(g	h̃n+1(x,−)(g	NOUN
ejpam-6640	588	7	)	)	PUNCT
ejpam-6640	588	8	//	//	NOUN
ejpam-6640	589	1	h̃n+1(x,−)((t	h̃n+1(x,−)((t	PROPN
ejpam-6640	589	2	,	,	PUNCT
ejpam-6640	589	3	γ	γ	NOUN
ejpam-6640	589	4	)	)	PUNCT
ejpam-6640	589	5	)	)	PUNCT
ejpam-6640	589	6	λn+1(−,x	λn+1(−,x	ADV
ejpam-6640	589	7	)	)	PUNCT
ejpam-6640	589	8	//	//	NOUN
ejpam-6640	589	9	.	.	PUNCT
ejpam-6640	589	10	.	.	PUNCT
ejpam-6640	590	1	.	.	PUNCT
ejpam-6640	591	1	is	be	AUX
ejpam-6640	591	2	a	a	DET
ejpam-6640	591	3	long	long	ADJ
ejpam-6640	591	4	exact	exact	ADJ
ejpam-6640	591	5	sequence	sequence	NOUN
ejpam-6640	591	6	of	of	ADP
ejpam-6640	591	7	abelian	abelian	ADJ
ejpam-6640	591	8	group	group	NOUN
ejpam-6640	591	9	morphisms	morphism	VERB
ejpam-6640	591	10	.	.	PUNCT
ejpam-6640	592	1	[	[	X
ejpam-6640	592	2	h̃n(−	h̃n(−	NOUN
ejpam-6640	592	3	,	,	PUNCT
ejpam-6640	592	4	x	x	NOUN
ejpam-6640	592	5	)	)	PUNCT
ejpam-6640	592	6	]	]	PUNCT
ejpam-6640	592	7	let	let	VERB
ejpam-6640	592	8	a	a	PRON
ejpam-6640	592	9	be	be	AUX
ejpam-6640	592	10	a	a	DET
ejpam-6640	592	11	balanced	balanced	ADJ
ejpam-6640	592	12	abelian	abelian	ADJ
ejpam-6640	592	13	category	category	NOUN
ejpam-6640	592	14	and	and	CCONJ
ejpam-6640	592	15	x	x	SYM
ejpam-6640	592	16	an	an	DET
ejpam-6640	592	17	injective	injective	ADJ
ejpam-6640	592	18	object	object	NOUN
ejpam-6640	592	19	in	in	ADP
ejpam-6640	592	20	a	a	PRON
ejpam-6640	592	21	.	.	PUNCT
ejpam-6640	593	1	then	then	ADV
ejpam-6640	593	2	the	the	DET
ejpam-6640	593	3	homological	homological	ADJ
ejpam-6640	593	4	functor	functor	NOUN
ejpam-6640	593	5	of	of	ADP
ejpam-6640	593	6	degree	degree	NOUN
ejpam-6640	593	7	n	n	CCONJ
ejpam-6640	593	8	(	(	PUNCT
ejpam-6640	593	9	n	n	X
ejpam-6640	593	10	∈	∈	PROPN
ejpam-6640	593	11	z	z	PROPN
ejpam-6640	593	12	)	)	PUNCT
ejpam-6640	593	13	,	,	PUNCT
ejpam-6640	593	14	denoted	denote	VERB
ejpam-6640	593	15	h̃n(−	h̃n(−	PROPN
ejpam-6640	593	16	,	,	PUNCT
ejpam-6640	593	17	x	x	X
ejpam-6640	593	18	)	)	PUNCT
ejpam-6640	594	1	=	=	SYM
ejpam-6640	594	2	hn	hn	PROPN
ejpam-6640	594	3	◦	◦	NOUN
ejpam-6640	594	4	homcomp(a	homcomp(a	NOUN
ejpam-6640	594	5	)	)	PUNCT
ejpam-6640	594	6	(	(	PUNCT
ejpam-6640	594	7	−	−	PROPN
ejpam-6640	594	8	,	,	PUNCT
ejpam-6640	594	9	x	x	NOUN
ejpam-6640	594	10	)	)	PUNCT
ejpam-6640	594	11	,	,	PUNCT
ejpam-6640	594	12	where	where	SCONJ
ejpam-6640	594	13	hn	hn	PROPN
ejpam-6640	594	14	:	:	PUNCT
ejpam-6640	594	15	comp(ab	comp(ab	PROPN
ejpam-6640	594	16	)	)	PUNCT
ejpam-6640	594	17	−→	−→	PROPN
ejpam-6640	594	18	ab	ab	PROPN
ejpam-6640	594	19	,	,	PUNCT
ejpam-6640	594	20	h̃n(−	h̃n(−	PROPN
ejpam-6640	594	21	,	,	PUNCT
ejpam-6640	594	22	x	x	NOUN
ejpam-6640	594	23	)	)	PUNCT
ejpam-6640	594	24	:	:	PUNCT
ejpam-6640	594	25	comp(a	comp(a	INTJ
ejpam-6640	594	26	)	)	PUNCT
ejpam-6640	594	27	−→	−→	PROPN
ejpam-6640	594	28	ab	ab	PROPN
ejpam-6640	594	29	is	be	AUX
ejpam-6640	594	30	defined	define	VERB
ejpam-6640	594	31	by	by	ADP
ejpam-6640	594	32	:	:	PUNCT
ejpam-6640	594	33	(	(	PUNCT
ejpam-6640	594	34	i	i	NOUN
ejpam-6640	594	35	)	)	PUNCT
ejpam-6640	594	36	for	for	ADP
ejpam-6640	594	37	any	any	DET
ejpam-6640	594	38	complex	complex	ADJ
ejpam-6640	594	39	(	(	PUNCT
ejpam-6640	594	40	y	y	PROPN
ejpam-6640	594	41	,	,	PUNCT
ejpam-6640	594	42	β	β	NOUN
ejpam-6640	594	43	)	)	PUNCT
ejpam-6640	594	44	=	=	SYM
ejpam-6640	594	45	(	(	PUNCT
ejpam-6640	594	46	βn	βn	NOUN
ejpam-6640	594	47	:	:	PUNCT
ejpam-6640	594	48	yn	yn	PROPN
ejpam-6640	594	49	→	→	SYM
ejpam-6640	594	50	yn+1)n∈z	yn+1)n∈z	NOUN
ejpam-6640	594	51	in	in	ADP
ejpam-6640	594	52	comp(a	comp(a	NOUN
ejpam-6640	594	53	)	)	PUNCT
ejpam-6640	594	54	,	,	PUNCT
ejpam-6640	594	55	we	we	PRON
ejpam-6640	594	56	associate	associate	VERB
ejpam-6640	594	57	:	:	PUNCT
ejpam-6640	594	58	h̃n(−	h̃n(−	PROPN
ejpam-6640	594	59	,	,	PUNCT
ejpam-6640	594	60	x)((y	x)((y	PROPN
ejpam-6640	594	61	,	,	PUNCT
ejpam-6640	594	62	β	β	NOUN
ejpam-6640	594	63	)	)	PUNCT
ejpam-6640	594	64	)	)	PUNCT
ejpam-6640	595	1	=	=	SYM
ejpam-6640	595	2	hn(homcomp(a	hn(homcomp(a	NOUN
ejpam-6640	595	3	)	)	PUNCT
ejpam-6640	595	4	(	(	PUNCT
ejpam-6640	595	5	−	−	NOUN
ejpam-6640	595	6	,	,	PUNCT
ejpam-6640	595	7	x))((y	x))((y	PROPN
ejpam-6640	595	8	,	,	PUNCT
ejpam-6640	595	9	β	β	NOUN
ejpam-6640	595	10	)	)	PUNCT
ejpam-6640	595	11	)	)	PUNCT
ejpam-6640	596	1	=	=	PUNCT
ejpam-6640	596	2	kerβ∗n+1	kerβ∗n+1	VERB
ejpam-6640	596	3	/	/	SYM
ejpam-6640	596	4	imβ	imβ	PRON
ejpam-6640	596	5	∗	∗	NOUN
ejpam-6640	596	6	n	n	CCONJ
ejpam-6640	596	7	∀n	∀n	NUM
ejpam-6640	596	8	∈	∈	PROPN
ejpam-6640	596	9	z	z	X
ejpam-6640	596	10	(	(	PUNCT
ejpam-6640	596	11	ii	ii	NOUN
ejpam-6640	596	12	)	)	PUNCT
ejpam-6640	596	13	for	for	ADP
ejpam-6640	596	14	any	any	DET
ejpam-6640	596	15	complex	complex	ADJ
ejpam-6640	596	16	morphism	morphism	NOUN
ejpam-6640	596	17	f	f	PROPN
ejpam-6640	596	18	:	:	PUNCT
ejpam-6640	596	19	(	(	PUNCT
ejpam-6640	596	20	y	y	NOUN
ejpam-6640	596	21	,	,	PUNCT
ejpam-6640	596	22	β	β	NOUN
ejpam-6640	596	23	)	)	PUNCT
ejpam-6640	596	24	→	→	SYM
ejpam-6640	596	25	(	(	PUNCT
ejpam-6640	596	26	z	z	NOUN
ejpam-6640	596	27	,	,	PUNCT
ejpam-6640	596	28	α	α	NOUN
ejpam-6640	596	29	)	)	PUNCT
ejpam-6640	596	30	=	=	PUNCT
ejpam-6640	596	31	(	(	PUNCT
ejpam-6640	596	32	fn	fn	X
ejpam-6640	596	33	:	:	PUNCT
ejpam-6640	596	34	yn	yn	PROPN
ejpam-6640	596	35	→	→	SYM
ejpam-6640	596	36	zn)n∈z	zn)n∈z	NUM
ejpam-6640	596	37	,	,	PUNCT
ejpam-6640	596	38	we	we	PRON
ejpam-6640	596	39	associate	associate	VERB
ejpam-6640	596	40	:	:	PUNCT
ejpam-6640	596	41	h̃n(f	h̃n(f	INTJ
ejpam-6640	596	42	,	,	PUNCT
ejpam-6640	596	43	x	x	X
ejpam-6640	596	44	)	)	PUNCT
ejpam-6640	596	45	:	:	PUNCT
ejpam-6640	597	1	h̃n(−	h̃n(−	PROPN
ejpam-6640	597	2	,	,	PUNCT
ejpam-6640	597	3	x)((z	x)((z	PROPN
ejpam-6640	597	4	,	,	PUNCT
ejpam-6640	597	5	α	α	NOUN
ejpam-6640	597	6	)	)	PUNCT
ejpam-6640	597	7	)	)	PUNCT
ejpam-6640	598	1	−→	−→	NOUN
ejpam-6640	598	2	h̃n(−	h̃n(−	PROPN
ejpam-6640	598	3	,	,	PUNCT
ejpam-6640	598	4	x)((y	x)((y	PROPN
ejpam-6640	598	5	,	,	PUNCT
ejpam-6640	598	6	β	β	NOUN
ejpam-6640	598	7	)	)	PUNCT
ejpam-6640	598	8	)	)	PUNCT
ejpam-6640	599	1	gn	gn	PROPN
ejpam-6640	599	2	7−→	7−→	PROPN
ejpam-6640	599	3	gn(fn	gn(fn	NOUN
ejpam-6640	599	4	)	)	PUNCT
ejpam-6640	599	5	is	be	AUX
ejpam-6640	599	6	a	a	DET
ejpam-6640	599	7	contravariant	contravariant	ADJ
ejpam-6640	599	8	additive	additive	ADJ
ejpam-6640	599	9	functor	functor	NOUN
ejpam-6640	599	10	.	.	PUNCT
ejpam-6640	600	1	proof	proof	NOUN
ejpam-6640	600	2	.	.	PUNCT
ejpam-6640	601	1	we	we	PRON
ejpam-6640	601	2	know	know	VERB
ejpam-6640	601	3	that	that	SCONJ
ejpam-6640	601	4	the	the	DET
ejpam-6640	601	5	homology	homology	NOUN
ejpam-6640	601	6	functor	functor	PROPN
ejpam-6640	601	7	hn	hn	PROPN
ejpam-6640	601	8	:	:	PUNCT
ejpam-6640	601	9	comp(a	comp(a	NOUN
ejpam-6640	601	10	-	-	PUNCT
ejpam-6640	601	11	mod	mod	NOUN
ejpam-6640	601	12	)	)	PUNCT
ejpam-6640	601	13	−→	−→	NOUN
ejpam-6640	601	14	ab	ab	PROPN
ejpam-6640	601	15	is	be	AUX
ejpam-6640	601	16	defined	define	VERB
ejpam-6640	601	17	by	by	ADP
ejpam-6640	601	18	:	:	PUNCT
ejpam-6640	601	19	a.	a.	PROPN
ejpam-6640	601	20	diallo	diallo	PROPN
ejpam-6640	601	21	,	,	PUNCT
ejpam-6640	601	22	m.	m.	PROPN
ejpam-6640	601	23	b.	b.	PROPN
ejpam-6640	601	24	f.	f.	PROPN
ejpam-6640	601	25	b.	b.	PROPN
ejpam-6640	601	26	maaouia	maaouia	PROPN
ejpam-6640	601	27	,	,	PUNCT
ejpam-6640	601	28	m.	m.	NOUN
ejpam-6640	601	29	sanghare	sanghare	PROPN
ejpam-6640	601	30	/	/	SYM
ejpam-6640	601	31	eur	eur	PROPN
ejpam-6640	601	32	.	.	PUNCT
ejpam-6640	602	1	j.	j.	PROPN
ejpam-6640	602	2	pure	pure	PROPN
ejpam-6640	602	3	appl	appl	PROPN
ejpam-6640	602	4	.	.	PROPN
ejpam-6640	602	5	math	math	PROPN
ejpam-6640	602	6	,	,	PUNCT
ejpam-6640	602	7	18	18	NUM
ejpam-6640	602	8	(	(	PUNCT
ejpam-6640	602	9	4	4	NUM
ejpam-6640	602	10	)	)	PUNCT
ejpam-6640	602	11	(	(	PUNCT
ejpam-6640	602	12	2025	2025	NUM
ejpam-6640	602	13	)	)	PUNCT
ejpam-6640	602	14	,	,	PUNCT
ejpam-6640	602	15	6640	6640	NUM
ejpam-6640	602	16	25	25	NUM
ejpam-6640	602	17	of	of	ADP
ejpam-6640	602	18	28	28	NUM
ejpam-6640	602	19	(	(	PUNCT
ejpam-6640	602	20	i	i	NOUN
ejpam-6640	602	21	)	)	PUNCT
ejpam-6640	602	22	for	for	ADP
ejpam-6640	602	23	any	any	DET
ejpam-6640	602	24	complex	complex	ADJ
ejpam-6640	602	25	(	(	PUNCT
ejpam-6640	602	26	y	y	PROPN
ejpam-6640	602	27	,	,	PUNCT
ejpam-6640	602	28	β	β	NOUN
ejpam-6640	602	29	)	)	PUNCT
ejpam-6640	602	30	=	=	SYM
ejpam-6640	602	31	(	(	PUNCT
ejpam-6640	602	32	βn	βn	NOUN
ejpam-6640	602	33	:	:	PUNCT
ejpam-6640	602	34	yn	yn	PROPN
ejpam-6640	602	35	→	→	SYM
ejpam-6640	602	36	yn+1)n∈z	yn+1)n∈z	NOUN
ejpam-6640	602	37	in	in	ADP
ejpam-6640	602	38	comp(a	comp(a	NOUN
ejpam-6640	602	39	-	-	PUNCT
ejpam-6640	602	40	mod	mod	NOUN
ejpam-6640	602	41	)	)	PUNCT
ejpam-6640	602	42	,	,	PUNCT
ejpam-6640	602	43	we	we	PRON
ejpam-6640	602	44	associate	associate	VERB
ejpam-6640	602	45	:	:	PUNCT
ejpam-6640	602	46	hn((y	hn((y	ADJ
ejpam-6640	602	47	,	,	PUNCT
ejpam-6640	602	48	β	β	NOUN
ejpam-6640	602	49	)	)	PUNCT
ejpam-6640	602	50	)	)	PUNCT
ejpam-6640	603	1	=	=	SYM
ejpam-6640	603	2	kerβn+1	kerβn+1	PROPN
ejpam-6640	603	3	/	/	SYM
ejpam-6640	603	4	imβn	imβn	NOUN
ejpam-6640	603	5	∀n	∀n	PUNCT
ejpam-6640	603	6	∈	∈	PROPN
ejpam-6640	603	7	z	z	X
ejpam-6640	603	8	(	(	PUNCT
ejpam-6640	603	9	ii	ii	NOUN
ejpam-6640	603	10	)	)	PUNCT
ejpam-6640	603	11	for	for	ADP
ejpam-6640	603	12	any	any	DET
ejpam-6640	603	13	complex	complex	ADJ
ejpam-6640	603	14	morphism	morphism	NOUN
ejpam-6640	603	15	f	f	PROPN
ejpam-6640	603	16	:	:	PUNCT
ejpam-6640	603	17	(	(	PUNCT
ejpam-6640	603	18	y	y	NOUN
ejpam-6640	603	19	,	,	PUNCT
ejpam-6640	603	20	β	β	NOUN
ejpam-6640	603	21	)	)	PUNCT
ejpam-6640	603	22	→	→	SYM
ejpam-6640	603	23	(	(	PUNCT
ejpam-6640	603	24	z	z	NOUN
ejpam-6640	603	25	,	,	PUNCT
ejpam-6640	603	26	α	α	NOUN
ejpam-6640	603	27	)	)	PUNCT
ejpam-6640	603	28	,	,	PUNCT
ejpam-6640	603	29	we	we	PRON
ejpam-6640	603	30	associate	associate	VERB
ejpam-6640	603	31	:	:	PUNCT
ejpam-6640	603	32	hn(f	hn(f	PUNCT
ejpam-6640	603	33	)	)	PUNCT
ejpam-6640	603	34	:	:	PUNCT
ejpam-6640	604	1	hn((z	hn((z	NOUN
ejpam-6640	604	2	,	,	PUNCT
ejpam-6640	604	3	α	α	NOUN
ejpam-6640	604	4	)	)	PUNCT
ejpam-6640	604	5	)	)	PUNCT
ejpam-6640	605	1	−→	−→	NOUN
ejpam-6640	605	2	hn((y	hn((y	ADJ
ejpam-6640	605	3	,	,	PUNCT
ejpam-6640	605	4	β	β	NOUN
ejpam-6640	605	5	)	)	PUNCT
ejpam-6640	605	6	)	)	PUNCT
ejpam-6640	606	1	gn	gn	PROPN
ejpam-6640	606	2	7−→	7−→	PROPN
ejpam-6640	606	3	gn(fn	gn(fn	NOUN
ejpam-6640	606	4	)	)	PUNCT
ejpam-6640	606	5	since	since	SCONJ
ejpam-6640	606	6	hn	hn	PROPN
ejpam-6640	606	7	is	be	AUX
ejpam-6640	606	8	a	a	DET
ejpam-6640	606	9	covariant	covariant	ADJ
ejpam-6640	606	10	additive	additive	ADJ
ejpam-6640	606	11	functor	functor	NOUN
ejpam-6640	606	12	,	,	PUNCT
ejpam-6640	606	13	and	and	CCONJ
ejpam-6640	606	14	comp(ab	comp(ab	NOUN
ejpam-6640	606	15	)	)	PUNCT
ejpam-6640	606	16	=	=	SYM
ejpam-6640	606	17	comp(z	comp(z	NOUN
ejpam-6640	606	18	−	−	PROPN
ejpam-6640	606	19	mod	mod	PROPN
ejpam-6640	606	20	)	)	PUNCT
ejpam-6640	606	21	is	be	AUX
ejpam-6640	606	22	a	a	DET
ejpam-6640	606	23	special	special	ADJ
ejpam-6640	606	24	case	case	NOUN
ejpam-6640	606	25	of	of	ADP
ejpam-6640	606	26	comp(a	comp(a	NOUN
ejpam-6640	606	27	-	-	PUNCT
ejpam-6640	606	28	mod	mod	NOUN
ejpam-6640	606	29	)	)	PUNCT
ejpam-6640	606	30	,	,	PUNCT
ejpam-6640	606	31	the	the	DET
ejpam-6640	606	32	functor	functor	PROPN
ejpam-6640	606	33	h̃n	h̃n	NOUN
ejpam-6640	606	34	is	be	AUX
ejpam-6640	606	35	covariant	covariant	ADJ
ejpam-6640	606	36	.	.	PUNCT
ejpam-6640	607	1	according	accord	VERB
ejpam-6640	607	2	to	to	ADP
ejpam-6640	607	3	theorem	theorem	ADJ
ejpam-6640	607	4	3	3	NUM
ejpam-6640	607	5	,	,	PUNCT
ejpam-6640	607	6	homcomp(a	homcomp(a	NOUN
ejpam-6640	607	7	)	)	PUNCT
ejpam-6640	607	8	(	(	PUNCT
ejpam-6640	607	9	−	−	PROPN
ejpam-6640	607	10	,	,	PUNCT
ejpam-6640	607	11	x	x	X
ejpam-6640	607	12	)	)	PUNCT
ejpam-6640	607	13	is	be	AUX
ejpam-6640	607	14	contravariant	contravariant	ADJ
ejpam-6640	607	15	.	.	PUNCT
ejpam-6640	608	1	however	however	ADV
ejpam-6640	608	2	,	,	PUNCT
ejpam-6640	608	3	the	the	DET
ejpam-6640	608	4	composition	composition	NOUN
ejpam-6640	608	5	of	of	ADP
ejpam-6640	608	6	a	a	DET
ejpam-6640	608	7	covariant	covariant	ADJ
ejpam-6640	608	8	functor	functor	NOUN
ejpam-6640	608	9	and	and	CCONJ
ejpam-6640	608	10	a	a	DET
ejpam-6640	608	11	contravariant	contravariant	ADJ
ejpam-6640	608	12	functor	functor	PROPN
ejpam-6640	608	13	is	be	AUX
ejpam-6640	608	14	contravariant	contravariant	ADJ
ejpam-6640	608	15	,	,	PUNCT
ejpam-6640	608	16	so	so	ADV
ejpam-6640	608	17	h̃n(−	h̃n(−	PROPN
ejpam-6640	608	18	,	,	PUNCT
ejpam-6640	608	19	x	x	NOUN
ejpam-6640	608	20	)	)	PUNCT
ejpam-6640	608	21	:	:	PUNCT
ejpam-6640	608	22	comp(a	comp(a	INTJ
ejpam-6640	608	23	)	)	PUNCT
ejpam-6640	609	1	−→	−→	PROPN
ejpam-6640	609	2	ab	ab	PROPN
ejpam-6640	609	3	is	be	AUX
ejpam-6640	609	4	welldefined	welldefine	VERB
ejpam-6640	609	5	and	and	CCONJ
ejpam-6640	609	6	is	be	AUX
ejpam-6640	609	7	a	a	DET
ejpam-6640	609	8	contravariant	contravariant	ADJ
ejpam-6640	609	9	functor	functor	NOUN
ejpam-6640	609	10	.	.	PUNCT
ejpam-6640	610	1	by	by	ADP
ejpam-6640	610	2	proposition	proposition	NOUN
ejpam-6640	610	3	1	1	NUM
ejpam-6640	610	4	and	and	CCONJ
ejpam-6640	610	5	theorem	theorem	VERB
ejpam-6640	610	6	2	2	NUM
ejpam-6640	610	7	,	,	PUNCT
ejpam-6640	610	8	h̃n(−	h̃n(−	PROPN
ejpam-6640	610	9	,	,	PUNCT
ejpam-6640	610	10	x	x	X
ejpam-6640	610	11	)	)	PUNCT
ejpam-6640	610	12	is	be	AUX
ejpam-6640	610	13	an	an	DET
ejpam-6640	610	14	additive	additive	ADJ
ejpam-6640	610	15	functor	functor	NOUN
ejpam-6640	610	16	.	.	PUNCT
ejpam-6640	611	1	thus	thus	ADV
ejpam-6640	611	2	,	,	PUNCT
ejpam-6640	611	3	h̃n(−	h̃n(−	PROPN
ejpam-6640	611	4	,	,	PUNCT
ejpam-6640	611	5	x	x	X
ejpam-6640	611	6	)	)	PUNCT
ejpam-6640	611	7	is	be	AUX
ejpam-6640	611	8	a	a	DET
ejpam-6640	611	9	contravariant	contravariant	ADJ
ejpam-6640	611	10	additive	additive	ADJ
ejpam-6640	611	11	functor	functor	NOUN
ejpam-6640	611	12	.	.	PUNCT
ejpam-6640	612	1	let	let	VERB
ejpam-6640	612	2	(	(	PUNCT
ejpam-6640	612	3	0	0	NUM
ejpam-6640	612	4	)	)	PUNCT
ejpam-6640	612	5	//	//	NOUN
ejpam-6640	613	1	(	(	PUNCT
ejpam-6640	613	2	y	y	PROPN
ejpam-6640	613	3	,	,	PUNCT
ejpam-6640	613	4	α	α	NOUN
ejpam-6640	613	5	)	)	PUNCT
ejpam-6640	613	6	f	f	PROPN
ejpam-6640	613	7	//	//	X
ejpam-6640	613	8	(	(	PUNCT
ejpam-6640	613	9	z	z	NOUN
ejpam-6640	613	10	,	,	PUNCT
ejpam-6640	613	11	β	β	NOUN
ejpam-6640	613	12	)	)	PUNCT
ejpam-6640	613	13	g	g	PROPN
ejpam-6640	613	14	//	//	SYM
ejpam-6640	613	15	(	(	PUNCT
ejpam-6640	613	16	t	t	PROPN
ejpam-6640	613	17	,	,	PUNCT
ejpam-6640	613	18	γ	γ	PROPN
ejpam-6640	613	19	)	)	PUNCT
ejpam-6640	613	20	//	//	NOUN
ejpam-6640	613	21	(	(	PUNCT
ejpam-6640	613	22	0	0	NUM
ejpam-6640	613	23	)	)	PUNCT
ejpam-6640	613	24	be	be	AUX
ejpam-6640	613	25	a	a	DET
ejpam-6640	613	26	short	short	ADJ
ejpam-6640	613	27	exact	exact	ADJ
ejpam-6640	613	28	sequence	sequence	NOUN
ejpam-6640	613	29	in	in	ADP
ejpam-6640	613	30	comp(a	comp(a	NOUN
ejpam-6640	613	31	)	)	PUNCT
ejpam-6640	613	32	,	,	PUNCT
ejpam-6640	613	33	where	where	SCONJ
ejpam-6640	613	34	a	a	PRON
ejpam-6640	613	35	is	be	AUX
ejpam-6640	613	36	a	a	DET
ejpam-6640	613	37	balanced	balanced	ADJ
ejpam-6640	613	38	abelian	abelian	ADJ
ejpam-6640	613	39	category	category	NOUN
ejpam-6640	613	40	and	and	CCONJ
ejpam-6640	613	41	x	x	SYM
ejpam-6640	613	42	an	an	DET
ejpam-6640	613	43	injective	injective	ADJ
ejpam-6640	613	44	object	object	NOUN
ejpam-6640	613	45	in	in	ADP
ejpam-6640	613	46	a	a	PRON
ejpam-6640	613	47	.	.	PUNCT
ejpam-6640	614	1	then	then	ADV
ejpam-6640	614	2	:	:	PUNCT
ejpam-6640	614	3	(	(	PUNCT
ejpam-6640	614	4	i	i	NOUN
ejpam-6640	614	5	)	)	PUNCT
ejpam-6640	614	6	the	the	DET
ejpam-6640	614	7	morphism	morphism	NOUN
ejpam-6640	614	8	of	of	ADP
ejpam-6640	614	9	connection	connection	NOUN
ejpam-6640	614	10	associated	associate	VERB
ejpam-6640	614	11	to	to	ADP
ejpam-6640	614	12	the	the	DET
ejpam-6640	614	13	contravariant	contravariant	PROPN
ejpam-6640	614	14	functor	functor	PROPN
ejpam-6640	614	15	h̃n(−	h̃n(−	PROPN
ejpam-6640	614	16	,	,	PUNCT
ejpam-6640	614	17	x	x	X
ejpam-6640	614	18	)	)	PUNCT
ejpam-6640	614	19	is	be	AUX
ejpam-6640	614	20	defined	define	VERB
ejpam-6640	614	21	by	by	ADP
ejpam-6640	614	22	:	:	PUNCT
ejpam-6640	614	23	δn	δn	NOUN
ejpam-6640	614	24	:	:	PUNCT
ejpam-6640	614	25	h̃n(−	h̃n(−	PROPN
ejpam-6640	614	26	,	,	PUNCT
ejpam-6640	614	27	x)((y	x)((y	PROPN
ejpam-6640	614	28	,	,	PUNCT
ejpam-6640	614	29	α	α	NOUN
ejpam-6640	614	30	)	)	PUNCT
ejpam-6640	614	31	)	)	PUNCT
ejpam-6640	614	32	−→	−→	NOUN
ejpam-6640	614	33	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	614	34	,	,	PUNCT
ejpam-6640	614	35	x)((t	x)((t	PROPN
ejpam-6640	614	36	,	,	PUNCT
ejpam-6640	614	37	γ	γ	NOUN
ejpam-6640	614	38	)	)	PUNCT
ejpam-6640	614	39	)	)	PUNCT
ejpam-6640	615	1	kn+1	kn+1	PROPN
ejpam-6640	615	2	7−→	7−→	PROPN
ejpam-6640	615	3	g∗−1	g∗−1	PROPN
ejpam-6640	615	4	n+2(β	n+2(β	PROPN
ejpam-6640	615	5	∗	∗	NOUN
ejpam-6640	615	6	n+1(f	n+1(f	ADJ
ejpam-6640	615	7	∗−1	∗−1	NOUN
ejpam-6640	615	8	n+1(kn+1	n+1(kn+1	PROPN
ejpam-6640	615	9	)	)	PUNCT
ejpam-6640	615	10	)	)	PUNCT
ejpam-6640	615	11	)	)	PUNCT
ejpam-6640	615	12	,	,	PUNCT
ejpam-6640	615	13	∀n	∀n	NUM
ejpam-6640	615	14	∈	∈	PROPN
ejpam-6640	615	15	z	z	X
ejpam-6640	615	16	(	(	PUNCT
ejpam-6640	615	17	ii	ii	PROPN
ejpam-6640	615	18	)	)	PUNCT
ejpam-6640	615	19	the	the	DET
ejpam-6640	615	20	sequence	sequence	NOUN
ejpam-6640	615	21	·	·	PUNCT
ejpam-6640	615	22	·	·	PUNCT
ejpam-6640	615	23	·	·	PUNCT
ejpam-6640	616	1	//	//	PUNCT
ejpam-6640	616	2	h̃n(−	h̃n(−	PROPN
ejpam-6640	616	3	,	,	PUNCT
ejpam-6640	616	4	x)((t	x)((t	PROPN
ejpam-6640	616	5	,	,	PUNCT
ejpam-6640	616	6	γ	γ	NOUN
ejpam-6640	616	7	)	)	PUNCT
ejpam-6640	616	8	)	)	PUNCT
ejpam-6640	616	9	h̃n(−,x)(g	h̃n(−,x)(g	PROPN
ejpam-6640	616	10	)	)	PUNCT
ejpam-6640	616	11	//	//	X
ejpam-6640	617	1	h̃n(−	h̃n(−	PROPN
ejpam-6640	617	2	,	,	PUNCT
ejpam-6640	617	3	x)((z	x)((z	PROPN
ejpam-6640	617	4	,	,	PUNCT
ejpam-6640	617	5	β	β	NOUN
ejpam-6640	617	6	)	)	PUNCT
ejpam-6640	617	7	)	)	PUNCT
ejpam-6640	617	8	h̃n(−,x)(f	h̃n(−,x)(f	PROPN
ejpam-6640	617	9	)	)	PUNCT
ejpam-6640	617	10	//	//	PUNCT
ejpam-6640	618	1	h̃n(−	h̃n(−	PROPN
ejpam-6640	618	2	,	,	PUNCT
ejpam-6640	618	3	x)((y	x)((y	PROPN
ejpam-6640	618	4	,	,	PUNCT
ejpam-6640	618	5	α	α	NOUN
ejpam-6640	618	6	)	)	PUNCT
ejpam-6640	618	7	)	)	PUNCT
ejpam-6640	618	8	δn//	δn//	PROPN
ejpam-6640	618	9	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	618	10	,	,	PUNCT
ejpam-6640	618	11	x)((t	x)((t	PROPN
ejpam-6640	618	12	,	,	PUNCT
ejpam-6640	618	13	γ	γ	NOUN
ejpam-6640	618	14	)	)	PUNCT
ejpam-6640	618	15	)	)	PUNCT
ejpam-6640	618	16	h̃n+1(−,x)(g	h̃n+1(−,x)(g	NOUN
ejpam-6640	618	17	)	)	PUNCT
ejpam-6640	618	18	//	//	SYM
ejpam-6640	618	19	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	618	20	,	,	PUNCT
ejpam-6640	618	21	x)((z	x)((z	PROPN
ejpam-6640	618	22	,	,	PUNCT
ejpam-6640	618	23	β	β	NOUN
ejpam-6640	618	24	)	)	PUNCT
ejpam-6640	618	25	)	)	PUNCT
ejpam-6640	619	1	h̃n+1(−,x)(f	h̃n+1(−,x)(f	PROPN
ejpam-6640	619	2	)	)	PUNCT
ejpam-6640	619	3	//	//	SYM
ejpam-6640	619	4	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	619	5	,	,	PUNCT
ejpam-6640	619	6	x)((y	x)((y	PROPN
ejpam-6640	619	7	,	,	PUNCT
ejpam-6640	619	8	α	α	NOUN
ejpam-6640	619	9	)	)	PUNCT
ejpam-6640	619	10	)	)	PUNCT
ejpam-6640	619	11	δn+1	δn+1	PROPN
ejpam-6640	619	12	//	//	X
ejpam-6640	619	13	·	·	PUNCT
ejpam-6640	619	14	·	·	PUNCT
ejpam-6640	619	15	·	·	PUNCT
ejpam-6640	619	16	is	be	AUX
ejpam-6640	619	17	a	a	DET
ejpam-6640	619	18	long	long	ADJ
ejpam-6640	619	19	exact	exact	ADJ
ejpam-6640	619	20	sequence	sequence	NOUN
ejpam-6640	619	21	in	in	ADP
ejpam-6640	619	22	ab	ab	PROPN
ejpam-6640	619	23	.	.	PUNCT
ejpam-6640	620	1	that	that	PRON
ejpam-6640	620	2	is	is	ADV
ejpam-6640	620	3	(	(	PUNCT
ejpam-6640	620	4	∀n	∀n	CCONJ
ejpam-6640	620	5	∈	∈	PROPN
ejpam-6640	620	6	z):	z):	NOUN
ejpam-6640	620	7	im(h̃n(−	im(h̃n(−	NOUN
ejpam-6640	620	8	,	,	PUNCT
ejpam-6640	620	9	x)(g	x)(g	NUM
ejpam-6640	620	10	)	)	PUNCT
ejpam-6640	620	11	)	)	PUNCT
ejpam-6640	621	1	=	=	PUNCT
ejpam-6640	621	2	ker(h̃n(−	ker(h̃n(−	PROPN
ejpam-6640	621	3	,	,	PUNCT
ejpam-6640	621	4	x)(f	x)(f	PROPN
ejpam-6640	621	5	)	)	PUNCT
ejpam-6640	621	6	)	)	PUNCT
ejpam-6640	622	1	im(h̃n(−	im(h̃n(−	NOUN
ejpam-6640	622	2	,	,	PUNCT
ejpam-6640	622	3	x)(f	x)(f	PROPN
ejpam-6640	622	4	)	)	PUNCT
ejpam-6640	622	5	)	)	PUNCT
ejpam-6640	623	1	=	=	SYM
ejpam-6640	623	2	ker(δn	ker(δn	X
ejpam-6640	623	3	)	)	PUNCT
ejpam-6640	623	4	im(δn	im(δn	PROPN
ejpam-6640	623	5	)	)	PUNCT
ejpam-6640	623	6	=	=	SYM
ejpam-6640	623	7	ker(h̃n+1(−	ker(h̃n+1(−	PROPN
ejpam-6640	623	8	,	,	PUNCT
ejpam-6640	623	9	x)(g	x)(g	NUM
ejpam-6640	623	10	)	)	PUNCT
ejpam-6640	623	11	)	)	PUNCT
ejpam-6640	623	12	proof	proof	NOUN
ejpam-6640	623	13	.	.	PUNCT
ejpam-6640	624	1	a.	a.	PROPN
ejpam-6640	624	2	diallo	diallo	PROPN
ejpam-6640	624	3	,	,	PUNCT
ejpam-6640	624	4	m.	m.	PROPN
ejpam-6640	624	5	b.	b.	PROPN
ejpam-6640	624	6	f.	f.	PROPN
ejpam-6640	624	7	b.	b.	PROPN
ejpam-6640	624	8	maaouia	maaouia	PROPN
ejpam-6640	624	9	,	,	PUNCT
ejpam-6640	624	10	m.	m.	NOUN
ejpam-6640	624	11	sanghare	sanghare	PROPN
ejpam-6640	624	12	/	/	SYM
ejpam-6640	624	13	eur	eur	PROPN
ejpam-6640	624	14	.	.	PUNCT
ejpam-6640	625	1	j.	j.	PROPN
ejpam-6640	625	2	pure	pure	PROPN
ejpam-6640	625	3	appl	appl	PROPN
ejpam-6640	625	4	.	.	PROPN
ejpam-6640	625	5	math	math	PROPN
ejpam-6640	625	6	,	,	PUNCT
ejpam-6640	625	7	18	18	NUM
ejpam-6640	625	8	(	(	PUNCT
ejpam-6640	625	9	4	4	NUM
ejpam-6640	625	10	)	)	PUNCT
ejpam-6640	625	11	(	(	PUNCT
ejpam-6640	625	12	2025	2025	NUM
ejpam-6640	625	13	)	)	PUNCT
ejpam-6640	625	14	,	,	PUNCT
ejpam-6640	625	15	6640	6640	NUM
ejpam-6640	625	16	26	26	NUM
ejpam-6640	625	17	of	of	ADP
ejpam-6640	625	18	28	28	NUM
ejpam-6640	625	19	(	(	PUNCT
ejpam-6640	625	20	i	i	NOUN
ejpam-6640	625	21	)	)	PUNCT
ejpam-6640	625	22	we	we	PRON
ejpam-6640	625	23	know	know	VERB
ejpam-6640	625	24	that	that	SCONJ
ejpam-6640	625	25	if	if	SCONJ
ejpam-6640	625	26	the	the	DET
ejpam-6640	625	27	homological	homological	ADJ
ejpam-6640	625	28	functor	functor	NOUN
ejpam-6640	625	29	hn	hn	PROPN
ejpam-6640	625	30	:	:	PUNCT
ejpam-6640	625	31	comp(a	comp(a	NOUN
ejpam-6640	625	32	-	-	PUNCT
ejpam-6640	625	33	mod	mod	NOUN
ejpam-6640	625	34	)	)	PUNCT
ejpam-6640	625	35	−→	−→	NOUN
ejpam-6640	625	36	ab	ab	PROPN
ejpam-6640	625	37	is	be	AUX
ejpam-6640	625	38	covariant	covariant	ADJ
ejpam-6640	625	39	,	,	PUNCT
ejpam-6640	625	40	then	then	ADV
ejpam-6640	625	41	for	for	ADP
ejpam-6640	625	42	every	every	DET
ejpam-6640	625	43	short	short	ADJ
ejpam-6640	625	44	exact	exact	ADJ
ejpam-6640	625	45	sequence	sequence	NOUN
ejpam-6640	625	46	of	of	ADP
ejpam-6640	625	47	morphisms	morphism	NOUN
ejpam-6640	625	48	in	in	ADP
ejpam-6640	625	49	comp(a	comp(a	NOUN
ejpam-6640	625	50	-	-	PUNCT
ejpam-6640	625	51	mod	mod	NOUN
ejpam-6640	625	52	)	)	PUNCT
ejpam-6640	625	53	(	(	PUNCT
ejpam-6640	625	54	0	0	NUM
ejpam-6640	625	55	)	)	PUNCT
ejpam-6640	625	56	//	//	NOUN
ejpam-6640	626	1	(	(	PUNCT
ejpam-6640	626	2	y	y	PROPN
ejpam-6640	626	3	,	,	PUNCT
ejpam-6640	626	4	α	α	NOUN
ejpam-6640	626	5	)	)	PUNCT
ejpam-6640	626	6	f	f	PROPN
ejpam-6640	626	7	//	//	X
ejpam-6640	627	1	(	(	PUNCT
ejpam-6640	627	2	z	z	NOUN
ejpam-6640	627	3	,	,	PUNCT
ejpam-6640	627	4	β	β	NOUN
ejpam-6640	627	5	)	)	PUNCT
ejpam-6640	627	6	g	g	PROPN
ejpam-6640	627	7	//	//	SYM
ejpam-6640	627	8	(	(	PUNCT
ejpam-6640	627	9	t	t	PROPN
ejpam-6640	627	10	,	,	PUNCT
ejpam-6640	627	11	γ	γ	PROPN
ejpam-6640	627	12	)	)	PUNCT
ejpam-6640	627	13	//	//	NOUN
ejpam-6640	627	14	(	(	PUNCT
ejpam-6640	627	15	0	0	NUM
ejpam-6640	627	16	)	)	PUNCT
ejpam-6640	627	17	the	the	DET
ejpam-6640	627	18	connecting	connect	VERB
ejpam-6640	627	19	morphism	morphism	NOUN
ejpam-6640	627	20	is	be	AUX
ejpam-6640	627	21	defined	define	VERB
ejpam-6640	627	22	by	by	ADP
ejpam-6640	627	23	λn	λn	PROPN
ejpam-6640	627	24	:	:	PUNCT
ejpam-6640	627	25	hn((y	hn((y	ADJ
ejpam-6640	627	26	,	,	PUNCT
ejpam-6640	627	27	α	α	NOUN
ejpam-6640	627	28	)	)	PUNCT
ejpam-6640	627	29	)	)	PUNCT
ejpam-6640	628	1	−→	−→	PROPN
ejpam-6640	628	2	hn+1((t	hn+1((t	PROPN
ejpam-6640	628	3	,	,	PUNCT
ejpam-6640	628	4	γ	γ	NOUN
ejpam-6640	628	5	)	)	PUNCT
ejpam-6640	628	6	)	)	PUNCT
ejpam-6640	628	7	kn+1	kn+1	PROPN
ejpam-6640	628	8	7−→	7−→	PROPN
ejpam-6640	628	9	g−1	g−1	PROPN
ejpam-6640	628	10	n+2(βn+1(f	n+2(βn+1(f	ADP
ejpam-6640	628	11	−1	−1	NOUN
ejpam-6640	628	12	n+1(kn+1	n+1(kn+1	PROPN
ejpam-6640	628	13	)	)	PUNCT
ejpam-6640	628	14	)	)	PUNCT
ejpam-6640	628	15	)	)	PUNCT
ejpam-6640	629	1	∀n	∀n	NUM
ejpam-6640	630	1	∈	∈	PROPN
ejpam-6640	630	2	z	z	NOUN
ejpam-6640	630	3	since	since	SCONJ
ejpam-6640	630	4	comp(ab	comp(ab	NOUN
ejpam-6640	630	5	)	)	PUNCT
ejpam-6640	630	6	=	=	SYM
ejpam-6640	630	7	comp(z−mod	comp(z−mod	X
ejpam-6640	630	8	)	)	PUNCT
ejpam-6640	630	9	is	be	AUX
ejpam-6640	630	10	a	a	DET
ejpam-6640	630	11	special	special	ADJ
ejpam-6640	630	12	case	case	NOUN
ejpam-6640	630	13	of	of	ADP
ejpam-6640	630	14	comp(a	comp(a	NOUN
ejpam-6640	630	15	-	-	PUNCT
ejpam-6640	630	16	mod	mod	NOUN
ejpam-6640	630	17	)	)	PUNCT
ejpam-6640	630	18	,	,	PUNCT
ejpam-6640	630	19	by	by	ADP
ejpam-6640	630	20	theorem	theorem	NOUN
ejpam-6640	630	21	3	3	NUM
ejpam-6640	630	22	if	if	SCONJ
ejpam-6640	630	23	x	x	PRON
ejpam-6640	630	24	is	be	AUX
ejpam-6640	630	25	an	an	DET
ejpam-6640	630	26	injective	injective	ADJ
ejpam-6640	630	27	object	object	NOUN
ejpam-6640	630	28	in	in	ADP
ejpam-6640	630	29	a	a	DET
ejpam-6640	630	30	where	where	SCONJ
ejpam-6640	630	31	a	a	PRON
ejpam-6640	630	32	is	be	AUX
ejpam-6640	630	33	a	a	DET
ejpam-6640	630	34	balanced	balanced	ADJ
ejpam-6640	630	35	abelian	abelian	ADJ
ejpam-6640	630	36	category	category	NOUN
ejpam-6640	630	37	,	,	PUNCT
ejpam-6640	630	38	then	then	ADV
ejpam-6640	630	39	by	by	ADP
ejpam-6640	630	40	definition	definition	NOUN
ejpam-6640	630	41	of	of	ADP
ejpam-6640	630	42	h̃n(−	h̃n(−	PROPN
ejpam-6640	630	43	,	,	PUNCT
ejpam-6640	630	44	x	x	X
ejpam-6640	630	45	):	):	PUNCT
ejpam-6640	630	46	δn	δn	NOUN
ejpam-6640	630	47	:	:	PUNCT
ejpam-6640	630	48	h̃n(−	h̃n(−	PROPN
ejpam-6640	630	49	,	,	PUNCT
ejpam-6640	630	50	x)((y	x)((y	PROPN
ejpam-6640	630	51	,	,	PUNCT
ejpam-6640	630	52	α	α	NOUN
ejpam-6640	630	53	)	)	PUNCT
ejpam-6640	630	54	)	)	PUNCT
ejpam-6640	630	55	−→	−→	NOUN
ejpam-6640	630	56	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	630	57	,	,	PUNCT
ejpam-6640	630	58	x)((t	x)((t	PROPN
ejpam-6640	630	59	,	,	PUNCT
ejpam-6640	630	60	γ	γ	NOUN
ejpam-6640	630	61	)	)	PUNCT
ejpam-6640	630	62	)	)	PUNCT
ejpam-6640	631	1	kn+1	kn+1	PROPN
ejpam-6640	631	2	7−→	7−→	PROPN
ejpam-6640	631	3	g∗−1	g∗−1	PROPN
ejpam-6640	631	4	n+2(β	n+2(β	PROPN
ejpam-6640	631	5	∗	∗	NOUN
ejpam-6640	631	6	n+1(f	n+1(f	ADJ
ejpam-6640	631	7	∗−1	∗−1	NOUN
ejpam-6640	631	8	n+1(kn+1	n+1(kn+1	PROPN
ejpam-6640	631	9	)	)	PUNCT
ejpam-6640	631	10	)	)	PUNCT
ejpam-6640	631	11	)	)	PUNCT
ejpam-6640	632	1	∀n	∀n	PUNCT
ejpam-6640	633	1	∈	∈	PROPN
ejpam-6640	633	2	z	z	NOUN
ejpam-6640	633	3	is	be	AUX
ejpam-6640	633	4	well	well	ADV
ejpam-6640	633	5	-	-	PUNCT
ejpam-6640	633	6	defined	define	VERB
ejpam-6640	633	7	with	with	ADP
ejpam-6640	633	8	hn	hn	PRON
ejpam-6640	633	9	:	:	PUNCT
ejpam-6640	633	10	comp(ab	comp(ab	PROPN
ejpam-6640	633	11	)	)	PUNCT
ejpam-6640	633	12	−→	−→	PROPN
ejpam-6640	633	13	ab	ab	PROPN
ejpam-6640	633	14	.	.	PUNCT
ejpam-6640	634	1	(	(	PUNCT
ejpam-6640	634	2	ii	ii	PROPN
ejpam-6640	634	3	)	)	PUNCT
ejpam-6640	634	4	according	accord	VERB
ejpam-6640	634	5	to	to	ADP
ejpam-6640	634	6	theorem	theorem	ADJ
ejpam-6640	634	7	3	3	NUM
ejpam-6640	634	8	,	,	PUNCT
ejpam-6640	634	9	if	if	SCONJ
ejpam-6640	634	10	x	x	PRON
ejpam-6640	634	11	is	be	AUX
ejpam-6640	634	12	an	an	DET
ejpam-6640	634	13	injective	injective	ADJ
ejpam-6640	634	14	object	object	NOUN
ejpam-6640	634	15	in	in	ADP
ejpam-6640	634	16	a	a	PRON
ejpam-6640	634	17	,	,	PUNCT
ejpam-6640	634	18	where	where	SCONJ
ejpam-6640	634	19	a	a	PRON
ejpam-6640	634	20	is	be	AUX
ejpam-6640	634	21	a	a	DET
ejpam-6640	634	22	balanced	balanced	ADJ
ejpam-6640	634	23	abelian	abelian	ADJ
ejpam-6640	634	24	category	category	NOUN
ejpam-6640	634	25	,	,	PUNCT
ejpam-6640	634	26	then	then	ADV
ejpam-6640	634	27	homcomp(a	homcomp(a	NOUN
ejpam-6640	634	28	)	)	PUNCT
ejpam-6640	634	29	(	(	PUNCT
ejpam-6640	634	30	−	−	PROPN
ejpam-6640	634	31	,	,	PUNCT
ejpam-6640	634	32	x	x	X
ejpam-6640	634	33	)	)	PUNCT
ejpam-6640	634	34	transforms	transform	VERB
ejpam-6640	634	35	any	any	DET
ejpam-6640	634	36	complex	complex	ADJ
ejpam-6640	634	37	sequence	sequence	NOUN
ejpam-6640	634	38	in	in	ADP
ejpam-6640	634	39	comp(a	comp(a	NOUN
ejpam-6640	634	40	)	)	PUNCT
ejpam-6640	634	41	into	into	ADP
ejpam-6640	634	42	a	a	DET
ejpam-6640	634	43	complex	complex	ADJ
ejpam-6640	634	44	sequence	sequence	NOUN
ejpam-6640	634	45	in	in	ADP
ejpam-6640	634	46	comp(ab	comp(ab	PROPN
ejpam-6640	634	47	)	)	PUNCT
ejpam-6640	634	48	.	.	PUNCT
ejpam-6640	635	1	however	however	ADV
ejpam-6640	635	2	,	,	PUNCT
ejpam-6640	635	3	hn	hn	PROPN
ejpam-6640	635	4	transforms	transform	VERB
ejpam-6640	635	5	every	every	DET
ejpam-6640	635	6	short	short	ADJ
ejpam-6640	635	7	exact	exact	ADJ
ejpam-6640	635	8	sequence	sequence	NOUN
ejpam-6640	635	9	in	in	ADP
ejpam-6640	635	10	comp(a	comp(a	NOUN
ejpam-6640	635	11	-	-	PUNCT
ejpam-6640	635	12	mod	mod	NOUN
ejpam-6640	635	13	)	)	PUNCT
ejpam-6640	635	14	into	into	ADP
ejpam-6640	635	15	a	a	DET
ejpam-6640	635	16	long	long	ADJ
ejpam-6640	635	17	exact	exact	ADJ
ejpam-6640	635	18	sequence	sequence	NOUN
ejpam-6640	635	19	of	of	ADP
ejpam-6640	635	20	morphisms	morphism	NOUN
ejpam-6640	635	21	in	in	ADP
ejpam-6640	635	22	ab	ab	PROPN
ejpam-6640	635	23	.	.	PUNCT
ejpam-6640	636	1	in	in	ADP
ejpam-6640	636	2	particular	particular	ADJ
ejpam-6640	636	3	,	,	PUNCT
ejpam-6640	636	4	hn	hn	PROPN
ejpam-6640	636	5	transforms	transform	VERB
ejpam-6640	636	6	any	any	DET
ejpam-6640	636	7	complex	complex	ADJ
ejpam-6640	636	8	sequence	sequence	NOUN
ejpam-6640	636	9	of	of	ADP
ejpam-6640	636	10	morphisms	morphism	NOUN
ejpam-6640	636	11	in	in	ADP
ejpam-6640	636	12	comp(ab	comp(ab	NOUN
ejpam-6640	636	13	)	)	PUNCT
ejpam-6640	636	14	=	=	SYM
ejpam-6640	636	15	comp(z	comp(z	NOUN
ejpam-6640	636	16	−	−	PROPN
ejpam-6640	636	17	mod	mod	PROPN
ejpam-6640	636	18	)	)	PUNCT
ejpam-6640	636	19	into	into	ADP
ejpam-6640	636	20	a	a	DET
ejpam-6640	636	21	long	long	ADJ
ejpam-6640	636	22	exact	exact	ADJ
ejpam-6640	636	23	sequence	sequence	NOUN
ejpam-6640	636	24	of	of	ADP
ejpam-6640	636	25	morphisms	morphism	NOUN
ejpam-6640	636	26	in	in	ADP
ejpam-6640	636	27	ab	ab	PROPN
ejpam-6640	636	28	.	.	PUNCT
ejpam-6640	637	1	now	now	ADV
ejpam-6640	637	2	,	,	PUNCT
ejpam-6640	637	3	h̃n(−	h̃n(−	PROPN
ejpam-6640	637	4	,	,	PUNCT
ejpam-6640	637	5	x	x	X
ejpam-6640	637	6	)	)	PUNCT
ejpam-6640	638	1	=	=	SYM
ejpam-6640	638	2	hn	hn	PROPN
ejpam-6640	638	3	◦	◦	NOUN
ejpam-6640	638	4	homcomp(a	homcomp(a	NOUN
ejpam-6640	638	5	)	)	PUNCT
ejpam-6640	638	6	(	(	PUNCT
ejpam-6640	638	7	−	−	PROPN
ejpam-6640	638	8	,	,	PUNCT
ejpam-6640	638	9	x	x	NOUN
ejpam-6640	638	10	)	)	PUNCT
ejpam-6640	638	11	,	,	PUNCT
ejpam-6640	638	12	where	where	SCONJ
ejpam-6640	638	13	hn	hn	PROPN
ejpam-6640	638	14	:	:	PUNCT
ejpam-6640	638	15	comp(ab	comp(ab	PROPN
ejpam-6640	638	16	)	)	PUNCT
ejpam-6640	638	17	−→	−→	PROPN
ejpam-6640	638	18	ab	ab	PROPN
ejpam-6640	638	19	,	,	PUNCT
ejpam-6640	638	20	and	and	CCONJ
ejpam-6640	638	21	h̃n(−	h̃n(−	PROPN
ejpam-6640	638	22	,	,	PUNCT
ejpam-6640	638	23	x	x	NOUN
ejpam-6640	638	24	)	)	PUNCT
ejpam-6640	638	25	:	:	PUNCT
ejpam-6640	638	26	comp(a	comp(a	INTJ
ejpam-6640	638	27	)	)	PUNCT
ejpam-6640	638	28	−→	−→	PROPN
ejpam-6640	638	29	ab	ab	PROPN
ejpam-6640	638	30	.	.	PUNCT
ejpam-6640	639	1	thus	thus	ADV
ejpam-6640	639	2	,	,	PUNCT
ejpam-6640	639	3	the	the	DET
ejpam-6640	639	4	sequence	sequence	NOUN
ejpam-6640	639	5	·	·	PUNCT
ejpam-6640	639	6	·	·	PUNCT
ejpam-6640	639	7	·	·	PUNCT
ejpam-6640	640	1	//	//	PUNCT
ejpam-6640	640	2	h̃n(−	h̃n(−	PROPN
ejpam-6640	640	3	,	,	PUNCT
ejpam-6640	640	4	x)((t	x)((t	PROPN
ejpam-6640	640	5	,	,	PUNCT
ejpam-6640	640	6	γ	γ	NOUN
ejpam-6640	640	7	)	)	PUNCT
ejpam-6640	640	8	)	)	PUNCT
ejpam-6640	640	9	h̃n(−,x)(g	h̃n(−,x)(g	PROPN
ejpam-6640	640	10	)	)	PUNCT
ejpam-6640	640	11	//	//	X
ejpam-6640	641	1	h̃n(−	h̃n(−	PROPN
ejpam-6640	641	2	,	,	PUNCT
ejpam-6640	641	3	x)((z	x)((z	PROPN
ejpam-6640	641	4	,	,	PUNCT
ejpam-6640	641	5	β	β	NOUN
ejpam-6640	641	6	)	)	PUNCT
ejpam-6640	641	7	)	)	PUNCT
ejpam-6640	641	8	h̃n(−,x)(f	h̃n(−,x)(f	PROPN
ejpam-6640	641	9	)	)	PUNCT
ejpam-6640	641	10	//	//	PUNCT
ejpam-6640	642	1	h̃n(−	h̃n(−	PROPN
ejpam-6640	642	2	,	,	PUNCT
ejpam-6640	642	3	x)((y	x)((y	PROPN
ejpam-6640	642	4	,	,	PUNCT
ejpam-6640	642	5	α	α	NOUN
ejpam-6640	642	6	)	)	PUNCT
ejpam-6640	642	7	)	)	PUNCT
ejpam-6640	642	8	λn//	λn//	PROPN
ejpam-6640	642	9	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	642	10	,	,	PUNCT
ejpam-6640	642	11	x)((t	x)((t	PROPN
ejpam-6640	642	12	,	,	PUNCT
ejpam-6640	642	13	γ	γ	NOUN
ejpam-6640	642	14	)	)	PUNCT
ejpam-6640	642	15	)	)	PUNCT
ejpam-6640	642	16	h̃n+1(−,x)(g	h̃n+1(−,x)(g	NOUN
ejpam-6640	642	17	)	)	PUNCT
ejpam-6640	642	18	//	//	SYM
ejpam-6640	642	19	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	642	20	,	,	PUNCT
ejpam-6640	642	21	x)((z	x)((z	PROPN
ejpam-6640	642	22	,	,	PUNCT
ejpam-6640	642	23	β	β	NOUN
ejpam-6640	642	24	)	)	PUNCT
ejpam-6640	642	25	)	)	PUNCT
ejpam-6640	643	1	h̃n+1(−,x)(f	h̃n+1(−,x)(f	PROPN
ejpam-6640	643	2	)	)	PUNCT
ejpam-6640	643	3	//	//	SYM
ejpam-6640	643	4	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	643	5	,	,	PUNCT
ejpam-6640	643	6	x)((y	x)((y	PROPN
ejpam-6640	643	7	,	,	PUNCT
ejpam-6640	643	8	α	α	NOUN
ejpam-6640	643	9	)	)	PUNCT
ejpam-6640	643	10	)	)	PUNCT
ejpam-6640	643	11	//	//	X
ejpam-6640	643	12	·	·	PUNCT
ejpam-6640	643	13	·	·	PUNCT
ejpam-6640	643	14	·	·	PUNCT
ejpam-6640	643	15	is	be	AUX
ejpam-6640	643	16	a	a	DET
ejpam-6640	643	17	long	long	ADJ
ejpam-6640	643	18	exact	exact	ADJ
ejpam-6640	643	19	sequence	sequence	NOUN
ejpam-6640	643	20	of	of	ADP
ejpam-6640	643	21	abelian	abelian	ADJ
ejpam-6640	643	22	group	group	NOUN
ejpam-6640	643	23	morphisms	morphism	VERB
ejpam-6640	643	24	.	.	PUNCT
ejpam-6640	644	1	5	5	X
ejpam-6640	644	2	.	.	X
ejpam-6640	644	3	conclusion	conclusion	NOUN
ejpam-6640	644	4	in	in	ADP
ejpam-6640	644	5	this	this	DET
ejpam-6640	644	6	article	article	NOUN
ejpam-6640	644	7	,	,	PUNCT
ejpam-6640	644	8	by	by	ADP
ejpam-6640	644	9	using	use	VERB
ejpam-6640	644	10	the	the	DET
ejpam-6640	644	11	exacteness	exacteness	NOUN
ejpam-6640	644	12	of	of	ADP
ejpam-6640	644	13	we	we	PRON
ejpam-6640	644	14	have	have	AUX
ejpam-6640	644	15	shown	show	VERB
ejpam-6640	644	16	the	the	DET
ejpam-6640	644	17	exactness	exactness	NOUN
ejpam-6640	644	18	of	of	ADP
ejpam-6640	644	19	the	the	DET
ejpam-6640	644	20	functors	functors	PROPN
ejpam-6640	644	21	homa	homa	PROPN
ejpam-6640	644	22	(	(	PUNCT
ejpam-6640	644	23	x,−	x,−	PROPN
ejpam-6640	644	24	)	)	PUNCT
ejpam-6640	644	25	,	,	PUNCT
ejpam-6640	644	26	homa	homa	NOUN
ejpam-6640	644	27	(	(	PUNCT
ejpam-6640	644	28	−	−	PROPN
ejpam-6640	644	29	,	,	PUNCT
ejpam-6640	644	30	x	x	NOUN
ejpam-6640	644	31	)	)	PUNCT
ejpam-6640	644	32	:	:	PUNCT
ejpam-6640	644	33	comp(a	comp(a	NOUN
ejpam-6640	644	34	)	)	PUNCT
ejpam-6640	644	35	→	→	SYM
ejpam-6640	644	36	comp(ab	comp(ab	PROPN
ejpam-6640	644	37	)	)	PUNCT
ejpam-6640	644	38	and	and	CCONJ
ejpam-6640	644	39	the	the	DET
ejpam-6640	644	40	exactness	exactness	NOUN
ejpam-6640	644	41	of	of	ADP
ejpam-6640	644	42	the	the	DET
ejpam-6640	644	43	functors	functors	PROPN
ejpam-6640	644	44	homcomp(a	homcomp(a	PROPN
ejpam-6640	644	45	)	)	PUNCT
ejpam-6640	644	46	(	(	PUNCT
ejpam-6640	644	47	x,−	x,−	PROPN
ejpam-6640	644	48	)	)	PUNCT
ejpam-6640	644	49	,	,	PUNCT
ejpam-6640	644	50	homcomp(a	homcomp(a	NOUN
ejpam-6640	644	51	)	)	PUNCT
ejpam-6640	644	52	(	(	PUNCT
ejpam-6640	644	53	−	−	PROPN
ejpam-6640	644	54	,	,	PUNCT
ejpam-6640	644	55	x	x	NOUN
ejpam-6640	644	56	)	)	PUNCT
ejpam-6640	644	57	:	:	PUNCT
ejpam-6640	644	58	comp(a	comp(a	NOUN
ejpam-6640	644	59	)	)	PUNCT
ejpam-6640	644	60	→	→	SYM
ejpam-6640	644	61	comp(ab	comp(ab	PROPN
ejpam-6640	644	62	)	)	PUNCT
ejpam-6640	644	63	where	where	SCONJ
ejpam-6640	644	64	a	a	PRON
ejpam-6640	644	65	is	be	AUX
ejpam-6640	644	66	a	a	DET
ejpam-6640	644	67	balanced	balanced	ADJ
ejpam-6640	644	68	abelian	abelian	ADJ
ejpam-6640	644	69	category	category	NOUN
ejpam-6640	644	70	.	.	PUNCT
ejpam-6640	645	1	we	we	PRON
ejpam-6640	645	2	then	then	ADV
ejpam-6640	645	3	constructed	construct	VERB
ejpam-6640	645	4	the	the	DET
ejpam-6640	645	5	additive	additive	ADJ
ejpam-6640	645	6	covariant	covariant	ADJ
ejpam-6640	645	7	homological	homological	PROPN
ejpam-6640	645	8	functor	functor	NOUN
ejpam-6640	645	9	:	:	PUNCT
ejpam-6640	645	10	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	645	11	)	)	PUNCT
ejpam-6640	646	1	=	=	PUNCT
ejpam-6640	646	2	hn	hn	PROPN
ejpam-6640	646	3	◦	◦	NOUN
ejpam-6640	646	4	homcomp(a	homcomp(a	NOUN
ejpam-6640	646	5	)	)	PUNCT
ejpam-6640	646	6	(	(	PUNCT
ejpam-6640	646	7	x,−	x,−	PROPN
ejpam-6640	646	8	)	)	PUNCT
ejpam-6640	646	9	and	and	CCONJ
ejpam-6640	646	10	the	the	DET
ejpam-6640	646	11	additive	additive	ADJ
ejpam-6640	646	12	contravariant	contravariant	PROPN
ejpam-6640	646	13	homological	homological	PROPN
ejpam-6640	646	14	functor	functor	NOUN
ejpam-6640	646	15	:	:	PUNCT
ejpam-6640	646	16	h̃n(−	h̃n(−	PROPN
ejpam-6640	646	17	,	,	PUNCT
ejpam-6640	646	18	x	x	X
ejpam-6640	646	19	)	)	PUNCT
ejpam-6640	647	1	=	=	SYM
ejpam-6640	647	2	hn	hn	PROPN
ejpam-6640	647	3	◦	◦	NOUN
ejpam-6640	647	4	homcomp(a	homcomp(a	NOUN
ejpam-6640	647	5	)	)	PUNCT
ejpam-6640	647	6	(	(	PUNCT
ejpam-6640	647	7	−	−	PROPN
ejpam-6640	647	8	,	,	PUNCT
ejpam-6640	647	9	x	x	X
ejpam-6640	647	10	)	)	PUNCT
ejpam-6640	647	11	wherehn	wherehn	NOUN
ejpam-6640	647	12	:	:	PUNCT
ejpam-6640	647	13	comp(ab	comp(ab	X
ejpam-6640	647	14	)	)	PUNCT
ejpam-6640	647	15	−→	−→	NOUN
ejpam-6640	647	16	ab	ab	PROPN
ejpam-6640	647	17	and	and	CCONJ
ejpam-6640	647	18	homcomp(a	homcomp(a	NOUN
ejpam-6640	647	19	)	)	PUNCT
ejpam-6640	647	20	(	(	PUNCT
ejpam-6640	647	21	x,−	x,−	PROPN
ejpam-6640	647	22	)	)	PUNCT
ejpam-6640	647	23	,	,	PUNCT
ejpam-6640	647	24	homcomp(a	homcomp(a	NOUN
ejpam-6640	647	25	)	)	PUNCT
ejpam-6640	647	26	(	(	PUNCT
ejpam-6640	647	27	−	−	PROPN
ejpam-6640	647	28	,	,	PUNCT
ejpam-6640	647	29	x	x	NOUN
ejpam-6640	647	30	)	)	PUNCT
ejpam-6640	647	31	:	:	PUNCT
ejpam-6640	647	32	comp(a	comp(a	INTJ
ejpam-6640	647	33	)	)	PUNCT
ejpam-6640	647	34	−→	−→	NOUN
ejpam-6640	647	35	a.	a.	PROPN
ejpam-6640	647	36	diallo	diallo	PROPN
ejpam-6640	647	37	,	,	PUNCT
ejpam-6640	647	38	m.	m.	PROPN
ejpam-6640	647	39	b.	b.	PROPN
ejpam-6640	647	40	f.	f.	PROPN
ejpam-6640	647	41	b.	b.	PROPN
ejpam-6640	647	42	maaouia	maaouia	PROPN
ejpam-6640	647	43	,	,	PUNCT
ejpam-6640	647	44	m.	m.	NOUN
ejpam-6640	647	45	sanghare	sanghare	PROPN
ejpam-6640	647	46	/	/	SYM
ejpam-6640	647	47	eur	eur	PROPN
ejpam-6640	647	48	.	.	PUNCT
ejpam-6640	648	1	j.	j.	PROPN
ejpam-6640	648	2	pure	pure	PROPN
ejpam-6640	648	3	appl	appl	PROPN
ejpam-6640	648	4	.	.	PROPN
ejpam-6640	648	5	math	math	PROPN
ejpam-6640	648	6	,	,	PUNCT
ejpam-6640	648	7	18	18	NUM
ejpam-6640	648	8	(	(	PUNCT
ejpam-6640	648	9	4	4	NUM
ejpam-6640	648	10	)	)	PUNCT
ejpam-6640	648	11	(	(	PUNCT
ejpam-6640	648	12	2025	2025	NUM
ejpam-6640	648	13	)	)	PUNCT
ejpam-6640	648	14	,	,	PUNCT
ejpam-6640	648	15	6640	6640	NUM
ejpam-6640	648	16	27	27	NUM
ejpam-6640	648	17	of	of	ADP
ejpam-6640	648	18	28	28	NUM
ejpam-6640	648	19	comp(ab	comp(ab	NOUN
ejpam-6640	648	20	)	)	PUNCT
ejpam-6640	648	21	∀n	∀n	NUM
ejpam-6640	648	22	∈	∈	PROPN
ejpam-6640	648	23	z.moreover	z.moreover	PROPN
ejpam-6640	648	24	,	,	PUNCT
ejpam-6640	648	25	we	we	PRON
ejpam-6640	648	26	constructed	construct	VERB
ejpam-6640	648	27	the	the	DET
ejpam-6640	648	28	connecting	connect	VERB
ejpam-6640	648	29	morphism	morphism	NOUN
ejpam-6640	648	30	λn	λn	PROPN
ejpam-6640	648	31	:	:	PUNCT
ejpam-6640	648	32	h̃n(x,−)((t	h̃n(x,−)((t	PROPN
ejpam-6640	648	33	,	,	PUNCT
ejpam-6640	648	34	γ	γ	NOUN
ejpam-6640	648	35	)	)	PUNCT
ejpam-6640	648	36	)	)	PUNCT
ejpam-6640	649	1	→	→	PUNCT
ejpam-6640	649	2	h̃n+1(x,−)((y	h̃n+1(x,−)((y	PROPN
ejpam-6640	649	3	,	,	PUNCT
ejpam-6640	649	4	α	α	NOUN
ejpam-6640	649	5	)	)	PUNCT
ejpam-6640	649	6	)	)	PUNCT
ejpam-6640	649	7	associated	associate	VERB
ejpam-6640	649	8	to	to	ADP
ejpam-6640	649	9	the	the	DET
ejpam-6640	649	10	covariant	covariant	ADJ
ejpam-6640	649	11	functor	functor	PROPN
ejpam-6640	649	12	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	649	13	)	)	PUNCT
ejpam-6640	649	14	,	,	PUNCT
ejpam-6640	649	15	by	by	ADP
ejpam-6640	649	16	showing	show	VERB
ejpam-6640	649	17	how	how	SCONJ
ejpam-6640	649	18	the	the	DET
ejpam-6640	649	19	functor	functor	PROPN
ejpam-6640	649	20	h̃n(x,−	h̃n(x,−	PROPN
ejpam-6640	649	21	)	)	PUNCT
ejpam-6640	649	22	transforms	transform	VERB
ejpam-6640	649	23	a	a	DET
ejpam-6640	649	24	short	short	ADJ
ejpam-6640	649	25	exact	exact	ADJ
ejpam-6640	649	26	sequence	sequence	NOUN
ejpam-6640	649	27	of	of	ADP
ejpam-6640	649	28	morphisms	morphism	NOUN
ejpam-6640	649	29	in	in	ADP
ejpam-6640	649	30	comp(a	comp(a	NOUN
ejpam-6640	649	31	)	)	PUNCT
ejpam-6640	649	32	into	into	ADP
ejpam-6640	649	33	a	a	DET
ejpam-6640	649	34	long	long	ADJ
ejpam-6640	649	35	exact	exact	ADJ
ejpam-6640	649	36	sequence	sequence	NOUN
ejpam-6640	649	37	of	of	ADP
ejpam-6640	649	38	morphisms	morphism	NOUN
ejpam-6640	649	39	in	in	ADP
ejpam-6640	649	40	ab	ab	PROPN
ejpam-6640	649	41	,	,	PUNCT
ejpam-6640	649	42	where	where	SCONJ
ejpam-6640	649	43	x	x	PRON
ejpam-6640	649	44	is	be	AUX
ejpam-6640	649	45	an	an	DET
ejpam-6640	649	46	projective	projective	ADJ
ejpam-6640	649	47	object	object	NOUN
ejpam-6640	649	48	of	of	ADP
ejpam-6640	649	49	a	a	PRON
ejpam-6640	649	50	and	and	CCONJ
ejpam-6640	649	51	a	a	PRON
ejpam-6640	649	52	is	be	AUX
ejpam-6640	649	53	a	a	DET
ejpam-6640	649	54	balanced	balanced	ADJ
ejpam-6640	649	55	abelian	abelian	ADJ
ejpam-6640	649	56	category	category	NOUN
ejpam-6640	649	57	.	.	PUNCT
ejpam-6640	650	1	then	then	ADV
ejpam-6640	650	2	we	we	PRON
ejpam-6640	650	3	again	again	ADV
ejpam-6640	650	4	constructed	construct	VERB
ejpam-6640	650	5	the	the	DET
ejpam-6640	650	6	connecting	connect	VERB
ejpam-6640	650	7	morphism	morphism	NOUN
ejpam-6640	650	8	δn	δn	NOUN
ejpam-6640	650	9	:	:	PUNCT
ejpam-6640	650	10	h̃n(−	h̃n(−	PROPN
ejpam-6640	650	11	,	,	PUNCT
ejpam-6640	650	12	x)((y	x)((y	PROPN
ejpam-6640	650	13	,	,	PUNCT
ejpam-6640	650	14	α	α	NOUN
ejpam-6640	650	15	)	)	PUNCT
ejpam-6640	650	16	)	)	PUNCT
ejpam-6640	650	17	→	→	SYM
ejpam-6640	650	18	h̃n+1(−	h̃n+1(−	PROPN
ejpam-6640	650	19	,	,	PUNCT
ejpam-6640	650	20	x)((t	x)((t	PROPN
ejpam-6640	650	21	,	,	PUNCT
ejpam-6640	650	22	γ	γ	NOUN
ejpam-6640	650	23	)	)	PUNCT
ejpam-6640	650	24	)	)	PUNCT
ejpam-6640	650	25	associated	associate	VERB
ejpam-6640	650	26	to	to	ADP
ejpam-6640	650	27	the	the	DET
ejpam-6640	650	28	contravariant	contravariant	PROPN
ejpam-6640	650	29	functor	functor	PROPN
ejpam-6640	650	30	h̃n(−	h̃n(−	PROPN
ejpam-6640	650	31	,	,	PUNCT
ejpam-6640	650	32	x	x	NOUN
ejpam-6640	650	33	)	)	PUNCT
ejpam-6640	650	34	also	also	ADV
ejpam-6640	650	35	showing	show	VERB
ejpam-6640	650	36	how	how	SCONJ
ejpam-6640	650	37	the	the	DET
ejpam-6640	650	38	functor	functor	PROPN
ejpam-6640	650	39	h̃n(−	h̃n(−	PROPN
ejpam-6640	650	40	,	,	PUNCT
ejpam-6640	650	41	x	x	X
ejpam-6640	650	42	)	)	PUNCT
ejpam-6640	650	43	transforms	transform	VERB
ejpam-6640	650	44	a	a	DET
ejpam-6640	650	45	short	short	ADJ
ejpam-6640	650	46	exact	exact	ADJ
ejpam-6640	650	47	sequence	sequence	NOUN
ejpam-6640	650	48	of	of	ADP
ejpam-6640	650	49	morphisms	morphism	NOUN
ejpam-6640	650	50	in	in	ADP
ejpam-6640	650	51	comp(a	comp(a	NOUN
ejpam-6640	650	52	)	)	PUNCT
ejpam-6640	650	53	into	into	ADP
ejpam-6640	650	54	a	a	DET
ejpam-6640	650	55	long	long	ADJ
ejpam-6640	650	56	exact	exact	ADJ
ejpam-6640	650	57	sequence	sequence	NOUN
ejpam-6640	650	58	of	of	ADP
ejpam-6640	650	59	morphisms	morphism	NOUN
ejpam-6640	650	60	in	in	ADP
ejpam-6640	650	61	ab	ab	PROPN
ejpam-6640	650	62	,	,	PUNCT
ejpam-6640	650	63	where	where	SCONJ
ejpam-6640	650	64	x	x	PRON
ejpam-6640	650	65	is	be	AUX
ejpam-6640	650	66	an	an	DET
ejpam-6640	650	67	injective	injective	ADJ
ejpam-6640	650	68	object	object	NOUN
ejpam-6640	650	69	of	of	ADP
ejpam-6640	650	70	a	a	PRON
ejpam-6640	650	71	and	and	CCONJ
ejpam-6640	650	72	a	a	PRON
ejpam-6640	650	73	is	be	AUX
ejpam-6640	650	74	a	a	DET
ejpam-6640	650	75	balanced	balanced	ADJ
ejpam-6640	650	76	abelian	abelian	ADJ
ejpam-6640	650	77	category	category	NOUN
ejpam-6640	650	78	.	.	PUNCT
ejpam-6640	651	1	references	reference	NOUN
ejpam-6640	651	2	[	[	X
ejpam-6640	651	3	1	1	NUM
ejpam-6640	651	4	]	]	PUNCT
ejpam-6640	651	5	bassirou	bassirou	NOUN
ejpam-6640	651	6	dembele	dembele	PROPN
ejpam-6640	651	7	,	,	PUNCT
ejpam-6640	651	8	mohamed	mohamed	PROPN
ejpam-6640	651	9	ben	ben	PROPN
ejpam-6640	651	10	faraj	faraj	PROPN
ejpam-6640	651	11	ben	ben	PROPN
ejpam-6640	651	12	maaouia	maaouia	PROPN
ejpam-6640	651	13	,	,	PUNCT
ejpam-6640	651	14	and	and	CCONJ
ejpam-6640	651	15	mamadou	mamadou	PROPN
ejpam-6640	651	16	sanghare	sanghare	NOUN
ejpam-6640	651	17	.	.	PUNCT
ejpam-6640	652	1	the	the	DET
ejpam-6640	652	2	functor	functor	PROPN
ejpam-6640	652	3	and	and	CCONJ
ejpam-6640	652	4	its	its	PRON
ejpam-6640	652	5	relationship	relationship	NOUN
ejpam-6640	652	6	with	with	ADP
ejpam-6640	652	7	homological	homological	ADJ
ejpam-6640	652	8	functors	functor	NOUN
ejpam-6640	652	9	torn	tear	VERB
ejpam-6640	652	10	and	and	CCONJ
ejpam-6640	652	11	extn	extn	NOUN
ejpam-6640	652	12	.	.	PUNCT
ejpam-6640	653	1	in	in	ADP
ejpam-6640	653	2	the	the	DET
ejpam-6640	653	3	moroccan	moroccan	ADJ
ejpam-6640	653	4	andalusian	andalusian	PROPN
ejpam-6640	653	5	meeting	meeting	NOUN
ejpam-6640	653	6	on	on	ADP
ejpam-6640	653	7	algebras	algebra	NOUN
ejpam-6640	653	8	and	and	CCONJ
ejpam-6640	653	9	their	their	PRON
ejpam-6640	653	10	applications	application	NOUN
ejpam-6640	653	11	,	,	PUNCT
ejpam-6640	653	12	pages	page	NOUN
ejpam-6640	653	13	253–271	253–271	NUM
ejpam-6640	653	14	.	.	PUNCT
ejpam-6640	654	1	springer	springer	NOUN
ejpam-6640	654	2	,	,	PUNCT
ejpam-6640	654	3	2018	2018	NUM
ejpam-6640	654	4	.	.	PUNCT
ejpam-6640	655	1	[	[	X
ejpam-6640	655	2	2	2	NUM
ejpam-6640	655	3	]	]	PUNCT
ejpam-6640	655	4	bassirou	bassirou	NOUN
ejpam-6640	655	5	dembele	dembele	PROPN
ejpam-6640	655	6	,	,	PUNCT
ejpam-6640	655	7	mohamed	mohamed	PROPN
ejpam-6640	655	8	ben	ben	PROPN
ejpam-6640	655	9	faraj	faraj	PROPN
ejpam-6640	655	10	ben	ben	PROPN
ejpam-6640	655	11	maaouia	maaouia	PROPN
ejpam-6640	655	12	,	,	PUNCT
ejpam-6640	655	13	and	and	CCONJ
ejpam-6640	655	14	mamadou	mamadou	PROPN
ejpam-6640	655	15	sanghare	sanghare	NOUN
ejpam-6640	655	16	.	.	PUNCT
ejpam-6640	656	1	localization	localization	NOUN
ejpam-6640	656	2	,	,	PUNCT
ejpam-6640	656	3	isomorphisms	isomorphism	NOUN
ejpam-6640	656	4	and	and	CCONJ
ejpam-6640	656	5	adjoint	adjoint	VERB
ejpam-6640	656	6	isomorphism	isomorphism	NOUN
ejpam-6640	656	7	in	in	ADP
ejpam-6640	656	8	the	the	DET
ejpam-6640	656	9	category	category	NOUN
ejpam-6640	656	10	comp(amod	comp(amod	PROPN
ejpam-6640	656	11	)	)	PUNCT
ejpam-6640	656	12	.	.	PUNCT
ejpam-6640	657	1	journal	journal	PROPN
ejpam-6640	657	2	of	of	ADP
ejpam-6640	657	3	mathematics	mathematics	PROPN
ejpam-6640	657	4	research	research	NOUN
ejpam-6640	657	5	,	,	PUNCT
ejpam-6640	657	6	12(4):1–65	12(4):1–65	NUM
ejpam-6640	657	7	,	,	PUNCT
ejpam-6640	657	8	2020	2020	NUM
ejpam-6640	657	9	.	.	PUNCT
ejpam-6640	658	1	[	[	X
ejpam-6640	658	2	3	3	NUM
ejpam-6640	658	3	]	]	X
ejpam-6640	658	4	seydina	seydina	NOUN
ejpam-6640	658	5	ababacar	ababacar	PROPN
ejpam-6640	658	6	balde	balde	PROPN
ejpam-6640	658	7	,	,	PUNCT
ejpam-6640	658	8	mohamed	mohamed	PROPN
ejpam-6640	658	9	ben	ben	PROPN
ejpam-6640	658	10	faraj	faraj	PROPN
ejpam-6640	658	11	ben	ben	PROPN
ejpam-6640	658	12	maaouia	maaouia	PROPN
ejpam-6640	658	13	,	,	PUNCT
ejpam-6640	658	14	and	and	CCONJ
ejpam-6640	658	15	ahmed	ahmed	PROPN
ejpam-6640	658	16	ould	ould	AUX
ejpam-6640	658	17	chbih	chbih	VERB
ejpam-6640	658	18	.	.	PUNCT
ejpam-6640	659	1	localization	localization	NOUN
ejpam-6640	659	2	of	of	ADP
ejpam-6640	659	3	hopfian	hopfian	ADJ
ejpam-6640	659	4	and	and	CCONJ
ejpam-6640	659	5	cohopfian	cohopfian	ADJ
ejpam-6640	659	6	objects	object	NOUN
ejpam-6640	659	7	in	in	ADP
ejpam-6640	659	8	the	the	DET
ejpam-6640	659	9	categories	category	NOUN
ejpam-6640	659	10	of	of	ADP
ejpam-6640	659	11	a	a	DET
ejpam-6640	659	12	-	-	PUNCT
ejpam-6640	659	13	mod	mod	ADJ
ejpam-6640	659	14	,	,	PUNCT
ejpam-6640	659	15	agr(amod	agr(amod	NOUN
ejpam-6640	659	16	)	)	PUNCT
ejpam-6640	659	17	and	and	CCONJ
ejpam-6640	659	18	comp(agr(a	comp(agr(a	NOUN
ejpam-6640	659	19	-	-	NOUN
ejpam-6640	659	20	mod	mod	ADJ
ejpam-6640	659	21	)	)	PUNCT
ejpam-6640	659	22	)	)	PUNCT
ejpam-6640	659	23	.	.	PUNCT
ejpam-6640	660	1	european	european	PROPN
ejpam-6640	660	2	journal	journal	PROPN
ejpam-6640	660	3	of	of	ADP
ejpam-6640	660	4	pure	pure	ADJ
ejpam-6640	660	5	and	and	CCONJ
ejpam-6640	660	6	applied	applied	ADJ
ejpam-6640	660	7	mathematics	mathematic	NOUN
ejpam-6640	660	8	,	,	PUNCT
ejpam-6640	660	9	14(2):404–422	14(2):404–422	NUM
ejpam-6640	660	10	,	,	PUNCT
ejpam-6640	660	11	2021	2021	NUM
ejpam-6640	660	12	.	.	PUNCT
ejpam-6640	661	1	[	[	X
ejpam-6640	661	2	4	4	X
ejpam-6640	661	3	]	]	PUNCT
ejpam-6640	661	4	moussa	moussa	PROPN
ejpam-6640	661	5	thiaw	thiaw	PROPN
ejpam-6640	661	6	.	.	PUNCT
ejpam-6640	662	1	relation	relation	NOUN
ejpam-6640	662	2	entre	entre	PROPN
ejpam-6640	662	3	foncteur	foncteur	NOUN
ejpam-6640	662	4	localisation	localisation	NOUN
ejpam-6640	662	5	s−1	s−1	PROPN
ejpam-6640	662	6	(	(	PUNCT
ejpam-6640	662	7	)	)	PUNCT
ejpam-6640	662	8	et	et	PROPN
ejpam-6640	662	9	les	les	PROPN
ejpam-6640	662	10	foncteurs	foncteurs	PROPN
ejpam-6640	662	11	homologiques	homologique	NOUN
ejpam-6640	662	12	ext	ext	PROPN
ejpam-6640	662	13	et	et	PROPN
ejpam-6640	662	14	tor	tor	PROPN
ejpam-6640	662	15	dans	dan	NOUN
ejpam-6640	662	16	la	la	X
ejpam-6640	662	17	catégorie	catégorie	PROPN
ejpam-6640	662	18	a	a	PROPN
ejpam-6640	662	19	-	-	PUNCT
ejpam-6640	662	20	alg(resp.alg	alg(resp.alg	NOUN
ejpam-6640	662	21	-	-	PUNCT
ejpam-6640	662	22	a	a	NOUN
ejpam-6640	662	23	)	)	PUNCT
ejpam-6640	662	24	.	.	PUNCT
ejpam-6640	663	1	thèse	thèse	PROPN
ejpam-6640	663	2	,	,	PUNCT
ejpam-6640	663	3	université	université	ADJ
ejpam-6640	663	4	gaston	gaston	PROPN
ejpam-6640	663	5	berger	berger	PROPN
ejpam-6640	663	6	,	,	PUNCT
ejpam-6640	663	7	saint	saint	PROPN
ejpam-6640	663	8	-	-	PUNCT
ejpam-6640	663	9	louis	louis	NOUN
ejpam-6640	663	10	,	,	PUNCT
ejpam-6640	663	11	février	février	PROPN
ejpam-6640	663	12	2020	2020	NUM
ejpam-6640	663	13	.	.	PUNCT
ejpam-6640	664	1	[	[	X
ejpam-6640	664	2	5	5	X
ejpam-6640	664	3	]	]	X
ejpam-6640	664	4	friedrich	friedrich	PROPN
ejpam-6640	664	5	kasch	kasch	PROPN
ejpam-6640	664	6	.	.	PUNCT
ejpam-6640	664	7	modules	module	NOUN
ejpam-6640	664	8	and	and	CCONJ
ejpam-6640	664	9	rings	ring	NOUN
ejpam-6640	664	10	,	,	PUNCT
ejpam-6640	664	11	volume	volume	NOUN
ejpam-6640	664	12	17	17	NUM
ejpam-6640	664	13	.	.	PUNCT
ejpam-6640	665	1	academic	academic	ADJ
ejpam-6640	665	2	press	press	NOUN
ejpam-6640	665	3	,	,	PUNCT
ejpam-6640	665	4	1982	1982	NUM
ejpam-6640	665	5	.	.	PUNCT
ejpam-6640	666	1	[	[	X
ejpam-6640	666	2	6	6	NUM
ejpam-6640	666	3	]	]	X
ejpam-6640	666	4	joseph	joseph	PROPN
ejpam-6640	666	5	j	j	PROPN
ejpam-6640	666	6	rotman	rotman	PROPN
ejpam-6640	666	7	.	.	PUNCT
ejpam-6640	667	1	notes	note	NOUN
ejpam-6640	667	2	on	on	ADP
ejpam-6640	667	3	homological	homological	ADJ
ejpam-6640	667	4	algebras	algebra	NOUN
ejpam-6640	667	5	,	,	PUNCT
ejpam-6640	667	6	university	university	PROPN
ejpam-6640	667	7	of	of	ADP
ejpam-6640	667	8	illinois	illinois	PROPN
ejpam-6640	667	9	.	.	PUNCT
ejpam-6640	668	1	urbana	urbana	PROPN
ejpam-6640	668	2	,	,	PUNCT
ejpam-6640	668	3	1968	1968	NUM
ejpam-6640	668	4	.	.	PUNCT
ejpam-6640	669	1	[	[	X
ejpam-6640	669	2	7	7	X
ejpam-6640	669	3	]	]	X
ejpam-6640	669	4	peter	peter	PROPN
ejpam-6640	669	5	j	j	PROPN
ejpam-6640	669	6	freyd	freyd	PROPN
ejpam-6640	669	7	.	.	PUNCT
ejpam-6640	670	1	abelian	abelian	PROPN
ejpam-6640	670	2	categories	category	NOUN
ejpam-6640	670	3	,	,	PUNCT
ejpam-6640	670	4	volume	volume	NOUN
ejpam-6640	670	5	1964	1964	NUM
ejpam-6640	670	6	.	.	PUNCT
ejpam-6640	671	1	harper	harper	NOUN
ejpam-6640	671	2	&	&	CCONJ
ejpam-6640	671	3	row	row	VERB
ejpam-6640	671	4	new	new	PROPN
ejpam-6640	671	5	york	york	PROPN
ejpam-6640	671	6	,	,	PUNCT
ejpam-6640	671	7	1964	1964	NUM
ejpam-6640	671	8	.	.	PUNCT
ejpam-6640	672	1	[	[	X
ejpam-6640	672	2	8	8	X
ejpam-6640	672	3	]	]	PUNCT
ejpam-6640	672	4	pierre	pierre	PROPN
ejpam-6640	672	5	gabriel	gabriel	PROPN
ejpam-6640	672	6	.	.	PUNCT
ejpam-6640	673	1	des	des	PROPN
ejpam-6640	673	2	catégories	catégories	PROPN
ejpam-6640	673	3	abéliennes	abéliennes	PROPN
ejpam-6640	673	4	.	.	PUNCT
ejpam-6640	674	1	bulletin	bulletin	PROPN
ejpam-6640	674	2	de	de	PROPN
ejpam-6640	674	3	la	la	PROPN
ejpam-6640	674	4	société	société	PROPN
ejpam-6640	674	5	mathématique	mathématique	PROPN
ejpam-6640	674	6	de	de	X
ejpam-6640	674	7	france	france	PROPN
ejpam-6640	674	8	,	,	PUNCT
ejpam-6640	674	9	90:323–448	90:323–448	NUM
ejpam-6640	674	10	,	,	PUNCT
ejpam-6640	674	11	1962	1962	NUM
ejpam-6640	674	12	.	.	PUNCT
ejpam-6640	675	1	[	[	X
ejpam-6640	675	2	9	9	NUM
ejpam-6640	675	3	]	]	X
ejpam-6640	675	4	joseph	joseph	PROPN
ejpam-6640	675	5	j	j	PROPN
ejpam-6640	675	6	rotman	rotman	PROPN
ejpam-6640	675	7	.	.	PUNCT
ejpam-6640	676	1	an	an	DET
ejpam-6640	676	2	introduction	introduction	NOUN
ejpam-6640	676	3	to	to	ADP
ejpam-6640	676	4	homological	homological	ADJ
ejpam-6640	676	5	algebra	algebra	NOUN
ejpam-6640	676	6	.	.	PUNCT
ejpam-6640	677	1	springer	springer	NOUN
ejpam-6640	677	2	,	,	PUNCT
ejpam-6640	677	3	2nd	2nd	PROPN
ejpam-6640	677	4	edition	edition	NOUN
ejpam-6640	677	5	,	,	PUNCT
ejpam-6640	677	6	2009	2009	NUM
ejpam-6640	677	7	.	.	PUNCT
ejpam-6640	678	1	[	[	X
ejpam-6640	678	2	10	10	NUM
ejpam-6640	678	3	]	]	X
ejpam-6640	678	4	charles	charle	VERB
ejpam-6640	678	5	a	a	DET
ejpam-6640	678	6	weibel	weibel	NOUN
ejpam-6640	678	7	.	.	PUNCT
ejpam-6640	679	1	an	an	DET
ejpam-6640	679	2	introduction	introduction	NOUN
ejpam-6640	679	3	to	to	ADP
ejpam-6640	679	4	homological	homological	ADJ
ejpam-6640	679	5	algebra	algebra	NOUN
ejpam-6640	679	6	,	,	PUNCT
ejpam-6640	679	7	volume	volume	NOUN
ejpam-6640	679	8	38	38	NUM
ejpam-6640	679	9	.	.	PUNCT
ejpam-6640	680	1	cambridge	cambridge	PROPN
ejpam-6640	680	2	university	university	PROPN
ejpam-6640	680	3	press	press	NOUN
ejpam-6640	680	4	,	,	PUNCT
ejpam-6640	680	5	1994	1994	NUM
ejpam-6640	680	6	.	.	PUNCT
ejpam-6640	681	1	[	[	X
ejpam-6640	681	2	11	11	NUM
ejpam-6640	681	3	]	]	X
ejpam-6640	681	4	el	el	PROPN
ejpam-6640	681	5	hadji	hadji	PROPN
ejpam-6640	681	6	ousseynou	ousseynou	PROPN
ejpam-6640	681	7	diallo	diallo	PROPN
ejpam-6640	681	8	.	.	PUNCT
ejpam-6640	682	1	hopficité	hopficité	PROPN
ejpam-6640	682	2	et	et	PROPN
ejpam-6640	682	3	co	co	PROPN
ejpam-6640	682	4	-	-	NOUN
ejpam-6640	682	5	hopficité	hopficité	NOUN
ejpam-6640	682	6	dans	dans	PROPN
ejpam-6640	682	7	la	la	PROPN
ejpam-6640	682	8	catégorie	catégorie	PROPN
ejpam-6640	682	9	comp	comp	PROPN
ejpam-6640	682	10	des	des	PROPN
ejpam-6640	682	11	complexes	complex	NOUN
ejpam-6640	682	12	.	.	PUNCT
ejpam-6640	683	1	thèse	thèse	PROPN
ejpam-6640	683	2	,	,	PUNCT
ejpam-6640	683	3	faculté	faculté	NOUN
ejpam-6640	683	4	des	des	PROPN
ejpam-6640	683	5	sciences	sciences	PROPN
ejpam-6640	683	6	et	et	PROPN
ejpam-6640	683	7	techniques	technique	NOUN
ejpam-6640	683	8	,	,	PUNCT
ejpam-6640	683	9	université	université	NOUN
ejpam-6640	683	10	cheikh	cheikh	PROPN
ejpam-6640	683	11	anta	anta	PROPN
ejpam-6640	683	12	diop	diop	PROPN
ejpam-6640	683	13	,	,	PUNCT
ejpam-6640	683	14	2014	2014	NUM
ejpam-6640	683	15	.	.	PUNCT
ejpam-6640	684	1	[	[	X
ejpam-6640	684	2	12	12	NUM
ejpam-6640	684	3	]	]	X
ejpam-6640	684	4	mathieu	mathieu	PROPN
ejpam-6640	684	5	dupont	dupont	PROPN
ejpam-6640	684	6	et	et	PROPN
ejpam-6640	684	7	al	al	PROPN
ejpam-6640	684	8	.	.	PUNCT
ejpam-6640	685	1	catégories	catégorie	NOUN
ejpam-6640	685	2	abéliennes	abélienne	NOUN
ejpam-6640	685	3	en	en	X
ejpam-6640	685	4	dimension	dimension	NOUN
ejpam-6640	685	5	2	2	NUM
ejpam-6640	685	6	.	.	PUNCT
ejpam-6640	685	7	phd	phd	NOUN
ejpam-6640	685	8	thesis	thesis	NOUN
ejpam-6640	685	9	,	,	PUNCT
ejpam-6640	685	10	université	université	ADJ
ejpam-6640	685	11	catholique	catholique	X
ejpam-6640	685	12	de	de	X
ejpam-6640	685	13	louvain	louvain	NOUN
ejpam-6640	685	14	,	,	PUNCT
ejpam-6640	685	15	2008	2008	NUM
ejpam-6640	685	16	(	(	PUNCT
ejpam-6640	685	17	english	english	ADJ
ejpam-6640	685	18	version	version	NOUN
ejpam-6640	685	19	)	)	PUNCT
ejpam-6640	685	20	,	,	PUNCT
ejpam-6640	685	21	2008	2008	NUM
ejpam-6640	685	22	.	.	PUNCT
ejpam-6640	686	1	[	[	X
ejpam-6640	686	2	13	13	NUM
ejpam-6640	686	3	]	]	PUNCT
ejpam-6640	686	4	sebastian	sebastian	PROPN
ejpam-6640	686	5	posur	posur	PROPN
ejpam-6640	686	6	.	.	PUNCT
ejpam-6640	687	1	a	a	DET
ejpam-6640	687	2	constructive	constructive	ADJ
ejpam-6640	687	3	approach	approach	NOUN
ejpam-6640	687	4	to	to	ADP
ejpam-6640	687	5	freyd	freyd	PROPN
ejpam-6640	687	6	categories	category	NOUN
ejpam-6640	687	7	.	.	PUNCT
ejpam-6640	688	1	applied	apply	VERB
ejpam-6640	688	2	categorical	categorical	ADJ
ejpam-6640	688	3	structures	structure	NOUN
ejpam-6640	688	4	,	,	PUNCT
ejpam-6640	688	5	29(1):171–211	29(1):171–211	NUM
ejpam-6640	688	6	,	,	PUNCT
ejpam-6640	688	7	2021	2021	NUM
ejpam-6640	688	8	.	.	PUNCT
ejpam-6640	689	1	[	[	X
ejpam-6640	689	2	14	14	NUM
ejpam-6640	689	3	]	]	PUNCT
ejpam-6640	689	4	bassirou	bassirou	NOUN
ejpam-6640	689	5	dembele	dembele	PROPN
ejpam-6640	689	6	.	.	PUNCT
ejpam-6640	690	1	foncteur	foncteur	NOUN
ejpam-6640	690	2	localisation	localisation	NOUN
ejpam-6640	690	3	dans	dan	NOUN
ejpam-6640	690	4	la	la	PROPN
ejpam-6640	690	5	catégorie	catégorie	PROPN
ejpam-6640	690	6	comp(a	comp(a	PROPN
ejpam-6640	690	7	-	-	PUNCT
ejpam-6640	690	8	mod	mod	NOUN
ejpam-6640	690	9	)	)	PUNCT
ejpam-6640	690	10	des	des	PROPN
ejpam-6640	690	11	suites	suit	VERB
ejpam-6640	690	12	a.	a.	PROPN
ejpam-6640	690	13	diallo	diallo	PROPN
ejpam-6640	690	14	,	,	PUNCT
ejpam-6640	690	15	m.	m.	PROPN
ejpam-6640	690	16	b.	b.	PROPN
ejpam-6640	690	17	f.	f.	PROPN
ejpam-6640	690	18	b.	b.	PROPN
ejpam-6640	690	19	maaouia	maaouia	PROPN
ejpam-6640	690	20	,	,	PUNCT
ejpam-6640	690	21	m.	m.	NOUN
ejpam-6640	690	22	sanghare	sanghare	PROPN
ejpam-6640	690	23	/	/	SYM
ejpam-6640	690	24	eur	eur	PROPN
ejpam-6640	690	25	.	.	PUNCT
ejpam-6640	691	1	j.	j.	PROPN
ejpam-6640	691	2	pure	pure	PROPN
ejpam-6640	691	3	appl	appl	PROPN
ejpam-6640	691	4	.	.	PROPN
ejpam-6640	691	5	math	math	PROPN
ejpam-6640	691	6	,	,	PUNCT
ejpam-6640	691	7	18	18	NUM
ejpam-6640	691	8	(	(	PUNCT
ejpam-6640	691	9	4	4	NUM
ejpam-6640	691	10	)	)	PUNCT
ejpam-6640	691	11	(	(	PUNCT
ejpam-6640	691	12	2025	2025	NUM
ejpam-6640	691	13	)	)	PUNCT
ejpam-6640	691	14	,	,	PUNCT
ejpam-6640	691	15	6640	6640	NUM
ejpam-6640	691	16	28	28	NUM
ejpam-6640	691	17	of	of	ADP
ejpam-6640	691	18	28	28	NUM
ejpam-6640	691	19	complexes	complex	NOUN
ejpam-6640	691	20	de	de	ADP
ejpam-6640	691	21	morphismes	morphisme	NOUN
ejpam-6640	691	22	de	de	PROPN
ejpam-6640	691	23	a	a	X
ejpam-6640	691	24	-	-	PUNCT
ejpam-6640	691	25	modules	module	NOUN
ejpam-6640	691	26	à	à	PROPN
ejpam-6640	691	27	gauche	gauche	PROPN
ejpam-6640	691	28	et	et	PROPN
ejpam-6640	691	29	applications	application	NOUN
ejpam-6640	691	30	sur	sur	PROPN
ejpam-6640	691	31	les	les	PROPN
ejpam-6640	691	32	dimensions	dimensions	PROPN
ejpam-6640	691	33	homologiques	homologique	NOUN
ejpam-6640	691	34	et	et	PROPN
ejpam-6640	691	35	sur	sur	PROPN
ejpam-6640	691	36	les	les	PROPN
ejpam-6640	691	37	enveloppes	enveloppes	PROPN
ejpam-6640	691	38	et	et	PROPN
ejpam-6640	691	39	couvertures	couverture	VERB
ejpam-6640	691	40	plates	plate	NOUN
ejpam-6640	691	41	dans	dan	NOUN
ejpam-6640	691	42	comp(a	comp(a	NOUN
ejpam-6640	691	43	-	-	PUNCT
ejpam-6640	691	44	mod	mod	NOUN
ejpam-6640	691	45	)	)	PUNCT
ejpam-6640	691	46	.	.	PUNCT
ejpam-6640	692	1	thèse	thèse	PROPN
ejpam-6640	692	2	,	,	PUNCT
ejpam-6640	692	3	université	université	ADJ
ejpam-6640	692	4	gaston	gaston	PROPN
ejpam-6640	692	5	berger	berger	PROPN
ejpam-6640	692	6	,	,	PUNCT
ejpam-6640	692	7	saint	saint	PROPN
ejpam-6640	692	8	-	-	PUNCT
ejpam-6640	692	9	louis	louis	NOUN
ejpam-6640	692	10	,	,	PUNCT
ejpam-6640	692	11	décembre	décembre	PROPN
ejpam-6640	692	12	2020	2020	NUM
ejpam-6640	692	13	.	.	PUNCT
ejpam-6640	693	1	[	[	X
ejpam-6640	693	2	15	15	NUM
ejpam-6640	693	3	]	]	X
ejpam-6640	693	4	ahmed	ahmed	PROPN
ejpam-6640	693	5	ould	ould	AUX
ejpam-6640	693	6	chbih	chbih	VERB
ejpam-6640	693	7	.	.	PUNCT
ejpam-6640	694	1	graduation	graduation	NOUN
ejpam-6640	694	2	et	et	PROPN
ejpam-6640	694	3	filtration	filtration	NOUN
ejpam-6640	694	4	des	des	X
ejpam-6640	694	5	modules	module	NOUN
ejpam-6640	694	6	de	de	X
ejpam-6640	694	7	fractions	fraction	NOUN
ejpam-6640	694	8	sur	sur	PROPN
ejpam-6640	694	9	des	des	X
ejpam-6640	694	10	anneaux	anneaux	PROPN
ejpam-6640	694	11	non	non	PROPN
ejpam-6640	694	12	nécessairement	nécessairement	PROPN
ejpam-6640	694	13	commutatifs	commutatifs	PROPN
ejpam-6640	694	14	.	.	PUNCT
ejpam-6640	695	1	thèse	thèse	PROPN
ejpam-6640	695	2	,	,	PUNCT
ejpam-6640	695	3	université	université	ADJ
ejpam-6640	695	4	gaston	gaston	PROPN
ejpam-6640	695	5	berger	berger	PROPN
ejpam-6640	695	6	,	,	PUNCT
ejpam-6640	695	7	saint	saint	PROPN
ejpam-6640	695	8	-	-	PUNCT
ejpam-6640	695	9	louis	louis	NOUN
ejpam-6640	695	10	,	,	PUNCT
ejpam-6640	695	11	avril	avril	PROPN
ejpam-6640	695	12	2016	2016	NUM
ejpam-6640	695	13	.	.	PUNCT
ejpam-6640	696	1	[	[	X
ejpam-6640	696	2	16	16	NUM
ejpam-6640	696	3	]	]	X
ejpam-6640	696	4	charles	charles	PROPN
ejpam-6640	696	5	weibel	weibel	PROPN
ejpam-6640	696	6	and	and	CCONJ
ejpam-6640	696	7	mcr	mcr	PROPN
ejpam-6640	696	8	butler	butler	PROPN
ejpam-6640	696	9	.	.	PUNCT
ejpam-6640	697	1	an	an	DET
ejpam-6640	697	2	introduction	introduction	NOUN
ejpam-6640	697	3	to	to	ADP
ejpam-6640	697	4	homological	homological	ADJ
ejpam-6640	697	5	algebra	algebra	NOUN
ejpam-6640	697	6	.	.	PUNCT
ejpam-6640	698	1	bulletin	bulletin	NOUN
ejpam-6640	698	2	of	of	ADP
ejpam-6640	698	3	the	the	DET
ejpam-6640	698	4	london	london	PROPN
ejpam-6640	698	5	mathematical	mathematical	ADJ
ejpam-6640	698	6	society	society	NOUN
ejpam-6640	698	7	,	,	PUNCT
ejpam-6640	698	8	28(132):322–323	28(132):322–323	PROPN
ejpam-6640	698	9	,	,	PUNCT
ejpam-6640	698	10	1996	1996	NUM
ejpam-6640	698	11	.	.	PUNCT
ejpam-6640	699	1	[	[	X
ejpam-6640	699	2	17	17	NUM
ejpam-6640	699	3	]	]	X
ejpam-6640	699	4	ahmed	ahmed	PROPN
ejpam-6640	699	5	ould	ould	AUX
ejpam-6640	699	6	chbih	chbih	PROPN
ejpam-6640	699	7	,	,	PUNCT
ejpam-6640	699	8	mbf	mbf	NOUN
ejpam-6640	699	9	maaouia	maaouia	NOUN
ejpam-6640	699	10	,	,	PUNCT
ejpam-6640	699	11	and	and	CCONJ
ejpam-6640	699	12	mamadou	mamadou	PROPN
ejpam-6640	699	13	sanghare	sanghare	NOUN
ejpam-6640	699	14	.	.	PUNCT
ejpam-6640	700	1	graduation	graduation	NOUN
ejpam-6640	700	2	of	of	ADP
ejpam-6640	700	3	module	module	NOUN
ejpam-6640	700	4	of	of	ADP
ejpam-6640	700	5	fraction	fraction	NOUN
ejpam-6640	700	6	on	on	ADP
ejpam-6640	700	7	a	a	DET
ejpam-6640	700	8	graded	grade	VERB
ejpam-6640	700	9	domain	domain	NOUN
ejpam-6640	700	10	ring	ring	NOUN
ejpam-6640	700	11	not	not	PART
ejpam-6640	700	12	necessarily	necessarily	ADV
ejpam-6640	700	13	commutative	commutative	ADJ
ejpam-6640	700	14	.	.	PUNCT
ejpam-6640	701	1	international	international	ADJ
ejpam-6640	701	2	journal	journal	PROPN
ejpam-6640	701	3	of	of	ADP
ejpam-6640	701	4	algebra	algebra	PROPN
ejpam-6640	701	5	,	,	PUNCT
ejpam-6640	701	6	9(10):457–474	9(10):457–474	NUM
ejpam-6640	701	7	,	,	PUNCT
ejpam-6640	701	8	2015	2015	NUM
ejpam-6640	701	9	.	.	PUNCT
ejpam-6640	702	1	[	[	X
ejpam-6640	702	2	18	18	NUM
ejpam-6640	702	3	]	]	X
ejpam-6640	702	4	ahmed	ahmed	PROPN
ejpam-6640	702	5	ould	ould	AUX
ejpam-6640	702	6	chbih	chbih	PROPN
ejpam-6640	702	7	,	,	PUNCT
ejpam-6640	702	8	mohamed	mohamed	PROPN
ejpam-6640	702	9	ben	ben	PROPN
ejpam-6640	702	10	faraj	faraj	PROPN
ejpam-6640	702	11	ben	ben	PROPN
ejpam-6640	702	12	maaouia	maaouia	PROPN
ejpam-6640	702	13	,	,	PUNCT
ejpam-6640	702	14	and	and	CCONJ
ejpam-6640	702	15	mamadou	mamadou	PROPN
ejpam-6640	702	16	sanghare	sanghare	NOUN
ejpam-6640	702	17	.	.	PUNCT
ejpam-6640	703	1	localization	localization	NOUN
ejpam-6640	703	2	in	in	ADP
ejpam-6640	703	3	the	the	DET
ejpam-6640	703	4	category	category	NOUN
ejpam-6640	703	5	comp(gr(a	comp(gr(a	NOUN
ejpam-6640	703	6	-	-	PUNCT
ejpam-6640	703	7	mod	mod	NOUN
ejpam-6640	703	8	)	)	PUNCT
ejpam-6640	703	9	)	)	PUNCT
ejpam-6640	703	10	of	of	ADP
ejpam-6640	703	11	complex	complex	ADJ
ejpam-6640	703	12	associated	associate	VERB
ejpam-6640	703	13	to	to	ADP
ejpam-6640	703	14	the	the	DET
ejpam-6640	703	15	category	category	NOUN
ejpam-6640	703	16	gr(a	gr(a	NOUN
ejpam-6640	703	17	-	-	PUNCT
ejpam-6640	703	18	mod	mod	NOUN
ejpam-6640	703	19	)	)	PUNCT
ejpam-6640	703	20	of	of	ADP
ejpam-6640	703	21	graded	grade	VERB
ejpam-6640	703	22	left	leave	VERB
ejpam-6640	703	23	a	a	DET
ejpam-6640	703	24	-	-	PUNCT
ejpam-6640	703	25	modules	module	NOUN
ejpam-6640	703	26	over	over	ADP
ejpam-6640	703	27	a	a	DET
ejpam-6640	703	28	graded	grade	VERB
ejpam-6640	703	29	ring	ring	NOUN
ejpam-6640	703	30	.	.	PUNCT
ejpam-6640	704	1	european	european	PROPN
ejpam-6640	704	2	journal	journal	PROPN
ejpam-6640	704	3	of	of	ADP
ejpam-6640	704	4	pure	pure	ADJ
ejpam-6640	704	5	and	and	CCONJ
ejpam-6640	704	6	applied	applied	ADJ
ejpam-6640	704	7	mathematics	mathematic	NOUN
ejpam-6640	704	8	,	,	PUNCT
ejpam-6640	704	9	16(3):1913–1939	16(3):1913–1939	NUM
ejpam-6640	704	10	,	,	PUNCT
ejpam-6640	704	11	2023	2023	NUM
ejpam-6640	704	12	.	.	PUNCT
ejpam-6640	705	1	[	[	X
ejpam-6640	705	2	19	19	NUM
ejpam-6640	705	3	]	]	X
ejpam-6640	705	4	moussa	moussa	PROPN
ejpam-6640	705	5	thiaw	thiaw	PROPN
ejpam-6640	705	6	and	and	CCONJ
ejpam-6640	705	7	mohamed	mohamed	PROPN
ejpam-6640	705	8	ben	ben	PROPN
ejpam-6640	705	9	faraj	faraj	PROPN
ejpam-6640	705	10	ben	ben	PROPN
ejpam-6640	705	11	maaouia	maaouia	PROPN
ejpam-6640	705	12	.	.	PUNCT
ejpam-6640	706	1	adjunction	adjunction	NOUN
ejpam-6640	706	2	and	and	CCONJ
ejpam-6640	706	3	localization	localization	NOUN
ejpam-6640	706	4	in	in	ADP
ejpam-6640	706	5	the	the	DET
ejpam-6640	706	6	category	category	NOUN
ejpam-6640	706	7	a	a	DET
ejpam-6640	706	8	-	-	PUNCT
ejpam-6640	706	9	alg	alg	NOUN
ejpam-6640	706	10	of	of	ADP
ejpam-6640	706	11	a	a	DET
ejpam-6640	706	12	-	-	PUNCT
ejpam-6640	706	13	algebras	algebra	VERB
ejpam-6640	706	14	.	.	PUNCT
ejpam-6640	707	1	european	european	PROPN
ejpam-6640	707	2	journal	journal	PROPN
ejpam-6640	707	3	of	of	ADP
ejpam-6640	707	4	pure	pure	ADJ
ejpam-6640	707	5	and	and	CCONJ
ejpam-6640	707	6	applied	applied	ADJ
ejpam-6640	707	7	mathematics	mathematic	NOUN
ejpam-6640	707	8	,	,	PUNCT
ejpam-6640	707	9	13(3):472–482	13(3):472–482	NUM
ejpam-6640	707	10	,	,	PUNCT
ejpam-6640	707	11	2020	2020	NUM
ejpam-6640	707	12	.	.	PUNCT