id	sid	tid	token	lemma	pos
ejpam-3322	1	1	on	on	ADP
ejpam-3322	1	2	non	non	ADJ
ejpam-3322	1	3	-	-	ADJ
ejpam-3322	1	4	trivially	trivially	ADV
ejpam-3322	1	5	associated	associated	ADJ
ejpam-3322	1	6	tensor	tensor	NOUN
ejpam-3322	1	7	categories	category	NOUN
ejpam-3322	1	8	european	european	PROPN
ejpam-3322	1	9	journal	journal	PROPN
ejpam-3322	1	10	of	of	ADP
ejpam-3322	1	11	pure	pure	ADJ
ejpam-3322	1	12	and	and	CCONJ
ejpam-3322	1	13	applied	apply	VERB
ejpam-3322	1	14	mathematics	mathematic	NOUN
ejpam-3322	1	15	vol	vol	NOUN
ejpam-3322	1	16	.	.	PUNCT
ejpam-3322	1	17	11	11	NUM
ejpam-3322	1	18	,	,	PUNCT
ejpam-3322	1	19	no	no	INTJ
ejpam-3322	1	20	.	.	NOUN
ejpam-3322	1	21	4	4	NUM
ejpam-3322	1	22	,	,	PUNCT
ejpam-3322	1	23	2018	2018	NUM
ejpam-3322	1	24	,	,	PUNCT
ejpam-3322	1	25	1027	1027	NUM
ejpam-3322	1	26	-	-	SYM
ejpam-3322	1	27	1045	1045	NUM
ejpam-3322	1	28	issn	issn	PROPN
ejpam-3322	1	29	1307	1307	NUM
ejpam-3322	1	30	-	-	SYM
ejpam-3322	1	31	5543	5543	NUM
ejpam-3322	1	32	–	–	PUNCT
ejpam-3322	1	33	www.ejpam.com	www.ejpam.com	X
ejpam-3322	1	34	published	publish	VERB
ejpam-3322	1	35	by	by	ADP
ejpam-3322	1	36	new	new	PROPN
ejpam-3322	1	37	york	york	PROPN
ejpam-3322	1	38	business	business	PROPN
ejpam-3322	1	39	global	global	PROPN
ejpam-3322	1	40	on	on	ADP
ejpam-3322	1	41	non	non	ADJ
ejpam-3322	1	42	-	-	ADJ
ejpam-3322	1	43	trivially	trivially	ADV
ejpam-3322	1	44	associated	associated	ADJ
ejpam-3322	1	45	tensor	tensor	NOUN
ejpam-3322	1	46	categories	category	NOUN
ejpam-3322	1	47	b.	b.	PROPN
ejpam-3322	1	48	al	al	PROPN
ejpam-3322	1	49	-	-	PUNCT
ejpam-3322	1	50	harbi1	harbi1	PROPN
ejpam-3322	1	51	,	,	PUNCT
ejpam-3322	1	52	w.	w.	PROPN
ejpam-3322	1	53	m.	m.	PROPN
ejpam-3322	1	54	fakieh2	fakieh2	PROPN
ejpam-3322	1	55	,	,	PUNCT
ejpam-3322	1	56	m.	m.	NOUN
ejpam-3322	1	57	m.	m.	PROPN
ejpam-3322	1	58	al	al	PROPN
ejpam-3322	1	59	-	-	PUNCT
ejpam-3322	1	60	shomrani2,∗	shomrani2,∗	PROPN
ejpam-3322	1	61	1	1	NUM
ejpam-3322	1	62	department	department	NOUN
ejpam-3322	1	63	of	of	ADP
ejpam-3322	1	64	mathematics	mathematics	PROPN
ejpam-3322	1	65	,	,	PUNCT
ejpam-3322	1	66	al	al	PROPN
ejpam-3322	1	67	-	-	PUNCT
ejpam-3322	1	68	baha	baha	PROPN
ejpam-3322	1	69	university	university	PROPN
ejpam-3322	1	70	,	,	PUNCT
ejpam-3322	1	71	al	al	PROPN
ejpam-3322	1	72	-	-	PUNCT
ejpam-3322	1	73	baha	baha	PROPN
ejpam-3322	1	74	,	,	PUNCT
ejpam-3322	1	75	saudi	saudi	PROPN
ejpam-3322	1	76	arabia	arabia	PROPN
ejpam-3322	1	77	2	2	NUM
ejpam-3322	1	78	department	department	NOUN
ejpam-3322	1	79	of	of	ADP
ejpam-3322	1	80	mathematics	mathematic	NOUN
ejpam-3322	1	81	,	,	PUNCT
ejpam-3322	1	82	faculty	faculty	NOUN
ejpam-3322	1	83	of	of	ADP
ejpam-3322	1	84	science	science	NOUN
ejpam-3322	1	85	,	,	PUNCT
ejpam-3322	1	86	king	king	PROPN
ejpam-3322	1	87	abdulaziz	abdulaziz	PROPN
ejpam-3322	1	88	university	university	PROPN
ejpam-3322	1	89	,	,	PUNCT
ejpam-3322	1	90	p.o.box	p.o.box	PROPN
ejpam-3322	1	91	80203	80203	NUM
ejpam-3322	1	92	,	,	PUNCT
ejpam-3322	1	93	jeddah	jeddah	PROPN
ejpam-3322	1	94	21589	21589	NUM
ejpam-3322	1	95	,	,	PUNCT
ejpam-3322	1	96	saudi	saudi	PROPN
ejpam-3322	1	97	arabia	arabia	PROPN
ejpam-3322	1	98	abstract	abstract	NOUN
ejpam-3322	1	99	.	.	PUNCT
ejpam-3322	2	1	the	the	DET
ejpam-3322	2	2	purpose	purpose	NOUN
ejpam-3322	2	3	of	of	ADP
ejpam-3322	2	4	this	this	DET
ejpam-3322	2	5	article	article	NOUN
ejpam-3322	2	6	is	be	AUX
ejpam-3322	2	7	to	to	PART
ejpam-3322	2	8	provide	provide	VERB
ejpam-3322	2	9	mathematical	mathematical	ADJ
ejpam-3322	2	10	formulas	formula	NOUN
ejpam-3322	2	11	for	for	ADP
ejpam-3322	2	12	some	some	DET
ejpam-3322	2	13	operations	operation	NOUN
ejpam-3322	2	14	on	on	ADP
ejpam-3322	2	15	the	the	DET
ejpam-3322	2	16	objects	object	NOUN
ejpam-3322	2	17	of	of	ADP
ejpam-3322	2	18	a	a	DET
ejpam-3322	2	19	non	non	ADJ
ejpam-3322	2	20	-	-	ADJ
ejpam-3322	2	21	trivially	trivially	ADV
ejpam-3322	2	22	associated	associated	ADJ
ejpam-3322	2	23	tensor	tensor	NOUN
ejpam-3322	2	24	category	category	NOUN
ejpam-3322	2	25	constructed	construct	VERB
ejpam-3322	2	26	from	from	ADP
ejpam-3322	2	27	a	a	DET
ejpam-3322	2	28	factorization	factorization	NOUN
ejpam-3322	2	29	of	of	ADP
ejpam-3322	2	30	a	a	DET
ejpam-3322	2	31	group	group	NOUN
ejpam-3322	2	32	into	into	ADP
ejpam-3322	2	33	a	a	DET
ejpam-3322	2	34	subgroup	subgroup	NOUN
ejpam-3322	2	35	and	and	CCONJ
ejpam-3322	2	36	a	a	DET
ejpam-3322	2	37	set	set	NOUN
ejpam-3322	2	38	of	of	ADP
ejpam-3322	2	39	left	left	ADJ
ejpam-3322	2	40	coset	coset	NOUN
ejpam-3322	2	41	representatives	representative	NOUN
ejpam-3322	2	42	.	.	PUNCT
ejpam-3322	3	1	a	a	DET
ejpam-3322	3	2	detailed	detailed	ADJ
ejpam-3322	3	3	example	example	NOUN
ejpam-3322	3	4	is	be	AUX
ejpam-3322	3	5	provided	provide	VERB
ejpam-3322	3	6	.	.	PUNCT
ejpam-3322	4	1	2010	2010	NUM
ejpam-3322	4	2	mathematics	mathematic	NOUN
ejpam-3322	4	3	subject	subject	NOUN
ejpam-3322	4	4	classifications	classification	NOUN
ejpam-3322	4	5	:	:	PUNCT
ejpam-3322	4	6	16w50	16w50	NUM
ejpam-3322	4	7	,	,	PUNCT
ejpam-3322	4	8	13a02	13a02	NUM
ejpam-3322	4	9	,	,	PUNCT
ejpam-3322	4	10	16d25	16d25	NUM
ejpam-3322	4	11	key	key	ADJ
ejpam-3322	4	12	words	word	NOUN
ejpam-3322	4	13	and	and	CCONJ
ejpam-3322	4	14	phrases	phrase	NOUN
ejpam-3322	4	15	:	:	PUNCT
ejpam-3322	4	16	non	non	ADJ
ejpam-3322	4	17	-	-	ADJ
ejpam-3322	4	18	trivially	trivially	ADV
ejpam-3322	4	19	associated	associated	ADJ
ejpam-3322	4	20	tensor	tensor	NOUN
ejpam-3322	4	21	categories	category	NOUN
ejpam-3322	4	22	,	,	PUNCT
ejpam-3322	4	23	algebras	algebra	VERB
ejpam-3322	4	24	in	in	ADP
ejpam-3322	4	25	tensor	tensor	NOUN
ejpam-3322	4	26	categories	category	NOUN
ejpam-3322	4	27	,	,	PUNCT
ejpam-3322	4	28	coalgebras	coalgebra	NOUN
ejpam-3322	4	29	in	in	ADP
ejpam-3322	4	30	tensor	tensor	NOUN
ejpam-3322	4	31	categories	category	NOUN
ejpam-3322	4	32	,	,	PUNCT
ejpam-3322	4	33	dual	dual	ADJ
ejpam-3322	4	34	of	of	ADP
ejpam-3322	4	35	algebras	algebra	NOUN
ejpam-3322	4	36	and	and	CCONJ
ejpam-3322	4	37	coalgebras	coalgebras	ADJ
ejpam-3322	4	38	1	1	NUM
ejpam-3322	4	39	.	.	PUNCT
ejpam-3322	4	40	introduction	introduction	NOUN
ejpam-3322	4	41	in	in	ADP
ejpam-3322	4	42	[	[	X
ejpam-3322	4	43	4	4	NUM
ejpam-3322	4	44	]	]	PUNCT
ejpam-3322	4	45	,	,	PUNCT
ejpam-3322	4	46	beggs	beggs	PROPN
ejpam-3322	4	47	form	form	VERB
ejpam-3322	4	48	a	a	DET
ejpam-3322	4	49	set	set	NOUN
ejpam-3322	4	50	m	m	NOUN
ejpam-3322	4	51	of	of	ADP
ejpam-3322	4	52	left	left	ADJ
ejpam-3322	4	53	coset	coset	NOUN
ejpam-3322	4	54	representatives	representative	NOUN
ejpam-3322	4	55	for	for	ADP
ejpam-3322	4	56	the	the	DET
ejpam-3322	4	57	left	left	ADJ
ejpam-3322	4	58	action	action	NOUN
ejpam-3322	4	59	of	of	ADP
ejpam-3322	4	60	a	a	DET
ejpam-3322	4	61	subgroup	subgroup	NOUN
ejpam-3322	4	62	g	g	NOUN
ejpam-3322	4	63	of	of	ADP
ejpam-3322	4	64	a	a	DET
ejpam-3322	4	65	group	group	NOUN
ejpam-3322	4	66	x	x	PUNCT
ejpam-3322	4	67	on	on	ADP
ejpam-3322	4	68	the	the	DET
ejpam-3322	4	69	group	group	NOUN
ejpam-3322	4	70	x.	x.	NOUN
ejpam-3322	5	1	moreover	moreover	ADV
ejpam-3322	5	2	,	,	PUNCT
ejpam-3322	5	3	he	he	PRON
ejpam-3322	5	4	defined	define	VERB
ejpam-3322	5	5	an	an	DET
ejpam-3322	5	6	operation	operation	NOUN
ejpam-3322	5	7	on	on	ADP
ejpam-3322	5	8	m	m	PROPN
ejpam-3322	5	9	which	which	PRON
ejpam-3322	5	10	has	have	VERB
ejpam-3322	5	11	a	a	DET
ejpam-3322	5	12	left	left	ADJ
ejpam-3322	5	13	identity	identity	NOUN
ejpam-3322	5	14	and	and	CCONJ
ejpam-3322	5	15	satisfies	satisfy	VERB
ejpam-3322	5	16	the	the	DET
ejpam-3322	5	17	right	right	ADJ
ejpam-3322	5	18	division	division	NOUN
ejpam-3322	5	19	property	property	NOUN
ejpam-3322	5	20	.	.	PUNCT
ejpam-3322	6	1	this	this	DET
ejpam-3322	6	2	binary	binary	ADJ
ejpam-3322	6	3	operation	operation	NOUN
ejpam-3322	6	4	is	be	AUX
ejpam-3322	6	5	not	not	PART
ejpam-3322	6	6	associative	associative	ADJ
ejpam-3322	6	7	.	.	PUNCT
ejpam-3322	7	1	however	however	ADV
ejpam-3322	7	2	,	,	PUNCT
ejpam-3322	7	3	associativity	associativity	NOUN
ejpam-3322	7	4	can	can	AUX
ejpam-3322	7	5	be	be	AUX
ejpam-3322	7	6	obtained	obtain	VERB
ejpam-3322	7	7	by	by	ADP
ejpam-3322	7	8	a	a	DET
ejpam-3322	7	9	”	"	PUNCT
ejpam-3322	7	10	cocycle	cocycle	NOUN
ejpam-3322	7	11	”	"	PUNCT
ejpam-3322	7	12	τ	τ	X
ejpam-3322	7	13	:	:	PUNCT
ejpam-3322	7	14	m	m	VERB
ejpam-3322	7	15	×m	×m	NOUN
ejpam-3322	7	16	−→	−→	NOUN
ejpam-3322	7	17	g.	g.	NOUN
ejpam-3322	7	18	by	by	ADP
ejpam-3322	7	19	using	use	VERB
ejpam-3322	7	20	this	this	DET
ejpam-3322	7	21	cocycle	cocycle	NOUN
ejpam-3322	7	22	,	,	PUNCT
ejpam-3322	7	23	one	one	PRON
ejpam-3322	7	24	can	can	AUX
ejpam-3322	7	25	construct	construct	VERB
ejpam-3322	7	26	a	a	DET
ejpam-3322	7	27	non	non	ADJ
ejpam-3322	7	28	-	-	ADJ
ejpam-3322	7	29	trivial	trivial	ADJ
ejpam-3322	7	30	associator	associator	NOUN
ejpam-3322	7	31	for	for	ADP
ejpam-3322	7	32	a	a	DET
ejpam-3322	7	33	category	category	NOUN
ejpam-3322	7	34	c	c	NOUN
ejpam-3322	7	35	whose	whose	DET
ejpam-3322	7	36	objects	object	NOUN
ejpam-3322	7	37	are	be	AUX
ejpam-3322	7	38	the	the	DET
ejpam-3322	7	39	m	m	ADV
ejpam-3322	7	40	-graded	-grade	VERB
ejpam-3322	7	41	right	right	ADJ
ejpam-3322	7	42	representations	representation	NOUN
ejpam-3322	7	43	of	of	ADP
ejpam-3322	7	44	g.	g.	PROPN
ejpam-3322	7	45	every	every	DET
ejpam-3322	7	46	object	object	NOUN
ejpam-3322	7	47	in	in	ADP
ejpam-3322	7	48	this	this	DET
ejpam-3322	7	49	category	category	NOUN
ejpam-3322	7	50	has	have	VERB
ejpam-3322	7	51	a	a	DET
ejpam-3322	7	52	dual	dual	ADJ
ejpam-3322	7	53	.	.	PUNCT
ejpam-3322	8	1	consequently	consequently	ADV
ejpam-3322	8	2	,	,	PUNCT
ejpam-3322	8	3	it	it	PRON
ejpam-3322	8	4	is	be	AUX
ejpam-3322	8	5	possible	possible	ADJ
ejpam-3322	8	6	to	to	PART
ejpam-3322	8	7	define	define	VERB
ejpam-3322	8	8	an	an	DET
ejpam-3322	8	9	evaluation	evaluation	NOUN
ejpam-3322	8	10	and	and	CCONJ
ejpam-3322	8	11	a	a	DET
ejpam-3322	8	12	coevaluation	coevaluation	NOUN
ejpam-3322	8	13	maps	map	NOUN
ejpam-3322	8	14	to	to	PART
ejpam-3322	8	15	make	make	VERB
ejpam-3322	8	16	the	the	DET
ejpam-3322	8	17	category	category	NOUN
ejpam-3322	8	18	into	into	ADP
ejpam-3322	8	19	a	a	DET
ejpam-3322	8	20	rigid	rigid	ADJ
ejpam-3322	8	21	tensor	tensor	NOUN
ejpam-3322	8	22	category	category	NOUN
ejpam-3322	8	23	.	.	PUNCT
ejpam-3322	9	1	if	if	SCONJ
ejpam-3322	9	2	we	we	PRON
ejpam-3322	9	3	assume	assume	VERB
ejpam-3322	9	4	that	that	SCONJ
ejpam-3322	9	5	the	the	DET
ejpam-3322	9	6	binary	binary	PROPN
ejpam-3322	9	7	operation	operation	NOUN
ejpam-3322	9	8	on	on	ADP
ejpam-3322	9	9	m	m	PROPN
ejpam-3322	9	10	satisfies	satisfie	NOUN
ejpam-3322	9	11	the	the	DET
ejpam-3322	9	12	left	left	ADJ
ejpam-3322	9	13	division	division	NOUN
ejpam-3322	9	14	property	property	NOUN
ejpam-3322	9	15	,	,	PUNCT
ejpam-3322	9	16	then	then	ADV
ejpam-3322	9	17	the	the	DET
ejpam-3322	9	18	grading	grading	NOUN
ejpam-3322	9	19	and	and	CCONJ
ejpam-3322	9	20	group	group	NOUN
ejpam-3322	9	21	action	action	NOUN
ejpam-3322	9	22	can	can	AUX
ejpam-3322	9	23	be	be	AUX
ejpam-3322	9	24	combined	combine	VERB
ejpam-3322	9	25	into	into	ADP
ejpam-3322	9	26	the	the	DET
ejpam-3322	9	27	action	action	NOUN
ejpam-3322	9	28	of	of	ADP
ejpam-3322	9	29	an	an	DET
ejpam-3322	9	30	algebra	algebra	NOUN
ejpam-3322	9	31	a	a	PRON
ejpam-3322	9	32	on	on	ADP
ejpam-3322	9	33	the	the	DET
ejpam-3322	9	34	objects	object	NOUN
ejpam-3322	9	35	in	in	ADP
ejpam-3322	9	36	the	the	DET
ejpam-3322	9	37	category	category	NOUN
ejpam-3322	9	38	.	.	PUNCT
ejpam-3322	10	1	it	it	PRON
ejpam-3322	10	2	turns	turn	VERB
ejpam-3322	10	3	out	out	ADP
ejpam-3322	10	4	that	that	SCONJ
ejpam-3322	10	5	a	a	DET
ejpam-3322	10	6	itself	itself	PRON
ejpam-3322	10	7	is	be	AUX
ejpam-3322	10	8	in	in	ADP
ejpam-3322	10	9	c	c	NOUN
ejpam-3322	10	10	,	,	PUNCT
ejpam-3322	10	11	and	and	CCONJ
ejpam-3322	10	12	that	that	SCONJ
ejpam-3322	10	13	the	the	DET
ejpam-3322	10	14	multiplication	multiplication	NOUN
ejpam-3322	10	15	is	be	AUX
ejpam-3322	10	16	associative	associative	ADJ
ejpam-3322	10	17	.	.	PUNCT
ejpam-3322	11	1	it	it	PRON
ejpam-3322	11	2	is	be	AUX
ejpam-3322	11	3	well	well	ADV
ejpam-3322	11	4	known	know	VERB
ejpam-3322	11	5	that	that	SCONJ
ejpam-3322	11	6	for	for	ADP
ejpam-3322	11	7	every	every	DET
ejpam-3322	11	8	factorization	factorization	NOUN
ejpam-3322	11	9	x	x	PUNCT
ejpam-3322	12	1	=	=	PRON
ejpam-3322	12	2	gm	gm	PROPN
ejpam-3322	12	3	of	of	ADP
ejpam-3322	12	4	a	a	DET
ejpam-3322	12	5	group	group	NOUN
ejpam-3322	12	6	into	into	ADP
ejpam-3322	12	7	two	two	NUM
ejpam-3322	12	8	subgroups	subgroup	NOUN
ejpam-3322	12	9	g	g	PROPN
ejpam-3322	12	10	and	and	CCONJ
ejpam-3322	12	11	m	m	PROPN
ejpam-3322	12	12	,	,	PUNCT
ejpam-3322	12	13	a	a	DET
ejpam-3322	12	14	hopf	hopf	ADJ
ejpam-3322	12	15	algebra	algebra	NOUN
ejpam-3322	12	16	h	h	NOUN
ejpam-3322	13	1	=	=	SYM
ejpam-3322	13	2	kmbj	kmbj	PROPN
ejpam-3322	13	3	k(g	k(g	PROPN
ejpam-3322	13	4	)	)	PUNCT
ejpam-3322	13	5	can	can	AUX
ejpam-3322	13	6	be	be	AUX
ejpam-3322	13	7	constructed	construct	VERB
ejpam-3322	13	8	,	,	PUNCT
ejpam-3322	13	9	where	where	SCONJ
ejpam-3322	13	10	k	k	PROPN
ejpam-3322	13	11	is	be	AUX
ejpam-3322	13	12	a	a	DET
ejpam-3322	13	13	field	field	NOUN
ejpam-3322	13	14	,	,	PUNCT
ejpam-3322	13	15	km	km	PROPN
ejpam-3322	13	16	is	be	AUX
ejpam-3322	13	17	the	the	DET
ejpam-3322	13	18	group	group	NOUN
ejpam-3322	13	19	hopf	hopf	ADJ
ejpam-3322	13	20	algebra	algebra	NOUN
ejpam-3322	13	21	of	of	ADP
ejpam-3322	13	22	m	m	PROPN
ejpam-3322	13	23	and	and	CCONJ
ejpam-3322	13	24	k(g	k(g	PROPN
ejpam-3322	13	25	)	)	PUNCT
ejpam-3322	13	26	is	be	AUX
ejpam-3322	13	27	the	the	DET
ejpam-3322	13	28	hopf	hopf	ADJ
ejpam-3322	13	29	algebra	algebra	NOUN
ejpam-3322	13	30	functions	function	NOUN
ejpam-3322	13	31	on	on	ADP
ejpam-3322	13	32	g.	g.	PROPN
ejpam-3322	13	33	in	in	ADP
ejpam-3322	13	34	the	the	DET
ejpam-3322	13	35	symbol	symbol	NOUN
ejpam-3322	13	36	kmbj	kmbj	PROPN
ejpam-3322	13	37	k(g	k(g	PROPN
ejpam-3322	13	38	)	)	PUNCT
ejpam-3322	13	39	,	,	PUNCT
ejpam-3322	13	40	the	the	DET
ejpam-3322	13	41	b	b	NOUN
ejpam-3322	13	42	part	part	NOUN
ejpam-3322	13	43	means	mean	VERB
ejpam-3322	13	44	that	that	SCONJ
ejpam-3322	13	45	km	km	NOUN
ejpam-3322	13	46	acts	act	VERB
ejpam-3322	13	47	on	on	ADP
ejpam-3322	13	48	k(g	k(g	PROPN
ejpam-3322	13	49	)	)	PUNCT
ejpam-3322	13	50	,	,	PUNCT
ejpam-3322	13	51	and	and	CCONJ
ejpam-3322	13	52	the	the	DET
ejpam-3322	13	53	j	j	PROPN
ejpam-3322	13	54	part	part	NOUN
ejpam-3322	13	55	means	mean	VERB
ejpam-3322	13	56	that	that	SCONJ
ejpam-3322	13	57	k(g	k(g	NOUN
ejpam-3322	13	58	)	)	PUNCT
ejpam-3322	13	59	coacts	coact	NOUN
ejpam-3322	13	60	on	on	ADP
ejpam-3322	13	61	km	km	PROPN
ejpam-3322	13	62	,	,	PUNCT
ejpam-3322	13	63	[	[	X
ejpam-3322	13	64	3	3	NUM
ejpam-3322	13	65	]	]	PUNCT
ejpam-3322	13	66	.	.	PUNCT
ejpam-3322	14	1	moreover	moreover	ADV
ejpam-3322	14	2	,	,	PUNCT
ejpam-3322	14	3	if	if	SCONJ
ejpam-3322	14	4	a	a	PRON
ejpam-3322	14	5	is	be	AUX
ejpam-3322	14	6	an	an	DET
ejpam-3322	14	7	algebra	algebra	NOUN
ejpam-3322	14	8	(	(	PUNCT
ejpam-3322	14	9	resp	resp	NOUN
ejpam-3322	14	10	.	.	PUNCT
ejpam-3322	15	1	a	a	DET
ejpam-3322	15	2	coalgebra	coalgebra	NOUN
ejpam-3322	15	3	)	)	PUNCT
ejpam-3322	15	4	in	in	ADP
ejpam-3322	15	5	a	a	DET
ejpam-3322	15	6	rigid	rigid	ADJ
ejpam-3322	15	7	∗corresponding	∗corresponding	NOUN
ejpam-3322	15	8	author	author	NOUN
ejpam-3322	15	9	.	.	PUNCT
ejpam-3322	16	1	doi	doi	NOUN
ejpam-3322	16	2	:	:	PUNCT
ejpam-3322	16	3	https://doi.org/10.29020/nybg.ejpam.v11i4.3222	https://doi.org/10.29020/nybg.ejpam.v11i4.3222	ADJ
ejpam-3322	16	4	email	email	NOUN
ejpam-3322	16	5	addresses	address	VERB
ejpam-3322	16	6	:	:	PUNCT
ejpam-3322	16	7	b.s.alharbi@hotmail.com	b.s.alharbi@hotmail.com	X
ejpam-3322	16	8	(	(	PUNCT
ejpam-3322	16	9	b.	b.	PROPN
ejpam-3322	16	10	al	al	PROPN
ejpam-3322	16	11	-	-	PUNCT
ejpam-3322	16	12	harbi	harbi	PROPN
ejpam-3322	16	13	)	)	PUNCT
ejpam-3322	16	14	,	,	PUNCT
ejpam-3322	16	15	wfakieh@kau.edu.sa	wfakieh@kau.edu.sa	PROPN
ejpam-3322	16	16	(	(	PUNCT
ejpam-3322	16	17	w.	w.	PROPN
ejpam-3322	16	18	fakieh	fakieh	PROPN
ejpam-3322	16	19	)	)	PUNCT
ejpam-3322	16	20	,	,	PUNCT
ejpam-3322	16	21	malshomrani@hotmail.com	malshomrani@hotmail.com	X
ejpam-3322	16	22	(	(	PUNCT
ejpam-3322	16	23	m.	m.	PROPN
ejpam-3322	16	24	al	al	PROPN
ejpam-3322	16	25	-	-	PUNCT
ejpam-3322	16	26	shomrani	shomrani	PROPN
ejpam-3322	16	27	)	)	PUNCT
ejpam-3322	16	28	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3322	16	29	1027	1027	NUM
ejpam-3322	17	1	c	c	NOUN
ejpam-3322	17	2	©	©	PROPN
ejpam-3322	17	3	2018	2018	NUM
ejpam-3322	17	4	ejpam	ejpam	VERB
ejpam-3322	17	5	all	all	DET
ejpam-3322	17	6	rights	right	NOUN
ejpam-3322	17	7	reserved	reserve	VERB
ejpam-3322	17	8	.	.	PUNCT
ejpam-3322	18	1	b.	b.	PROPN
ejpam-3322	18	2	al	al	PROPN
ejpam-3322	18	3	-	-	PUNCT
ejpam-3322	18	4	harbi	harbi	PROPN
ejpam-3322	18	5	,	,	PUNCT
ejpam-3322	18	6	w.	w.	PROPN
ejpam-3322	18	7	m.	m.	PROPN
ejpam-3322	18	8	fakieh	fakieh	PROPN
ejpam-3322	18	9	,	,	PUNCT
ejpam-3322	18	10	m.	m.	NOUN
ejpam-3322	18	11	m.	m.	PROPN
ejpam-3322	18	12	al	al	PROPN
ejpam-3322	18	13	-	-	PUNCT
ejpam-3322	18	14	shomrani	shomrani	PROPN
ejpam-3322	18	15	/	/	SYM
ejpam-3322	18	16	eur	eur	NOUN
ejpam-3322	18	17	.	.	PUNCT
ejpam-3322	19	1	j.	j.	PROPN
ejpam-3322	19	2	pure	pure	PROPN
ejpam-3322	19	3	appl	appl	PROPN
ejpam-3322	19	4	.	.	PROPN
ejpam-3322	19	5	math	math	PROPN
ejpam-3322	19	6	,	,	PUNCT
ejpam-3322	19	7	11	11	NUM
ejpam-3322	19	8	(	(	PUNCT
ejpam-3322	19	9	4	4	NUM
ejpam-3322	19	10	)	)	PUNCT
ejpam-3322	19	11	(	(	PUNCT
ejpam-3322	19	12	2018	2018	NUM
ejpam-3322	19	13	)	)	PUNCT
ejpam-3322	19	14	,	,	PUNCT
ejpam-3322	19	15	1027	1027	NUM
ejpam-3322	19	16	-	-	SYM
ejpam-3322	19	17	1045	1045	NUM
ejpam-3322	19	18	1028	1028	NUM
ejpam-3322	19	19	tensor	tensor	NOUN
ejpam-3322	19	20	category	category	NOUN
ejpam-3322	19	21	,	,	PUNCT
ejpam-3322	19	22	then	then	ADV
ejpam-3322	19	23	its	its	PRON
ejpam-3322	19	24	dual	dual	ADJ
ejpam-3322	19	25	a∗	a∗	NOUN
ejpam-3322	19	26	is	be	AUX
ejpam-3322	19	27	a	a	DET
ejpam-3322	19	28	coalgebra	coalgebra	NOUN
ejpam-3322	19	29	(	(	PUNCT
ejpam-3322	19	30	resp	resp	NOUN
ejpam-3322	19	31	.	.	PUNCT
ejpam-3322	20	1	an	an	DET
ejpam-3322	20	2	algebra	algebra	NOUN
ejpam-3322	20	3	)	)	PUNCT
ejpam-3322	20	4	in	in	ADP
ejpam-3322	20	5	the	the	DET
ejpam-3322	20	6	same	same	ADJ
ejpam-3322	20	7	category	category	NOUN
ejpam-3322	20	8	.	.	PUNCT
ejpam-3322	21	1	in	in	ADP
ejpam-3322	21	2	[	[	X
ejpam-3322	21	3	1	1	NUM
ejpam-3322	21	4	]	]	PUNCT
ejpam-3322	21	5	,	,	PUNCT
ejpam-3322	21	6	al	al	PROPN
ejpam-3322	21	7	-	-	PUNCT
ejpam-3322	21	8	shomrani	shomrani	PROPN
ejpam-3322	21	9	reproved	reprove	VERB
ejpam-3322	21	10	this	this	DET
ejpam-3322	21	11	result	result	NOUN
ejpam-3322	21	12	by	by	ADP
ejpam-3322	21	13	using	use	VERB
ejpam-3322	21	14	specific	specific	ADJ
ejpam-3322	21	15	definitions	definition	NOUN
ejpam-3322	21	16	in	in	ADP
ejpam-3322	21	17	terms	term	NOUN
ejpam-3322	21	18	of	of	ADP
ejpam-3322	21	19	diagrams	diagram	NOUN
ejpam-3322	21	20	that	that	PRON
ejpam-3322	21	21	had	have	AUX
ejpam-3322	21	22	been	be	AUX
ejpam-3322	21	23	used	use	VERB
ejpam-3322	21	24	in	in	ADP
ejpam-3322	21	25	[	[	X
ejpam-3322	21	26	2	2	NUM
ejpam-3322	21	27	]	]	PUNCT
ejpam-3322	21	28	,	,	PUNCT
ejpam-3322	21	29	[	[	X
ejpam-3322	21	30	5	5	NUM
ejpam-3322	21	31	]	]	PUNCT
ejpam-3322	21	32	,	,	PUNCT
ejpam-3322	22	1	[	[	X
ejpam-3322	22	2	7]and	7]and	NOUN
ejpam-3322	22	3	[	[	X
ejpam-3322	22	4	8	8	NUM
ejpam-3322	22	5	]	]	PUNCT
ejpam-3322	22	6	.	.	PUNCT
ejpam-3322	23	1	in	in	ADP
ejpam-3322	23	2	this	this	DET
ejpam-3322	23	3	article	article	NOUN
ejpam-3322	23	4	we	we	PRON
ejpam-3322	23	5	obtain	obtain	VERB
ejpam-3322	23	6	mathematical	mathematical	ADJ
ejpam-3322	23	7	formulas	formula	NOUN
ejpam-3322	23	8	for	for	ADP
ejpam-3322	23	9	some	some	DET
ejpam-3322	23	10	operations	operation	NOUN
ejpam-3322	23	11	on	on	ADP
ejpam-3322	23	12	the	the	DET
ejpam-3322	23	13	objects	object	NOUN
ejpam-3322	23	14	of	of	ADP
ejpam-3322	23	15	a	a	DET
ejpam-3322	23	16	non	non	ADJ
ejpam-3322	23	17	-	-	ADJ
ejpam-3322	23	18	trivially	trivially	ADV
ejpam-3322	23	19	associated	associated	ADJ
ejpam-3322	23	20	tensor	tensor	NOUN
ejpam-3322	23	21	category	category	NOUN
ejpam-3322	23	22	constructed	construct	VERB
ejpam-3322	23	23	from	from	ADP
ejpam-3322	23	24	a	a	DET
ejpam-3322	23	25	factorization	factorization	NOUN
ejpam-3322	23	26	of	of	ADP
ejpam-3322	23	27	a	a	DET
ejpam-3322	23	28	group	group	NOUN
ejpam-3322	23	29	into	into	ADP
ejpam-3322	23	30	a	a	DET
ejpam-3322	23	31	subgroup	subgroup	NOUN
ejpam-3322	23	32	and	and	CCONJ
ejpam-3322	23	33	a	a	DET
ejpam-3322	23	34	set	set	NOUN
ejpam-3322	23	35	of	of	ADP
ejpam-3322	23	36	left	left	ADJ
ejpam-3322	23	37	coset	coset	NOUN
ejpam-3322	23	38	representatives	representative	NOUN
ejpam-3322	23	39	.	.	PUNCT
ejpam-3322	24	1	we	we	PRON
ejpam-3322	24	2	consider	consider	VERB
ejpam-3322	24	3	the	the	DET
ejpam-3322	24	4	same	same	ADJ
ejpam-3322	24	5	non	non	ADJ
ejpam-3322	24	6	-	-	ADJ
ejpam-3322	24	7	trivially	trivially	ADV
ejpam-3322	24	8	associated	associated	ADJ
ejpam-3322	24	9	tensor	tensor	NOUN
ejpam-3322	24	10	category	category	NOUN
ejpam-3322	24	11	c	c	NOUN
ejpam-3322	24	12	as	as	SCONJ
ejpam-3322	24	13	defined	define	VERB
ejpam-3322	24	14	in	in	ADP
ejpam-3322	24	15	[	[	X
ejpam-3322	24	16	4	4	NUM
ejpam-3322	24	17	]	]	PUNCT
ejpam-3322	24	18	.	.	PUNCT
ejpam-3322	25	1	throughout	throughout	ADP
ejpam-3322	25	2	this	this	DET
ejpam-3322	25	3	article	article	NOUN
ejpam-3322	25	4	,	,	PUNCT
ejpam-3322	25	5	we	we	PRON
ejpam-3322	25	6	use	use	VERB
ejpam-3322	25	7	the	the	DET
ejpam-3322	25	8	same	same	ADJ
ejpam-3322	25	9	formulas	formula	NOUN
ejpam-3322	25	10	and	and	CCONJ
ejpam-3322	25	11	ideas	idea	NOUN
ejpam-3322	25	12	from	from	ADP
ejpam-3322	25	13	[	[	X
ejpam-3322	25	14	4	4	X
ejpam-3322	25	15	]	]	PUNCT
ejpam-3322	25	16	which	which	PRON
ejpam-3322	25	17	is	be	AUX
ejpam-3322	25	18	itself	itself	PRON
ejpam-3322	25	19	based	base	VERB
ejpam-3322	25	20	on	on	ADP
ejpam-3322	25	21	[	[	X
ejpam-3322	25	22	3	3	NUM
ejpam-3322	25	23	]	]	PUNCT
ejpam-3322	25	24	,	,	PUNCT
ejpam-3322	25	25	[	[	X
ejpam-3322	25	26	5	5	NUM
ejpam-3322	25	27	]	]	PUNCT
ejpam-3322	25	28	and	and	CCONJ
ejpam-3322	25	29	[	[	X
ejpam-3322	25	30	6	6	NUM
ejpam-3322	25	31	]	]	PUNCT
ejpam-3322	25	32	,	,	PUNCT
ejpam-3322	25	33	but	but	CCONJ
ejpam-3322	25	34	is	be	AUX
ejpam-3322	25	35	mostly	mostly	ADV
ejpam-3322	25	36	self	self	NOUN
ejpam-3322	25	37	-	-	PUNCT
ejpam-3322	25	38	contained	contain	VERB
ejpam-3322	25	39	in	in	ADP
ejpam-3322	25	40	terms	term	NOUN
ejpam-3322	25	41	of	of	ADP
ejpam-3322	25	42	notation	notation	NOUN
ejpam-3322	25	43	and	and	CCONJ
ejpam-3322	25	44	definitions	definition	NOUN
ejpam-3322	25	45	.	.	PUNCT
ejpam-3322	26	1	in	in	ADP
ejpam-3322	26	2	addition	addition	NOUN
ejpam-3322	26	3	,	,	PUNCT
ejpam-3322	26	4	we	we	PRON
ejpam-3322	26	5	assume	assume	VERB
ejpam-3322	26	6	that	that	SCONJ
ejpam-3322	26	7	all	all	DET
ejpam-3322	26	8	groups	group	NOUN
ejpam-3322	26	9	mentioned	mention	VERB
ejpam-3322	26	10	,	,	PUNCT
ejpam-3322	26	11	unless	unless	SCONJ
ejpam-3322	26	12	otherwise	otherwise	ADV
ejpam-3322	26	13	stated	state	VERB
ejpam-3322	26	14	,	,	PUNCT
ejpam-3322	26	15	are	be	AUX
ejpam-3322	26	16	finite	finite	ADJ
ejpam-3322	26	17	,	,	PUNCT
ejpam-3322	26	18	and	and	CCONJ
ejpam-3322	26	19	that	that	SCONJ
ejpam-3322	26	20	all	all	DET
ejpam-3322	26	21	vector	vector	NOUN
ejpam-3322	26	22	spaces	space	NOUN
ejpam-3322	26	23	are	be	AUX
ejpam-3322	26	24	finite	finite	ADJ
ejpam-3322	26	25	dimensional	dimensional	ADJ
ejpam-3322	26	26	over	over	ADP
ejpam-3322	26	27	a	a	DET
ejpam-3322	26	28	field	field	NOUN
ejpam-3322	26	29	k	k	NOUN
ejpam-3322	26	30	,	,	PUNCT
ejpam-3322	26	31	which	which	PRON
ejpam-3322	26	32	will	will	AUX
ejpam-3322	26	33	be	be	AUX
ejpam-3322	26	34	denoted	denote	VERB
ejpam-3322	26	35	by	by	ADP
ejpam-3322	26	36	1	1	NUM
ejpam-3322	26	37	as	as	ADP
ejpam-3322	26	38	an	an	DET
ejpam-3322	26	39	object	object	NOUN
ejpam-3322	26	40	in	in	ADP
ejpam-3322	26	41	the	the	DET
ejpam-3322	26	42	category	category	NOUN
ejpam-3322	26	43	.	.	PUNCT
ejpam-3322	27	1	moreover	moreover	ADV
ejpam-3322	27	2	we	we	PRON
ejpam-3322	27	3	are	be	AUX
ejpam-3322	27	4	going	go	VERB
ejpam-3322	27	5	to	to	PART
ejpam-3322	27	6	restrict	restrict	VERB
ejpam-3322	27	7	ourselves	ourselves	PRON
ejpam-3322	27	8	to	to	ADP
ejpam-3322	27	9	the	the	DET
ejpam-3322	27	10	finite	finite	ADJ
ejpam-3322	27	11	case	case	NOUN
ejpam-3322	27	12	of	of	ADP
ejpam-3322	27	13	algebras	algebras	PROPN
ejpam-3322	27	14	,	,	PUNCT
ejpam-3322	27	15	coalgebras	coalgebra	NOUN
ejpam-3322	27	16	and	and	CCONJ
ejpam-3322	27	17	hopf	hopf	ADJ
ejpam-3322	27	18	algebras	algebra	NOUN
ejpam-3322	27	19	although	although	SCONJ
ejpam-3322	27	20	many	many	ADJ
ejpam-3322	27	21	results	result	NOUN
ejpam-3322	27	22	are	be	AUX
ejpam-3322	27	23	still	still	ADV
ejpam-3322	27	24	true	true	ADJ
ejpam-3322	27	25	in	in	ADP
ejpam-3322	27	26	the	the	DET
ejpam-3322	27	27	infinite	infinite	ADJ
ejpam-3322	27	28	case	case	NOUN
ejpam-3322	27	29	(	(	PUNCT
ejpam-3322	27	30	see	see	VERB
ejpam-3322	27	31	[	[	X
ejpam-3322	27	32	10	10	NUM
ejpam-3322	27	33	]	]	NUM
ejpam-3322	27	34	)	)	PUNCT
ejpam-3322	27	35	.	.	PUNCT
ejpam-3322	28	1	2	2	X
ejpam-3322	28	2	.	.	X
ejpam-3322	28	3	preliminaries	preliminary	NOUN
ejpam-3322	28	4	in	in	ADP
ejpam-3322	28	5	this	this	DET
ejpam-3322	28	6	section	section	NOUN
ejpam-3322	28	7	,	,	PUNCT
ejpam-3322	28	8	we	we	PRON
ejpam-3322	28	9	include	include	VERB
ejpam-3322	28	10	some	some	DET
ejpam-3322	28	11	definitions	definition	NOUN
ejpam-3322	28	12	and	and	CCONJ
ejpam-3322	28	13	results	result	NOUN
ejpam-3322	28	14	that	that	PRON
ejpam-3322	28	15	will	will	AUX
ejpam-3322	28	16	be	be	AUX
ejpam-3322	28	17	used	use	VERB
ejpam-3322	28	18	later	later	ADV
ejpam-3322	28	19	in	in	ADP
ejpam-3322	28	20	this	this	DET
ejpam-3322	28	21	article	article	NOUN
ejpam-3322	28	22	.	.	PUNCT
ejpam-3322	29	1	definition	definition	NOUN
ejpam-3322	29	2	2.1	2.1	NUM
ejpam-3322	29	3	.	.	PUNCT
ejpam-3322	30	1	[	[	X
ejpam-3322	30	2	11	11	NUM
ejpam-3322	30	3	]	]	PUNCT
ejpam-3322	30	4	a	a	DET
ejpam-3322	30	5	k	k	X
ejpam-3322	30	6	-	-	NOUN
ejpam-3322	30	7	algebra	algebra	NOUN
ejpam-3322	30	8	is	be	AUX
ejpam-3322	30	9	a	a	DET
ejpam-3322	30	10	triple	triple	ADJ
ejpam-3322	30	11	(	(	PUNCT
ejpam-3322	30	12	a,µa	a,µa	PROPN
ejpam-3322	30	13	,	,	PUNCT
ejpam-3322	30	14	ηa	ηa	ADV
ejpam-3322	30	15	)	)	PUNCT
ejpam-3322	30	16	consisting	consist	VERB
ejpam-3322	30	17	of	of	ADP
ejpam-3322	30	18	a	a	DET
ejpam-3322	30	19	vector	vector	NOUN
ejpam-3322	30	20	space	space	NOUN
ejpam-3322	30	21	a	a	PRON
ejpam-3322	30	22	over	over	ADP
ejpam-3322	30	23	a	a	DET
ejpam-3322	30	24	field	field	NOUN
ejpam-3322	30	25	k	k	PROPN
ejpam-3322	30	26	and	and	CCONJ
ejpam-3322	30	27	k	k	ADJ
ejpam-3322	30	28	-	-	PUNCT
ejpam-3322	30	29	linear	linear	ADJ
ejpam-3322	30	30	maps	map	NOUN
ejpam-3322	30	31	µa	µa	NOUN
ejpam-3322	30	32	:	:	PUNCT
ejpam-3322	30	33	a	a	DET
ejpam-3322	30	34	⊗	⊗	NOUN
ejpam-3322	30	35	a	a	DET
ejpam-3322	30	36	−→	−→	NOUN
ejpam-3322	30	37	a	a	PRON
ejpam-3322	31	1	and	and	CCONJ
ejpam-3322	31	2	ηa	ηa	INTJ
ejpam-3322	31	3	:	:	PUNCT
ejpam-3322	32	1	k	k	X
ejpam-3322	32	2	−→	−→	ADV
ejpam-3322	32	3	a	a	DET
ejpam-3322	32	4	such	such	ADJ
ejpam-3322	32	5	that	that	SCONJ
ejpam-3322	32	6	the	the	DET
ejpam-3322	32	7	following	follow	VERB
ejpam-3322	32	8	diagrams	diagram	NOUN
ejpam-3322	32	9	commute	commute	NOUN
ejpam-3322	32	10	:	:	PUNCT
ejpam-3322	32	11	−−−−−−−→	−−−−−−−→	X
ejpam-3322	32	12	−−−−−−−−→	−−−−−−−−→	X
ejpam-3322	32	13	y	y	VERB
ejpam-3322	32	14	y	y	NOUN
ejpam-3322	32	15	k	k	PROPN
ejpam-3322	32	16	⊗a	⊗a	PROPN
ejpam-3322	32	17	a⊗a	a⊗a	NOUN
ejpam-3322	32	18	a	a	PRON
ejpam-3322	32	19	a	a	DET
ejpam-3322	32	20	ηa	ηa	NOUN
ejpam-3322	32	21	⊗	⊗	PROPN
ejpam-3322	32	22	ia	ia	PROPN
ejpam-3322	32	23	ia	ia	PROPN
ejpam-3322	32	24	∼=	∼=	PROPN
ejpam-3322	32	25	µa	µa	ADP
ejpam-3322	32	26	←−−−−−−−−	←−−−−−−−−	PROPN
ejpam-3322	32	27	←−−−−−−−−−	←−−−−−−−−−	PROPN
ejpam-3322	32	28	a⊗k	a⊗k	PROPN
ejpam-3322	32	29	a	a	DET
ejpam-3322	32	30	ia	ia	PROPN
ejpam-3322	32	31	⊗	⊗	PROPN
ejpam-3322	32	32	ηa	ηa	PROPN
ejpam-3322	32	33	ia	ia	PROPN
ejpam-3322	32	34	y∼=	y∼=	ADP
ejpam-3322	32	35	−−−−−−→	−−−−−−→	PROPN
ejpam-3322	32	36	−−−−−−−→	−−−−−−−→	X
ejpam-3322	32	37	y	y	PROPN
ejpam-3322	32	38	y	y	NOUN
ejpam-3322	32	39	a⊗a⊗a	a⊗a⊗a	NOUN
ejpam-3322	32	40	a⊗a	a⊗a	NOUN
ejpam-3322	32	41	a⊗a	a⊗a	NOUN
ejpam-3322	32	42	a	a	DET
ejpam-3322	32	43	µa	µa	NOUN
ejpam-3322	32	44	⊗	⊗	PROPN
ejpam-3322	32	45	ia	ia	PROPN
ejpam-3322	32	46	µa	µa	PROPN
ejpam-3322	32	47	ia	ia	PROPN
ejpam-3322	32	48	⊗	⊗	PROPN
ejpam-3322	32	49	µa	µa	PROPN
ejpam-3322	32	50	µa	µa	ADP
ejpam-3322	32	51	figure	figure	NOUN
ejpam-3322	32	52	1	1	NUM
ejpam-3322	32	53	:	:	PUNCT
ejpam-3322	32	54	unit	unit	NOUN
ejpam-3322	32	55	and	and	CCONJ
ejpam-3322	32	56	the	the	DET
ejpam-3322	32	57	associative	associative	ADJ
ejpam-3322	32	58	property	property	NOUN
ejpam-3322	32	59	on	on	ADP
ejpam-3322	32	60	a.	a.	NOUN
ejpam-3322	32	61	here	here	ADV
ejpam-3322	32	62	the	the	DET
ejpam-3322	32	63	map	map	NOUN
ejpam-3322	32	64	ia	ia	PROPN
ejpam-3322	32	65	:	:	PUNCT
ejpam-3322	32	66	a	a	DET
ejpam-3322	32	67	−→	−→	NOUN
ejpam-3322	32	68	a	a	PRON
ejpam-3322	32	69	is	be	AUX
ejpam-3322	32	70	the	the	DET
ejpam-3322	32	71	identity	identity	NOUN
ejpam-3322	32	72	map	map	NOUN
ejpam-3322	32	73	and	and	CCONJ
ejpam-3322	32	74	the	the	DET
ejpam-3322	32	75	maps	map	NOUN
ejpam-3322	32	76	ia⊗µa	ia⊗µa	NOUN
ejpam-3322	32	77	:	:	PUNCT
ejpam-3322	32	78	a⊗a⊗a	a⊗a⊗a	ADJ
ejpam-3322	32	79	−→	−→	NOUN
ejpam-3322	32	80	a⊗a	a⊗a	NOUN
ejpam-3322	32	81	and	and	CCONJ
ejpam-3322	32	82	µa	µa	ADP
ejpam-3322	32	83	⊗	⊗	PROPN
ejpam-3322	32	84	ia	ia	PROPN
ejpam-3322	32	85	:	:	PUNCT
ejpam-3322	32	86	a⊗a⊗a	a⊗a⊗a	ADJ
ejpam-3322	32	87	−→	−→	ADJ
ejpam-3322	32	88	a⊗a	a⊗a	NOUN
ejpam-3322	32	89	are	be	AUX
ejpam-3322	32	90	defined	define	VERB
ejpam-3322	32	91	by	by	ADP
ejpam-3322	32	92	a⊗	a⊗	PROPN
ejpam-3322	32	93	b⊗	b⊗	NOUN
ejpam-3322	32	94	c	c	PROPN
ejpam-3322	32	95	7−→	7−→	PROPN
ejpam-3322	32	96	a⊗	a⊗	NOUN
ejpam-3322	32	97	µa(b⊗	µa(b⊗	ADP
ejpam-3322	32	98	c	c	X
ejpam-3322	32	99	)	)	PUNCT
ejpam-3322	32	100	and	and	CCONJ
ejpam-3322	32	101	a⊗	a⊗	NOUN
ejpam-3322	32	102	b⊗	b⊗	NOUN
ejpam-3322	32	103	c	c	PROPN
ejpam-3322	32	104	7−→	7−→	PROPN
ejpam-3322	32	105	µa(a⊗	µa(a⊗	PROPN
ejpam-3322	32	106	b)⊗	b)⊗	PROPN
ejpam-3322	32	107	c	c	PROPN
ejpam-3322	32	108	,	,	PUNCT
ejpam-3322	32	109	respectively	respectively	ADV
ejpam-3322	32	110	,	,	PUNCT
ejpam-3322	32	111	for	for	ADP
ejpam-3322	32	112	all	all	DET
ejpam-3322	32	113	a	a	DET
ejpam-3322	32	114	,	,	PUNCT
ejpam-3322	32	115	b	b	NOUN
ejpam-3322	32	116	,	,	PUNCT
ejpam-3322	32	117	c	c	PROPN
ejpam-3322	32	118	∈	∈	PROPN
ejpam-3322	32	119	a.	a.	NOUN
ejpam-3322	32	120	the	the	DET
ejpam-3322	32	121	maps	map	NOUN
ejpam-3322	32	122	ia⊗	ia⊗	NOUN
ejpam-3322	32	123	ηa	ηa	PROPN
ejpam-3322	32	124	,	,	PUNCT
ejpam-3322	32	125	ηa⊗	ηa⊗	PROPN
ejpam-3322	32	126	ia	ia	NOUN
ejpam-3322	32	127	are	be	AUX
ejpam-3322	32	128	defined	define	VERB
ejpam-3322	32	129	by	by	ADP
ejpam-3322	32	130	a⊗k	a⊗k	PROPN
ejpam-3322	32	131	7−→	7−→	PROPN
ejpam-3322	32	132	a⊗ηa(k	a⊗ηa(k	PROPN
ejpam-3322	32	133	)	)	PUNCT
ejpam-3322	32	134	,	,	PUNCT
ejpam-3322	32	135	k⊗a	k⊗a	VERB
ejpam-3322	32	136	7−→	7−→	NOUN
ejpam-3322	32	137	ηa(k)⊗a	ηa(k)⊗a	NOUN
ejpam-3322	32	138	for	for	ADP
ejpam-3322	32	139	all	all	DET
ejpam-3322	32	140	k	k	PROPN
ejpam-3322	32	141	∈	∈	PROPN
ejpam-3322	32	142	k	k	PROPN
ejpam-3322	32	143	,	,	PUNCT
ejpam-3322	32	144	a	a	DET
ejpam-3322	32	145	∈	∈	PROPN
ejpam-3322	32	146	a	a	PRON
ejpam-3322	32	147	,	,	PUNCT
ejpam-3322	32	148	respectively	respectively	ADV
ejpam-3322	32	149	.	.	PUNCT
ejpam-3322	33	1	these	these	DET
ejpam-3322	33	2	commuted	commute	VERB
ejpam-3322	33	3	diagrams	diagram	NOUN
ejpam-3322	33	4	can	can	AUX
ejpam-3322	33	5	be	be	AUX
ejpam-3322	33	6	represented	represent	VERB
ejpam-3322	33	7	in	in	ADP
ejpam-3322	33	8	terms	term	NOUN
ejpam-3322	33	9	of	of	ADP
ejpam-3322	33	10	equations	equation	NOUN
ejpam-3322	33	11	as	as	SCONJ
ejpam-3322	33	12	follows	follow	VERB
ejpam-3322	33	13	for	for	ADP
ejpam-3322	33	14	all	all	DET
ejpam-3322	33	15	k	k	PROPN
ejpam-3322	33	16	∈	∈	PROPN
ejpam-3322	33	17	k	k	PROPN
ejpam-3322	33	18	and	and	CCONJ
ejpam-3322	33	19	a	a	DET
ejpam-3322	33	20	,	,	PUNCT
ejpam-3322	33	21	b	b	NOUN
ejpam-3322	33	22	,	,	PUNCT
ejpam-3322	33	23	c	c	PROPN
ejpam-3322	33	24	∈	∈	PROPN
ejpam-3322	33	25	a	a	DET
ejpam-3322	33	26	:	:	PUNCT
ejpam-3322	33	27	µa(ia	µa(ia	PROPN
ejpam-3322	33	28	⊗	⊗	ADJ
ejpam-3322	33	29	µa)(a⊗	µa)(a⊗	PROPN
ejpam-3322	33	30	b⊗	b⊗	NOUN
ejpam-3322	33	31	c	c	NOUN
ejpam-3322	33	32	)	)	PUNCT
ejpam-3322	34	1	=	=	PUNCT
ejpam-3322	34	2	µa(µa	µa(µa	VERB
ejpam-3322	34	3	⊗	⊗	PROPN
ejpam-3322	34	4	ia)(a⊗	ia)(a⊗	PROPN
ejpam-3322	34	5	b⊗	b⊗	NOUN
ejpam-3322	34	6	c	c	X
ejpam-3322	34	7	)	)	PUNCT
ejpam-3322	34	8	(	(	PUNCT
ejpam-3322	34	9	1	1	X
ejpam-3322	34	10	)	)	PUNCT
ejpam-3322	34	11	b.	b.	PROPN
ejpam-3322	34	12	al	al	PROPN
ejpam-3322	34	13	-	-	PUNCT
ejpam-3322	34	14	harbi	harbi	PROPN
ejpam-3322	34	15	,	,	PUNCT
ejpam-3322	34	16	w.	w.	PROPN
ejpam-3322	34	17	m.	m.	PROPN
ejpam-3322	34	18	fakieh	fakieh	PROPN
ejpam-3322	34	19	,	,	PUNCT
ejpam-3322	34	20	m.	m.	NOUN
ejpam-3322	34	21	m.	m.	PROPN
ejpam-3322	34	22	al	al	PROPN
ejpam-3322	34	23	-	-	PUNCT
ejpam-3322	34	24	shomrani	shomrani	PROPN
ejpam-3322	34	25	/	/	SYM
ejpam-3322	34	26	eur	eur	NOUN
ejpam-3322	34	27	.	.	PUNCT
ejpam-3322	35	1	j.	j.	PROPN
ejpam-3322	35	2	pure	pure	PROPN
ejpam-3322	35	3	appl	appl	PROPN
ejpam-3322	35	4	.	.	PROPN
ejpam-3322	35	5	math	math	PROPN
ejpam-3322	35	6	,	,	PUNCT
ejpam-3322	35	7	11	11	NUM
ejpam-3322	35	8	(	(	PUNCT
ejpam-3322	35	9	4	4	NUM
ejpam-3322	35	10	)	)	PUNCT
ejpam-3322	35	11	(	(	PUNCT
ejpam-3322	35	12	2018	2018	NUM
ejpam-3322	35	13	)	)	PUNCT
ejpam-3322	35	14	,	,	PUNCT
ejpam-3322	35	15	1027	1027	NUM
ejpam-3322	35	16	-	-	SYM
ejpam-3322	35	17	1045	1045	NUM
ejpam-3322	35	18	1029	1029	NUM
ejpam-3322	35	19	and	and	CCONJ
ejpam-3322	35	20	µa(ia	µa(ia	PROPN
ejpam-3322	35	21	⊗	⊗	PROPN
ejpam-3322	35	22	ηa)(a⊗	ηa)(a⊗	PROPN
ejpam-3322	35	23	k	k	NOUN
ejpam-3322	35	24	)	)	PUNCT
ejpam-3322	35	25	=	=	PUNCT
ejpam-3322	35	26	ka	ka	PROPN
ejpam-3322	36	1	=	=	PUNCT
ejpam-3322	36	2	µa(ηa	µa(ηa	PROPN
ejpam-3322	36	3	⊗	⊗	ADJ
ejpam-3322	36	4	ia)(k	ia)(k	PROPN
ejpam-3322	37	1	⊗	⊗	PROPN
ejpam-3322	37	2	a	a	NOUN
ejpam-3322	37	3	)	)	PUNCT
ejpam-3322	37	4	(	(	PUNCT
ejpam-3322	37	5	2	2	X
ejpam-3322	37	6	)	)	PUNCT
ejpam-3322	37	7	the	the	DET
ejpam-3322	37	8	map	map	NOUN
ejpam-3322	37	9	µa	µa	NOUN
ejpam-3322	37	10	is	be	AUX
ejpam-3322	37	11	the	the	DET
ejpam-3322	37	12	multiplication	multiplication	NOUN
ejpam-3322	37	13	map	map	NOUN
ejpam-3322	37	14	and	and	CCONJ
ejpam-3322	37	15	ηa	ηa	PRON
ejpam-3322	37	16	is	be	AUX
ejpam-3322	37	17	the	the	DET
ejpam-3322	37	18	unit	unit	NOUN
ejpam-3322	37	19	map	map	NOUN
ejpam-3322	37	20	.	.	PUNCT
ejpam-3322	38	1	the	the	DET
ejpam-3322	38	2	associative	associative	ADJ
ejpam-3322	38	3	property	property	NOUN
ejpam-3322	38	4	follows	follow	VERB
ejpam-3322	38	5	from	from	ADP
ejpam-3322	38	6	(	(	PUNCT
ejpam-3322	38	7	1	1	NUM
ejpam-3322	38	8	)	)	PUNCT
ejpam-3322	38	9	and	and	CCONJ
ejpam-3322	38	10	the	the	DET
ejpam-3322	38	11	unit	unit	NOUN
ejpam-3322	38	12	property	property	NOUN
ejpam-3322	38	13	follows	follow	VERB
ejpam-3322	38	14	from	from	ADP
ejpam-3322	38	15	(	(	PUNCT
ejpam-3322	38	16	2	2	NUM
ejpam-3322	38	17	)	)	PUNCT
ejpam-3322	38	18	.	.	PUNCT
ejpam-3322	39	1	we	we	PRON
ejpam-3322	39	2	say	say	VERB
ejpam-3322	39	3	that	that	SCONJ
ejpam-3322	39	4	the	the	DET
ejpam-3322	39	5	k	k	NOUN
ejpam-3322	39	6	-	-	NOUN
ejpam-3322	39	7	algebra	algebra	NOUN
ejpam-3322	39	8	a	a	PRON
ejpam-3322	39	9	is	be	AUX
ejpam-3322	39	10	commutative	commutative	ADJ
ejpam-3322	39	11	if	if	SCONJ
ejpam-3322	39	12	µaτ	µaτ	PROPN
ejpam-3322	39	13	=	=	SYM
ejpam-3322	39	14	µa	µa	NOUN
ejpam-3322	39	15	,	,	PUNCT
ejpam-3322	39	16	where	where	SCONJ
ejpam-3322	39	17	τ	τ	PROPN
ejpam-3322	39	18	is	be	AUX
ejpam-3322	39	19	the	the	DET
ejpam-3322	39	20	twist	twist	NOUN
ejpam-3322	39	21	map	map	NOUN
ejpam-3322	39	22	which	which	PRON
ejpam-3322	39	23	is	be	AUX
ejpam-3322	39	24	defined	define	VERB
ejpam-3322	39	25	by	by	ADP
ejpam-3322	39	26	τ(a⊗	τ(a⊗	PROPN
ejpam-3322	39	27	b	b	PROPN
ejpam-3322	39	28	)	)	PUNCT
ejpam-3322	39	29	=	=	NOUN
ejpam-3322	39	30	b⊗	b⊗	NOUN
ejpam-3322	39	31	a	a	PRON
ejpam-3322	39	32	for	for	ADP
ejpam-3322	39	33	a	a	DET
ejpam-3322	39	34	,	,	PUNCT
ejpam-3322	39	35	b	b	X
ejpam-3322	39	36	∈	∈	PROPN
ejpam-3322	39	37	a.	a.	NOUN
ejpam-3322	39	38	definition	definition	NOUN
ejpam-3322	39	39	2.2	2.2	NUM
ejpam-3322	39	40	.	.	PUNCT
ejpam-3322	40	1	[	[	X
ejpam-3322	40	2	11	11	NUM
ejpam-3322	40	3	]	]	PUNCT
ejpam-3322	40	4	a	a	PRON
ejpam-3322	40	5	k	k	NOUN
ejpam-3322	40	6	-	-	NOUN
ejpam-3322	40	7	coalgebra	coalgebra	NOUN
ejpam-3322	40	8	is	be	AUX
ejpam-3322	40	9	a	a	DET
ejpam-3322	40	10	triple	triple	ADJ
ejpam-3322	40	11	(	(	PUNCT
ejpam-3322	40	12	c,∆c	c,∆c	NOUN
ejpam-3322	40	13	,	,	PUNCT
ejpam-3322	40	14	εc	εc	NOUN
ejpam-3322	40	15	)	)	PUNCT
ejpam-3322	40	16	consisting	consist	VERB
ejpam-3322	40	17	of	of	ADP
ejpam-3322	40	18	a	a	DET
ejpam-3322	40	19	vector	vector	NOUN
ejpam-3322	40	20	space	space	NOUN
ejpam-3322	40	21	c	c	NOUN
ejpam-3322	40	22	over	over	ADP
ejpam-3322	40	23	a	a	DET
ejpam-3322	40	24	field	field	NOUN
ejpam-3322	40	25	k	k	PROPN
ejpam-3322	40	26	and	and	CCONJ
ejpam-3322	40	27	k	k	ADJ
ejpam-3322	40	28	-	-	PUNCT
ejpam-3322	40	29	linear	linear	ADJ
ejpam-3322	40	30	maps	map	NOUN
ejpam-3322	41	1	∆c	∆c	NOUN
ejpam-3322	41	2	:	:	PUNCT
ejpam-3322	41	3	c	c	X
ejpam-3322	42	1	−→	−→	NOUN
ejpam-3322	42	2	c	c	PROPN
ejpam-3322	42	3	⊗	⊗	PROPN
ejpam-3322	42	4	c	c	PROPN
ejpam-3322	42	5	and	and	CCONJ
ejpam-3322	42	6	εc	εc	INTJ
ejpam-3322	42	7	:	:	PUNCT
ejpam-3322	42	8	c	c	VERB
ejpam-3322	42	9	−→	−→	ADV
ejpam-3322	43	1	k	k	INTJ
ejpam-3322	43	2	such	such	ADJ
ejpam-3322	43	3	that	that	SCONJ
ejpam-3322	43	4	the	the	DET
ejpam-3322	43	5	following	follow	VERB
ejpam-3322	43	6	diagrams	diagram	NOUN
ejpam-3322	43	7	commute	commute	NOUN
ejpam-3322	43	8	:	:	PUNCT
ejpam-3322	44	1	←−−−−−−−	←−−−−−−−	PROPN
ejpam-3322	44	2	←−−−−−−−−	←−−−−−−−−	PROPN
ejpam-3322	44	3	x	x	PROPN
ejpam-3322	44	4	x	x	PROPN
ejpam-3322	45	1	k	k	PROPN
ejpam-3322	46	1	⊗	⊗	PROPN
ejpam-3322	46	2	c	c	PROPN
ejpam-3322	47	1	c	c	PROPN
ejpam-3322	48	1	⊗	⊗	PROPN
ejpam-3322	48	2	c	c	PROPN
ejpam-3322	49	1	c	c	NOUN
ejpam-3322	49	2	c	c	NOUN
ejpam-3322	50	1	εc	εc	NOUN
ejpam-3322	50	2	⊗	⊗	PROPN
ejpam-3322	50	3	ic	ic	PROPN
ejpam-3322	51	1	ic	ic	NUM
ejpam-3322	51	2	1⊗−	1⊗−	NUM
ejpam-3322	51	3	∆c	∆c	PROPN
ejpam-3322	51	4	−−−−−−−−→	−−−−−−−−→	NOUN
ejpam-3322	51	5	−−−−−−−−−→	−−−−−−−−−→	X
ejpam-3322	51	6	c	c	NOUN
ejpam-3322	52	1	⊗	⊗	PROPN
ejpam-3322	52	2	k	k	PROPN
ejpam-3322	53	1	c	c	PROPN
ejpam-3322	53	2	ic	ic	PROPN
ejpam-3322	54	1	⊗	⊗	PROPN
ejpam-3322	54	2	εc	εc	PROPN
ejpam-3322	54	3	ic	ic	PROPN
ejpam-3322	54	4	x−⊗	x−⊗	PROPN
ejpam-3322	54	5	1	1	NUM
ejpam-3322	54	6	←−−−−−	←−−−−−	PROPN
ejpam-3322	54	7	←−−−−−−−	←−−−−−−−	PROPN
ejpam-3322	54	8	x	x	PROPN
ejpam-3322	55	1	x	x	PROPN
ejpam-3322	56	1	c	c	PROPN
ejpam-3322	57	1	⊗	⊗	PROPN
ejpam-3322	57	2	c	c	PROPN
ejpam-3322	58	1	⊗	⊗	PROPN
ejpam-3322	59	1	c	c	PROPN
ejpam-3322	59	2	c	c	PROPN
ejpam-3322	60	1	⊗	⊗	PROPN
ejpam-3322	60	2	c	c	PROPN
ejpam-3322	61	1	c	c	PROPN
ejpam-3322	62	1	⊗	⊗	PROPN
ejpam-3322	62	2	c	c	PROPN
ejpam-3322	62	3	c	c	PROPN
ejpam-3322	63	1	∆c	∆c	NOUN
ejpam-3322	63	2	⊗	⊗	PROPN
ejpam-3322	63	3	ic	ic	PROPN
ejpam-3322	64	1	∆c	∆c	NOUN
ejpam-3322	64	2	ic	ic	PROPN
ejpam-3322	64	3	⊗∆c	⊗∆c	PROPN
ejpam-3322	64	4	∆c	∆c	PROPN
ejpam-3322	64	5	figure	figure	NOUN
ejpam-3322	64	6	2	2	NUM
ejpam-3322	64	7	:	:	PUNCT
ejpam-3322	64	8	counit	counit	VERB
ejpam-3322	64	9	and	and	CCONJ
ejpam-3322	64	10	the	the	DET
ejpam-3322	64	11	coassociative	coassociative	ADJ
ejpam-3322	64	12	property	property	NOUN
ejpam-3322	64	13	on	on	ADP
ejpam-3322	64	14	c.	c.	PROPN
ejpam-3322	64	15	here	here	ADV
ejpam-3322	64	16	the	the	DET
ejpam-3322	64	17	map	map	NOUN
ejpam-3322	65	1	ic	ic	INTJ
ejpam-3322	65	2	:	:	PUNCT
ejpam-3322	65	3	c	c	AUX
ejpam-3322	65	4	−→	−→	NOUN
ejpam-3322	65	5	c	c	PROPN
ejpam-3322	65	6	is	be	AUX
ejpam-3322	65	7	the	the	DET
ejpam-3322	65	8	the	the	DET
ejpam-3322	65	9	identity	identity	NOUN
ejpam-3322	65	10	map	map	NOUN
ejpam-3322	65	11	on	on	ADP
ejpam-3322	65	12	c.	c.	PROPN
ejpam-3322	65	13	also	also	ADV
ejpam-3322	65	14	,	,	PUNCT
ejpam-3322	65	15	the	the	DET
ejpam-3322	65	16	maps	map	NOUN
ejpam-3322	65	17	ic	ic	PROPN
ejpam-3322	65	18	⊗∆c	⊗∆c	NOUN
ejpam-3322	65	19	:	:	PUNCT
ejpam-3322	65	20	c⊗c	c⊗c	PROPN
ejpam-3322	65	21	−→	−→	NOUN
ejpam-3322	65	22	c⊗c⊗c	c⊗c⊗c	NOUN
ejpam-3322	65	23	and	and	CCONJ
ejpam-3322	65	24	∆c⊗ic	∆c⊗ic	NOUN
ejpam-3322	65	25	:	:	PUNCT
ejpam-3322	65	26	c⊗c	c⊗c	PROPN
ejpam-3322	65	27	−→	−→	NOUN
ejpam-3322	65	28	c⊗c⊗c	c⊗c⊗c	NOUN
ejpam-3322	65	29	are	be	AUX
ejpam-3322	65	30	defined	define	VERB
ejpam-3322	65	31	by	by	ADP
ejpam-3322	65	32	a⊗b	a⊗b	PROPN
ejpam-3322	65	33	7−→	7−→	PROPN
ejpam-3322	65	34	a⊗∆c(b	a⊗∆c(b	PROPN
ejpam-3322	65	35	)	)	PUNCT
ejpam-3322	65	36	and	and	CCONJ
ejpam-3322	65	37	a	a	DET
ejpam-3322	65	38	⊗	⊗	PROPN
ejpam-3322	65	39	b	b	PROPN
ejpam-3322	65	40	7−→	7−→	PROPN
ejpam-3322	65	41	∆c(a	∆c(a	PROPN
ejpam-3322	65	42	)	)	PUNCT
ejpam-3322	65	43	⊗	⊗	PROPN
ejpam-3322	65	44	b	b	PROPN
ejpam-3322	65	45	,	,	PUNCT
ejpam-3322	65	46	for	for	ADP
ejpam-3322	65	47	all	all	DET
ejpam-3322	65	48	a	a	DET
ejpam-3322	65	49	,	,	PUNCT
ejpam-3322	65	50	b	b	X
ejpam-3322	65	51	∈	∈	PROPN
ejpam-3322	65	52	c	c	NOUN
ejpam-3322	65	53	,	,	PUNCT
ejpam-3322	65	54	respectively	respectively	ADV
ejpam-3322	65	55	.	.	PUNCT
ejpam-3322	66	1	in	in	ADP
ejpam-3322	66	2	addition	addition	NOUN
ejpam-3322	66	3	,	,	PUNCT
ejpam-3322	66	4	the	the	DET
ejpam-3322	66	5	maps	map	NOUN
ejpam-3322	66	6	−	−	PROPN
ejpam-3322	66	7	⊗	⊗	PROPN
ejpam-3322	66	8	1	1	NUM
ejpam-3322	66	9	and	and	CCONJ
ejpam-3322	66	10	1⊗−	1⊗−	NUM
ejpam-3322	66	11	are	be	AUX
ejpam-3322	66	12	defined	define	VERB
ejpam-3322	66	13	by	by	ADP
ejpam-3322	66	14	c	c	PROPN
ejpam-3322	66	15	7−→	7−→	PROPN
ejpam-3322	66	16	c⊗	c⊗	NOUN
ejpam-3322	66	17	1	1	NUM
ejpam-3322	66	18	and	and	CCONJ
ejpam-3322	66	19	c	c	NOUN
ejpam-3322	66	20	7−→	7−→	NOUN
ejpam-3322	66	21	1⊗	1⊗	NUM
ejpam-3322	66	22	c	c	NOUN
ejpam-3322	66	23	,	,	PUNCT
ejpam-3322	66	24	respectively	respectively	ADV
ejpam-3322	66	25	.	.	PUNCT
ejpam-3322	67	1	these	these	DET
ejpam-3322	67	2	commuted	commute	VERB
ejpam-3322	67	3	diagrams	diagram	NOUN
ejpam-3322	67	4	can	can	AUX
ejpam-3322	67	5	be	be	AUX
ejpam-3322	67	6	represented	represent	VERB
ejpam-3322	67	7	in	in	ADP
ejpam-3322	67	8	terms	term	NOUN
ejpam-3322	67	9	of	of	ADP
ejpam-3322	67	10	equations	equation	NOUN
ejpam-3322	67	11	as	as	SCONJ
ejpam-3322	67	12	follows	follow	VERB
ejpam-3322	67	13	for	for	ADP
ejpam-3322	67	14	all	all	DET
ejpam-3322	67	15	c	c	NOUN
ejpam-3322	67	16	∈	∈	PROPN
ejpam-3322	68	1	c	c	NOUN
ejpam-3322	68	2	:	:	PUNCT
ejpam-3322	68	3	(	(	PUNCT
ejpam-3322	68	4	ic	ic	PROPN
ejpam-3322	68	5	⊗∆c)∆c(c	⊗∆c)∆c(c	NUM
ejpam-3322	68	6	)	)	PUNCT
ejpam-3322	68	7	=	=	SYM
ejpam-3322	69	1	(	(	PUNCT
ejpam-3322	69	2	∆c	∆c	PROPN
ejpam-3322	69	3	⊗	⊗	PROPN
ejpam-3322	69	4	ic)∆c(c	ic)∆c(c	PROPN
ejpam-3322	69	5	)	)	PUNCT
ejpam-3322	69	6	(	(	PUNCT
ejpam-3322	69	7	3	3	X
ejpam-3322	69	8	)	)	PUNCT
ejpam-3322	69	9	and	and	CCONJ
ejpam-3322	69	10	(	(	PUNCT
ejpam-3322	69	11	εc	εc	INTJ
ejpam-3322	69	12	⊗	⊗	PROPN
ejpam-3322	69	13	ic)∆c(c	ic)∆c(c	PROPN
ejpam-3322	69	14	)	)	PUNCT
ejpam-3322	69	15	=	=	PUNCT
ejpam-3322	70	1	1⊗	1⊗	NUM
ejpam-3322	70	2	c	c	X
ejpam-3322	70	3	,	,	PUNCT
ejpam-3322	70	4	(	(	PUNCT
ejpam-3322	70	5	ic	ic	PROPN
ejpam-3322	70	6	⊗	⊗	PROPN
ejpam-3322	70	7	εc)∆c(c	εc)∆c(c	NUM
ejpam-3322	70	8	)	)	PUNCT
ejpam-3322	70	9	=	=	SYM
ejpam-3322	70	10	c⊗	c⊗	NOUN
ejpam-3322	70	11	1	1	NUM
ejpam-3322	70	12	.	.	PUNCT
ejpam-3322	71	1	(	(	PUNCT
ejpam-3322	71	2	4	4	X
ejpam-3322	71	3	)	)	PUNCT
ejpam-3322	71	4	the	the	DET
ejpam-3322	71	5	maps	map	NOUN
ejpam-3322	71	6	∆c	∆c	PROPN
ejpam-3322	71	7	and	and	CCONJ
ejpam-3322	71	8	εc	εc	NOUN
ejpam-3322	71	9	are	be	AUX
ejpam-3322	71	10	called	call	VERB
ejpam-3322	71	11	the	the	DET
ejpam-3322	71	12	comultiplication	comultiplication	NOUN
ejpam-3322	71	13	and	and	CCONJ
ejpam-3322	71	14	counit	counit	VERB
ejpam-3322	71	15	maps	map	NOUN
ejpam-3322	71	16	on	on	ADP
ejpam-3322	71	17	the	the	DET
ejpam-3322	71	18	coalgebra	coalgebra	NOUN
ejpam-3322	71	19	c	c	NOUN
ejpam-3322	71	20	,	,	PUNCT
ejpam-3322	71	21	respectively	respectively	ADV
ejpam-3322	71	22	.	.	PUNCT
ejpam-3322	72	1	the	the	DET
ejpam-3322	72	2	coassociative	coassociative	ADJ
ejpam-3322	72	3	property	property	NOUN
ejpam-3322	72	4	is	be	AUX
ejpam-3322	72	5	presented	present	VERB
ejpam-3322	72	6	by	by	ADP
ejpam-3322	72	7	equation	equation	NOUN
ejpam-3322	72	8	(	(	PUNCT
ejpam-3322	72	9	3	3	NUM
ejpam-3322	72	10	)	)	PUNCT
ejpam-3322	72	11	and	and	CCONJ
ejpam-3322	72	12	the	the	DET
ejpam-3322	72	13	counit	counit	VERB
ejpam-3322	72	14	property	property	NOUN
ejpam-3322	72	15	is	be	AUX
ejpam-3322	72	16	presented	present	VERB
ejpam-3322	72	17	by	by	ADP
ejpam-3322	72	18	equation	equation	NOUN
ejpam-3322	72	19	(	(	PUNCT
ejpam-3322	72	20	4	4	NUM
ejpam-3322	72	21	)	)	PUNCT
ejpam-3322	72	22	.	.	PUNCT
ejpam-3322	73	1	a	a	DET
ejpam-3322	73	2	k	k	NOUN
ejpam-3322	73	3	-	-	NOUN
ejpam-3322	73	4	coalgebra	coalgebra	NOUN
ejpam-3322	73	5	c	c	NOUN
ejpam-3322	73	6	is	be	AUX
ejpam-3322	73	7	cocommutative	cocommutative	ADJ
ejpam-3322	73	8	if	if	SCONJ
ejpam-3322	73	9	τ(∆c(c	τ(∆c(c	NOUN
ejpam-3322	73	10	)	)	PUNCT
ejpam-3322	73	11	)	)	PUNCT
ejpam-3322	74	1	=	=	PUNCT
ejpam-3322	74	2	∆c(c	∆c(c	ADJ
ejpam-3322	74	3	)	)	PUNCT
ejpam-3322	74	4	,	,	PUNCT
ejpam-3322	74	5	for	for	ADP
ejpam-3322	74	6	all	all	DET
ejpam-3322	74	7	c	c	PROPN
ejpam-3322	74	8	∈	∈	PROPN
ejpam-3322	74	9	c.	c.	NOUN
ejpam-3322	74	10	we	we	PRON
ejpam-3322	74	11	use	use	VERB
ejpam-3322	74	12	the	the	DET
ejpam-3322	74	13	notation	notation	NOUN
ejpam-3322	74	14	of	of	ADP
ejpam-3322	74	15	sweedler	sweedler	NOUN
ejpam-3322	74	16	[	[	X
ejpam-3322	74	17	9	9	NUM
ejpam-3322	74	18	]	]	PUNCT
ejpam-3322	74	19	to	to	PART
ejpam-3322	74	20	write	write	VERB
ejpam-3322	74	21	∆c(c	∆c(c	PROPN
ejpam-3322	74	22	)	)	PUNCT
ejpam-3322	74	23	=	=	PUNCT
ejpam-3322	75	1	∑	∑	PUNCT
ejpam-3322	75	2	(	(	PUNCT
ejpam-3322	75	3	c	c	NOUN
ejpam-3322	75	4	)	)	PUNCT
ejpam-3322	75	5	c(1	c(1	NOUN
ejpam-3322	75	6	)	)	PUNCT
ejpam-3322	75	7	⊗	⊗	PROPN
ejpam-3322	75	8	c(2	c(2	PROPN
ejpam-3322	75	9	)	)	PUNCT
ejpam-3322	75	10	.	.	PUNCT
ejpam-3322	76	1	since	since	SCONJ
ejpam-3322	76	2	(	(	PUNCT
ejpam-3322	76	3	1	1	NUM
ejpam-3322	76	4	⊗	⊗	PROPN
ejpam-3322	76	5	c	c	NOUN
ejpam-3322	76	6	)	)	PUNCT
ejpam-3322	76	7	=	=	SYM
ejpam-3322	76	8	c	c	NOUN
ejpam-3322	76	9	=	=	SYM
ejpam-3322	76	10	(	(	PUNCT
ejpam-3322	76	11	c	c	PROPN
ejpam-3322	76	12	⊗	⊗	PROPN
ejpam-3322	76	13	1	1	NUM
ejpam-3322	76	14	)	)	PUNCT
ejpam-3322	76	15	,	,	PUNCT
ejpam-3322	76	16	equation	equation	NOUN
ejpam-3322	76	17	(	(	PUNCT
ejpam-3322	76	18	4	4	NUM
ejpam-3322	76	19	)	)	PUNCT
ejpam-3322	76	20	implies	imply	VERB
ejpam-3322	76	21	that	that	SCONJ
ejpam-3322	76	22	∑	∑	PROPN
ejpam-3322	76	23	(	(	PUNCT
ejpam-3322	76	24	c	c	NOUN
ejpam-3322	76	25	)	)	PUNCT
ejpam-3322	76	26	εc(c(1))c(2	εc(c(1))c(2	NOUN
ejpam-3322	76	27	)	)	PUNCT
ejpam-3322	77	1	=	=	PUNCT
ejpam-3322	77	2	c	c	NOUN
ejpam-3322	77	3	=	=	PUNCT
ejpam-3322	77	4	∑	∑	PUNCT
ejpam-3322	77	5	(	(	PUNCT
ejpam-3322	77	6	c	c	NOUN
ejpam-3322	77	7	)	)	PUNCT
ejpam-3322	77	8	εc(c(2))c(1	εc(c(2))c(1	NOUN
ejpam-3322	77	9	)	)	PUNCT
ejpam-3322	77	10	.	.	PUNCT
ejpam-3322	78	1	moreover	moreover	ADV
ejpam-3322	78	2	,	,	PUNCT
ejpam-3322	78	3	we	we	PRON
ejpam-3322	78	4	have	have	VERB
ejpam-3322	78	5	(	(	PUNCT
ejpam-3322	78	6	ic⊗∆c)∆c(c	ic⊗∆c)∆c(c	NOUN
ejpam-3322	78	7	)	)	PUNCT
ejpam-3322	78	8	=	=	PUNCT
ejpam-3322	78	9	(	(	PUNCT
ejpam-3322	78	10	ic⊗∆c	ic⊗∆c	NUM
ejpam-3322	78	11	)	)	PUNCT
ejpam-3322	78	12	(	(	PUNCT
ejpam-3322	78	13	∑	∑	PUNCT
ejpam-3322	78	14	(	(	PUNCT
ejpam-3322	78	15	c	c	NOUN
ejpam-3322	78	16	)	)	PUNCT
ejpam-3322	78	17	c(1)⊗c(2	c(1)⊗c(2	NUM
ejpam-3322	78	18	)	)	PUNCT
ejpam-3322	78	19	)	)	PUNCT
ejpam-3322	79	1	=	=	PUNCT
ejpam-3322	79	2	∑	∑	PUNCT
ejpam-3322	79	3	(	(	PUNCT
ejpam-3322	79	4	c	c	NOUN
ejpam-3322	79	5	)	)	PUNCT
ejpam-3322	79	6	c(1)⊗∆c(c(2	c(1)⊗∆c(c(2	NOUN
ejpam-3322	79	7	)	)	PUNCT
ejpam-3322	79	8	)	)	PUNCT
ejpam-3322	80	1	=	=	PUNCT
ejpam-3322	80	2	∑	∑	PUNCT
ejpam-3322	80	3	(	(	PUNCT
ejpam-3322	80	4	c),(c(2	c),(c(2	PROPN
ejpam-3322	80	5	)	)	PUNCT
ejpam-3322	80	6	)	)	PUNCT
ejpam-3322	80	7	c(1)⊗c(2)(1)⊗c(2)(2	c(1)⊗c(2)(1)⊗c(2)(2	PROPN
ejpam-3322	80	8	)	)	PUNCT
ejpam-3322	80	9	b.	b.	PROPN
ejpam-3322	80	10	al	al	PROPN
ejpam-3322	80	11	-	-	PUNCT
ejpam-3322	80	12	harbi	harbi	PROPN
ejpam-3322	80	13	,	,	PUNCT
ejpam-3322	80	14	w.	w.	PROPN
ejpam-3322	80	15	m.	m.	PROPN
ejpam-3322	80	16	fakieh	fakieh	PROPN
ejpam-3322	80	17	,	,	PUNCT
ejpam-3322	80	18	m.	m.	NOUN
ejpam-3322	80	19	m.	m.	PROPN
ejpam-3322	80	20	al	al	PROPN
ejpam-3322	80	21	-	-	PUNCT
ejpam-3322	80	22	shomrani	shomrani	PROPN
ejpam-3322	80	23	/	/	SYM
ejpam-3322	80	24	eur	eur	NOUN
ejpam-3322	80	25	.	.	PUNCT
ejpam-3322	81	1	j.	j.	PROPN
ejpam-3322	81	2	pure	pure	PROPN
ejpam-3322	81	3	appl	appl	PROPN
ejpam-3322	81	4	.	.	PROPN
ejpam-3322	81	5	math	math	PROPN
ejpam-3322	81	6	,	,	PUNCT
ejpam-3322	81	7	11	11	NUM
ejpam-3322	81	8	(	(	PUNCT
ejpam-3322	81	9	4	4	NUM
ejpam-3322	81	10	)	)	PUNCT
ejpam-3322	81	11	(	(	PUNCT
ejpam-3322	81	12	2018	2018	NUM
ejpam-3322	81	13	)	)	PUNCT
ejpam-3322	81	14	,	,	PUNCT
ejpam-3322	81	15	1027	1027	NUM
ejpam-3322	81	16	-	-	SYM
ejpam-3322	81	17	1045	1045	NUM
ejpam-3322	81	18	1030	1030	NUM
ejpam-3322	81	19	and	and	CCONJ
ejpam-3322	81	20	(	(	PUNCT
ejpam-3322	81	21	∆c⊗ic)∆c(c	∆c⊗ic)∆c(c	NOUN
ejpam-3322	81	22	)	)	PUNCT
ejpam-3322	81	23	=	=	SYM
ejpam-3322	81	24	(	(	PUNCT
ejpam-3322	81	25	∆c⊗ic	∆c⊗ic	NOUN
ejpam-3322	81	26	)	)	PUNCT
ejpam-3322	81	27	(	(	PUNCT
ejpam-3322	81	28	∑	∑	PUNCT
ejpam-3322	81	29	(	(	PUNCT
ejpam-3322	81	30	c	c	NOUN
ejpam-3322	81	31	)	)	PUNCT
ejpam-3322	81	32	c(1)⊗c(2	c(1)⊗c(2	NUM
ejpam-3322	81	33	)	)	PUNCT
ejpam-3322	81	34	)	)	PUNCT
ejpam-3322	82	1	=	=	PUNCT
ejpam-3322	82	2	∑	∑	PUNCT
ejpam-3322	82	3	(	(	PUNCT
ejpam-3322	82	4	c	c	NOUN
ejpam-3322	82	5	)	)	PUNCT
ejpam-3322	82	6	∆c(c(1))⊗c(2	∆c(c(1))⊗c(2	PROPN
ejpam-3322	82	7	)	)	PUNCT
ejpam-3322	82	8	=	=	SYM
ejpam-3322	83	1	∑	∑	PUNCT
ejpam-3322	83	2	(	(	PUNCT
ejpam-3322	83	3	c),(c(1	c),(c(1	NOUN
ejpam-3322	83	4	)	)	PUNCT
ejpam-3322	83	5	)	)	PUNCT
ejpam-3322	84	1	c(1)(1)⊗c(1)(2)⊗c(2	c(1)(1)⊗c(1)(2)⊗c(2	PROPN
ejpam-3322	84	2	)	)	PUNCT
ejpam-3322	84	3	.	.	PUNCT
ejpam-3322	85	1	but	but	CCONJ
ejpam-3322	85	2	,	,	PUNCT
ejpam-3322	85	3	(	(	PUNCT
ejpam-3322	85	4	ic	ic	PROPN
ejpam-3322	85	5	⊗	⊗	PROPN
ejpam-3322	85	6	∆c)∆c	∆c)∆c	NOUN
ejpam-3322	85	7	=	=	SYM
ejpam-3322	85	8	(	(	PUNCT
ejpam-3322	85	9	∆c	∆c	PROPN
ejpam-3322	85	10	⊗	⊗	PROPN
ejpam-3322	85	11	ic)∆c	ic)∆c	PROPN
ejpam-3322	85	12	by	by	ADP
ejpam-3322	85	13	(	(	PUNCT
ejpam-3322	85	14	3	3	NUM
ejpam-3322	85	15	)	)	PUNCT
ejpam-3322	85	16	.	.	PUNCT
ejpam-3322	86	1	so	so	ADV
ejpam-3322	86	2	,	,	PUNCT
ejpam-3322	86	3	the	the	DET
ejpam-3322	86	4	expressions	expression	NOUN
ejpam-3322	86	5	in	in	ADP
ejpam-3322	86	6	both	both	PRON
ejpam-3322	86	7	of	of	ADP
ejpam-3322	86	8	the	the	DET
ejpam-3322	86	9	above	above	ADJ
ejpam-3322	86	10	equations	equation	NOUN
ejpam-3322	86	11	are	be	AUX
ejpam-3322	86	12	equal	equal	ADJ
ejpam-3322	86	13	.	.	PUNCT
ejpam-3322	87	1	the	the	DET
ejpam-3322	87	2	common	common	ADJ
ejpam-3322	87	3	value	value	NOUN
ejpam-3322	87	4	in	in	ADP
ejpam-3322	87	5	both	both	PRON
ejpam-3322	87	6	is	be	AUX
ejpam-3322	87	7	denoted	denote	VERB
ejpam-3322	87	8	by∑	by∑	NOUN
ejpam-3322	87	9	(	(	PUNCT
ejpam-3322	87	10	c	c	NOUN
ejpam-3322	87	11	)	)	PUNCT
ejpam-3322	87	12	c(1	c(1	NOUN
ejpam-3322	87	13	)	)	PUNCT
ejpam-3322	87	14	⊗	⊗	PROPN
ejpam-3322	87	15	c(2	c(2	PROPN
ejpam-3322	87	16	)	)	PUNCT
ejpam-3322	87	17	⊗	⊗	PROPN
ejpam-3322	87	18	c(3	c(3	PROPN
ejpam-3322	87	19	)	)	PUNCT
ejpam-3322	87	20	.	.	PUNCT
ejpam-3322	88	1	in	in	ADP
ejpam-3322	88	2	general	general	ADJ
ejpam-3322	88	3	we	we	PRON
ejpam-3322	88	4	write	write	VERB
ejpam-3322	88	5	∆n−1(c	∆n−1(c	NOUN
ejpam-3322	88	6	)	)	PUNCT
ejpam-3322	88	7	=	=	PUNCT
ejpam-3322	89	1	∑	∑	PUNCT
ejpam-3322	89	2	(	(	PUNCT
ejpam-3322	89	3	c	c	NOUN
ejpam-3322	89	4	)	)	PUNCT
ejpam-3322	89	5	c(1	c(1	NOUN
ejpam-3322	89	6	)	)	PUNCT
ejpam-3322	89	7	⊗	⊗	NOUN
ejpam-3322	89	8	.	.	PUNCT
ejpam-3322	89	9	.	.	PUNCT
ejpam-3322	89	10	.	.	PUNCT
ejpam-3322	89	11	.	.	PUNCT
ejpam-3322	90	1	⊗	⊗	PROPN
ejpam-3322	90	2	c(n	c(n	NOUN
ejpam-3322	90	3	)	)	PUNCT
ejpam-3322	90	4	.	.	PUNCT
ejpam-3322	91	1	∆n−1(c	∆n−1(c	X
ejpam-3322	91	2	)	)	PUNCT
ejpam-3322	91	3	is	be	AUX
ejpam-3322	91	4	the	the	DET
ejpam-3322	91	5	element	element	NOUN
ejpam-3322	91	6	obtained	obtain	VERB
ejpam-3322	91	7	by	by	ADP
ejpam-3322	91	8	applying	apply	VERB
ejpam-3322	91	9	the	the	DET
ejpam-3322	91	10	coassociativity	coassociativity	NOUN
ejpam-3322	91	11	(	(	PUNCT
ejpam-3322	91	12	n−	n−	NOUN
ejpam-3322	91	13	1	1	NUM
ejpam-3322	91	14	)	)	PUNCT
ejpam-3322	91	15	times	time	NOUN
ejpam-3322	91	16	.	.	PUNCT
ejpam-3322	92	1	definition	definition	NOUN
ejpam-3322	92	2	2.3	2.3	NUM
ejpam-3322	92	3	.	.	PUNCT
ejpam-3322	93	1	[	[	X
ejpam-3322	93	2	11	11	NUM
ejpam-3322	93	3	]	]	PUNCT
ejpam-3322	93	4	a	a	DET
ejpam-3322	93	5	k	k	ADJ
ejpam-3322	93	6	-	-	ADJ
ejpam-3322	93	7	vector	vector	NOUN
ejpam-3322	93	8	space	space	NOUN
ejpam-3322	93	9	h	h	NOUN
ejpam-3322	93	10	over	over	ADP
ejpam-3322	93	11	a	a	DET
ejpam-3322	93	12	field	field	NOUN
ejpam-3322	93	13	k	k	X
ejpam-3322	93	14	is	be	AUX
ejpam-3322	93	15	a	a	DET
ejpam-3322	93	16	bialgebra	bialgebra	NOUN
ejpam-3322	93	17	if	if	SCONJ
ejpam-3322	93	18	(	(	PUNCT
ejpam-3322	93	19	h,µh	h,µh	PROPN
ejpam-3322	93	20	,	,	PUNCT
ejpam-3322	93	21	ηh	ηh	PROPN
ejpam-3322	93	22	)	)	PUNCT
ejpam-3322	93	23	is	be	AUX
ejpam-3322	93	24	an	an	DET
ejpam-3322	93	25	algebra	algebra	NOUN
ejpam-3322	93	26	,	,	PUNCT
ejpam-3322	93	27	(	(	PUNCT
ejpam-3322	93	28	h,∆h	h,∆h	NOUN
ejpam-3322	93	29	,	,	PUNCT
ejpam-3322	93	30	εh	εh	PROPN
ejpam-3322	93	31	)	)	PUNCT
ejpam-3322	93	32	is	be	AUX
ejpam-3322	93	33	a	a	DET
ejpam-3322	93	34	coalgebra	coalgebra	NOUN
ejpam-3322	93	35	and	and	CCONJ
ejpam-3322	93	36	either	either	PRON
ejpam-3322	93	37	of	of	ADP
ejpam-3322	93	38	the	the	DET
ejpam-3322	93	39	following	follow	VERB
ejpam-3322	93	40	equivalent	equivalent	ADJ
ejpam-3322	93	41	conditions	condition	NOUN
ejpam-3322	93	42	holds	hold	VERB
ejpam-3322	93	43	:	:	PUNCT
ejpam-3322	93	44	1	1	X
ejpam-3322	93	45	)	)	PUNCT
ejpam-3322	93	46	∆h	∆h	PROPN
ejpam-3322	93	47	and	and	CCONJ
ejpam-3322	93	48	εh	εh	PROPN
ejpam-3322	93	49	are	be	AUX
ejpam-3322	93	50	algebra	algebra	NOUN
ejpam-3322	93	51	maps	map	NOUN
ejpam-3322	93	52	.	.	PUNCT
ejpam-3322	94	1	2	2	X
ejpam-3322	94	2	)	)	PUNCT
ejpam-3322	94	3	µh	µh	NOUN
ejpam-3322	94	4	and	and	CCONJ
ejpam-3322	94	5	ηh	ηh	PROPN
ejpam-3322	94	6	are	be	AUX
ejpam-3322	94	7	coalgebra	coalgebra	NOUN
ejpam-3322	94	8	maps	map	NOUN
ejpam-3322	94	9	.	.	PUNCT
ejpam-3322	95	1	corollary	corollary	ADJ
ejpam-3322	95	2	2.4	2.4	NUM
ejpam-3322	95	3	.	.	PUNCT
ejpam-3322	96	1	[	[	X
ejpam-3322	96	2	11	11	NUM
ejpam-3322	96	3	]	]	PUNCT
ejpam-3322	96	4	let	let	VERB
ejpam-3322	96	5	k	k	PRON
ejpam-3322	96	6	be	be	AUX
ejpam-3322	96	7	a	a	DET
ejpam-3322	96	8	filed	file	VERB
ejpam-3322	96	9	and	and	CCONJ
ejpam-3322	96	10	let	let	VERB
ejpam-3322	96	11	vi	vi	NOUN
ejpam-3322	96	12	,	,	PUNCT
ejpam-3322	96	13	1	1	NUM
ejpam-3322	96	14	≤	≤	NUM
ejpam-3322	96	15	i	i	PRON
ejpam-3322	96	16	≤	≤	PROPN
ejpam-3322	96	17	n	n	CCONJ
ejpam-3322	96	18	,	,	PUNCT
ejpam-3322	96	19	be	be	AUX
ejpam-3322	96	20	a	a	DET
ejpam-3322	96	21	finite	finite	ADJ
ejpam-3322	96	22	set	set	NOUN
ejpam-3322	96	23	of	of	ADP
ejpam-3322	96	24	vector	vector	NOUN
ejpam-3322	96	25	spaces	space	NOUN
ejpam-3322	96	26	over	over	ADP
ejpam-3322	96	27	k.	k.	PROPN
ejpam-3322	96	28	then	then	ADV
ejpam-3322	96	29	v	v	ADP
ejpam-3322	97	1	∗1	∗1	PROPN
ejpam-3322	97	2	⊗	⊗	PROPN
ejpam-3322	97	3	v	v	PROPN
ejpam-3322	97	4	∗2	∗2	PROPN
ejpam-3322	97	5	⊗	⊗	NOUN
ejpam-3322	97	6	...	...	PUNCT
ejpam-3322	98	1	⊗	⊗	PROPN
ejpam-3322	98	2	v	v	ADP
ejpam-3322	98	3	∗n	∗n	PROPN
ejpam-3322	98	4	⊆	⊆	NUM
ejpam-3322	98	5	(	(	PUNCT
ejpam-3322	98	6	v1	v1	PROPN
ejpam-3322	98	7	⊗	⊗	PROPN
ejpam-3322	98	8	v2	v2	PROPN
ejpam-3322	98	9	⊗	⊗	PROPN
ejpam-3322	98	10	...	...	PUNCT
ejpam-3322	99	1	⊗	⊗	NUM
ejpam-3322	99	2	vn)∗.	vn)∗.	NOUN
ejpam-3322	99	3	definition	definition	NOUN
ejpam-3322	99	4	2.5	2.5	NUM
ejpam-3322	99	5	.	.	PUNCT
ejpam-3322	100	1	[	[	X
ejpam-3322	100	2	4	4	X
ejpam-3322	100	3	]	]	PUNCT
ejpam-3322	100	4	for	for	ADP
ejpam-3322	100	5	a	a	DET
ejpam-3322	100	6	group	group	NOUN
ejpam-3322	100	7	x	x	X
ejpam-3322	100	8	and	and	CCONJ
ejpam-3322	100	9	a	a	DET
ejpam-3322	100	10	subgroup	subgroup	NOUN
ejpam-3322	100	11	g	g	NOUN
ejpam-3322	100	12	,	,	PUNCT
ejpam-3322	100	13	we	we	PRON
ejpam-3322	100	14	call	call	VERB
ejpam-3322	100	15	m	m	VERB
ejpam-3322	100	16	⊂	⊂	X
ejpam-3322	100	17	x	x	PUNCT
ejpam-3322	100	18	a	a	DET
ejpam-3322	100	19	set	set	NOUN
ejpam-3322	100	20	of	of	ADP
ejpam-3322	100	21	left	left	ADJ
ejpam-3322	100	22	coset	coset	NOUN
ejpam-3322	100	23	representatives	representative	NOUN
ejpam-3322	100	24	if	if	SCONJ
ejpam-3322	100	25	for	for	ADP
ejpam-3322	100	26	every	every	DET
ejpam-3322	100	27	x	x	SYM
ejpam-3322	100	28	∈	∈	PROPN
ejpam-3322	100	29	x	x	PUNCT
ejpam-3322	100	30	there	there	PRON
ejpam-3322	100	31	is	be	VERB
ejpam-3322	100	32	a	a	DET
ejpam-3322	100	33	unique	unique	ADJ
ejpam-3322	100	34	s	s	X
ejpam-3322	100	35	∈	∈	NOUN
ejpam-3322	100	36	m	m	VERB
ejpam-3322	101	1	such	such	ADJ
ejpam-3322	101	2	that	that	SCONJ
ejpam-3322	101	3	x	x	SYM
ejpam-3322	101	4	∈	∈	PROPN
ejpam-3322	101	5	gs	gs	NOUN
ejpam-3322	101	6	.	.	PUNCT
ejpam-3322	102	1	the	the	DET
ejpam-3322	102	2	decomposition	decomposition	NOUN
ejpam-3322	102	3	x	x	PUNCT
ejpam-3322	103	1	=	=	PUNCT
ejpam-3322	103	2	us	us	PROPN
ejpam-3322	103	3	is	be	AUX
ejpam-3322	103	4	called	call	VERB
ejpam-3322	103	5	the	the	DET
ejpam-3322	103	6	unique	unique	ADJ
ejpam-3322	103	7	factorization	factorization	NOUN
ejpam-3322	103	8	of	of	ADP
ejpam-3322	103	9	x	x	PUNCT
ejpam-3322	103	10	where	where	SCONJ
ejpam-3322	103	11	u	u	PROPN
ejpam-3322	103	12	∈	∈	PROPN
ejpam-3322	103	13	g	g	PROPN
ejpam-3322	103	14	and	and	CCONJ
ejpam-3322	103	15	s	s	X
ejpam-3322	103	16	∈m	∈m	NOUN
ejpam-3322	103	17	.	.	PUNCT
ejpam-3322	104	1	in	in	ADP
ejpam-3322	104	2	what	what	PRON
ejpam-3322	104	3	follows	follow	VERB
ejpam-3322	104	4	,	,	PUNCT
ejpam-3322	104	5	m	m	VERB
ejpam-3322	104	6	⊂	⊂	PROPN
ejpam-3322	104	7	x	x	VERB
ejpam-3322	104	8	is	be	AUX
ejpam-3322	104	9	assumed	assume	VERB
ejpam-3322	104	10	to	to	PART
ejpam-3322	104	11	be	be	AUX
ejpam-3322	104	12	a	a	DET
ejpam-3322	104	13	set	set	NOUN
ejpam-3322	104	14	of	of	ADP
ejpam-3322	104	15	left	left	ADJ
ejpam-3322	104	16	coset	coset	NOUN
ejpam-3322	104	17	representatives	representative	NOUN
ejpam-3322	104	18	for	for	ADP
ejpam-3322	104	19	the	the	DET
ejpam-3322	104	20	subgroup	subgroup	NOUN
ejpam-3322	104	21	g	g	PROPN
ejpam-3322	104	22	⊂	⊂	PROPN
ejpam-3322	104	23	x.	x.	PROPN
ejpam-3322	105	1	in	in	ADP
ejpam-3322	105	2	addition	addition	NOUN
ejpam-3322	105	3	,	,	PUNCT
ejpam-3322	105	4	the	the	DET
ejpam-3322	105	5	identity	identity	NOUN
ejpam-3322	105	6	in	in	ADP
ejpam-3322	105	7	x	x	X
ejpam-3322	105	8	will	will	AUX
ejpam-3322	105	9	be	be	AUX
ejpam-3322	105	10	denoted	denote	VERB
ejpam-3322	105	11	by	by	ADP
ejpam-3322	105	12	e.	e.	PROPN
ejpam-3322	105	13	definition	definition	PROPN
ejpam-3322	105	14	2.6	2.6	NUM
ejpam-3322	105	15	.	.	PUNCT
ejpam-3322	106	1	[	[	X
ejpam-3322	106	2	4	4	X
ejpam-3322	106	3	]	]	PUNCT
ejpam-3322	106	4	for	for	ADP
ejpam-3322	106	5	s	s	PROPN
ejpam-3322	106	6	,	,	PUNCT
ejpam-3322	106	7	t	t	PROPN
ejpam-3322	106	8	∈	∈	PROPN
ejpam-3322	106	9	m	m	AUX
ejpam-3322	106	10	we	we	PRON
ejpam-3322	106	11	define	define	VERB
ejpam-3322	106	12	τ(s	τ(s	PROPN
ejpam-3322	106	13	,	,	PUNCT
ejpam-3322	106	14	t	t	PROPN
ejpam-3322	106	15	)	)	PUNCT
ejpam-3322	106	16	∈	∈	PROPN
ejpam-3322	106	17	g	g	PROPN
ejpam-3322	106	18	and	and	CCONJ
ejpam-3322	106	19	s	s	PROPN
ejpam-3322	106	20	·	·	PUNCT
ejpam-3322	106	21	t	t	PROPN
ejpam-3322	106	22	∈	∈	PROPN
ejpam-3322	106	23	m	m	VERB
ejpam-3322	106	24	by	by	ADP
ejpam-3322	106	25	the	the	DET
ejpam-3322	106	26	unique	unique	ADJ
ejpam-3322	106	27	factorization	factorization	NOUN
ejpam-3322	106	28	st	st	PROPN
ejpam-3322	106	29	=	=	PUNCT
ejpam-3322	106	30	τ(s	τ(s	NOUN
ejpam-3322	106	31	,	,	PUNCT
ejpam-3322	106	32	t)(s	t)(s	PROPN
ejpam-3322	106	33	·	·	PUNCT
ejpam-3322	106	34	t	t	X
ejpam-3322	106	35	)	)	PUNCT
ejpam-3322	106	36	in	in	ADP
ejpam-3322	106	37	x.	x.	NOUN
ejpam-3322	106	38	the	the	DET
ejpam-3322	106	39	functions	function	NOUN
ejpam-3322	106	40	.	.	PUNCT
ejpam-3322	107	1	:	:	PUNCT
ejpam-3322	108	1	m	m	VERB
ejpam-3322	108	2	×g→	×g→	VERB
ejpam-3322	108	3	g	g	NOUN
ejpam-3322	108	4	and	and	CCONJ
ejpam-3322	108	5	/	/	SYM
ejpam-3322	108	6	:	:	PUNCT
ejpam-3322	109	1	m	m	VERB
ejpam-3322	109	2	×g→	×g→	NOUN
ejpam-3322	109	3	m	m	NOUN
ejpam-3322	109	4	are	be	AUX
ejpam-3322	109	5	also	also	ADV
ejpam-3322	109	6	defined	define	VERB
ejpam-3322	109	7	by	by	ADP
ejpam-3322	109	8	the	the	DET
ejpam-3322	109	9	unique	unique	ADJ
ejpam-3322	109	10	factorization	factorization	NOUN
ejpam-3322	109	11	su	su	PROPN
ejpam-3322	110	1	=	=	PUNCT
ejpam-3322	110	2	(	(	PUNCT
ejpam-3322	110	3	s	s	NOUN
ejpam-3322	110	4	.	.	PUNCT
ejpam-3322	110	5	u)(s	u)(s	NOUN
ejpam-3322	110	6	/	/	SYM
ejpam-3322	110	7	u	u	NOUN
ejpam-3322	110	8	)	)	PUNCT
ejpam-3322	110	9	for	for	ADP
ejpam-3322	110	10	s	s	PROPN
ejpam-3322	110	11	,	,	PUNCT
ejpam-3322	110	12	s	s	PART
ejpam-3322	110	13	/	/	SYM
ejpam-3322	110	14	u	u	NOUN
ejpam-3322	110	15	∈	∈	NOUN
ejpam-3322	110	16	m	m	NOUN
ejpam-3322	110	17	and	and	CCONJ
ejpam-3322	110	18	u	u	NOUN
ejpam-3322	110	19	,	,	PUNCT
ejpam-3322	110	20	s	s	PART
ejpam-3322	110	21	.	.	PUNCT
ejpam-3322	111	1	u	u	PROPN
ejpam-3322	111	2	∈	∈	PROPN
ejpam-3322	111	3	g.	g.	NOUN
ejpam-3322	111	4	it	it	PRON
ejpam-3322	111	5	was	be	AUX
ejpam-3322	111	6	shown	show	VERB
ejpam-3322	111	7	in	in	ADP
ejpam-3322	111	8	[	[	X
ejpam-3322	111	9	4	4	X
ejpam-3322	111	10	]	]	PUNCT
ejpam-3322	111	11	that	that	SCONJ
ejpam-3322	111	12	the	the	DET
ejpam-3322	111	13	binary	binary	PROPN
ejpam-3322	111	14	operation	operation	NOUN
ejpam-3322	111	15	(	(	PUNCT
ejpam-3322	111	16	m	m	PROPN
ejpam-3322	111	17	,	,	PUNCT
ejpam-3322	111	18	·	·	PUNCT
ejpam-3322	111	19	)	)	PUNCT
ejpam-3322	111	20	has	have	VERB
ejpam-3322	111	21	a	a	DET
ejpam-3322	111	22	unique	unique	ADJ
ejpam-3322	111	23	left	leave	VERB
ejpam-3322	111	24	identity	identity	NOUN
ejpam-3322	111	25	em	em	PRON
ejpam-3322	111	26	∈m	∈m	VERB
ejpam-3322	111	27	and	and	CCONJ
ejpam-3322	111	28	also	also	ADV
ejpam-3322	111	29	has	have	VERB
ejpam-3322	111	30	the	the	DET
ejpam-3322	111	31	right	right	ADJ
ejpam-3322	111	32	division	division	NOUN
ejpam-3322	111	33	property	property	NOUN
ejpam-3322	111	34	(	(	PUNCT
ejpam-3322	111	35	i.e.	i.e.	X
ejpam-3322	111	36	there	there	PRON
ejpam-3322	111	37	is	be	VERB
ejpam-3322	111	38	a	a	DET
ejpam-3322	111	39	unique	unique	ADJ
ejpam-3322	111	40	solution	solution	NOUN
ejpam-3322	111	41	p	p	X
ejpam-3322	111	42	∈	∈	NOUN
ejpam-3322	111	43	m	m	VERB
ejpam-3322	111	44	to	to	ADP
ejpam-3322	111	45	the	the	DET
ejpam-3322	111	46	equation	equation	NOUN
ejpam-3322	112	1	p	p	X
ejpam-3322	112	2	·	·	PUNCT
ejpam-3322	112	3	s	s	PART
ejpam-3322	112	4	=	=	X
ejpam-3322	112	5	t	t	PROPN
ejpam-3322	112	6	for	for	ADP
ejpam-3322	112	7	all	all	DET
ejpam-3322	112	8	s	s	PROPN
ejpam-3322	112	9	,	,	PUNCT
ejpam-3322	112	10	t	t	NOUN
ejpam-3322	112	11	∈m	∈m	NOUN
ejpam-3322	112	12	)	)	PUNCT
ejpam-3322	112	13	.	.	PUNCT
ejpam-3322	113	1	if	if	SCONJ
ejpam-3322	113	2	e	e	PROPN
ejpam-3322	113	3	∈m	∈m	NOUN
ejpam-3322	113	4	then	then	ADV
ejpam-3322	113	5	em	em	PRON
ejpam-3322	113	6	=	=	PUNCT
ejpam-3322	113	7	e	e	NOUN
ejpam-3322	113	8	is	be	AUX
ejpam-3322	113	9	also	also	ADV
ejpam-3322	113	10	a	a	DET
ejpam-3322	113	11	right	right	ADJ
ejpam-3322	113	12	identity	identity	NOUN
ejpam-3322	113	13	[	[	X
ejpam-3322	113	14	4	4	NUM
ejpam-3322	113	15	]	]	PUNCT
ejpam-3322	113	16	.	.	PUNCT
ejpam-3322	114	1	the	the	DET
ejpam-3322	114	2	next	next	ADJ
ejpam-3322	114	3	proposition	proposition	NOUN
ejpam-3322	114	4	will	will	AUX
ejpam-3322	114	5	be	be	AUX
ejpam-3322	114	6	used	use	VERB
ejpam-3322	114	7	at	at	ADP
ejpam-3322	114	8	many	many	ADJ
ejpam-3322	114	9	places	place	NOUN
ejpam-3322	114	10	in	in	ADP
ejpam-3322	114	11	this	this	DET
ejpam-3322	114	12	article	article	NOUN
ejpam-3322	114	13	:	:	PUNCT
ejpam-3322	114	14	proposition	proposition	NOUN
ejpam-3322	114	15	2.7	2.7	NUM
ejpam-3322	114	16	.	.	PUNCT
ejpam-3322	115	1	[	[	X
ejpam-3322	115	2	4	4	X
ejpam-3322	115	3	]	]	PUNCT
ejpam-3322	115	4	for	for	ADP
ejpam-3322	115	5	t	t	PROPN
ejpam-3322	115	6	,	,	PUNCT
ejpam-3322	115	7	s	s	PROPN
ejpam-3322	115	8	,	,	PUNCT
ejpam-3322	115	9	p	p	NOUN
ejpam-3322	115	10	∈m	∈m	NOUN
ejpam-3322	115	11	and	and	CCONJ
ejpam-3322	115	12	u	u	NOUN
ejpam-3322	115	13	,	,	PUNCT
ejpam-3322	115	14	v	v	ADP
ejpam-3322	115	15	∈	∈	PROPN
ejpam-3322	115	16	g	g	NOUN
ejpam-3322	115	17	,	,	PUNCT
ejpam-3322	115	18	the	the	DET
ejpam-3322	115	19	following	follow	VERB
ejpam-3322	115	20	identities	identity	NOUN
ejpam-3322	115	21	between	between	ADP
ejpam-3322	115	22	(	(	PUNCT
ejpam-3322	115	23	m	m	PROPN
ejpam-3322	115	24	,	,	PUNCT
ejpam-3322	115	25	·	·	PUNCT
ejpam-3322	115	26	)	)	PUNCT
ejpam-3322	115	27	and	and	CCONJ
ejpam-3322	115	28	τ	τ	PROPN
ejpam-3322	115	29	are	be	AUX
ejpam-3322	115	30	satisfied	satisfied	ADJ
ejpam-3322	115	31	:	:	PUNCT
ejpam-3322	115	32	s	s	X
ejpam-3322	115	33	.	.	PUNCT
ejpam-3322	116	1	(	(	PUNCT
ejpam-3322	116	2	t	t	PROPN
ejpam-3322	116	3	.	.	PUNCT
ejpam-3322	117	1	u	u	NOUN
ejpam-3322	117	2	)	)	PUNCT
ejpam-3322	117	3	=	=	SYM
ejpam-3322	117	4	τ(s	τ(s	PROPN
ejpam-3322	117	5	,	,	PUNCT
ejpam-3322	117	6	t	t	PROPN
ejpam-3322	117	7	)	)	PUNCT
ejpam-3322	117	8	(	(	PUNCT
ejpam-3322	117	9	(	(	PUNCT
ejpam-3322	117	10	s	s	X
ejpam-3322	117	11	·	·	PUNCT
ejpam-3322	117	12	t	t	PROPN
ejpam-3322	117	13	)	)	PUNCT
ejpam-3322	117	14	.	.	PUNCT
ejpam-3322	118	1	u)τ	u)τ	PUNCT
ejpam-3322	118	2	(	(	PUNCT
ejpam-3322	118	3	s	s	X
ejpam-3322	118	4	/	/	SYM
ejpam-3322	118	5	(	(	PUNCT
ejpam-3322	118	6	t	t	PROPN
ejpam-3322	118	7	.	.	PUNCT
ejpam-3322	119	1	u	u	NOUN
ejpam-3322	119	2	)	)	PUNCT
ejpam-3322	119	3	,	,	PUNCT
ejpam-3322	119	4	t	t	PROPN
ejpam-3322	119	5	/	/	SYM
ejpam-3322	119	6	u	u	PROPN
ejpam-3322	119	7	)	)	PUNCT
ejpam-3322	119	8	−1	−1	NOUN
ejpam-3322	119	9	and	and	CCONJ
ejpam-3322	119	10	(	(	PUNCT
ejpam-3322	119	11	s	s	X
ejpam-3322	119	12	·	·	SYM
ejpam-3322	119	13	t	t	PROPN
ejpam-3322	119	14	)	)	PUNCT
ejpam-3322	119	15	/	/	SYM
ejpam-3322	119	16	u	u	NOUN
ejpam-3322	119	17	=	=	PUNCT
ejpam-3322	119	18	(	(	PUNCT
ejpam-3322	119	19	s	s	NOUN
ejpam-3322	119	20	/	/	SYM
ejpam-3322	119	21	(	(	PUNCT
ejpam-3322	119	22	t	t	PROPN
ejpam-3322	119	23	.	.	PUNCT
ejpam-3322	120	1	u	u	NOUN
ejpam-3322	120	2	)	)	PUNCT
ejpam-3322	120	3	)	)	PUNCT
ejpam-3322	120	4	·	·	PUNCT
ejpam-3322	121	1	(	(	PUNCT
ejpam-3322	121	2	t	t	NOUN
ejpam-3322	121	3	/	/	SYM
ejpam-3322	121	4	u	u	NOUN
ejpam-3322	121	5	)	)	PUNCT
ejpam-3322	121	6	,	,	PUNCT
ejpam-3322	121	7	s	s	X
ejpam-3322	121	8	.	.	PUNCT
ejpam-3322	122	1	uv	uv	NOUN
ejpam-3322	122	2	=	=	PUNCT
ejpam-3322	122	3	(	(	PUNCT
ejpam-3322	122	4	s	s	NOUN
ejpam-3322	122	5	.	.	PUNCT
ejpam-3322	122	6	u	u	NOUN
ejpam-3322	122	7	)	)	PUNCT
ejpam-3322	122	8	(	(	PUNCT
ejpam-3322	122	9	(	(	PUNCT
ejpam-3322	122	10	s	s	NOUN
ejpam-3322	122	11	/	/	SYM
ejpam-3322	122	12	u	u	NOUN
ejpam-3322	122	13	)	)	PUNCT
ejpam-3322	122	14	.	.	PUNCT
ejpam-3322	123	1	v	v	X
ejpam-3322	123	2	)	)	PUNCT
ejpam-3322	123	3	and	and	CCONJ
ejpam-3322	123	4	s	s	NOUN
ejpam-3322	123	5	/	/	SYM
ejpam-3322	123	6	uv	uv	NOUN
ejpam-3322	123	7	=	=	SYM
ejpam-3322	123	8	(	(	PUNCT
ejpam-3322	123	9	s/	s/	NOUN
ejpam-3322	123	10	)	)	PUNCT
ejpam-3322	123	11	/	/	SYM
ejpam-3322	123	12	v	v	NOUN
ejpam-3322	123	13	,	,	PUNCT
ejpam-3322	123	14	τ(p	τ(p	NOUN
ejpam-3322	123	15	,	,	PUNCT
ejpam-3322	123	16	s)τ(p	s)τ(p	NOUN
ejpam-3322	123	17	·	·	PUNCT
ejpam-3322	123	18	s	s	X
ejpam-3322	123	19	,	,	PUNCT
ejpam-3322	123	20	t	t	PROPN
ejpam-3322	123	21	)	)	PUNCT
ejpam-3322	123	22	=	=	PUNCT
ejpam-3322	124	1	(	(	PUNCT
ejpam-3322	124	2	p	p	X
ejpam-3322	124	3	.	.	PUNCT
ejpam-3322	125	1	τ(s	τ(s	PROPN
ejpam-3322	125	2	,	,	PUNCT
ejpam-3322	125	3	t	t	PROPN
ejpam-3322	125	4	)	)	PUNCT
ejpam-3322	125	5	)	)	PUNCT
ejpam-3322	126	1	τ	τ	X
ejpam-3322	126	2	(	(	PUNCT
ejpam-3322	126	3	p	p	NOUN
ejpam-3322	126	4	/	/	SYM
ejpam-3322	126	5	τ(s	τ(s	NOUN
ejpam-3322	126	6	,	,	PUNCT
ejpam-3322	126	7	t	t	PROPN
ejpam-3322	126	8	)	)	PUNCT
ejpam-3322	126	9	,	,	PUNCT
ejpam-3322	126	10	s	s	PART
ejpam-3322	126	11	·	·	PUNCT
ejpam-3322	126	12	t	t	PROPN
ejpam-3322	126	13	)	)	PUNCT
ejpam-3322	126	14	and	and	CCONJ
ejpam-3322	126	15	(	(	PUNCT
ejpam-3322	126	16	p	p	NOUN
ejpam-3322	126	17	/	/	SYM
ejpam-3322	126	18	τ(s	τ(s	NOUN
ejpam-3322	126	19	,	,	PUNCT
ejpam-3322	126	20	t	t	PROPN
ejpam-3322	126	21	)	)	PUNCT
ejpam-3322	126	22	)	)	PUNCT
ejpam-3322	126	23	·	·	PUNCT
ejpam-3322	127	1	(	(	PUNCT
ejpam-3322	127	2	s	s	X
ejpam-3322	127	3	·	·	SYM
ejpam-3322	127	4	t	t	X
ejpam-3322	127	5	)	)	PUNCT
ejpam-3322	127	6	=	=	PUNCT
ejpam-3322	128	1	(	(	PUNCT
ejpam-3322	128	2	p	p	X
ejpam-3322	128	3	·	·	PUNCT
ejpam-3322	128	4	s	s	X
ejpam-3322	128	5	)	)	PUNCT
ejpam-3322	128	6	·	·	PUNCT
ejpam-3322	128	7	t	t	X
ejpam-3322	128	8	.	.	PUNCT
ejpam-3322	129	1	b.	b.	PROPN
ejpam-3322	129	2	al	al	PROPN
ejpam-3322	129	3	-	-	PUNCT
ejpam-3322	129	4	harbi	harbi	PROPN
ejpam-3322	129	5	,	,	PUNCT
ejpam-3322	129	6	w.	w.	PROPN
ejpam-3322	129	7	m.	m.	PROPN
ejpam-3322	129	8	fakieh	fakieh	PROPN
ejpam-3322	129	9	,	,	PUNCT
ejpam-3322	129	10	m.	m.	NOUN
ejpam-3322	129	11	m.	m.	PROPN
ejpam-3322	129	12	al	al	PROPN
ejpam-3322	129	13	-	-	PUNCT
ejpam-3322	129	14	shomrani	shomrani	PROPN
ejpam-3322	129	15	/	/	SYM
ejpam-3322	129	16	eur	eur	NOUN
ejpam-3322	129	17	.	.	PUNCT
ejpam-3322	130	1	j.	j.	PROPN
ejpam-3322	130	2	pure	pure	PROPN
ejpam-3322	130	3	appl	appl	PROPN
ejpam-3322	130	4	.	.	PROPN
ejpam-3322	130	5	math	math	PROPN
ejpam-3322	130	6	,	,	PUNCT
ejpam-3322	130	7	11	11	NUM
ejpam-3322	130	8	(	(	PUNCT
ejpam-3322	130	9	4	4	NUM
ejpam-3322	130	10	)	)	PUNCT
ejpam-3322	130	11	(	(	PUNCT
ejpam-3322	130	12	2018	2018	NUM
ejpam-3322	130	13	)	)	PUNCT
ejpam-3322	130	14	,	,	PUNCT
ejpam-3322	130	15	1027	1027	NUM
ejpam-3322	130	16	-	-	SYM
ejpam-3322	130	17	1045	1045	NUM
ejpam-3322	130	18	1031	1031	NUM
ejpam-3322	130	19	in	in	ADP
ejpam-3322	130	20	what	what	PRON
ejpam-3322	130	21	follows	follow	VERB
ejpam-3322	130	22	,	,	PUNCT
ejpam-3322	130	23	unless	unless	SCONJ
ejpam-3322	130	24	otherwise	otherwise	ADV
ejpam-3322	130	25	stated	state	VERB
ejpam-3322	130	26	,	,	PUNCT
ejpam-3322	130	27	we	we	PRON
ejpam-3322	130	28	assume	assume	VERB
ejpam-3322	130	29	that	that	SCONJ
ejpam-3322	130	30	e	e	PROPN
ejpam-3322	130	31	∈	∈	PROPN
ejpam-3322	130	32	m	m	VERB
ejpam-3322	130	33	for	for	ADP
ejpam-3322	130	34	the	the	DET
ejpam-3322	130	35	sake	sake	NOUN
ejpam-3322	130	36	of	of	ADP
ejpam-3322	130	37	simplicity	simplicity	NOUN
ejpam-3322	130	38	.	.	PUNCT
ejpam-3322	131	1	in	in	ADP
ejpam-3322	131	2	[	[	X
ejpam-3322	131	3	4	4	NUM
ejpam-3322	131	4	]	]	PUNCT
ejpam-3322	131	5	,	,	PUNCT
ejpam-3322	131	6	it	it	PRON
ejpam-3322	131	7	was	be	AUX
ejpam-3322	131	8	proved	prove	VERB
ejpam-3322	131	9	that	that	SCONJ
ejpam-3322	131	10	for	for	ADP
ejpam-3322	131	11	all	all	DET
ejpam-3322	131	12	t	t	NOUN
ejpam-3322	131	13	∈m	∈m	NOUN
ejpam-3322	131	14	and	and	CCONJ
ejpam-3322	131	15	v	v	ADP
ejpam-3322	131	16	∈	∈	PROPN
ejpam-3322	131	17	g	g	NOUN
ejpam-3322	131	18	,	,	PUNCT
ejpam-3322	131	19	the	the	DET
ejpam-3322	131	20	following	follow	VERB
ejpam-3322	131	21	identities	identity	NOUN
ejpam-3322	131	22	hold	hold	VERB
ejpam-3322	131	23	:	:	PUNCT
ejpam-3322	131	24	e	e	X
ejpam-3322	131	25	/	/	SYM
ejpam-3322	131	26	v	v	NOUN
ejpam-3322	131	27	=	=	SYM
ejpam-3322	131	28	e	e	X
ejpam-3322	131	29	,	,	PUNCT
ejpam-3322	131	30	e	e	X
ejpam-3322	131	31	.	.	PUNCT
ejpam-3322	132	1	v	v	X
ejpam-3322	132	2	=	=	SYM
ejpam-3322	132	3	v	v	NOUN
ejpam-3322	132	4	,	,	PUNCT
ejpam-3322	132	5	t	t	PROPN
ejpam-3322	132	6	.	.	PUNCT
ejpam-3322	133	1	e	e	X
ejpam-3322	133	2	=	=	SYM
ejpam-3322	133	3	e	e	PROPN
ejpam-3322	133	4	,	,	PUNCT
ejpam-3322	133	5	t	t	PROPN
ejpam-3322	133	6	/	/	SYM
ejpam-3322	133	7	e	e	PROPN
ejpam-3322	133	8	=	=	PROPN
ejpam-3322	133	9	t	t	PROPN
ejpam-3322	133	10	.	.	PUNCT
ejpam-3322	134	1	let	let	VERB
ejpam-3322	134	2	x	x	SYM
ejpam-3322	134	3	=	=	PRON
ejpam-3322	134	4	gm	gm	PROPN
ejpam-3322	134	5	be	be	AUX
ejpam-3322	134	6	a	a	DET
ejpam-3322	134	7	factorization	factorization	NOUN
ejpam-3322	134	8	of	of	ADP
ejpam-3322	134	9	a	a	DET
ejpam-3322	134	10	finite	finite	ADJ
ejpam-3322	134	11	group	group	NOUN
ejpam-3322	134	12	as	as	SCONJ
ejpam-3322	134	13	defined	define	VERB
ejpam-3322	134	14	before	before	ADV
ejpam-3322	134	15	,	,	PUNCT
ejpam-3322	134	16	the	the	DET
ejpam-3322	134	17	category	category	NOUN
ejpam-3322	134	18	c	c	NOUN
ejpam-3322	134	19	is	be	AUX
ejpam-3322	134	20	defined	define	VERB
ejpam-3322	134	21	as	as	ADP
ejpam-3322	134	22	the	the	DET
ejpam-3322	134	23	following	following	NOUN
ejpam-3322	134	24	[	[	X
ejpam-3322	134	25	4	4	NUM
ejpam-3322	134	26	]	]	PUNCT
ejpam-3322	134	27	:	:	PUNCT
ejpam-3322	134	28	take	take	VERB
ejpam-3322	134	29	a	a	DET
ejpam-3322	134	30	category	category	NOUN
ejpam-3322	134	31	c	c	NOUN
ejpam-3322	134	32	of	of	ADP
ejpam-3322	134	33	finite	finite	ADJ
ejpam-3322	134	34	dimensional	dimensional	ADJ
ejpam-3322	134	35	vector	vector	NOUN
ejpam-3322	134	36	spaces	space	NOUN
ejpam-3322	134	37	over	over	ADP
ejpam-3322	134	38	a	a	DET
ejpam-3322	134	39	field	field	NOUN
ejpam-3322	134	40	k	k	NOUN
ejpam-3322	134	41	,	,	PUNCT
ejpam-3322	134	42	whose	whose	DET
ejpam-3322	134	43	objects	object	NOUN
ejpam-3322	134	44	are	be	AUX
ejpam-3322	134	45	right	right	ADJ
ejpam-3322	134	46	representations	representation	NOUN
ejpam-3322	134	47	of	of	ADP
ejpam-3322	134	48	the	the	DET
ejpam-3322	134	49	group	group	NOUN
ejpam-3322	134	50	g	g	PROPN
ejpam-3322	134	51	and	and	CCONJ
ejpam-3322	134	52	have	have	VERB
ejpam-3322	134	53	m	m	PROPN
ejpam-3322	134	54	-gradings	-grading	NOUN
ejpam-3322	134	55	.	.	PUNCT
ejpam-3322	135	1	the	the	DET
ejpam-3322	135	2	action	action	NOUN
ejpam-3322	135	3	for	for	ADP
ejpam-3322	135	4	the	the	DET
ejpam-3322	135	5	representation	representation	NOUN
ejpam-3322	135	6	is	be	AUX
ejpam-3322	135	7	written	write	VERB
ejpam-3322	135	8	as	as	ADP
ejpam-3322	135	9	/̄	/̄	PUNCT
ejpam-3322	135	10	:	:	PUNCT
ejpam-3322	135	11	v	v	NUM
ejpam-3322	135	12	×g→	×g→	NOUN
ejpam-3322	135	13	v	v	NOUN
ejpam-3322	135	14	.	.	PUNCT
ejpam-3322	136	1	in	in	ADP
ejpam-3322	136	2	addition	addition	NOUN
ejpam-3322	136	3	it	it	PRON
ejpam-3322	136	4	is	be	AUX
ejpam-3322	136	5	supposed	suppose	VERB
ejpam-3322	136	6	that	that	SCONJ
ejpam-3322	136	7	the	the	DET
ejpam-3322	136	8	action	action	NOUN
ejpam-3322	136	9	and	and	CCONJ
ejpam-3322	136	10	the	the	DET
ejpam-3322	136	11	grading	grading	NOUN
ejpam-3322	136	12	satisfy	satisfy	VERB
ejpam-3322	136	13	the	the	DET
ejpam-3322	136	14	compatibility	compatibility	NOUN
ejpam-3322	136	15	condition	condition	NOUN
ejpam-3322	136	16	,	,	PUNCT
ejpam-3322	137	1	i.e.	i.e.	X
ejpam-3322	137	2	〈	〈	PROPN
ejpam-3322	137	3	ξ/̄u	ξ/̄u	PROPN
ejpam-3322	137	4	〉	〉	NOUN
ejpam-3322	137	5	=	=	SYM
ejpam-3322	137	6	〈	〈	PROPN
ejpam-3322	137	7	ξ	ξ	PROPN
ejpam-3322	137	8	〉	〉	PROPN
ejpam-3322	137	9	/	/	SYM
ejpam-3322	137	10	u	u	NOUN
ejpam-3322	137	11	where	where	SCONJ
ejpam-3322	137	12	ξ	ξ	X
ejpam-3322	137	13	∈	∈	PROPN
ejpam-3322	137	14	vs	vs	ADP
ejpam-3322	137	15	corresponds	correspond	NOUN
ejpam-3322	137	16	to	to	ADP
ejpam-3322	137	17	〈	〈	PROPN
ejpam-3322	137	18	ξ	ξ	PROPN
ejpam-3322	137	19	〉	〉	NOUN
ejpam-3322	137	20	=	=	PUNCT
ejpam-3322	137	21	s.	s.	PROPN
ejpam-3322	137	22	the	the	DET
ejpam-3322	137	23	morphisms	morphism	NOUN
ejpam-3322	137	24	in	in	ADP
ejpam-3322	137	25	the	the	DET
ejpam-3322	137	26	category	category	NOUN
ejpam-3322	137	27	c	c	NOUN
ejpam-3322	137	28	is	be	AUX
ejpam-3322	137	29	defined	define	VERB
ejpam-3322	137	30	to	to	PART
ejpam-3322	137	31	be	be	AUX
ejpam-3322	137	32	linear	linear	ADJ
ejpam-3322	137	33	maps	map	NOUN
ejpam-3322	137	34	that	that	PRON
ejpam-3322	137	35	preserve	preserve	VERB
ejpam-3322	137	36	both	both	PRON
ejpam-3322	137	37	of	of	ADP
ejpam-3322	137	38	grading	grading	NOUN
ejpam-3322	137	39	and	and	CCONJ
ejpam-3322	137	40	action	action	NOUN
ejpam-3322	137	41	,	,	PUNCT
ejpam-3322	137	42	i.e.	i.e.	X
ejpam-3322	137	43	for	for	ADP
ejpam-3322	137	44	a	a	DET
ejpam-3322	137	45	morphism	morphism	NOUN
ejpam-3322	137	46	ϑ	ϑ	X
ejpam-3322	137	47	:	:	PUNCT
ejpam-3322	137	48	v	v	X
ejpam-3322	137	49	→	→	SYM
ejpam-3322	137	50	w	w	VERB
ejpam-3322	137	51	we	we	PRON
ejpam-3322	137	52	have	have	VERB
ejpam-3322	137	53	〈	〈	PROPN
ejpam-3322	137	54	ϑ(ξ	ϑ(ξ	NOUN
ejpam-3322	137	55	)	)	PUNCT
ejpam-3322	137	56	〉	〉	NOUN
ejpam-3322	137	57	=	=	SYM
ejpam-3322	138	1	〈	〈	PROPN
ejpam-3322	138	2	ξ	ξ	PROPN
ejpam-3322	138	3	〉	〉	PROPN
ejpam-3322	138	4	and	and	CCONJ
ejpam-3322	138	5	ϑ(ξ)/̄u	ϑ(ξ)/̄u	PROPN
ejpam-3322	138	6	=	=	SYM
ejpam-3322	138	7	ϑ(ξ/̄u	ϑ(ξ/̄u	PROPN
ejpam-3322	138	8	)	)	PUNCT
ejpam-3322	138	9	for	for	ADP
ejpam-3322	138	10	all	all	DET
ejpam-3322	138	11	ξ	ξ	PROPN
ejpam-3322	138	12	∈	∈	PROPN
ejpam-3322	138	13	v	v	NOUN
ejpam-3322	138	14	and	and	CCONJ
ejpam-3322	138	15	u	u	PROPN
ejpam-3322	138	16	∈	∈	PROPN
ejpam-3322	138	17	g.	g.	PROPN
ejpam-3322	138	18	c	c	PROPN
ejpam-3322	138	19	can	can	AUX
ejpam-3322	138	20	be	be	AUX
ejpam-3322	138	21	made	make	VERB
ejpam-3322	138	22	into	into	ADP
ejpam-3322	138	23	a	a	DET
ejpam-3322	138	24	tensor	tensor	NOUN
ejpam-3322	138	25	category	category	NOUN
ejpam-3322	138	26	by	by	ADP
ejpam-3322	138	27	taking	take	VERB
ejpam-3322	138	28	v	v	ADP
ejpam-3322	138	29	⊗w	⊗w	NOUN
ejpam-3322	138	30	to	to	PART
ejpam-3322	138	31	be	be	AUX
ejpam-3322	138	32	the	the	DET
ejpam-3322	138	33	usual	usual	ADJ
ejpam-3322	138	34	vector	vector	NOUN
ejpam-3322	138	35	space	space	NOUN
ejpam-3322	138	36	tensor	tensor	NOUN
ejpam-3322	138	37	product	product	NOUN
ejpam-3322	138	38	,	,	PUNCT
ejpam-3322	138	39	with	with	ADP
ejpam-3322	138	40	actions	action	NOUN
ejpam-3322	138	41	and	and	CCONJ
ejpam-3322	138	42	gradings	grading	NOUN
ejpam-3322	138	43	given	give	VERB
ejpam-3322	138	44	by	by	ADP
ejpam-3322	138	45	〈	〈	PROPN
ejpam-3322	138	46	ξ	ξ	PROPN
ejpam-3322	138	47	⊗	⊗	PROPN
ejpam-3322	138	48	η	η	PROPN
ejpam-3322	138	49	〉	〉	PROPN
ejpam-3322	138	50	=	=	SYM
ejpam-3322	138	51	〈	〈	PROPN
ejpam-3322	138	52	ξ	ξ	PROPN
ejpam-3322	138	53	〉	〉	PROPN
ejpam-3322	138	54	·	·	PUNCT
ejpam-3322	139	1	〈	〈	PROPN
ejpam-3322	139	2	η	η	PROPN
ejpam-3322	139	3	〉	〉	PROPN
ejpam-3322	139	4	and	and	CCONJ
ejpam-3322	139	5	(	(	PUNCT
ejpam-3322	139	6	ξ	ξ	PROPN
ejpam-3322	139	7	⊗	⊗	PROPN
ejpam-3322	139	8	η)/̄u	η)/̄u	NOUN
ejpam-3322	139	9	=	=	SYM
ejpam-3322	139	10	ξ/̄(〈η	ξ/̄(〈η	PROPN
ejpam-3322	139	11	〉	〉	PROPN
ejpam-3322	139	12	b	b	PROPN
ejpam-3322	139	13	u)⊗	u)⊗	PROPN
ejpam-3322	139	14	η/̄u	η/̄u	PROPN
ejpam-3322	139	15	.	.	PUNCT
ejpam-3322	140	1	there	there	PRON
ejpam-3322	140	2	is	be	VERB
ejpam-3322	140	3	an	an	DET
ejpam-3322	140	4	associator	associator	NOUN
ejpam-3322	140	5	φuvw	φuvw	NOUN
ejpam-3322	140	6	:	:	PUNCT
ejpam-3322	140	7	(	(	PUNCT
ejpam-3322	140	8	u	u	NOUN
ejpam-3322	140	9	⊗	⊗	PROPN
ejpam-3322	140	10	v	v	NOUN
ejpam-3322	140	11	)	)	PUNCT
ejpam-3322	140	12	⊗w	⊗w	NOUN
ejpam-3322	140	13	→	→	SYM
ejpam-3322	140	14	u	u	NOUN
ejpam-3322	140	15	⊗	⊗	PROPN
ejpam-3322	140	16	(	(	PUNCT
ejpam-3322	140	17	v	v	NOUN
ejpam-3322	140	18	⊗w	⊗w	NOUN
ejpam-3322	140	19	)	)	PUNCT
ejpam-3322	140	20	given	give	VERB
ejpam-3322	140	21	by	by	ADP
ejpam-3322	140	22	φ((ξ	φ((ξ	NOUN
ejpam-3322	140	23	⊗	⊗	PROPN
ejpam-3322	140	24	η)⊗	η)⊗	PROPN
ejpam-3322	140	25	ζ	ζ	NOUN
ejpam-3322	140	26	)	)	PUNCT
ejpam-3322	140	27	=	=	SYM
ejpam-3322	140	28	ξ/̄τ(〈η	ξ/̄τ(〈η	PROPN
ejpam-3322	140	29	〉	〉	PROPN
ejpam-3322	140	30	,	,	PUNCT
ejpam-3322	140	31	〈	〈	PROPN
ejpam-3322	140	32	ζ〉)⊗	ζ〉)⊗	NUM
ejpam-3322	140	33	(	(	PUNCT
ejpam-3322	140	34	η	η	PROPN
ejpam-3322	140	35	⊗	⊗	PROPN
ejpam-3322	140	36	ζ	ζ	PROPN
ejpam-3322	140	37	)	)	PUNCT
ejpam-3322	140	38	.	.	PUNCT
ejpam-3322	141	1	now	now	ADV
ejpam-3322	141	2	,	,	PUNCT
ejpam-3322	141	3	for	for	ADP
ejpam-3322	141	4	the	the	DET
ejpam-3322	141	5	rigidity	rigidity	NOUN
ejpam-3322	141	6	of	of	ADP
ejpam-3322	141	7	c	c	PROPN
ejpam-3322	141	8	,	,	PUNCT
ejpam-3322	141	9	suppose	suppose	VERB
ejpam-3322	141	10	that	that	SCONJ
ejpam-3322	141	11	(	(	PUNCT
ejpam-3322	141	12	m	m	NOUN
ejpam-3322	141	13	,	,	PUNCT
ejpam-3322	141	14	·	·	PUNCT
ejpam-3322	141	15	)	)	PUNCT
ejpam-3322	141	16	has	have	VERB
ejpam-3322	141	17	right	right	ADJ
ejpam-3322	141	18	inverses	inverse	NOUN
ejpam-3322	141	19	,	,	PUNCT
ejpam-3322	141	20	i.e.	i.e.	X
ejpam-3322	141	21	for	for	ADP
ejpam-3322	141	22	every	every	DET
ejpam-3322	141	23	s	s	NOUN
ejpam-3322	141	24	∈m	∈m	NOUN
ejpam-3322	141	25	there	there	PRON
ejpam-3322	141	26	is	be	VERB
ejpam-3322	141	27	an	an	DET
ejpam-3322	141	28	sr	sr	NOUN
ejpam-3322	141	29	∈m	∈m	NOUN
ejpam-3322	141	30	so	so	SCONJ
ejpam-3322	141	31	that	that	SCONJ
ejpam-3322	141	32	s	s	VERB
ejpam-3322	141	33	·	·	PUNCT
ejpam-3322	141	34	sr	sr	PROPN
ejpam-3322	141	35	=	=	SYM
ejpam-3322	141	36	e	e	PROPN
ejpam-3322	141	37	and	and	CCONJ
ejpam-3322	141	38	consider	consider	VERB
ejpam-3322	141	39	v	v	NOUN
ejpam-3322	141	40	=	=	SYM
ejpam-3322	141	41	⊕	⊕	PROPN
ejpam-3322	141	42	s∈m	s∈m	NOUN
ejpam-3322	141	43	vs	vs	ADP
ejpam-3322	141	44	,	,	PUNCT
ejpam-3322	141	45	where	where	SCONJ
ejpam-3322	141	46	ξ	ξ	X
ejpam-3322	141	47	∈	∈	PROPN
ejpam-3322	141	48	vs	vs	ADP
ejpam-3322	141	49	corresponds	correspond	NOUN
ejpam-3322	141	50	to	to	ADP
ejpam-3322	141	51	〈	〈	PROPN
ejpam-3322	141	52	ξ	ξ	PROPN
ejpam-3322	141	53	〉	〉	NOUN
ejpam-3322	141	54	=	=	PUNCT
ejpam-3322	141	55	s.	s.	PROPN
ejpam-3322	141	56	now	now	ADV
ejpam-3322	141	57	take	take	VERB
ejpam-3322	141	58	the	the	DET
ejpam-3322	141	59	dual	dual	ADJ
ejpam-3322	141	60	vector	vector	NOUN
ejpam-3322	141	61	space	space	NOUN
ejpam-3322	141	62	v	v	ADP
ejpam-3322	141	63	∗	∗	NOUN
ejpam-3322	141	64	,	,	PUNCT
ejpam-3322	141	65	and	and	CCONJ
ejpam-3322	141	66	set	set	VERB
ejpam-3322	141	67	v	v	NUM
ejpam-3322	141	68	∗	∗	NOUN
ejpam-3322	141	69	sl	sl	NOUN
ejpam-3322	141	70	=	=	SYM
ejpam-3322	141	71	{	{	PUNCT
ejpam-3322	141	72	α	α	NOUN
ejpam-3322	141	73	∈	∈	NOUN
ejpam-3322	141	74	v	v	ADP
ejpam-3322	141	75	∗	∗	NOUN
ejpam-3322	141	76	:	:	PUNCT
ejpam-3322	142	1	α|vt	α|vt	NOUN
ejpam-3322	142	2	=	=	SYM
ejpam-3322	142	3	0	0	NUM
ejpam-3322	142	4	∀t	∀t	PROPN
ejpam-3322	142	5	6=	6=	SYM
ejpam-3322	142	6	s	s	PART
ejpam-3322	142	7	}	}	PUNCT
ejpam-3322	142	8	.	.	PUNCT
ejpam-3322	143	1	then	then	ADV
ejpam-3322	143	2	v	v	X
ejpam-3322	143	3	∗	∗	NOUN
ejpam-3322	143	4	=	=	SYM
ejpam-3322	143	5	⊕	⊕	PROPN
ejpam-3322	143	6	s∈m	s∈m	NOUN
ejpam-3322	143	7	v	v	ADP
ejpam-3322	143	8	∗	∗	NOUN
ejpam-3322	143	9	sl	sl	NOUN
ejpam-3322	143	10	,	,	PUNCT
ejpam-3322	143	11	and	and	CCONJ
ejpam-3322	143	12	we	we	PRON
ejpam-3322	143	13	define	define	VERB
ejpam-3322	143	14	〈	〈	PROPN
ejpam-3322	143	15	α	α	NOUN
ejpam-3322	143	16	〉	〉	NOUN
ejpam-3322	143	17	=	=	PUNCT
ejpam-3322	143	18	sl	sl	VERB
ejpam-3322	143	19	when	when	SCONJ
ejpam-3322	143	20	α	α	PROPN
ejpam-3322	143	21	∈	∈	PROPN
ejpam-3322	143	22	v	v	ADP
ejpam-3322	143	23	∗	∗	NOUN
ejpam-3322	143	24	sl	sl	INTJ
ejpam-3322	143	25	,	,	PUNCT
ejpam-3322	143	26	where	where	SCONJ
ejpam-3322	143	27	sl	sl	NOUN
ejpam-3322	143	28	is	be	AUX
ejpam-3322	143	29	the	the	DET
ejpam-3322	143	30	left	left	ADJ
ejpam-3322	143	31	inverse	inverse	NOUN
ejpam-3322	143	32	of	of	ADP
ejpam-3322	143	33	s	s	PRON
ejpam-3322	143	34	in	in	ADP
ejpam-3322	143	35	m	m	PROPN
ejpam-3322	143	36	.	.	PUNCT
ejpam-3322	144	1	the	the	DET
ejpam-3322	144	2	evaluation	evaluation	NOUN
ejpam-3322	144	3	map	map	NOUN
ejpam-3322	144	4	ev	ev	X
ejpam-3322	144	5	:	:	PUNCT
ejpam-3322	144	6	v	v	NUM
ejpam-3322	144	7	∗	∗	NOUN
ejpam-3322	144	8	⊗	⊗	PROPN
ejpam-3322	144	9	v	v	NOUN
ejpam-3322	144	10	→	→	SYM
ejpam-3322	144	11	k	k	X
ejpam-3322	144	12	is	be	AUX
ejpam-3322	144	13	defined	define	VERB
ejpam-3322	144	14	by	by	ADP
ejpam-3322	144	15	ev(α	ev(α	NOUN
ejpam-3322	144	16	,	,	PUNCT
ejpam-3322	144	17	ξ	ξ	X
ejpam-3322	144	18	)	)	PUNCT
ejpam-3322	144	19	=	=	SYM
ejpam-3322	144	20	α(ξ	α(ξ	PROPN
ejpam-3322	144	21	)	)	PUNCT
ejpam-3322	144	22	.	.	PUNCT
ejpam-3322	145	1	considering	consider	VERB
ejpam-3322	145	2	the	the	DET
ejpam-3322	145	3	action	action	NOUN
ejpam-3322	145	4	/̄u	/̄u	PUNCT
ejpam-3322	145	5	,	,	PUNCT
ejpam-3322	145	6	if	if	SCONJ
ejpam-3322	145	7	we	we	PRON
ejpam-3322	145	8	apply	apply	VERB
ejpam-3322	145	9	evaluation	evaluation	NOUN
ejpam-3322	145	10	to	to	ADP
ejpam-3322	145	11	α/̄(〈ξ	α/̄(〈ξ	NOUN
ejpam-3322	145	12	〉	〉	PROPN
ejpam-3322	145	13	b	b	SYM
ejpam-3322	145	14	u	u	NOUN
ejpam-3322	145	15	)	)	PUNCT
ejpam-3322	145	16	⊗	⊗	PROPN
ejpam-3322	145	17	ξ/̄u	ξ/̄u	PROPN
ejpam-3322	145	18	we	we	PRON
ejpam-3322	145	19	should	should	AUX
ejpam-3322	145	20	get	get	VERB
ejpam-3322	145	21	α(ξ)/̄u	α(ξ)/̄u	NOUN
ejpam-3322	145	22	=	=	SYM
ejpam-3322	145	23	α(ξ	α(ξ	PROPN
ejpam-3322	145	24	)	)	PUNCT
ejpam-3322	145	25	.	.	PUNCT
ejpam-3322	146	1	so	so	ADV
ejpam-3322	146	2	we	we	PRON
ejpam-3322	146	3	define	define	VERB
ejpam-3322	146	4	(	(	PUNCT
ejpam-3322	146	5	α/̄(〈ξ	α/̄(〈ξ	NOUN
ejpam-3322	146	6	〉	〉	PROPN
ejpam-3322	146	7	b	b	SYM
ejpam-3322	146	8	u	u	NOUN
ejpam-3322	146	9	)	)	PUNCT
ejpam-3322	146	10	)	)	PUNCT
ejpam-3322	147	1	(	(	PUNCT
ejpam-3322	147	2	ξ/̄u	ξ/̄u	PROPN
ejpam-3322	147	3	)	)	PUNCT
ejpam-3322	147	4	=	=	SYM
ejpam-3322	147	5	α(ξ	α(ξ	PROPN
ejpam-3322	147	6	)	)	PUNCT
ejpam-3322	147	7	,	,	PUNCT
ejpam-3322	147	8	or	or	CCONJ
ejpam-3322	147	9	if	if	SCONJ
ejpam-3322	147	10	we	we	PRON
ejpam-3322	147	11	put	put	VERB
ejpam-3322	147	12	η	η	NOUN
ejpam-3322	147	13	=	=	SYM
ejpam-3322	147	14	ξ/̄u	ξ/̄u	PROPN
ejpam-3322	147	15	we	we	PRON
ejpam-3322	147	16	get	get	VERB
ejpam-3322	147	17	(	(	PUNCT
ejpam-3322	147	18	α/̄	α/̄	X
ejpam-3322	147	19	(	(	PUNCT
ejpam-3322	147	20	(	(	PUNCT
ejpam-3322	147	21	〈	〈	PROPN
ejpam-3322	147	22	η	η	PROPN
ejpam-3322	147	23	〉	〉	PROPN
ejpam-3322	147	24	c	c	PROPN
ejpam-3322	147	25	u−1	u−1	PROPN
ejpam-3322	147	26	)	)	PUNCT
ejpam-3322	147	27	b	b	PROPN
ejpam-3322	147	28	u	u	NOUN
ejpam-3322	147	29	)	)	PUNCT
ejpam-3322	147	30	)	)	PUNCT
ejpam-3322	147	31	(	(	PUNCT
ejpam-3322	147	32	η	η	NOUN
ejpam-3322	147	33	)	)	PUNCT
ejpam-3322	147	34	=	=	SYM
ejpam-3322	147	35	α(η/̄u−1	α(η/̄u−1	X
ejpam-3322	147	36	)	)	PUNCT
ejpam-3322	147	37	=	=	NOUN
ejpam-3322	147	38	(	(	PUNCT
ejpam-3322	147	39	α/̄(〈η	α/̄(〈η	PROPN
ejpam-3322	147	40	〉	〉	PROPN
ejpam-3322	147	41	b	b	PROPN
ejpam-3322	147	42	u−1)−1	u−1)−1	PROPN
ejpam-3322	147	43	)	)	PUNCT
ejpam-3322	147	44	(	(	PUNCT
ejpam-3322	147	45	η	η	NOUN
ejpam-3322	147	46	)	)	PUNCT
ejpam-3322	147	47	.	.	PUNCT
ejpam-3322	148	1	if	if	SCONJ
ejpam-3322	148	2	this	this	PRON
ejpam-3322	148	3	is	be	AUX
ejpam-3322	148	4	rearranged	rearrange	VERB
ejpam-3322	148	5	to	to	PART
ejpam-3322	148	6	give	give	VERB
ejpam-3322	148	7	α	α	PRON
ejpam-3322	148	8	/	/	SYM
ejpam-3322	148	9	v	v	NOUN
ejpam-3322	148	10	,	,	PUNCT
ejpam-3322	148	11	we	we	PRON
ejpam-3322	148	12	get	get	VERB
ejpam-3322	148	13	the	the	DET
ejpam-3322	148	14	following	follow	VERB
ejpam-3322	148	15	formula	formula	NOUN
ejpam-3322	148	16	:	:	PUNCT
ejpam-3322	148	17	(	(	PUNCT
ejpam-3322	148	18	α/̄v)(η	α/̄v)(η	NUM
ejpam-3322	148	19	)	)	PUNCT
ejpam-3322	149	1	=	=	SYM
ejpam-3322	149	2	α	α	PROPN
ejpam-3322	149	3	(	(	PUNCT
ejpam-3322	149	4	η/̄τ(〈η〉l	η/̄τ(〈η〉l	PROPN
ejpam-3322	149	5	,	,	PUNCT
ejpam-3322	149	6	〈	〈	PROPN
ejpam-3322	149	7	η〉)−1(〈η〉l	η〉)−1(〈η〉l	NOUN
ejpam-3322	149	8	b	b	X
ejpam-3322	149	9	v−1)τ(〈η〉l	v−1)τ(〈η〉l	NOUN
ejpam-3322	149	10	c	c	X
ejpam-3322	149	11	v−1	v−1	PROPN
ejpam-3322	149	12	,	,	PUNCT
ejpam-3322	149	13	(	(	PUNCT
ejpam-3322	149	14	〈	〈	PROPN
ejpam-3322	149	15	η〉l	η〉l	NOUN
ejpam-3322	149	16	c	c	NOUN
ejpam-3322	149	17	v−1)r	v−1)r	X
ejpam-3322	149	18	)	)	PUNCT
ejpam-3322	149	19	)	)	PUNCT
ejpam-3322	149	20	.	.	PUNCT
ejpam-3322	150	1	(	(	PUNCT
ejpam-3322	150	2	5	5	X
ejpam-3322	150	3	)	)	PUNCT
ejpam-3322	150	4	for	for	SCONJ
ejpam-3322	150	5	the	the	DET
ejpam-3322	150	6	coevaluation	coevaluation	NOUN
ejpam-3322	150	7	map	map	NOUN
ejpam-3322	150	8	to	to	PART
ejpam-3322	150	9	be	be	AUX
ejpam-3322	150	10	defined	define	VERB
ejpam-3322	150	11	,	,	PUNCT
ejpam-3322	150	12	a	a	DET
ejpam-3322	150	13	basis	basis	NOUN
ejpam-3322	150	14	{	{	PUNCT
ejpam-3322	150	15	ξ	ξ	NOUN
ejpam-3322	150	16	}	}	PUNCT
ejpam-3322	150	17	of	of	ADP
ejpam-3322	150	18	each	each	PRON
ejpam-3322	150	19	vs	vs	ADP
ejpam-3322	150	20	is	be	AUX
ejpam-3322	150	21	taken	take	VERB
ejpam-3322	150	22	and	and	CCONJ
ejpam-3322	150	23	a	a	DET
ejpam-3322	150	24	corresponding	correspond	VERB
ejpam-3322	150	25	dual	dual	ADJ
ejpam-3322	150	26	basis	basis	NOUN
ejpam-3322	150	27	{	{	PUNCT
ejpam-3322	150	28	ξ̂	ξ̂	NOUN
ejpam-3322	150	29	}	}	PUNCT
ejpam-3322	150	30	of	of	ADP
ejpam-3322	150	31	each	each	PRON
ejpam-3322	150	32	v	v	NOUN
ejpam-3322	150	33	∗	∗	NOUN
ejpam-3322	150	34	sl	sl	INTJ
ejpam-3322	150	35	,	,	PUNCT
ejpam-3322	150	36	i.e.	i.e.	X
ejpam-3322	150	37	η̂(ξ	η̂(ξ	ADJ
ejpam-3322	150	38	)	)	PUNCT
ejpam-3322	151	1	=	=	SYM
ejpam-3322	151	2	δξ	δξ	PROPN
ejpam-3322	151	3	,	,	PUNCT
ejpam-3322	151	4	η	η	PROPN
ejpam-3322	151	5	.	.	PROPN
ejpam-3322	151	6	then	then	ADV
ejpam-3322	151	7	these	these	DET
ejpam-3322	151	8	bases	basis	NOUN
ejpam-3322	151	9	are	be	AUX
ejpam-3322	151	10	put	put	VERB
ejpam-3322	151	11	together	together	ADV
ejpam-3322	151	12	for	for	ADP
ejpam-3322	151	13	all	all	DET
ejpam-3322	151	14	s	s	PART
ejpam-3322	151	15	∈m	∈m	NOUN
ejpam-3322	151	16	to	to	PART
ejpam-3322	151	17	get	get	VERB
ejpam-3322	151	18	the	the	DET
ejpam-3322	151	19	following	follow	VERB
ejpam-3322	151	20	definition	definition	NOUN
ejpam-3322	151	21	,	,	PUNCT
ejpam-3322	151	22	which	which	PRON
ejpam-3322	151	23	is	be	AUX
ejpam-3322	151	24	a	a	DET
ejpam-3322	151	25	morphism	morphism	NOUN
ejpam-3322	151	26	in	in	ADP
ejpam-3322	151	27	c	c	PROPN
ejpam-3322	152	1	[	[	X
ejpam-3322	152	2	4	4	NUM
ejpam-3322	152	3	]	]	NOUN
ejpam-3322	152	4	:	:	PUNCT
ejpam-3322	152	5	coev(1	coev(1	ADJ
ejpam-3322	152	6	)	)	PUNCT
ejpam-3322	152	7	=	=	PUNCT
ejpam-3322	153	1	∑	∑	PUNCT
ejpam-3322	153	2	ξ∈basis	ξ∈basis	PROPN
ejpam-3322	153	3	ξ/̄τ(〈ξ〉l	ξ/̄τ(〈ξ〉l	PROPN
ejpam-3322	153	4	,	,	PUNCT
ejpam-3322	153	5	〈	〈	PROPN
ejpam-3322	153	6	ξ〉)−1	ξ〉)−1	NOUN
ejpam-3322	153	7	⊗	⊗	PROPN
ejpam-3322	153	8	ξ̂	ξ̂	NUM
ejpam-3322	153	9	.	.	PUNCT
ejpam-3322	154	1	the	the	DET
ejpam-3322	154	2	algebra	algebra	NOUN
ejpam-3322	154	3	a	a	PRON
ejpam-3322	154	4	in	in	ADP
ejpam-3322	154	5	the	the	DET
ejpam-3322	154	6	tensor	tensor	NOUN
ejpam-3322	154	7	category	category	NOUN
ejpam-3322	154	8	c	c	PROPN
ejpam-3322	154	9	is	be	AUX
ejpam-3322	154	10	constructed	construct	VERB
ejpam-3322	154	11	such	such	ADJ
ejpam-3322	154	12	that	that	SCONJ
ejpam-3322	154	13	the	the	DET
ejpam-3322	154	14	group	group	NOUN
ejpam-3322	154	15	action	action	NOUN
ejpam-3322	154	16	and	and	CCONJ
ejpam-3322	154	17	the	the	DET
ejpam-3322	154	18	grading	grading	NOUN
ejpam-3322	154	19	in	in	ADP
ejpam-3322	154	20	the	the	DET
ejpam-3322	154	21	definition	definition	NOUN
ejpam-3322	154	22	of	of	ADP
ejpam-3322	154	23	c	c	NOUN
ejpam-3322	154	24	can	can	AUX
ejpam-3322	154	25	be	be	AUX
ejpam-3322	154	26	combined	combine	VERB
ejpam-3322	154	27	.	.	PUNCT
ejpam-3322	155	1	we	we	PRON
ejpam-3322	155	2	consider	consider	VERB
ejpam-3322	155	3	a	a	DET
ejpam-3322	155	4	single	single	ADJ
ejpam-3322	155	5	object	object	NOUN
ejpam-3322	155	6	a	a	DET
ejpam-3322	155	7	in	in	ADP
ejpam-3322	155	8	c	c	PROPN
ejpam-3322	155	9	,	,	PUNCT
ejpam-3322	155	10	a	a	DET
ejpam-3322	155	11	vector	vector	NOUN
ejpam-3322	155	12	space	space	NOUN
ejpam-3322	155	13	spanned	span	VERB
ejpam-3322	155	14	by	by	ADP
ejpam-3322	155	15	a	a	DET
ejpam-3322	155	16	basis	basis	NOUN
ejpam-3322	155	17	δs⊗u	δs⊗u	NOUN
ejpam-3322	155	18	for	for	ADP
ejpam-3322	155	19	s	s	PRON
ejpam-3322	155	20	∈m	∈m	NOUN
ejpam-3322	155	21	and	and	CCONJ
ejpam-3322	155	22	u	u	NOUN
ejpam-3322	155	23	∈	∈	PROPN
ejpam-3322	155	24	g.	g.	NOUN
ejpam-3322	155	25	for	for	ADP
ejpam-3322	155	26	any	any	DET
ejpam-3322	155	27	object	object	NOUN
ejpam-3322	155	28	v	v	NOUN
ejpam-3322	155	29	in	in	ADP
ejpam-3322	155	30	c	c	NOUN
ejpam-3322	155	31	define	define	VERB
ejpam-3322	155	32	a	a	DET
ejpam-3322	155	33	map	map	NOUN
ejpam-3322	155	34	/̄	/̄	PUNCT
ejpam-3322	156	1	:	:	PUNCT
ejpam-3322	156	2	v	v	NUM
ejpam-3322	156	3	⊗a→	⊗a→	PROPN
ejpam-3322	156	4	v	v	NOUN
ejpam-3322	156	5	by	by	ADP
ejpam-3322	156	6	ξ/̄(δs	ξ/̄(δs	PROPN
ejpam-3322	156	7	⊗	⊗	NUM
ejpam-3322	156	8	u	u	NOUN
ejpam-3322	156	9	)	)	PUNCT
ejpam-3322	156	10	=	=	SYM
ejpam-3322	156	11	δs	δs	NOUN
ejpam-3322	156	12	,	,	PUNCT
ejpam-3322	156	13	〈ξ〉ξ/̄u	〈ξ〉ξ/̄u	PROPN
ejpam-3322	156	14	.	.	PUNCT
ejpam-3322	157	1	this	this	DET
ejpam-3322	157	2	map	map	NOUN
ejpam-3322	157	3	is	be	AUX
ejpam-3322	157	4	a	a	DET
ejpam-3322	157	5	morphism	morphism	NOUN
ejpam-3322	157	6	in	in	ADP
ejpam-3322	157	7	c	c	NOUN
ejpam-3322	157	8	only	only	ADV
ejpam-3322	157	9	if	if	SCONJ
ejpam-3322	157	10	〈	〈	PROPN
ejpam-3322	157	11	ξ	ξ	PROPN
ejpam-3322	157	12	〉	〉	NOUN
ejpam-3322	158	1	·	·	PUNCT
ejpam-3322	158	2	〈	〈	NOUN
ejpam-3322	158	3	δs	δs	NOUN
ejpam-3322	158	4	⊗	⊗	NUM
ejpam-3322	158	5	u	u	PROPN
ejpam-3322	158	6	〉	〉	NOUN
ejpam-3322	158	7	=	=	SYM
ejpam-3322	158	8	〈	〈	PROPN
ejpam-3322	158	9	ξ/̄u	ξ/̄u	PROPN
ejpam-3322	158	10	〉	〉	PROPN
ejpam-3322	158	11	,	,	PUNCT
ejpam-3322	158	12	i.e.	i.e.	X
ejpam-3322	158	13	s	s	X
ejpam-3322	158	14	·	·	PUNCT
ejpam-3322	158	15	〈	〈	VERB
ejpam-3322	158	16	δs	δs	NOUN
ejpam-3322	158	17	⊗	⊗	NUM
ejpam-3322	158	18	u	u	PROPN
ejpam-3322	158	19	〉	〉	PROPN
ejpam-3322	158	20	=	=	SYM
ejpam-3322	158	21	s	s	PROPN
ejpam-3322	158	22	/	/	SYM
ejpam-3322	158	23	u	u	NOUN
ejpam-3322	158	24	,	,	PUNCT
ejpam-3322	158	25	where	where	SCONJ
ejpam-3322	158	26	〈	〈	PROPN
ejpam-3322	158	27	ξ	ξ	PROPN
ejpam-3322	158	28	〉	〉	NOUN
ejpam-3322	158	29	=	=	SYM
ejpam-3322	158	30	s.	s.	PROPN
ejpam-3322	158	31	if	if	SCONJ
ejpam-3322	158	32	we	we	PRON
ejpam-3322	158	33	put	put	VERB
ejpam-3322	158	34	a	a	DET
ejpam-3322	158	35	=	=	SYM
ejpam-3322	158	36	〈	〈	PROPN
ejpam-3322	158	37	δs	δs	NOUN
ejpam-3322	158	38	⊗	⊗	PROPN
ejpam-3322	158	39	u	u	PROPN
ejpam-3322	158	40	〉	〉	PROPN
ejpam-3322	158	41	,	,	PUNCT
ejpam-3322	158	42	the	the	DET
ejpam-3322	158	43	action	action	NOUN
ejpam-3322	158	44	of	of	ADP
ejpam-3322	158	45	v	v	NOUN
ejpam-3322	158	46	∈	∈	PROPN
ejpam-3322	158	47	g	g	NOUN
ejpam-3322	158	48	is	be	AUX
ejpam-3322	158	49	given	give	VERB
ejpam-3322	158	50	by	by	ADP
ejpam-3322	158	51	(	(	PUNCT
ejpam-3322	158	52	δs	δs	NOUN
ejpam-3322	158	53	⊗	⊗	NUM
ejpam-3322	158	54	u)/̄v	u)/̄v	NOUN
ejpam-3322	158	55	=	=	SYM
ejpam-3322	158	56	δsc(abv	δsc(abv	X
ejpam-3322	158	57	)	)	PUNCT
ejpam-3322	158	58	⊗	⊗	NOUN
ejpam-3322	158	59	(	(	PUNCT
ejpam-3322	158	60	a	a	DET
ejpam-3322	158	61	b	b	PROPN
ejpam-3322	158	62	v)−1uv	v)−1uv	NOUN
ejpam-3322	158	63	.	.	PUNCT
ejpam-3322	159	1	b.	b.	PROPN
ejpam-3322	160	1	al	al	PROPN
ejpam-3322	160	2	-	-	PUNCT
ejpam-3322	160	3	harbi	harbi	PROPN
ejpam-3322	160	4	,	,	PUNCT
ejpam-3322	160	5	w.	w.	PROPN
ejpam-3322	160	6	m.	m.	PROPN
ejpam-3322	160	7	fakieh	fakieh	PROPN
ejpam-3322	160	8	,	,	PUNCT
ejpam-3322	160	9	m.	m.	NOUN
ejpam-3322	160	10	m.	m.	PROPN
ejpam-3322	160	11	al	al	PROPN
ejpam-3322	160	12	-	-	PUNCT
ejpam-3322	160	13	shomrani	shomrani	PROPN
ejpam-3322	160	14	/	/	SYM
ejpam-3322	160	15	eur	eur	NOUN
ejpam-3322	160	16	.	.	PUNCT
ejpam-3322	161	1	j.	j.	PROPN
ejpam-3322	161	2	pure	pure	PROPN
ejpam-3322	161	3	appl	appl	PROPN
ejpam-3322	161	4	.	.	PROPN
ejpam-3322	161	5	math	math	PROPN
ejpam-3322	161	6	,	,	PUNCT
ejpam-3322	161	7	11	11	NUM
ejpam-3322	161	8	(	(	PUNCT
ejpam-3322	161	9	4	4	NUM
ejpam-3322	161	10	)	)	PUNCT
ejpam-3322	161	11	(	(	PUNCT
ejpam-3322	161	12	2018	2018	NUM
ejpam-3322	161	13	)	)	PUNCT
ejpam-3322	161	14	,	,	PUNCT
ejpam-3322	161	15	1027	1027	NUM
ejpam-3322	161	16	-	-	SYM
ejpam-3322	161	17	1045	1045	NUM
ejpam-3322	161	18	1032	1032	NUM
ejpam-3322	161	19	in	in	ADP
ejpam-3322	161	20	the	the	DET
ejpam-3322	161	21	remaining	remain	VERB
ejpam-3322	161	22	of	of	ADP
ejpam-3322	161	23	this	this	DET
ejpam-3322	161	24	article	article	NOUN
ejpam-3322	161	25	,	,	PUNCT
ejpam-3322	161	26	when	when	SCONJ
ejpam-3322	161	27	an	an	DET
ejpam-3322	161	28	algebra	algebra	NOUN
ejpam-3322	161	29	a	a	PRON
ejpam-3322	161	30	in	in	ADP
ejpam-3322	161	31	c	c	PROPN
ejpam-3322	161	32	is	be	AUX
ejpam-3322	161	33	mentioned	mention	VERB
ejpam-3322	161	34	,	,	PUNCT
ejpam-3322	161	35	it	it	PRON
ejpam-3322	161	36	is	be	AUX
ejpam-3322	161	37	meant	mean	VERB
ejpam-3322	161	38	to	to	PART
ejpam-3322	161	39	refer	refer	VERB
ejpam-3322	161	40	to	to	ADP
ejpam-3322	161	41	this	this	DET
ejpam-3322	161	42	construction	construction	NOUN
ejpam-3322	161	43	.	.	PUNCT
ejpam-3322	162	1	proposition	proposition	NOUN
ejpam-3322	162	2	2.8	2.8	NUM
ejpam-3322	162	3	.	.	PUNCT
ejpam-3322	163	1	[	[	X
ejpam-3322	163	2	4	4	X
ejpam-3322	163	3	]	]	PUNCT
ejpam-3322	163	4	the	the	DET
ejpam-3322	163	5	formula	formula	NOUN
ejpam-3322	163	6	of	of	ADP
ejpam-3322	163	7	the	the	DET
ejpam-3322	163	8	multiplication	multiplication	NOUN
ejpam-3322	163	9	µa	µa	NOUN
ejpam-3322	163	10	for	for	ADP
ejpam-3322	163	11	a	a	DET
ejpam-3322	163	12	in	in	ADP
ejpam-3322	163	13	c	c	NOUN
ejpam-3322	163	14	is	be	AUX
ejpam-3322	163	15	given	give	VERB
ejpam-3322	163	16	by	by	ADP
ejpam-3322	163	17	(	(	PUNCT
ejpam-3322	163	18	δs	δs	PROPN
ejpam-3322	163	19	⊗	⊗	PROPN
ejpam-3322	163	20	u)(δt	u)(δt	PROPN
ejpam-3322	163	21	⊗	⊗	PROPN
ejpam-3322	163	22	v	v	NOUN
ejpam-3322	163	23	)	)	PUNCT
ejpam-3322	163	24	=	=	SYM
ejpam-3322	163	25	δt	δt	PROPN
ejpam-3322	163	26	,	,	PUNCT
ejpam-3322	163	27	scuδscτ(a	scuδscτ(a	PROPN
ejpam-3322	163	28	,	,	PUNCT
ejpam-3322	163	29	b	b	NOUN
ejpam-3322	163	30	)	)	PUNCT
ejpam-3322	163	31	⊗	⊗	NUM
ejpam-3322	163	32	τ(a	τ(a	NOUN
ejpam-3322	163	33	,	,	PUNCT
ejpam-3322	163	34	b)−1uv	b)−1uv	NOUN
ejpam-3322	163	35	,	,	PUNCT
ejpam-3322	163	36	where	where	SCONJ
ejpam-3322	163	37	a	a	DET
ejpam-3322	163	38	=	=	X
ejpam-3322	163	39	〈	〈	NOUN
ejpam-3322	163	40	δs	δs	NOUN
ejpam-3322	163	41	⊗	⊗	PROPN
ejpam-3322	163	42	u	u	PROPN
ejpam-3322	163	43	〉	〉	PROPN
ejpam-3322	163	44	and	and	CCONJ
ejpam-3322	163	45	b	b	NOUN
ejpam-3322	163	46	=	=	SYM
ejpam-3322	163	47	〈	〈	PROPN
ejpam-3322	163	48	δt	δt	PROPN
ejpam-3322	163	49	⊗	⊗	PROPN
ejpam-3322	163	50	v	v	PROPN
ejpam-3322	163	51	〉	〉	PROPN
ejpam-3322	163	52	.	.	PUNCT
ejpam-3322	164	1	proposition	proposition	NOUN
ejpam-3322	164	2	2.9	2.9	NUM
ejpam-3322	164	3	.	.	PUNCT
ejpam-3322	165	1	[	[	X
ejpam-3322	165	2	4	4	NUM
ejpam-3322	165	3	]	]	ADJ
ejpam-3322	165	4	multiplication	multiplication	NOUN
ejpam-3322	165	5	µa	µa	NOUN
ejpam-3322	165	6	:	:	PUNCT
ejpam-3322	165	7	a⊗	a⊗	NOUN
ejpam-3322	165	8	a	a	DET
ejpam-3322	165	9	−→	−→	NOUN
ejpam-3322	165	10	a	a	PRON
ejpam-3322	165	11	is	be	AUX
ejpam-3322	165	12	a	a	DET
ejpam-3322	165	13	morphism	morphism	NOUN
ejpam-3322	165	14	and	and	CCONJ
ejpam-3322	165	15	associative	associative	NOUN
ejpam-3322	165	16	in	in	ADP
ejpam-3322	165	17	c.	c.	PROPN
ejpam-3322	165	18	also	also	ADV
ejpam-3322	165	19	there	there	PRON
ejpam-3322	165	20	are	be	VERB
ejpam-3322	165	21	an	an	DET
ejpam-3322	165	22	identity	identity	NOUN
ejpam-3322	165	23	i	i	PRON
ejpam-3322	165	24	for	for	ADP
ejpam-3322	165	25	the	the	DET
ejpam-3322	165	26	multiplication	multiplication	NOUN
ejpam-3322	165	27	and	and	CCONJ
ejpam-3322	165	28	an	an	DET
ejpam-3322	165	29	algebra	algebra	NOUN
ejpam-3322	165	30	map	map	NOUN
ejpam-3322	165	31	εa	εa	X
ejpam-3322	165	32	:	:	PUNCT
ejpam-3322	166	1	a	a	DET
ejpam-3322	166	2	−→	−→	NOUN
ejpam-3322	166	3	k	k	X
ejpam-3322	166	4	in	in	ADP
ejpam-3322	166	5	the	the	DET
ejpam-3322	166	6	category	category	NOUN
ejpam-3322	166	7	given	give	VERB
ejpam-3322	166	8	by	by	ADP
ejpam-3322	166	9	ia	ia	PROPN
ejpam-3322	166	10	=	=	SYM
ejpam-3322	166	11	∑	∑	PROPN
ejpam-3322	166	12	t	t	PROPN
ejpam-3322	166	13	δt	δt	X
ejpam-3322	166	14	⊗	⊗	PROPN
ejpam-3322	166	15	e	e	PROPN
ejpam-3322	166	16	,	,	PUNCT
ejpam-3322	166	17	εa(δs	εa(δs	NOUN
ejpam-3322	166	18	⊗	⊗	NUM
ejpam-3322	166	19	u	u	NOUN
ejpam-3322	166	20	)	)	PUNCT
ejpam-3322	166	21	=	=	SYM
ejpam-3322	166	22	δs	δs	NOUN
ejpam-3322	166	23	,	,	PUNCT
ejpam-3322	166	24	e.	e.	PROPN
ejpam-3322	167	1	the	the	DET
ejpam-3322	167	2	identity	identity	NOUN
ejpam-3322	167	3	ia	ia	PROPN
ejpam-3322	167	4	has	have	VERB
ejpam-3322	167	5	the	the	DET
ejpam-3322	167	6	trivial	trivial	ADJ
ejpam-3322	167	7	action	action	NOUN
ejpam-3322	167	8	on	on	ADP
ejpam-3322	167	9	the	the	DET
ejpam-3322	167	10	objects	object	NOUN
ejpam-3322	167	11	of	of	ADP
ejpam-3322	167	12	c.	c.	NOUN
ejpam-3322	167	13	also	also	ADV
ejpam-3322	167	14	the	the	DET
ejpam-3322	167	15	action	action	NOUN
ejpam-3322	167	16	of	of	ADP
ejpam-3322	167	17	h	h	NOUN
ejpam-3322	167	18	∈	∈	PROPN
ejpam-3322	167	19	a	a	PRON
ejpam-3322	167	20	on	on	ADP
ejpam-3322	167	21	the	the	DET
ejpam-3322	167	22	object	object	NOUN
ejpam-3322	167	23	k	k	X
ejpam-3322	167	24	is	be	AUX
ejpam-3322	167	25	just	just	ADV
ejpam-3322	167	26	multiplication	multiplication	NOUN
ejpam-3322	167	27	by	by	ADP
ejpam-3322	167	28	εa(h	εa(h	NOUN
ejpam-3322	167	29	)	)	PUNCT
ejpam-3322	167	30	,	,	PUNCT
ejpam-3322	167	31	and	and	CCONJ
ejpam-3322	167	32	εa(i	εa(i	NOUN
ejpam-3322	167	33	)	)	PUNCT
ejpam-3322	167	34	=	=	SYM
ejpam-3322	167	35	1	1	NUM
ejpam-3322	167	36	,	,	PUNCT
ejpam-3322	167	37	the	the	DET
ejpam-3322	167	38	identity	identity	NOUN
ejpam-3322	167	39	element	element	NOUN
ejpam-3322	167	40	in	in	ADP
ejpam-3322	167	41	k.	k.	PROPN
ejpam-3322	167	42	proposition	proposition	PROPN
ejpam-3322	167	43	2.10	2.10	NUM
ejpam-3322	167	44	.	.	PUNCT
ejpam-3322	168	1	[	[	X
ejpam-3322	168	2	1	1	X
ejpam-3322	168	3	]	]	PUNCT
ejpam-3322	168	4	define	define	VERB
ejpam-3322	168	5	a	a	DET
ejpam-3322	168	6	basis	basis	NOUN
ejpam-3322	168	7	s⊗	s⊗	NOUN
ejpam-3322	168	8	δu	δu	NOUN
ejpam-3322	168	9	of	of	ADP
ejpam-3322	168	10	a∗	a∗	PROPN
ejpam-3322	168	11	with	with	ADP
ejpam-3322	168	12	evaluation	evaluation	NOUN
ejpam-3322	168	13	map	map	NOUN
ejpam-3322	168	14	given	give	VERB
ejpam-3322	168	15	by	by	ADP
ejpam-3322	168	16	ev	ev	X
ejpam-3322	168	17	(	(	PUNCT
ejpam-3322	168	18	(	(	PUNCT
ejpam-3322	168	19	s⊗	s⊗	NOUN
ejpam-3322	168	20	δu)⊗	δu)⊗	PROPN
ejpam-3322	168	21	(	(	PUNCT
ejpam-3322	168	22	δt	δt	PROPN
ejpam-3322	168	23	⊗	⊗	PROPN
ejpam-3322	168	24	v	v	NOUN
ejpam-3322	168	25	)	)	PUNCT
ejpam-3322	168	26	)	)	PUNCT
ejpam-3322	169	1	=	=	SYM
ejpam-3322	169	2	δs	δs	NOUN
ejpam-3322	169	3	,	,	PUNCT
ejpam-3322	169	4	t	t	PROPN
ejpam-3322	169	5	δu	δu	NOUN
ejpam-3322	169	6	,	,	PUNCT
ejpam-3322	169	7	v	v	NOUN
ejpam-3322	169	8	,	,	PUNCT
ejpam-3322	169	9	for	for	ADP
ejpam-3322	169	10	s	s	PROPN
ejpam-3322	169	11	,	,	PUNCT
ejpam-3322	169	12	t	t	PROPN
ejpam-3322	169	13	∈	∈	PROPN
ejpam-3322	169	14	m	m	PROPN
ejpam-3322	169	15	and	and	CCONJ
ejpam-3322	169	16	u	u	NOUN
ejpam-3322	169	17	,	,	PUNCT
ejpam-3322	169	18	v	v	PROPN
ejpam-3322	169	19	∈	∈	NOUN
ejpam-3322	169	20	g.	g.	NOUN
ejpam-3322	170	1	then	then	ADV
ejpam-3322	170	2	the	the	DET
ejpam-3322	170	3	m	m	PROPN
ejpam-3322	170	4	-grade	-grade	PROPN
ejpam-3322	170	5	and	and	CCONJ
ejpam-3322	170	6	the	the	DET
ejpam-3322	170	7	g	g	NOUN
ejpam-3322	170	8	-	-	PUNCT
ejpam-3322	170	9	action	action	NOUN
ejpam-3322	170	10	on	on	ADP
ejpam-3322	170	11	a∗	a∗	PROPN
ejpam-3322	170	12	are	be	AUX
ejpam-3322	170	13	defined	define	VERB
ejpam-3322	170	14	as	as	SCONJ
ejpam-3322	170	15	follows	follow	VERB
ejpam-3322	170	16	:	:	PUNCT
ejpam-3322	171	1	〈	〈	NOUN
ejpam-3322	171	2	s⊗	s⊗	VERB
ejpam-3322	171	3	δu	δu	PRON
ejpam-3322	171	4	〉	〉	NOUN
ejpam-3322	171	5	=	=	SYM
ejpam-3322	171	6	〈	〈	PROPN
ejpam-3322	171	7	δs	δs	NOUN
ejpam-3322	171	8	⊗	⊗	PROPN
ejpam-3322	171	9	u〉l	u〉l	PROPN
ejpam-3322	171	10	,	,	PUNCT
ejpam-3322	171	11	and	and	CCONJ
ejpam-3322	171	12	for	for	ADP
ejpam-3322	171	13	any	any	DET
ejpam-3322	171	14	w	w	PROPN
ejpam-3322	171	15	∈	∈	PROPN
ejpam-3322	171	16	g	g	NOUN
ejpam-3322	171	17	(	(	PUNCT
ejpam-3322	171	18	s⊗	s⊗	VERB
ejpam-3322	171	19	δu)/̄(〈s⊗	δu)/̄(〈s⊗	PROPN
ejpam-3322	171	20	δu〉r	δu〉r	PROPN
ejpam-3322	171	21	b	b	PROPN
ejpam-3322	171	22	w	w	NOUN
ejpam-3322	171	23	)	)	PUNCT
ejpam-3322	171	24	=	=	VERB
ejpam-3322	171	25	s/(〈s⊗	s/(〈s⊗	PROPN
ejpam-3322	171	26	δu〉r	δu〉r	PROPN
ejpam-3322	171	27	b	b	PROPN
ejpam-3322	171	28	w)⊗	w)⊗	PROPN
ejpam-3322	171	29	δ	δ	PROPN
ejpam-3322	171	30	(	(	PUNCT
ejpam-3322	171	31	〈	〈	PROPN
ejpam-3322	171	32	s⊗δu〉rbw)−1uw	s⊗δu〉rbw)−1uw	PROPN
ejpam-3322	171	33	.	.	PUNCT
ejpam-3322	172	1	proposition	proposition	NOUN
ejpam-3322	172	2	2.11	2.11	NUM
ejpam-3322	172	3	.	.	PUNCT
ejpam-3322	173	1	[	[	X
ejpam-3322	173	2	1	1	X
ejpam-3322	173	3	]	]	X
ejpam-3322	173	4	if	if	SCONJ
ejpam-3322	173	5	a	a	PRON
ejpam-3322	173	6	is	be	AUX
ejpam-3322	173	7	an	an	DET
ejpam-3322	173	8	algebra	algebra	NOUN
ejpam-3322	173	9	in	in	ADP
ejpam-3322	173	10	a	a	DET
ejpam-3322	173	11	rigid	rigid	ADJ
ejpam-3322	173	12	tensor	tensor	NOUN
ejpam-3322	173	13	category	category	NOUN
ejpam-3322	173	14	,	,	PUNCT
ejpam-3322	173	15	then	then	ADV
ejpam-3322	173	16	its	its	PRON
ejpam-3322	173	17	dual	dual	ADJ
ejpam-3322	173	18	a∗	a∗	NOUN
ejpam-3322	173	19	is	be	AUX
ejpam-3322	173	20	a	a	DET
ejpam-3322	173	21	coalgebra	coalgebra	NOUN
ejpam-3322	173	22	in	in	ADP
ejpam-3322	173	23	the	the	DET
ejpam-3322	173	24	category	category	NOUN
ejpam-3322	173	25	using	use	VERB
ejpam-3322	173	26	the	the	DET
ejpam-3322	173	27	following	follow	VERB
ejpam-3322	173	28	definitions	definition	NOUN
ejpam-3322	173	29	:	:	PUNCT
ejpam-3322	173	30	@@	@@	X
ejpam-3322	173	31	�	�	PROPN
ejpam-3322	173	32	�	�	PROPN
ejpam-3322	173	33	@@	@@	PROPN
ejpam-3322	173	34	�	�	PROPN
ejpam-3322	173	35	�	�	PROPN
ejpam-3322	173	36	�	�	PROPN
ejpam-3322	173	37	�	�	PROPN
ejpam-3322	173	38	@@	@@	PROPN
ejpam-3322	173	39	�	�	PROPN
ejpam-3322	173	40	�	�	PROPN
ejpam-3322	173	41	@	@	ADP
ejpam-3322	173	42	@	@	ADP
ejpam-3322	173	43	@	@	ADP
ejpam-3322	173	44	@	@	ADP
ejpam-3322	173	45	�	�	PROPN
ejpam-3322	173	46	�	�	PROPN
ejpam-3322	173	47	a∗a∗	a∗a∗	PROPN
ejpam-3322	173	48	a∗	a∗	PROPN
ejpam-3322	173	49	=	=	SYM
ejpam-3322	173	50	�	�	PROPN
ejpam-3322	173	51	�	�	PROPN
ejpam-3322	173	52	@@	@@	PROPN
ejpam-3322	173	53	∗	∗	NOUN
ejpam-3322	173	54	a∗	a∗	PROPN
ejpam-3322	173	55	a∗	a∗	PROPN
ejpam-3322	173	56	a∗	a∗	PROPN
ejpam-3322	173	57	,	,	PUNCT
ejpam-3322	173	58	a∗	a∗	PROPN
ejpam-3322	173	59	@@	@@	SYM
ejpam-3322	173	60	�	�	PROPN
ejpam-3322	173	61	�	�	PROPN
ejpam-3322	173	62	�	�	PROPN
ejpam-3322	173	63	�	�	PROPN
ejpam-3322	173	64	�	�	PROPN
ejpam-3322	173	65	ηa=	ηa=	PROPN
ejpam-3322	173	66	�	�	PROPN
ejpam-3322	173	67	�	�	PROPN
ejpam-3322	173	68	�	�	PROPN
ejpam-3322	173	69	εa∗	εa∗	NOUN
ejpam-3322	173	70	a∗	a∗	ADJ
ejpam-3322	173	71	figure	figure	NOUN
ejpam-3322	173	72	3	3	NUM
ejpam-3322	173	73	:	:	PUNCT
ejpam-3322	173	74	comultiplication	comultiplication	NOUN
ejpam-3322	173	75	and	and	CCONJ
ejpam-3322	173	76	counit	counit	VERB
ejpam-3322	173	77	on	on	ADP
ejpam-3322	173	78	a∗.	a∗.	PROPN
ejpam-3322	173	79	b.	b.	PROPN
ejpam-3322	173	80	al	al	PROPN
ejpam-3322	173	81	-	-	PUNCT
ejpam-3322	173	82	harbi	harbi	PROPN
ejpam-3322	173	83	,	,	PUNCT
ejpam-3322	173	84	w.	w.	PROPN
ejpam-3322	173	85	m.	m.	PROPN
ejpam-3322	173	86	fakieh	fakieh	PROPN
ejpam-3322	173	87	,	,	PUNCT
ejpam-3322	173	88	m.	m.	NOUN
ejpam-3322	173	89	m.	m.	PROPN
ejpam-3322	173	90	al	al	PROPN
ejpam-3322	173	91	-	-	PUNCT
ejpam-3322	173	92	shomrani	shomrani	PROPN
ejpam-3322	173	93	/	/	SYM
ejpam-3322	173	94	eur	eur	NOUN
ejpam-3322	173	95	.	.	PUNCT
ejpam-3322	174	1	j.	j.	PROPN
ejpam-3322	174	2	pure	pure	PROPN
ejpam-3322	174	3	appl	appl	PROPN
ejpam-3322	174	4	.	.	PROPN
ejpam-3322	174	5	math	math	PROPN
ejpam-3322	174	6	,	,	PUNCT
ejpam-3322	174	7	11	11	NUM
ejpam-3322	174	8	(	(	PUNCT
ejpam-3322	174	9	4	4	NUM
ejpam-3322	174	10	)	)	PUNCT
ejpam-3322	174	11	(	(	PUNCT
ejpam-3322	174	12	2018	2018	NUM
ejpam-3322	174	13	)	)	PUNCT
ejpam-3322	174	14	,	,	PUNCT
ejpam-3322	174	15	1027	1027	NUM
ejpam-3322	174	16	-	-	SYM
ejpam-3322	174	17	1045	1045	NUM
ejpam-3322	174	18	1033	1033	NUM
ejpam-3322	174	19	proposition	proposition	NOUN
ejpam-3322	174	20	2.12	2.12	NUM
ejpam-3322	174	21	.	.	PUNCT
ejpam-3322	175	1	[	[	X
ejpam-3322	175	2	1	1	X
ejpam-3322	175	3	]	]	X
ejpam-3322	175	4	if	if	SCONJ
ejpam-3322	175	5	c	c	PROPN
ejpam-3322	175	6	is	be	AUX
ejpam-3322	175	7	a	a	DET
ejpam-3322	175	8	coalgebra	coalgebra	NOUN
ejpam-3322	175	9	in	in	ADP
ejpam-3322	175	10	a	a	DET
ejpam-3322	175	11	rigid	rigid	ADJ
ejpam-3322	175	12	tensor	tensor	NOUN
ejpam-3322	175	13	category	category	NOUN
ejpam-3322	175	14	,	,	PUNCT
ejpam-3322	175	15	then	then	ADV
ejpam-3322	175	16	its	its	PRON
ejpam-3322	175	17	dual	dual	ADJ
ejpam-3322	175	18	c∗	c∗	NOUN
ejpam-3322	175	19	is	be	AUX
ejpam-3322	175	20	an	an	DET
ejpam-3322	175	21	algebra	algebra	NOUN
ejpam-3322	175	22	in	in	ADP
ejpam-3322	175	23	the	the	DET
ejpam-3322	175	24	category	category	NOUN
ejpam-3322	175	25	using	use	VERB
ejpam-3322	175	26	the	the	DET
ejpam-3322	175	27	following	follow	VERB
ejpam-3322	175	28	definitions	definition	NOUN
ejpam-3322	175	29	:	:	PUNCT
ejpam-3322	175	30	�	�	PROPN
ejpam-3322	175	31	�	�	PROPN
ejpam-3322	175	32	@@	@@	PROPN
ejpam-3322	175	33	�	�	PROPN
ejpam-3322	175	34	�	�	PROPN
ejpam-3322	175	35	@@	@@	X
ejpam-3322	175	36	@@	@@	PROPN
ejpam-3322	175	37	�	�	PROPN
ejpam-3322	175	38	�	�	PROPN
ejpam-3322	175	39	@	@	ADP
ejpam-3322	175	40	@	@	ADP
ejpam-3322	175	41	�	�	PROPN
ejpam-3322	175	42	�	�	PROPN
ejpam-3322	175	43	�	�	PROPN
ejpam-3322	175	44	�	�	PROPN
ejpam-3322	175	45	@@	@@	X
ejpam-3322	175	46	c∗c∗	c∗c∗	VERB
ejpam-3322	175	47	c∗	c∗	PROPN
ejpam-3322	175	48	=	=	SYM
ejpam-3322	175	49	@@	@@	X
ejpam-3322	175	50	�	�	PROPN
ejpam-3322	175	51	�	�	PROPN
ejpam-3322	175	52	∗	∗	NOUN
ejpam-3322	175	53	c∗c∗	c∗c∗	VERB
ejpam-3322	175	54	c∗	c∗	PROPN
ejpam-3322	175	55	,	,	PUNCT
ejpam-3322	175	56	�	�	PROPN
ejpam-3322	175	57	�	�	PROPN
ejpam-3322	175	58	@@	@@	PROPN
ejpam-3322	175	59	c∗	c∗	PROPN
ejpam-3322	175	60	�	�	PROPN
ejpam-3322	175	61	�	�	PROPN
ejpam-3322	175	62	�	�	PROPN
ejpam-3322	175	63	εc	εc	ADP
ejpam-3322	175	64	=	=	PROPN
ejpam-3322	176	1	c∗	c∗	PROPN
ejpam-3322	176	2	�	�	PROPN
ejpam-3322	176	3	�	�	PROPN
ejpam-3322	176	4	�	�	PROPN
ejpam-3322	176	5	�	�	PROPN
ejpam-3322	176	6	ηc∗	ηc∗	PROPN
ejpam-3322	176	7	figure	figure	VERB
ejpam-3322	176	8	4	4	NUM
ejpam-3322	176	9	:	:	PUNCT
ejpam-3322	176	10	multiplication	multiplication	NOUN
ejpam-3322	176	11	and	and	CCONJ
ejpam-3322	176	12	unit	unit	NOUN
ejpam-3322	176	13	on	on	ADP
ejpam-3322	176	14	c∗.	c∗.	X
ejpam-3322	176	15	b.	b.	PROPN
ejpam-3322	176	16	al	al	PROPN
ejpam-3322	176	17	-	-	PUNCT
ejpam-3322	176	18	harbi	harbi	PROPN
ejpam-3322	176	19	,	,	PUNCT
ejpam-3322	176	20	w.	w.	PROPN
ejpam-3322	176	21	m.	m.	PROPN
ejpam-3322	176	22	fakieh	fakieh	PROPN
ejpam-3322	176	23	,	,	PUNCT
ejpam-3322	176	24	m.	m.	NOUN
ejpam-3322	176	25	m.	m.	PROPN
ejpam-3322	176	26	al	al	PROPN
ejpam-3322	176	27	-	-	PUNCT
ejpam-3322	176	28	shomrani	shomrani	PROPN
ejpam-3322	176	29	/	/	SYM
ejpam-3322	176	30	eur	eur	NOUN
ejpam-3322	176	31	.	.	PUNCT
ejpam-3322	177	1	j.	j.	PROPN
ejpam-3322	177	2	pure	pure	PROPN
ejpam-3322	177	3	appl	appl	PROPN
ejpam-3322	177	4	.	.	PROPN
ejpam-3322	177	5	math	math	PROPN
ejpam-3322	177	6	,	,	PUNCT
ejpam-3322	177	7	11	11	NUM
ejpam-3322	177	8	(	(	PUNCT
ejpam-3322	177	9	4	4	NUM
ejpam-3322	177	10	)	)	PUNCT
ejpam-3322	177	11	(	(	PUNCT
ejpam-3322	177	12	2018	2018	NUM
ejpam-3322	177	13	)	)	PUNCT
ejpam-3322	177	14	,	,	PUNCT
ejpam-3322	177	15	1027	1027	NUM
ejpam-3322	177	16	-	-	SYM
ejpam-3322	177	17	1045	1045	NUM
ejpam-3322	177	18	1034	1034	NUM
ejpam-3322	177	19	3	3	NUM
ejpam-3322	177	20	.	.	X
ejpam-3322	177	21	results	result	NOUN
ejpam-3322	177	22	in	in	ADP
ejpam-3322	177	23	this	this	DET
ejpam-3322	177	24	section	section	NOUN
ejpam-3322	177	25	,	,	PUNCT
ejpam-3322	177	26	we	we	PRON
ejpam-3322	177	27	consider	consider	VERB
ejpam-3322	177	28	an	an	DET
ejpam-3322	177	29	algebra	algebra	NOUN
ejpam-3322	177	30	a	a	PRON
ejpam-3322	177	31	and	and	CCONJ
ejpam-3322	177	32	a	a	DET
ejpam-3322	177	33	coalgebra	coalgebra	NOUN
ejpam-3322	177	34	c	c	NOUN
ejpam-3322	177	35	in	in	ADP
ejpam-3322	177	36	the	the	DET
ejpam-3322	177	37	rigid	rigid	ADJ
ejpam-3322	177	38	tensor	tensor	NOUN
ejpam-3322	177	39	category	category	NOUN
ejpam-3322	177	40	c	c	NOUN
ejpam-3322	177	41	as	as	SCONJ
ejpam-3322	177	42	defined	define	VERB
ejpam-3322	177	43	before	before	ADP
ejpam-3322	177	44	as	as	ADV
ejpam-3322	177	45	well	well	ADV
ejpam-3322	177	46	as	as	ADP
ejpam-3322	177	47	their	their	PRON
ejpam-3322	177	48	duals	dual	NOUN
ejpam-3322	177	49	in	in	ADP
ejpam-3322	177	50	the	the	DET
ejpam-3322	177	51	same	same	ADJ
ejpam-3322	177	52	category	category	NOUN
ejpam-3322	177	53	.	.	PUNCT
ejpam-3322	178	1	we	we	PRON
ejpam-3322	178	2	provide	provide	VERB
ejpam-3322	178	3	mathematical	mathematical	ADJ
ejpam-3322	178	4	formulas	formula	NOUN
ejpam-3322	178	5	for	for	ADP
ejpam-3322	178	6	some	some	DET
ejpam-3322	178	7	operations	operation	NOUN
ejpam-3322	178	8	on	on	ADP
ejpam-3322	178	9	the	the	DET
ejpam-3322	178	10	dual	dual	ADJ
ejpam-3322	178	11	objects	object	NOUN
ejpam-3322	178	12	of	of	ADP
ejpam-3322	178	13	c.	c.	NOUN
ejpam-3322	178	14	precisely	precisely	ADV
ejpam-3322	178	15	,	,	PUNCT
ejpam-3322	178	16	formulas	formula	NOUN
ejpam-3322	178	17	for	for	ADP
ejpam-3322	178	18	the	the	DET
ejpam-3322	178	19	multiplication	multiplication	NOUN
ejpam-3322	178	20	µc∗	µc∗	ADV
ejpam-3322	178	21	on	on	ADP
ejpam-3322	178	22	c∗	c∗	PROPN
ejpam-3322	178	23	,	,	PUNCT
ejpam-3322	178	24	the	the	DET
ejpam-3322	178	25	counit	counit	VERB
ejpam-3322	178	26	εa∗	εa∗	NOUN
ejpam-3322	178	27	on	on	ADP
ejpam-3322	178	28	a∗	a∗	PROPN
ejpam-3322	178	29	and	and	CCONJ
ejpam-3322	178	30	the	the	DET
ejpam-3322	178	31	unit	unit	NOUN
ejpam-3322	178	32	ηc∗	ηc∗	VERB
ejpam-3322	178	33	on	on	ADP
ejpam-3322	178	34	c∗	c∗	PROPN
ejpam-3322	178	35	are	be	AUX
ejpam-3322	178	36	obtained	obtain	VERB
ejpam-3322	178	37	.	.	PUNCT
ejpam-3322	179	1	moreover	moreover	ADV
ejpam-3322	179	2	,	,	PUNCT
ejpam-3322	179	3	the	the	DET
ejpam-3322	179	4	unit	unit	NOUN
ejpam-3322	179	5	property	property	NOUN
ejpam-3322	179	6	and	and	CCONJ
ejpam-3322	179	7	the	the	DET
ejpam-3322	179	8	counit	counit	VERB
ejpam-3322	179	9	property	property	NOUN
ejpam-3322	179	10	for	for	ADP
ejpam-3322	179	11	ηc∗	ηc∗	PRON
ejpam-3322	179	12	and	and	CCONJ
ejpam-3322	179	13	εa∗	εa∗	NOUN
ejpam-3322	179	14	,	,	PUNCT
ejpam-3322	179	15	respectively	respectively	ADV
ejpam-3322	179	16	,	,	PUNCT
ejpam-3322	179	17	are	be	AUX
ejpam-3322	179	18	checked	check	VERB
ejpam-3322	179	19	.	.	PUNCT
ejpam-3322	180	1	proposition	proposition	NOUN
ejpam-3322	180	2	3.1	3.1	NUM
ejpam-3322	180	3	.	.	PUNCT
ejpam-3322	181	1	let	let	VERB
ejpam-3322	181	2	c	c	PRON
ejpam-3322	181	3	be	be	AUX
ejpam-3322	181	4	a	a	DET
ejpam-3322	181	5	coalgebra	coalgebra	NOUN
ejpam-3322	181	6	in	in	ADP
ejpam-3322	181	7	the	the	DET
ejpam-3322	181	8	category	category	NOUN
ejpam-3322	181	9	c.	c.	NOUN
ejpam-3322	181	10	then	then	ADV
ejpam-3322	181	11	the	the	DET
ejpam-3322	181	12	multiplication	multiplication	NOUN
ejpam-3322	181	13	µc∗	µc∗	ADV
ejpam-3322	181	14	on	on	ADP
ejpam-3322	181	15	c∗	c∗	NOUN
ejpam-3322	181	16	for	for	ADP
ejpam-3322	181	17	any	any	DET
ejpam-3322	181	18	elements	element	NOUN
ejpam-3322	181	19	α	α	NOUN
ejpam-3322	181	20	′	′	NUM
ejpam-3322	182	1	=	=	PUNCT
ejpam-3322	182	2	(	(	PUNCT
ejpam-3322	182	3	t1⊗	t1⊗	NOUN
ejpam-3322	182	4	δv1	δv1	ADJ
ejpam-3322	182	5	)	)	PUNCT
ejpam-3322	182	6	and	and	CCONJ
ejpam-3322	182	7	α	α	X
ejpam-3322	182	8	=	=	SYM
ejpam-3322	182	9	(	(	PUNCT
ejpam-3322	182	10	t2⊗	t2⊗	PROPN
ejpam-3322	182	11	δv2	δv2	NOUN
ejpam-3322	182	12	)	)	PUNCT
ejpam-3322	182	13	in	in	ADP
ejpam-3322	182	14	c∗	c∗	PROPN
ejpam-3322	182	15	for	for	ADP
ejpam-3322	182	16	v1	v1	NOUN
ejpam-3322	182	17	,	,	PUNCT
ejpam-3322	182	18	v2	v2	PROPN
ejpam-3322	182	19	∈	∈	PROPN
ejpam-3322	182	20	g	g	NOUN
ejpam-3322	182	21	and	and	CCONJ
ejpam-3322	182	22	t1	t1	NOUN
ejpam-3322	182	23	,	,	PUNCT
ejpam-3322	182	24	t2	t2	NOUN
ejpam-3322	182	25	∈m	∈m	NOUN
ejpam-3322	182	26	,	,	PUNCT
ejpam-3322	182	27	can	can	AUX
ejpam-3322	182	28	be	be	AUX
ejpam-3322	182	29	given	give	VERB
ejpam-3322	182	30	by	by	ADP
ejpam-3322	182	31	µc∗(α⊗	µc∗(α⊗	NUM
ejpam-3322	182	32	α	α	NOUN
ejpam-3322	182	33	′	′	NUM
ejpam-3322	182	34	)	)	PUNCT
ejpam-3322	183	1	=	=	PUNCT
ejpam-3322	183	2	δt1cv1,t2	δt1cv1,t2	NOUN
ejpam-3322	183	3	(	(	PUNCT
ejpam-3322	183	4	t1	t1	NOUN
ejpam-3322	183	5	c	c	NOUN
ejpam-3322	183	6	τ(a1	τ(a1	NOUN
ejpam-3322	183	7	,	,	PUNCT
ejpam-3322	183	8	a2	a2	PROPN
ejpam-3322	183	9	)	)	PUNCT
ejpam-3322	183	10	⊗	⊗	PROPN
ejpam-3322	183	11	δτ(a1,a2)−1v1v2	δτ(a1,a2)−1v1v2	X
ejpam-3322	183	12	)	)	PUNCT
ejpam-3322	183	13	,	,	PUNCT
ejpam-3322	183	14	with	with	ADP
ejpam-3322	183	15	τ(a2	τ(a2	NOUN
ejpam-3322	183	16	,	,	PUNCT
ejpam-3322	183	17	a	a	DET
ejpam-3322	183	18	l	l	NOUN
ejpam-3322	183	19	)	)	PUNCT
ejpam-3322	183	20	=	=	SYM
ejpam-3322	184	1	e	e	X
ejpam-3322	184	2	where	where	SCONJ
ejpam-3322	184	3	a1	a1	NOUN
ejpam-3322	184	4	=	=	PUNCT
ejpam-3322	184	5	〈	〈	AUX
ejpam-3322	184	6	δt1	δt1	NOUN
ejpam-3322	184	7	⊗	⊗	PROPN
ejpam-3322	184	8	v1	v1	PROPN
ejpam-3322	184	9	〉	〉	PROPN
ejpam-3322	184	10	,	,	PUNCT
ejpam-3322	184	11	a2	a2	PROPN
ejpam-3322	184	12	=	=	PUNCT
ejpam-3322	185	1	〈	〈	PROPN
ejpam-3322	185	2	δt2	δt2	VERB
ejpam-3322	185	3	⊗	⊗	PROPN
ejpam-3322	185	4	v2	v2	PROPN
ejpam-3322	185	5	〉	〉	PROPN
ejpam-3322	185	6	and	and	CCONJ
ejpam-3322	185	7	a	a	DET
ejpam-3322	185	8	=	=	PUNCT
ejpam-3322	185	9	a1	a1	NOUN
ejpam-3322	185	10	·	·	PUNCT
ejpam-3322	185	11	a2	a2	PROPN
ejpam-3322	185	12	.	.	PUNCT
ejpam-3322	186	1	proof	proof	NOUN
ejpam-3322	186	2	.	.	PUNCT
ejpam-3322	187	1	from	from	ADP
ejpam-3322	187	2	proposition	proposition	NOUN
ejpam-3322	187	3	2.12	2.12	NUM
ejpam-3322	187	4	,	,	PUNCT
ejpam-3322	187	5	we	we	PRON
ejpam-3322	187	6	know	know	VERB
ejpam-3322	187	7	that	that	SCONJ
ejpam-3322	187	8	�	�	PROPN
ejpam-3322	187	9	�	�	PROPN
ejpam-3322	187	10	@@	@@	PROPN
ejpam-3322	187	11	�	�	PROPN
ejpam-3322	187	12	�	�	PROPN
ejpam-3322	187	13	@@	@@	X
ejpam-3322	187	14	@@	@@	PROPN
ejpam-3322	187	15	�	�	PROPN
ejpam-3322	187	16	�	�	PROPN
ejpam-3322	187	17	@	@	ADP
ejpam-3322	187	18	@	@	ADP
ejpam-3322	187	19	�	�	PROPN
ejpam-3322	187	20	�	�	PROPN
ejpam-3322	187	21	�	�	PROPN
ejpam-3322	187	22	�	�	PROPN
ejpam-3322	187	23	@@	@@	X
ejpam-3322	187	24	c∗c∗	c∗c∗	VERB
ejpam-3322	187	25	c∗	c∗	PROPN
ejpam-3322	187	26	=	=	SYM
ejpam-3322	187	27	@@	@@	X
ejpam-3322	187	28	�	�	PROPN
ejpam-3322	187	29	�	�	PROPN
ejpam-3322	187	30	∗	∗	NOUN
ejpam-3322	187	31	c∗c∗	c∗c∗	VERB
ejpam-3322	187	32	c∗	c∗	NOUN
ejpam-3322	187	33	for	for	ADP
ejpam-3322	187	34	α	α	NOUN
ejpam-3322	187	35	,	,	PUNCT
ejpam-3322	187	36	α	α	NOUN
ejpam-3322	187	37	′	′	NOUN
ejpam-3322	187	38	∈	∈	PROPN
ejpam-3322	187	39	c∗	c∗	NOUN
ejpam-3322	187	40	,	,	PUNCT
ejpam-3322	187	41	we	we	PRON
ejpam-3322	187	42	follow	follow	VERB
ejpam-3322	187	43	the	the	DET
ejpam-3322	187	44	above	above	ADJ
ejpam-3322	187	45	figure	figure	NOUN
ejpam-3322	187	46	from	from	ADP
ejpam-3322	187	47	top	top	NOUN
ejpam-3322	187	48	to	to	ADP
ejpam-3322	187	49	bottom	bottom	NOUN
ejpam-3322	187	50	and	and	CCONJ
ejpam-3322	187	51	calculate	calculate	VERB
ejpam-3322	187	52	the	the	DET
ejpam-3322	187	53	following	following	NOUN
ejpam-3322	187	54	:	:	PUNCT
ejpam-3322	187	55	put	put	VERB
ejpam-3322	187	56	coev(1	coev(1	ADJ
ejpam-3322	187	57	)	)	PUNCT
ejpam-3322	188	1	=	=	PUNCT
ejpam-3322	188	2	β	β	PROPN
ejpam-3322	188	3	⊗	⊗	PROPN
ejpam-3322	188	4	γ	γ	X
ejpam-3322	188	5	for	for	ADP
ejpam-3322	188	6	some	some	DET
ejpam-3322	188	7	β	β	NOUN
ejpam-3322	188	8	∈	∈	PROPN
ejpam-3322	188	9	c	c	NOUN
ejpam-3322	188	10	and	and	CCONJ
ejpam-3322	188	11	γ	γ	PROPN
ejpam-3322	188	12	∈	∈	PROPN
ejpam-3322	188	13	c∗with	c∗with	ADP
ejpam-3322	188	14	4c	4c	NOUN
ejpam-3322	188	15	(	(	PUNCT
ejpam-3322	188	16	β	β	NOUN
ejpam-3322	188	17	)	)	PUNCT
ejpam-3322	188	18	=	=	SYM
ejpam-3322	188	19	β1	β1	PROPN
ejpam-3322	188	20	⊗	⊗	PROPN
ejpam-3322	188	21	β2	β2	PROPN
ejpam-3322	188	22	,	,	PUNCT
ejpam-3322	188	23	α	α	PROPN
ejpam-3322	188	24	⊗	⊗	PROPN
ejpam-3322	188	25	α′	α′	NUM
ejpam-3322	188	26	=	=	SYM
ejpam-3322	188	27	γ	γ	X
ejpam-3322	188	28	,	,	PUNCT
ejpam-3322	188	29	ev	ev	X
ejpam-3322	188	30	(	(	PUNCT
ejpam-3322	188	31	α⊗	α⊗	NOUN
ejpam-3322	188	32	β2	β2	PROPN
ejpam-3322	188	33	)	)	PUNCT
ejpam-3322	188	34	=	=	SYM
ejpam-3322	188	35	1	1	NUM
ejpam-3322	188	36	and	and	CCONJ
ejpam-3322	188	37	ev	ev	INTJ
ejpam-3322	188	38	(	(	PUNCT
ejpam-3322	188	39	α	α	PROPN
ejpam-3322	188	40	′	′	PROPN
ejpam-3322	189	1	⊗	⊗	PROPN
ejpam-3322	189	2	β1	β1	PROPN
ejpam-3322	189	3	)	)	PUNCT
ejpam-3322	190	1	=	=	PUNCT
ejpam-3322	190	2	1	1	NUM
ejpam-3322	190	3	that	that	PRON
ejpam-3322	190	4	imply	imply	VERB
ejpam-3322	190	5	〈	〈	PROPN
ejpam-3322	190	6	β〉·〈γ	β〉·〈γ	NOUN
ejpam-3322	190	7	〉	〉	NOUN
ejpam-3322	190	8	=	=	SYM
ejpam-3322	190	9	e	e	NOUN
ejpam-3322	190	10	,	,	PUNCT
ejpam-3322	190	11	〈	〈	PROPN
ejpam-3322	190	12	α〉·〈β2	α〉·〈β2	PROPN
ejpam-3322	190	13	〉	〉	PROPN
ejpam-3322	190	14	=	=	SYM
ejpam-3322	190	15	e	e	NOUN
ejpam-3322	190	16	,	,	PUNCT
ejpam-3322	190	17	〈	〈	PROPN
ejpam-3322	190	18	α	α	NOUN
ejpam-3322	190	19	′	′	NUM
ejpam-3322	190	20	〉	〉	NOUN
ejpam-3322	190	21	·	·	PUNCT
ejpam-3322	190	22	〈	〈	VERB
ejpam-3322	191	1	β1	β1	PROPN
ejpam-3322	191	2	〉	〉	NOUN
ejpam-3322	191	3	=	=	SYM
ejpam-3322	191	4	e	e	NOUN
ejpam-3322	191	5	,	,	PUNCT
ejpam-3322	191	6	〈	〈	PROPN
ejpam-3322	191	7	β	β	NOUN
ejpam-3322	191	8	〉	〉	NOUN
ejpam-3322	191	9	=	=	SYM
ejpam-3322	191	10	〈	〈	PROPN
ejpam-3322	191	11	β1	β1	PROPN
ejpam-3322	191	12	〉	〉	PROPN
ejpam-3322	191	13	·	·	PUNCT
ejpam-3322	192	1	〈	〈	PROPN
ejpam-3322	192	2	β2	β2	NOUN
ejpam-3322	192	3	〉	〉	PROPN
ejpam-3322	192	4	and	and	CCONJ
ejpam-3322	192	5	〈	〈	PROPN
ejpam-3322	192	6	α〉	α〉	PROPN
ejpam-3322	192	7	.	.	PUNCT
ejpam-3322	192	8	〈α′	〈α′	NOUN
ejpam-3322	193	1	〉	〉	NOUN
ejpam-3322	193	2	=	=	SYM
ejpam-3322	193	3	〈	〈	PROPN
ejpam-3322	193	4	γ	γ	X
ejpam-3322	193	5	〉	〉	PROPN
ejpam-3322	193	6	.	.	PUNCT
ejpam-3322	194	1	we	we	PRON
ejpam-3322	194	2	start	start	VERB
ejpam-3322	194	3	with	with	ADP
ejpam-3322	194	4	(	(	PUNCT
ejpam-3322	194	5	α⊗	α⊗	X
ejpam-3322	194	6	α′)⊗	α′)⊗	NUM
ejpam-3322	194	7	coev(1	coev(1	ADJ
ejpam-3322	194	8	)	)	PUNCT
ejpam-3322	195	1	=	=	PUNCT
ejpam-3322	195	2	(	(	PUNCT
ejpam-3322	195	3	α⊗	α⊗	NOUN
ejpam-3322	195	4	α′)⊗	α′)⊗	PROPN
ejpam-3322	195	5	(	(	PUNCT
ejpam-3322	195	6	β	β	PROPN
ejpam-3322	195	7	⊗	⊗	PROPN
ejpam-3322	195	8	γ	γ	X
ejpam-3322	195	9	)	)	PUNCT
ejpam-3322	195	10	.	.	PUNCT
ejpam-3322	196	1	(	(	PUNCT
ejpam-3322	196	2	6	6	X
ejpam-3322	196	3	)	)	PUNCT
ejpam-3322	196	4	applying	apply	VERB
ejpam-3322	196	5	the	the	DET
ejpam-3322	196	6	associator	associator	NOUN
ejpam-3322	196	7	φ	φ	PROPN
ejpam-3322	196	8	on	on	ADP
ejpam-3322	196	9	the	the	DET
ejpam-3322	196	10	right	right	ADJ
ejpam-3322	196	11	hand	hand	NOUN
ejpam-3322	196	12	side	side	NOUN
ejpam-3322	196	13	of	of	ADP
ejpam-3322	196	14	(	(	PUNCT
ejpam-3322	196	15	6	6	NUM
ejpam-3322	196	16	)	)	PUNCT
ejpam-3322	196	17	and	and	CCONJ
ejpam-3322	196	18	then	then	ADV
ejpam-3322	196	19	the	the	DET
ejpam-3322	196	20	comultiplication	comultiplication	NOUN
ejpam-3322	196	21	on	on	ADP
ejpam-3322	196	22	β	β	NOUN
ejpam-3322	196	23	give	give	VERB
ejpam-3322	196	24	α/̄τ(〈α′	α/̄τ(〈α′	PROPN
ejpam-3322	196	25	〉	〉	NOUN
ejpam-3322	196	26	,	,	PUNCT
ejpam-3322	196	27	〈	〈	PROPN
ejpam-3322	196	28	β	β	X
ejpam-3322	196	29	〉	〉	NUM
ejpam-3322	196	30	·	·	PUNCT
ejpam-3322	197	1	〈	〈	NOUN
ejpam-3322	197	2	γ〉)⊗	γ〉)⊗	NUM
ejpam-3322	197	3	(	(	PUNCT
ejpam-3322	197	4	α′	α′	NUM
ejpam-3322	197	5	⊗	⊗	PROPN
ejpam-3322	197	6	(	(	PUNCT
ejpam-3322	197	7	β	β	PROPN
ejpam-3322	197	8	⊗	⊗	PROPN
ejpam-3322	197	9	γ	γ	X
ejpam-3322	197	10	)	)	PUNCT
ejpam-3322	197	11	)	)	PUNCT
ejpam-3322	198	1	=	=	SYM
ejpam-3322	198	2	α⊗	α⊗	X
ejpam-3322	198	3	(	(	PUNCT
ejpam-3322	198	4	α′	α′	NUM
ejpam-3322	198	5	⊗	⊗	PROPN
ejpam-3322	198	6	(	(	PUNCT
ejpam-3322	198	7	β	β	PROPN
ejpam-3322	198	8	⊗	⊗	PROPN
ejpam-3322	198	9	γ	γ	X
ejpam-3322	198	10	)	)	PUNCT
ejpam-3322	198	11	)	)	PUNCT
ejpam-3322	199	1	=	=	SYM
ejpam-3322	199	2	α⊗	α⊗	INTJ
ejpam-3322	199	3	(	(	PUNCT
ejpam-3322	199	4	α	α	NOUN
ejpam-3322	199	5	′	′	NOUN
ejpam-3322	199	6	⊗	⊗	NOUN
ejpam-3322	199	7	(	(	PUNCT
ejpam-3322	199	8	(	(	PUNCT
ejpam-3322	199	9	β1	β1	PROPN
ejpam-3322	199	10	⊗	⊗	PROPN
ejpam-3322	199	11	β2)⊗	β2)⊗	PROPN
ejpam-3322	199	12	γ	γ	PROPN
ejpam-3322	199	13	)	)	PUNCT
ejpam-3322	199	14	)	)	PUNCT
ejpam-3322	199	15	,	,	PUNCT
ejpam-3322	199	16	(	(	PUNCT
ejpam-3322	199	17	7	7	X
ejpam-3322	199	18	)	)	PUNCT
ejpam-3322	199	19	since	since	SCONJ
ejpam-3322	199	20	α/̄τ((〈α′	α/̄τ((〈α′	NOUN
ejpam-3322	199	21	〉	〉	NOUN
ejpam-3322	199	22	,	,	PUNCT
ejpam-3322	199	23	〈	〈	PROPN
ejpam-3322	199	24	β	β	X
ejpam-3322	199	25	〉	〉	NOUN
ejpam-3322	199	26	·	·	PUNCT
ejpam-3322	200	1	〈	〈	PROPN
ejpam-3322	200	2	γ	γ	X
ejpam-3322	200	3	〉	〉	NUM
ejpam-3322	200	4	)	)	PUNCT
ejpam-3322	200	5	=	=	PUNCT
ejpam-3322	200	6	α/̄τ(〈α′	α/̄τ(〈α′	ADP
ejpam-3322	200	7	〉	〉	PROPN
ejpam-3322	200	8	,	,	PUNCT
ejpam-3322	200	9	e	e	NOUN
ejpam-3322	200	10	)	)	PUNCT
ejpam-3322	200	11	=	=	SYM
ejpam-3322	200	12	α/̄e	α/̄e	PROPN
ejpam-3322	200	13	=	=	SYM
ejpam-3322	200	14	α	α	PROPN
ejpam-3322	200	15	and	and	CCONJ
ejpam-3322	200	16	4c	4c	NOUN
ejpam-3322	200	17	(	(	PUNCT
ejpam-3322	200	18	β	β	NOUN
ejpam-3322	200	19	)	)	PUNCT
ejpam-3322	200	20	=	=	SYM
ejpam-3322	200	21	β1	β1	PROPN
ejpam-3322	200	22	⊗	⊗	PROPN
ejpam-3322	200	23	β2	β2	PROPN
ejpam-3322	200	24	.	.	PUNCT
ejpam-3322	201	1	now	now	ADV
ejpam-3322	201	2	,	,	PUNCT
ejpam-3322	201	3	applying	apply	VERB
ejpam-3322	201	4	the	the	DET
ejpam-3322	201	5	associator	associator	NOUN
ejpam-3322	201	6	φ	φ	PROPN
ejpam-3322	201	7	and	and	CCONJ
ejpam-3322	201	8	then	then	ADV
ejpam-3322	201	9	the	the	DET
ejpam-3322	201	10	associator	associator	NOUN
ejpam-3322	201	11	inverse	inverse	NOUN
ejpam-3322	201	12	φ−1	φ−1	PROPN
ejpam-3322	201	13	on	on	ADP
ejpam-3322	201	14	the	the	DET
ejpam-3322	201	15	right	right	ADJ
ejpam-3322	201	16	hand	hand	NOUN
ejpam-3322	201	17	side	side	NOUN
ejpam-3322	201	18	of	of	ADP
ejpam-3322	201	19	(	(	PUNCT
ejpam-3322	201	20	7	7	X
ejpam-3322	201	21	)	)	PUNCT
ejpam-3322	201	22	give	give	VERB
ejpam-3322	201	23	α⊗	α⊗	NOUN
ejpam-3322	201	24	(	(	PUNCT
ejpam-3322	201	25	α	α	NOUN
ejpam-3322	201	26	′	′	NOUN
ejpam-3322	202	1	⊗	⊗	PROPN
ejpam-3322	202	2	(	(	PUNCT
ejpam-3322	202	3	β1/̄τ(〈β2	β1/̄τ(〈β2	PROPN
ejpam-3322	202	4	〉	〉	NOUN
ejpam-3322	202	5	,	,	PUNCT
ejpam-3322	202	6	〈	〈	PROPN
ejpam-3322	202	7	γ	γ	PROPN
ejpam-3322	202	8	〉	〉	NUM
ejpam-3322	202	9	)	)	PUNCT
ejpam-3322	203	1	⊗	⊗	PROPN
ejpam-3322	203	2	(	(	PUNCT
ejpam-3322	203	3	β2	β2	PROPN
ejpam-3322	203	4	⊗	⊗	PROPN
ejpam-3322	203	5	γ	γ	PROPN
ejpam-3322	203	6	)	)	PUNCT
ejpam-3322	203	7	)	)	PUNCT
ejpam-3322	203	8	,	,	PUNCT
ejpam-3322	203	9	b.	b.	PROPN
ejpam-3322	203	10	al	al	PROPN
ejpam-3322	203	11	-	-	PUNCT
ejpam-3322	203	12	harbi	harbi	PROPN
ejpam-3322	203	13	,	,	PUNCT
ejpam-3322	203	14	w.	w.	PROPN
ejpam-3322	203	15	m.	m.	PROPN
ejpam-3322	203	16	fakieh	fakieh	PROPN
ejpam-3322	203	17	,	,	PUNCT
ejpam-3322	203	18	m.	m.	NOUN
ejpam-3322	203	19	m.	m.	PROPN
ejpam-3322	203	20	al	al	PROPN
ejpam-3322	203	21	-	-	PUNCT
ejpam-3322	203	22	shomrani	shomrani	PROPN
ejpam-3322	203	23	/	/	SYM
ejpam-3322	203	24	eur	eur	NOUN
ejpam-3322	203	25	.	.	PUNCT
ejpam-3322	204	1	j.	j.	PROPN
ejpam-3322	204	2	pure	pure	PROPN
ejpam-3322	204	3	appl	appl	PROPN
ejpam-3322	204	4	.	.	PROPN
ejpam-3322	204	5	math	math	PROPN
ejpam-3322	204	6	,	,	PUNCT
ejpam-3322	204	7	11	11	NUM
ejpam-3322	204	8	(	(	PUNCT
ejpam-3322	204	9	4	4	NUM
ejpam-3322	204	10	)	)	PUNCT
ejpam-3322	204	11	(	(	PUNCT
ejpam-3322	204	12	2018	2018	NUM
ejpam-3322	204	13	)	)	PUNCT
ejpam-3322	204	14	,	,	PUNCT
ejpam-3322	204	15	1027	1027	NUM
ejpam-3322	204	16	-	-	SYM
ejpam-3322	204	17	1045	1045	NUM
ejpam-3322	204	18	1035	1035	NUM
ejpam-3322	204	19	α⊗	α⊗	NOUN
ejpam-3322	204	20	(	(	PUNCT
ejpam-3322	204	21	(	(	PUNCT
ejpam-3322	204	22	α	α	NOUN
ejpam-3322	204	23	′	′	NUM
ejpam-3322	204	24	/̄τ(〈β′	/̄τ(〈β′	PROPN
ejpam-3322	204	25	〉	〉	PROPN
ejpam-3322	204	26	,	,	PUNCT
ejpam-3322	204	27	〈	〈	PROPN
ejpam-3322	204	28	β2〉	β2〉	NOUN
ejpam-3322	204	29	.	.	PUNCT
ejpam-3322	204	30	〈γ〉)−1	〈γ〉)−1	PROPN
ejpam-3322	204	31	⊗	⊗	PROPN
ejpam-3322	204	32	β′	β′	NUM
ejpam-3322	204	33	)	)	PUNCT
ejpam-3322	205	1	⊗	⊗	PROPN
ejpam-3322	205	2	(	(	PUNCT
ejpam-3322	205	3	β2	β2	PROPN
ejpam-3322	205	4	⊗	⊗	PROPN
ejpam-3322	205	5	γ	γ	PROPN
ejpam-3322	205	6	)	)	PUNCT
ejpam-3322	205	7	)	)	PUNCT
ejpam-3322	205	8	,	,	PUNCT
ejpam-3322	205	9	(	(	PUNCT
ejpam-3322	205	10	8)	8)	NUM
ejpam-3322	205	11	where	where	SCONJ
ejpam-3322	205	12	β	β	X
ejpam-3322	205	13	′	′	NUM
ejpam-3322	205	14	=	=	PUNCT
ejpam-3322	206	1	β1/̄τ(〈β2	β1/̄τ(〈β2	PROPN
ejpam-3322	206	2	〉	〉	NUM
ejpam-3322	206	3	,	,	PUNCT
ejpam-3322	206	4	〈	〈	PROPN
ejpam-3322	206	5	γ	γ	PROPN
ejpam-3322	206	6	〉	〉	NUM
ejpam-3322	206	7	)	)	PUNCT
ejpam-3322	206	8	.	.	PUNCT
ejpam-3322	207	1	next	next	ADV
ejpam-3322	207	2	,	,	PUNCT
ejpam-3322	207	3	we	we	PRON
ejpam-3322	207	4	apply	apply	VERB
ejpam-3322	207	5	the	the	DET
ejpam-3322	207	6	evaluation	evaluation	NOUN
ejpam-3322	207	7	map	map	NOUN
ejpam-3322	207	8	on	on	ADP
ejpam-3322	207	9	(	(	PUNCT
ejpam-3322	207	10	(	(	PUNCT
ejpam-3322	207	11	α	α	NOUN
ejpam-3322	207	12	′	′	NUM
ejpam-3322	207	13	/̄τ(〈β′	/̄τ(〈β′	PROPN
ejpam-3322	207	14	〉	〉	PROPN
ejpam-3322	207	15	,	,	PUNCT
ejpam-3322	207	16	〈	〈	PROPN
ejpam-3322	207	17	β2〉	β2〉	NOUN
ejpam-3322	207	18	.	.	PUNCT
ejpam-3322	207	19	〈γ〉)−1	〈γ〉)−1	PROPN
ejpam-3322	207	20	⊗	⊗	PROPN
ejpam-3322	207	21	β′	β′	NUM
ejpam-3322	207	22	)	)	PUNCT
ejpam-3322	207	23	of	of	ADP
ejpam-3322	207	24	(	(	PUNCT
ejpam-3322	207	25	8)	8)	NUM
ejpam-3322	207	26	to	to	PART
ejpam-3322	207	27	get	get	VERB
ejpam-3322	207	28	α	α	NOUN
ejpam-3322	207	29	′	′	NUM
ejpam-3322	207	30	/̄τ(〈β′	/̄τ(〈β′	PROPN
ejpam-3322	207	31	〉	〉	PROPN
ejpam-3322	207	32	,	,	PUNCT
ejpam-3322	207	33	〈	〈	PROPN
ejpam-3322	207	34	β2	β2	PROPN
ejpam-3322	207	35	〉	〉	NOUN
ejpam-3322	207	36	·	·	PUNCT
ejpam-3322	208	1	〈	〈	VERB
ejpam-3322	208	2	γ〉)−1(β	γ〉)−1(β	NOUN
ejpam-3322	208	3	′	′	NUM
ejpam-3322	208	4	)	)	PUNCT
ejpam-3322	208	5	(	(	PUNCT
ejpam-3322	208	6	9	9	X
ejpam-3322	208	7	)	)	PUNCT
ejpam-3322	208	8	=	=	SYM
ejpam-3322	209	1	α	α	NOUN
ejpam-3322	209	2	′	′	NUM
ejpam-3322	210	1	(	(	PUNCT
ejpam-3322	210	2	β	β	NOUN
ejpam-3322	210	3	′	′	NUM
ejpam-3322	210	4	/̄τ(〈β′〉l	/̄τ(〈β′〉l	PROPN
ejpam-3322	210	5	,	,	PUNCT
ejpam-3322	210	6	〈	〈	PROPN
ejpam-3322	210	7	β′〉)−1(〈β′〉l.τ(〈β′	β′〉)−1(〈β′〉l.τ(〈β′	PROPN
ejpam-3322	210	8	〉	〉	PROPN
ejpam-3322	210	9	,	,	PUNCT
ejpam-3322	210	10	〈	〈	PROPN
ejpam-3322	210	11	β2〉·〈γ〉))τ(〈β′〉l	β2〉·〈γ〉))τ(〈β′〉l	NUM
ejpam-3322	210	12	c	c	PROPN
ejpam-3322	210	13	τ(〈β′	τ(〈β′	PROPN
ejpam-3322	210	14	〉	〉	PROPN
ejpam-3322	210	15	,	,	PUNCT
ejpam-3322	210	16	〈	〈	PROPN
ejpam-3322	210	17	β2〉·〈γ	β2〉·〈γ	NOUN
ejpam-3322	210	18	〉	〉	NOUN
ejpam-3322	210	19	)	)	PUNCT
ejpam-3322	210	20	,	,	PUNCT
ejpam-3322	210	21	(	(	PUNCT
ejpam-3322	210	22	〈	〈	PROPN
ejpam-3322	210	23	β	β	X
ejpam-3322	210	24	′〉l	′〉l	NOUN
ejpam-3322	210	25	c	c	PROPN
ejpam-3322	210	26	τ(〈β′	τ(〈β′	PROPN
ejpam-3322	210	27	〉	〉	PROPN
ejpam-3322	210	28	,	,	PUNCT
ejpam-3322	210	29	〈	〈	PROPN
ejpam-3322	210	30	β2〉·〈γ〉))r	β2〉·〈γ〉))r	NUM
ejpam-3322	210	31	)	)	PUNCT
ejpam-3322	210	32	)	)	PUNCT
ejpam-3322	210	33	.	.	PUNCT
ejpam-3322	211	1	to	to	PART
ejpam-3322	211	2	make	make	VERB
ejpam-3322	211	3	this	this	DET
ejpam-3322	211	4	equation	equation	NOUN
ejpam-3322	211	5	simpler	simple	ADJ
ejpam-3322	211	6	we	we	PRON
ejpam-3322	211	7	need	need	VERB
ejpam-3322	211	8	to	to	PART
ejpam-3322	211	9	do	do	VERB
ejpam-3322	211	10	following	follow	VERB
ejpam-3322	211	11	calculations	calculation	NOUN
ejpam-3322	211	12	:	:	PUNCT
ejpam-3322	211	13	we	we	PRON
ejpam-3322	211	14	first	first	ADV
ejpam-3322	211	15	show	show	VERB
ejpam-3322	211	16	that	that	SCONJ
ejpam-3322	211	17	〈	〈	PROPN
ejpam-3322	211	18	β′	β′	PROPN
ejpam-3322	211	19	〉	〉	NOUN
ejpam-3322	211	20	=	=	SYM
ejpam-3322	211	21	(	(	PUNCT
ejpam-3322	211	22	〈	〈	PROPN
ejpam-3322	211	23	β2	β2	PROPN
ejpam-3322	211	24	〉	〉	NOUN
ejpam-3322	211	25	·	·	PUNCT
ejpam-3322	211	26	〈	〈	PROPN
ejpam-3322	211	27	γ〉)l	γ〉)l	NOUN
ejpam-3322	211	28	as	as	SCONJ
ejpam-3322	211	29	follows	follow	VERB
ejpam-3322	211	30	:	:	PUNCT
ejpam-3322	211	31	〈	〈	PROPN
ejpam-3322	211	32	β′	β′	PROPN
ejpam-3322	211	33	〉	〉	NOUN
ejpam-3322	211	34	·	·	PUNCT
ejpam-3322	212	1	(	(	PUNCT
ejpam-3322	212	2	〈	〈	PROPN
ejpam-3322	212	3	β2	β2	PROPN
ejpam-3322	212	4	〉	〉	PROPN
ejpam-3322	212	5	·	·	PUNCT
ejpam-3322	213	1	〈	〈	PROPN
ejpam-3322	213	2	γ	γ	X
ejpam-3322	213	3	〉	〉	NUM
ejpam-3322	213	4	)	)	PUNCT
ejpam-3322	213	5	=	=	PUNCT
ejpam-3322	214	1	(	(	PUNCT
ejpam-3322	214	2	〈	〈	PROPN
ejpam-3322	214	3	β1	β1	PROPN
ejpam-3322	214	4	〉	〉	PROPN
ejpam-3322	214	5	c	c	PROPN
ejpam-3322	214	6	τ(〈β2	τ(〈β2	PROPN
ejpam-3322	214	7	〉	〉	PROPN
ejpam-3322	214	8	,	,	PUNCT
ejpam-3322	214	9	〈	〈	PROPN
ejpam-3322	214	10	γ	γ	PROPN
ejpam-3322	214	11	〉	〉	NUM
ejpam-3322	214	12	)	)	PUNCT
ejpam-3322	214	13	)	)	PUNCT
ejpam-3322	214	14	·	·	PUNCT
ejpam-3322	215	1	(	(	PUNCT
ejpam-3322	215	2	〈	〈	PROPN
ejpam-3322	215	3	β2	β2	PROPN
ejpam-3322	215	4	〉	〉	PROPN
ejpam-3322	215	5	·	·	PUNCT
ejpam-3322	215	6	〈	〈	PROPN
ejpam-3322	215	7	γ	γ	X
ejpam-3322	215	8	〉	〉	NUM
ejpam-3322	215	9	)	)	PUNCT
ejpam-3322	215	10	=	=	PUNCT
ejpam-3322	216	1	(	(	PUNCT
ejpam-3322	216	2	〈	〈	PROPN
ejpam-3322	216	3	β1	β1	PROPN
ejpam-3322	216	4	〉	〉	PROPN
ejpam-3322	216	5	·	·	PUNCT
ejpam-3322	217	1	〈	〈	PROPN
ejpam-3322	217	2	β2	β2	PROPN
ejpam-3322	217	3	〉	〉	PROPN
ejpam-3322	217	4	)	)	PUNCT
ejpam-3322	217	5	·	·	PUNCT
ejpam-3322	218	1	〈	〈	PROPN
ejpam-3322	218	2	γ	γ	X
ejpam-3322	218	3	〉	〉	NOUN
ejpam-3322	218	4	=	=	SYM
ejpam-3322	218	5	〈	〈	PROPN
ejpam-3322	218	6	β	β	NOUN
ejpam-3322	218	7	〉	〉	NOUN
ejpam-3322	218	8	·	·	PUNCT
ejpam-3322	219	1	〈	〈	PROPN
ejpam-3322	219	2	γ	γ	X
ejpam-3322	219	3	〉	〉	PROPN
ejpam-3322	219	4	=	=	SYM
ejpam-3322	219	5	e.	e.	PROPN
ejpam-3322	220	1	but	but	CCONJ
ejpam-3322	220	2	we	we	PRON
ejpam-3322	220	3	know	know	VERB
ejpam-3322	220	4	〈	〈	PROPN
ejpam-3322	220	5	α	α	NOUN
ejpam-3322	220	6	〉	〉	NOUN
ejpam-3322	220	7	·	·	PUNCT
ejpam-3322	221	1	〈	〈	PROPN
ejpam-3322	221	2	α′	α′	NUM
ejpam-3322	221	3	〉	〉	NUM
ejpam-3322	221	4	=	=	SYM
ejpam-3322	221	5	〈	〈	PROPN
ejpam-3322	221	6	γ	γ	NOUN
ejpam-3322	221	7	〉	〉	NOUN
ejpam-3322	221	8	and	and	CCONJ
ejpam-3322	221	9	〈	〈	PROPN
ejpam-3322	221	10	α	α	PRON
ejpam-3322	221	11	〉	〉	NOUN
ejpam-3322	221	12	·	·	PUNCT
ejpam-3322	221	13	〈	〈	NOUN
ejpam-3322	221	14	β2	β2	NOUN
ejpam-3322	221	15	〉	〉	NOUN
ejpam-3322	221	16	=	=	SYM
ejpam-3322	221	17	e	e	NOUN
ejpam-3322	221	18	,	,	PUNCT
ejpam-3322	221	19	that	that	PRON
ejpam-3322	221	20	imply	imply	VERB
ejpam-3322	221	21	〈	〈	PROPN
ejpam-3322	221	22	β2	β2	ADJ
ejpam-3322	221	23	〉	〉	PROPN
ejpam-3322	221	24	·	·	PUNCT
ejpam-3322	222	1	〈	〈	PROPN
ejpam-3322	222	2	γ	γ	X
ejpam-3322	222	3	〉	〉	NOUN
ejpam-3322	222	4	=	=	SYM
ejpam-3322	222	5	〈	〈	PROPN
ejpam-3322	222	6	α′	α′	NUM
ejpam-3322	222	7	〉	〉	NUM
ejpam-3322	222	8	.	.	PUNCT
ejpam-3322	223	1	hence	hence	ADV
ejpam-3322	223	2	,	,	PUNCT
ejpam-3322	223	3	〈	〈	PROPN
ejpam-3322	223	4	β′	β′	PROPN
ejpam-3322	223	5	〉	〉	NOUN
ejpam-3322	223	6	=	=	SYM
ejpam-3322	223	7	(	(	PUNCT
ejpam-3322	223	8	〈	〈	PROPN
ejpam-3322	223	9	β2〉	β2〉	X
ejpam-3322	223	10	.	.	PUNCT
ejpam-3322	223	11	〈γ〉)l	〈γ〉)l	NOUN
ejpam-3322	224	1	=	=	PUNCT
ejpam-3322	225	1	〈	〈	PROPN
ejpam-3322	225	2	α′〉l	α′〉l	PROPN
ejpam-3322	225	3	.	.	PUNCT
ejpam-3322	226	1	substituting	substitute	VERB
ejpam-3322	226	2	in	in	ADP
ejpam-3322	226	3	(	(	PUNCT
ejpam-3322	226	4	9	9	NUM
ejpam-3322	226	5	)	)	PUNCT
ejpam-3322	226	6	gives	give	VERB
ejpam-3322	226	7	α	α	NOUN
ejpam-3322	226	8	′	′	NUM
ejpam-3322	227	1	/̄τ(〈α′〉l	/̄τ(〈α′〉l	PROPN
ejpam-3322	227	2	,	,	PUNCT
ejpam-3322	227	3	〈	〈	PROPN
ejpam-3322	227	4	α′〉)−1(β	α′〉)−1(β	PROPN
ejpam-3322	227	5	′	′	NUM
ejpam-3322	227	6	)	)	PUNCT
ejpam-3322	228	1	=	=	PUNCT
ejpam-3322	228	2	(	(	PUNCT
ejpam-3322	228	3	10	10	NUM
ejpam-3322	228	4	)	)	PUNCT
ejpam-3322	228	5	α	α	NOUN
ejpam-3322	228	6	′	′	NUM
ejpam-3322	228	7	(	(	PUNCT
ejpam-3322	228	8	β	β	NOUN
ejpam-3322	228	9	′	′	NUM
ejpam-3322	228	10	/̄τ(〈β′〉l	/̄τ(〈β′〉l	PROPN
ejpam-3322	228	11	,	,	PUNCT
ejpam-3322	228	12	〈	〈	PROPN
ejpam-3322	228	13	β′〉)−1(〈β′〉l.τ(〈α′〉l	β′〉)−1(〈β′〉l.τ(〈α′〉l	NOUN
ejpam-3322	228	14	,	,	PUNCT
ejpam-3322	228	15	〈	〈	PROPN
ejpam-3322	228	16	α′〉))τ(〈β′〉l	α′〉))τ(〈β′〉l	X
ejpam-3322	228	17	c	c	NOUN
ejpam-3322	228	18	τ(〈α′〉l	τ(〈α′〉l	NOUN
ejpam-3322	228	19	,	,	PUNCT
ejpam-3322	228	20	〈	〈	PROPN
ejpam-3322	228	21	α′	α′	NUM
ejpam-3322	228	22	〉	〉	NUM
ejpam-3322	228	23	)	)	PUNCT
ejpam-3322	228	24	,	,	PUNCT
ejpam-3322	228	25	(	(	PUNCT
ejpam-3322	228	26	〈	〈	PROPN
ejpam-3322	228	27	β′〉l	β′〉l	PROPN
ejpam-3322	228	28	c	c	PROPN
ejpam-3322	228	29	τ(〈α′〉l	τ(〈α′〉l	NOUN
ejpam-3322	228	30	,	,	PUNCT
ejpam-3322	228	31	〈	〈	PROPN
ejpam-3322	228	32	α′〉))r	α′〉))r	NUM
ejpam-3322	228	33	)	)	PUNCT
ejpam-3322	228	34	)	)	PUNCT
ejpam-3322	228	35	.	.	PUNCT
ejpam-3322	229	1	next	next	ADV
ejpam-3322	229	2	,	,	PUNCT
ejpam-3322	229	3	we	we	PRON
ejpam-3322	229	4	need	need	VERB
ejpam-3322	229	5	to	to	PART
ejpam-3322	229	6	do	do	VERB
ejpam-3322	229	7	the	the	DET
ejpam-3322	229	8	following	following	ADJ
ejpam-3322	229	9	calculations	calculation	NOUN
ejpam-3322	229	10	:(	:(	PUNCT
ejpam-3322	230	1	〈	〈	PROPN
ejpam-3322	230	2	α′	α′	PROPN
ejpam-3322	230	3	〉	〉	NUM
ejpam-3322	230	4	ll	ll	AUX
ejpam-3322	230	5	/τ(〈α′	/τ(〈α′	PROPN
ejpam-3322	230	6	〉	〉	PROPN
ejpam-3322	230	7	l	l	NOUN
ejpam-3322	230	8	,	,	PUNCT
ejpam-3322	230	9	〈	〈	PROPN
ejpam-3322	230	10	α′	α′	NUM
ejpam-3322	230	11	〉	〉	NUM
ejpam-3322	230	12	)	)	PUNCT
ejpam-3322	230	13	)	)	PUNCT
ejpam-3322	230	14	·	·	PUNCT
ejpam-3322	231	1	(	(	PUNCT
ejpam-3322	231	2	〈	〈	PROPN
ejpam-3322	231	3	α′	α′	NUM
ejpam-3322	231	4	〉	〉	NUM
ejpam-3322	231	5	l	l	NOUN
ejpam-3322	231	6	·	·	PUNCT
ejpam-3322	232	1	〈	〈	PROPN
ejpam-3322	232	2	α′	α′	NUM
ejpam-3322	232	3	〉	〉	NUM
ejpam-3322	232	4	)	)	PUNCT
ejpam-3322	233	1	=	=	PUNCT
ejpam-3322	233	2	(	(	PUNCT
ejpam-3322	233	3	〈	〈	PROPN
ejpam-3322	233	4	α′	α′	NUM
ejpam-3322	233	5	〉	〉	PROPN
ejpam-3322	233	6	ll	ll	NOUN
ejpam-3322	233	7	·	·	PUNCT
ejpam-3322	233	8	〈	〈	PROPN
ejpam-3322	233	9	α′	α′	NUM
ejpam-3322	233	10	〉	〉	NUM
ejpam-3322	233	11	l	l	NOUN
ejpam-3322	233	12	)	)	PUNCT
ejpam-3322	233	13	·	·	PUNCT
ejpam-3322	234	1	〈	〈	PROPN
ejpam-3322	234	2	α′	α′	NUM
ejpam-3322	234	3	〉	〉	NUM
ejpam-3322	234	4	,	,	PUNCT
ejpam-3322	234	5	which	which	PRON
ejpam-3322	234	6	implies	imply	VERB
ejpam-3322	234	7	that	that	SCONJ
ejpam-3322	234	8	〈	〈	PROPN
ejpam-3322	234	9	α′	α′	ADP
ejpam-3322	234	10	〉	〉	NUM
ejpam-3322	234	11	ll	ll	AUX
ejpam-3322	234	12	c	c	X
ejpam-3322	234	13	τ(〈α′	τ(〈α′	VERB
ejpam-3322	234	14	〉	〉	PROPN
ejpam-3322	234	15	l	l	NOUN
ejpam-3322	234	16	,	,	PUNCT
ejpam-3322	234	17	〈	〈	PROPN
ejpam-3322	234	18	α′	α′	NUM
ejpam-3322	234	19	〉	〉	NUM
ejpam-3322	234	20	)	)	PUNCT
ejpam-3322	234	21	=	=	PUNCT
ejpam-3322	235	1	〈	〈	PROPN
ejpam-3322	235	2	α′	α′	NUM
ejpam-3322	235	3	〉	〉	NUM
ejpam-3322	235	4	.	.	PUNCT
ejpam-3322	236	1	thus	thus	ADV
ejpam-3322	236	2	,	,	PUNCT
ejpam-3322	236	3	we	we	PRON
ejpam-3322	236	4	can	can	AUX
ejpam-3322	236	5	consider	consider	VERB
ejpam-3322	236	6	the	the	DET
ejpam-3322	236	7	following	follow	VERB
ejpam-3322	236	8	〈	〈	PROPN
ejpam-3322	236	9	α′	α′	PROPN
ejpam-3322	236	10	〉	〉	PROPN
ejpam-3322	236	11	ll	ll	AUX
ejpam-3322	236	12	〈	〈	PROPN
ejpam-3322	236	13	α′	α′	ADP
ejpam-3322	236	14	〉	〉	NUM
ejpam-3322	236	15	l	l	NOUN
ejpam-3322	237	1	〈	〈	PROPN
ejpam-3322	237	2	α′	α′	NUM
ejpam-3322	237	3	〉	〉	NUM
ejpam-3322	237	4	=	=	SYM
ejpam-3322	237	5	〈	〈	PROPN
ejpam-3322	237	6	α′	α′	ADP
ejpam-3322	237	7	〉	〉	PROPN
ejpam-3322	237	8	ll	ll	AUX
ejpam-3322	237	9	τ(〈α′	τ(〈α′	VERB
ejpam-3322	237	10	〉	〉	PROPN
ejpam-3322	237	11	l	l	NOUN
ejpam-3322	237	12	,	,	PUNCT
ejpam-3322	237	13	〈	〈	PROPN
ejpam-3322	237	14	α′	α′	NUM
ejpam-3322	237	15	〉	〉	NUM
ejpam-3322	237	16	)	)	PUNCT
ejpam-3322	238	1	=	=	PRON
ejpam-3322	239	1	(	(	PUNCT
ejpam-3322	239	2	〈	〈	PROPN
ejpam-3322	239	3	α′〉)ll	α′〉)ll	PROPN
ejpam-3322	239	4	b	b	PROPN
ejpam-3322	239	5	τ(〈α′	τ(〈α′	NOUN
ejpam-3322	239	6	〉	〉	NOUN
ejpam-3322	239	7	l	l	NOUN
ejpam-3322	239	8	,	,	PUNCT
ejpam-3322	239	9	〈	〈	PROPN
ejpam-3322	239	10	α′	α′	NUM
ejpam-3322	239	11	〉	〉	NUM
ejpam-3322	239	12	)	)	PUNCT
ejpam-3322	239	13	)	)	PUNCT
ejpam-3322	240	1	〈	〈	PROPN
ejpam-3322	240	2	α′	α′	NUM
ejpam-3322	240	3	〉	〉	NUM
ejpam-3322	240	4	,	,	PUNCT
ejpam-3322	240	5	which	which	PRON
ejpam-3322	240	6	implies	imply	VERB
ejpam-3322	240	7	that	that	SCONJ
ejpam-3322	240	8	〈	〈	PROPN
ejpam-3322	240	9	α′	α′	ADP
ejpam-3322	240	10	〉	〉	NUM
ejpam-3322	240	11	ll	ll	AUX
ejpam-3322	240	12	〈	〈	VERB
ejpam-3322	240	13	α′	α′	ADP
ejpam-3322	240	14	〉	〉	NUM
ejpam-3322	240	15	l	l	NOUN
ejpam-3322	240	16	=	=	PUNCT
ejpam-3322	240	17	τ(〈α′	τ(〈α′	NOUN
ejpam-3322	240	18	〉	〉	NOUN
ejpam-3322	240	19	ll	ll	NOUN
ejpam-3322	240	20	,	,	PUNCT
ejpam-3322	240	21	〈	〈	PROPN
ejpam-3322	240	22	α′	α′	NUM
ejpam-3322	240	23	〉	〉	NUM
ejpam-3322	240	24	l	l	NOUN
ejpam-3322	240	25	)	)	PUNCT
ejpam-3322	241	1	=	=	PUNCT
ejpam-3322	242	1	〈	〈	PROPN
ejpam-3322	242	2	α′〉ll	α′〉ll	PROPN
ejpam-3322	242	3	b	b	NOUN
ejpam-3322	242	4	τ(〈′α〉l	τ(〈′α〉l	PROPN
ejpam-3322	242	5	,	,	PUNCT
ejpam-3322	242	6	〈	〈	PROPN
ejpam-3322	242	7	α′	α′	NUM
ejpam-3322	242	8	〉	〉	NUM
ejpam-3322	242	9	)	)	PUNCT
ejpam-3322	242	10	.	.	PUNCT
ejpam-3322	243	1	now	now	ADV
ejpam-3322	243	2	,	,	PUNCT
ejpam-3322	243	3	substituting	substitute	VERB
ejpam-3322	243	4	in	in	ADP
ejpam-3322	243	5	equation	equation	NOUN
ejpam-3322	243	6	(	(	PUNCT
ejpam-3322	243	7	10	10	NUM
ejpam-3322	243	8	)	)	PUNCT
ejpam-3322	243	9	gives	give	VERB
ejpam-3322	243	10	α	α	NOUN
ejpam-3322	243	11	′	′	NUM
ejpam-3322	244	1	/̄τ(〈α′〉l	/̄τ(〈α′〉l	PROPN
ejpam-3322	244	2	,	,	PUNCT
ejpam-3322	244	3	〈	〈	PROPN
ejpam-3322	244	4	α′〉)−1(β	α′〉)−1(β	PROPN
ejpam-3322	244	5	′	′	NUM
ejpam-3322	244	6	)	)	PUNCT
ejpam-3322	245	1	=	=	PUNCT
ejpam-3322	246	1	α	α	X
ejpam-3322	246	2	′	′	NUM
ejpam-3322	247	1	(	(	PUNCT
ejpam-3322	247	2	β	β	NOUN
ejpam-3322	247	3	′	′	NUM
ejpam-3322	247	4	/̄τ(〈α′	/̄τ(〈α′	PROPN
ejpam-3322	247	5	〉	〉	NUM
ejpam-3322	247	6	,	,	PUNCT
ejpam-3322	247	7	〈	〈	PROPN
ejpam-3322	247	8	α′〉r	α′〉r	NUM
ejpam-3322	247	9	)	)	PUNCT
ejpam-3322	247	10	)	)	PUNCT
ejpam-3322	247	11	.	.	PUNCT
ejpam-3322	248	1	after	after	ADP
ejpam-3322	248	2	applying	apply	VERB
ejpam-3322	248	3	the	the	DET
ejpam-3322	248	4	evaluation	evaluation	NOUN
ejpam-3322	248	5	map	map	NOUN
ejpam-3322	248	6	and	and	CCONJ
ejpam-3322	248	7	since	since	SCONJ
ejpam-3322	248	8	τ(〈α′	τ(〈α′	NOUN
ejpam-3322	248	9	〉	〉	NOUN
ejpam-3322	248	10	,	,	PUNCT
ejpam-3322	248	11	〈	〈	PROPN
ejpam-3322	248	12	α′〉r	α′〉r	NUM
ejpam-3322	248	13	)	)	PUNCT
ejpam-3322	248	14	=	=	SYM
ejpam-3322	248	15	e	e	NOUN
ejpam-3322	248	16	,	,	PUNCT
ejpam-3322	248	17	(	(	PUNCT
ejpam-3322	248	18	8)	8)	NUM
ejpam-3322	248	19	becomes	become	VERB
ejpam-3322	248	20	α⊗	α⊗	NOUN
ejpam-3322	248	21	(	(	PUNCT
ejpam-3322	248	22	(	(	PUNCT
ejpam-3322	248	23	α	α	NOUN
ejpam-3322	248	24	′	′	NUM
ejpam-3322	248	25	(	(	PUNCT
ejpam-3322	248	26	β	β	NOUN
ejpam-3322	248	27	′	′	NUM
ejpam-3322	249	1	/̄τ(〈α′	/̄τ(〈α′	PROPN
ejpam-3322	249	2	〉	〉	NUM
ejpam-3322	249	3	,	,	PUNCT
ejpam-3322	249	4	〈	〈	PROPN
ejpam-3322	249	5	α′〉r))⊗	α′〉r))⊗	NUM
ejpam-3322	249	6	(	(	PUNCT
ejpam-3322	249	7	β2	β2	NOUN
ejpam-3322	249	8	⊗	⊗	PROPN
ejpam-3322	249	9	γ	γ	PROPN
ejpam-3322	249	10	)	)	PUNCT
ejpam-3322	249	11	)	)	PUNCT
ejpam-3322	250	1	=	=	SYM
ejpam-3322	250	2	α⊗	α⊗	INTJ
ejpam-3322	250	3	(	(	PUNCT
ejpam-3322	250	4	α	α	NOUN
ejpam-3322	250	5	′	′	NUM
ejpam-3322	250	6	(	(	PUNCT
ejpam-3322	250	7	β	β	NOUN
ejpam-3322	250	8	′	′	NUM
ejpam-3322	250	9	)	)	PUNCT
ejpam-3322	251	1	⊗	⊗	PROPN
ejpam-3322	251	2	(	(	PUNCT
ejpam-3322	251	3	β2	β2	PROPN
ejpam-3322	251	4	⊗	⊗	PROPN
ejpam-3322	251	5	γ	γ	PROPN
ejpam-3322	251	6	)	)	PUNCT
ejpam-3322	251	7	)	)	PUNCT
ejpam-3322	251	8	.	.	PUNCT
ejpam-3322	252	1	(	(	PUNCT
ejpam-3322	252	2	11	11	NUM
ejpam-3322	252	3	)	)	PUNCT
ejpam-3322	252	4	b.	b.	PROPN
ejpam-3322	252	5	al	al	PROPN
ejpam-3322	252	6	-	-	PUNCT
ejpam-3322	252	7	harbi	harbi	PROPN
ejpam-3322	252	8	,	,	PUNCT
ejpam-3322	252	9	w.	w.	PROPN
ejpam-3322	252	10	m.	m.	PROPN
ejpam-3322	252	11	fakieh	fakieh	PROPN
ejpam-3322	252	12	,	,	PUNCT
ejpam-3322	252	13	m.	m.	NOUN
ejpam-3322	252	14	m.	m.	PROPN
ejpam-3322	252	15	al	al	PROPN
ejpam-3322	252	16	-	-	PUNCT
ejpam-3322	252	17	shomrani	shomrani	PROPN
ejpam-3322	252	18	/	/	SYM
ejpam-3322	252	19	eur	eur	NOUN
ejpam-3322	252	20	.	.	PUNCT
ejpam-3322	253	1	j.	j.	PROPN
ejpam-3322	253	2	pure	pure	PROPN
ejpam-3322	253	3	appl	appl	PROPN
ejpam-3322	253	4	.	.	PROPN
ejpam-3322	253	5	math	math	PROPN
ejpam-3322	253	6	,	,	PUNCT
ejpam-3322	253	7	11	11	NUM
ejpam-3322	253	8	(	(	PUNCT
ejpam-3322	253	9	4	4	NUM
ejpam-3322	253	10	)	)	PUNCT
ejpam-3322	253	11	(	(	PUNCT
ejpam-3322	253	12	2018	2018	NUM
ejpam-3322	253	13	)	)	PUNCT
ejpam-3322	253	14	,	,	PUNCT
ejpam-3322	253	15	1027	1027	NUM
ejpam-3322	253	16	-	-	SYM
ejpam-3322	253	17	1045	1045	NUM
ejpam-3322	253	18	1036	1036	NUM
ejpam-3322	253	19	we	we	PRON
ejpam-3322	253	20	now	now	ADV
ejpam-3322	253	21	apply	apply	VERB
ejpam-3322	253	22	the	the	DET
ejpam-3322	253	23	associator	associator	NOUN
ejpam-3322	253	24	inverse	inverse	NOUN
ejpam-3322	253	25	φ−1	φ−1	PROPN
ejpam-3322	253	26	on	on	ADP
ejpam-3322	253	27	(	(	PUNCT
ejpam-3322	253	28	11	11	NUM
ejpam-3322	253	29	)	)	PUNCT
ejpam-3322	253	30	to	to	PART
ejpam-3322	253	31	get	get	VERB
ejpam-3322	253	32	α⊗	α⊗	NOUN
ejpam-3322	253	33	(	(	PUNCT
ejpam-3322	253	34	α′(β	α′(β	X
ejpam-3322	253	35	′	′	NOUN
ejpam-3322	253	36	)	)	PUNCT
ejpam-3322	253	37	/̄τ(〈β2	/̄τ(〈β2	PUNCT
ejpam-3322	253	38	〉	〉	NUM
ejpam-3322	253	39	,	,	PUNCT
ejpam-3322	253	40	〈	〈	PROPN
ejpam-3322	253	41	γ〉)−1	γ〉)−1	NOUN
ejpam-3322	253	42	⊗	⊗	PROPN
ejpam-3322	253	43	β2	β2	PROPN
ejpam-3322	253	44	)	)	PUNCT
ejpam-3322	254	1	⊗	⊗	PROPN
ejpam-3322	254	2	γ	γ	X
ejpam-3322	254	3	.	.	PUNCT
ejpam-3322	254	4	applying	apply	VERB
ejpam-3322	254	5	the	the	DET
ejpam-3322	254	6	associator	associator	NOUN
ejpam-3322	254	7	inverse	inverse	NOUN
ejpam-3322	254	8	again	again	ADV
ejpam-3322	254	9	gives	give	VERB
ejpam-3322	254	10	(	(	PUNCT
ejpam-3322	254	11	α/̄τ(〈β′′	α/̄τ(〈β′′	NUM
ejpam-3322	254	12	〉	〉	NUM
ejpam-3322	254	13	,	,	PUNCT
ejpam-3322	254	14	〈	〈	PROPN
ejpam-3322	254	15	γ〉)−1	γ〉)−1	NOUN
ejpam-3322	254	16	⊗	⊗	PROPN
ejpam-3322	254	17	β′′	β′′	NOUN
ejpam-3322	254	18	)	)	PUNCT
ejpam-3322	254	19	⊗	⊗	PROPN
ejpam-3322	254	20	γ	γ	X
ejpam-3322	254	21	,	,	PUNCT
ejpam-3322	254	22	(	(	PUNCT
ejpam-3322	254	23	12	12	NUM
ejpam-3322	254	24	)	)	PUNCT
ejpam-3322	254	25	where	where	SCONJ
ejpam-3322	254	26	β′′	β′′	NOUN
ejpam-3322	254	27	=	=	SYM
ejpam-3322	254	28	α	α	NOUN
ejpam-3322	254	29	′	′	NUM
ejpam-3322	255	1	(	(	PUNCT
ejpam-3322	255	2	β	β	NOUN
ejpam-3322	255	3	′	′	NUM
ejpam-3322	255	4	)	)	PUNCT
ejpam-3322	255	5	/̄τ(〈β2	/̄τ(〈β2	PUNCT
ejpam-3322	256	1	〉	〉	NUM
ejpam-3322	256	2	,	,	PUNCT
ejpam-3322	256	3	〈	〈	PROPN
ejpam-3322	256	4	γ〉)−1⊗	γ〉)−1⊗	NOUN
ejpam-3322	256	5	β2	β2	NOUN
ejpam-3322	256	6	=	=	PROPN
ejpam-3322	256	7	α′	α′	NUM
ejpam-3322	256	8	(	(	PUNCT
ejpam-3322	256	9	β1	β1	PROPN
ejpam-3322	256	10	c	c	PROPN
ejpam-3322	256	11	τ(〈β2	τ(〈β2	PROPN
ejpam-3322	256	12	〉	〉	PROPN
ejpam-3322	256	13	,	,	PUNCT
ejpam-3322	256	14	〈	〈	PROPN
ejpam-3322	256	15	γ	γ	PROPN
ejpam-3322	256	16	〉	〉	NUM
ejpam-3322	256	17	)	)	PUNCT
ejpam-3322	256	18	)	)	PUNCT
ejpam-3322	256	19	/̄τ(〈β2	/̄τ(〈β2	PUNCT
ejpam-3322	257	1	〉	〉	NUM
ejpam-3322	257	2	,	,	PUNCT
ejpam-3322	257	3	〈	〈	PROPN
ejpam-3322	257	4	γ〉)−1⊗	γ〉)−1⊗	NOUN
ejpam-3322	257	5	β2	β2	NOUN
ejpam-3322	257	6	=	=	SYM
ejpam-3322	257	7	α′(β1)⊗	α′(β1)⊗	PROPN
ejpam-3322	257	8	β2	β2	PROPN
ejpam-3322	257	9	,	,	PUNCT
ejpam-3322	257	10	which	which	PRON
ejpam-3322	257	11	implies	imply	VERB
ejpam-3322	257	12	that	that	SCONJ
ejpam-3322	257	13	〈	〈	PROPN
ejpam-3322	257	14	β′′	β′′	NOUN
ejpam-3322	257	15	〉	〉	NOUN
ejpam-3322	257	16	=	=	SYM
ejpam-3322	257	17	(	(	PUNCT
ejpam-3322	257	18	〈	〈	PROPN
ejpam-3322	257	19	α′	α′	NUM
ejpam-3322	257	20	〉	〉	NUM
ejpam-3322	257	21	·	·	PUNCT
ejpam-3322	257	22	〈	〈	PROPN
ejpam-3322	257	23	β1	β1	PROPN
ejpam-3322	257	24	〉	〉	PROPN
ejpam-3322	257	25	)	)	PUNCT
ejpam-3322	257	26	·	·	PUNCT
ejpam-3322	258	1	〈	〈	PROPN
ejpam-3322	258	2	β2	β2	NOUN
ejpam-3322	258	3	〉	〉	NOUN
ejpam-3322	258	4	=	=	SYM
ejpam-3322	258	5	e	e	X
ejpam-3322	258	6	·	·	PUNCT
ejpam-3322	258	7	〈	〈	NOUN
ejpam-3322	258	8	β2	β2	NOUN
ejpam-3322	258	9	〉	〉	NOUN
ejpam-3322	258	10	=	=	PUNCT
ejpam-3322	258	11	〈	〈	PROPN
ejpam-3322	258	12	β2	β2	PROPN
ejpam-3322	258	13	〉	〉	PROPN
ejpam-3322	258	14	.	.	PUNCT
ejpam-3322	259	1	now	now	ADV
ejpam-3322	259	2	,	,	PUNCT
ejpam-3322	259	3	we	we	PRON
ejpam-3322	259	4	apply	apply	VERB
ejpam-3322	259	5	the	the	DET
ejpam-3322	259	6	evaluation	evaluation	NOUN
ejpam-3322	259	7	map	map	NOUN
ejpam-3322	259	8	on	on	ADP
ejpam-3322	259	9	(	(	PUNCT
ejpam-3322	259	10	12	12	NUM
ejpam-3322	259	11	)	)	PUNCT
ejpam-3322	259	12	to	to	PART
ejpam-3322	259	13	get	get	VERB
ejpam-3322	259	14	(	(	PUNCT
ejpam-3322	259	15	(	(	PUNCT
ejpam-3322	259	16	α/̄τ(〈β2	α/̄τ(〈β2	PROPN
ejpam-3322	259	17	〉	〉	PROPN
ejpam-3322	259	18	,	,	PUNCT
ejpam-3322	259	19	〈	〈	NOUN
ejpam-3322	259	20	γ〉)−1	γ〉)−1	NOUN
ejpam-3322	259	21	)	)	PUNCT
ejpam-3322	259	22	(	(	PUNCT
ejpam-3322	259	23	β′′	β′′	NOUN
ejpam-3322	259	24	)	)	PUNCT
ejpam-3322	259	25	)	)	PUNCT
ejpam-3322	260	1	(	(	PUNCT
ejpam-3322	260	2	γ	γ	X
ejpam-3322	260	3	)	)	PUNCT
ejpam-3322	260	4	=	=	SYM
ejpam-3322	260	5	α	α	PROPN
ejpam-3322	260	6	(	(	PUNCT
ejpam-3322	260	7	β′′/̄τ(〈β2〉l	β′′/̄τ(〈β2〉l	ADV
ejpam-3322	260	8	,	,	PUNCT
ejpam-3322	260	9	〈	〈	NOUN
ejpam-3322	260	10	β2〉)−1	β2〉)−1	X
ejpam-3322	260	11	(	(	PUNCT
ejpam-3322	260	12	〈	〈	PROPN
ejpam-3322	260	13	β2〉l	β2〉l	PROPN
ejpam-3322	260	14	b	b	PROPN
ejpam-3322	260	15	τ(〈β2	τ(〈β2	PROPN
ejpam-3322	260	16	〉	〉	PROPN
ejpam-3322	260	17	,	,	PUNCT
ejpam-3322	260	18	〈	〈	PROPN
ejpam-3322	260	19	γ	γ	PROPN
ejpam-3322	260	20	〉	〉	NUM
ejpam-3322	260	21	)	)	PUNCT
ejpam-3322	260	22	)	)	PUNCT
ejpam-3322	261	1	τ	τ	X
ejpam-3322	261	2	(	(	PUNCT
ejpam-3322	261	3	〈	〈	PROPN
ejpam-3322	261	4	β2〉l	β2〉l	PROPN
ejpam-3322	261	5	c	c	PROPN
ejpam-3322	261	6	τ(〈β2	τ(〈β2	PROPN
ejpam-3322	261	7	〉	〉	PROPN
ejpam-3322	261	8	,	,	PUNCT
ejpam-3322	261	9	〈	〈	PROPN
ejpam-3322	261	10	γ	γ	PROPN
ejpam-3322	261	11	〉	〉	NUM
ejpam-3322	261	12	)	)	PUNCT
ejpam-3322	261	13	,	,	PUNCT
ejpam-3322	261	14	(	(	PUNCT
ejpam-3322	261	15	〈	〈	PROPN
ejpam-3322	261	16	β2〉l	β2〉l	PROPN
ejpam-3322	261	17	c	c	PROPN
ejpam-3322	261	18	τ(〈β2	τ(〈β2	PROPN
ejpam-3322	261	19	〉	〉	PROPN
ejpam-3322	261	20	,	,	PUNCT
ejpam-3322	261	21	〈	〈	PROPN
ejpam-3322	261	22	γ〉))r	γ〉))r	PROPN
ejpam-3322	261	23	)	)	PUNCT
ejpam-3322	261	24	)	)	PUNCT
ejpam-3322	262	1	(	(	PUNCT
ejpam-3322	262	2	γ	γ	X
ejpam-3322	262	3	)	)	PUNCT
ejpam-3322	262	4	(	(	PUNCT
ejpam-3322	262	5	13	13	NUM
ejpam-3322	262	6	)	)	PUNCT
ejpam-3322	262	7	=	=	SYM
ejpam-3322	262	8	α	α	PROPN
ejpam-3322	262	9	(	(	PUNCT
ejpam-3322	262	10	β′′/̄(〈β2〉l	β′′/̄(〈β2〉l	PROPN
ejpam-3322	262	11	b	b	PROPN
ejpam-3322	262	12	τ(〈β2	τ(〈β2	PROPN
ejpam-3322	262	13	〉	〉	PROPN
ejpam-3322	262	14	,	,	PUNCT
ejpam-3322	262	15	〈	〈	PROPN
ejpam-3322	262	16	γ	γ	PROPN
ejpam-3322	262	17	〉	〉	NUM
ejpam-3322	262	18	)	)	PUNCT
ejpam-3322	262	19	)	)	PUNCT
ejpam-3322	262	20	(	(	PUNCT
ejpam-3322	262	21	γ	γ	X
ejpam-3322	262	22	)	)	PUNCT
ejpam-3322	262	23	.	.	PUNCT
ejpam-3322	263	1	considering	consider	VERB
ejpam-3322	263	2	the	the	DET
ejpam-3322	263	3	equality	equality	NOUN
ejpam-3322	263	4	of	of	ADP
ejpam-3322	263	5	the	the	DET
ejpam-3322	263	6	diagram	diagram	NOUN
ejpam-3322	263	7	,	,	PUNCT
ejpam-3322	263	8	we	we	PRON
ejpam-3322	263	9	should	should	AUX
ejpam-3322	263	10	have	have	VERB
ejpam-3322	263	11	µc∗(α⊗	µc∗(α⊗	NUM
ejpam-3322	263	12	α′	α′	NUM
ejpam-3322	263	13	)	)	PUNCT
ejpam-3322	264	1	=	=	SYM
ejpam-3322	264	2	α	α	PROPN
ejpam-3322	264	3	(	(	PUNCT
ejpam-3322	264	4	β′′/̄	β′′/̄	PROPN
ejpam-3322	264	5	(	(	PUNCT
ejpam-3322	264	6	〈	〈	PROPN
ejpam-3322	264	7	β2〉l	β2〉l	PROPN
ejpam-3322	264	8	b	b	PROPN
ejpam-3322	264	9	τ(〈β2	τ(〈β2	PROPN
ejpam-3322	264	10	〉	〉	PROPN
ejpam-3322	264	11	,	,	PUNCT
ejpam-3322	264	12	〈	〈	PROPN
ejpam-3322	264	13	γ	γ	PROPN
ejpam-3322	264	14	〉	〉	NUM
ejpam-3322	264	15	)	)	PUNCT
ejpam-3322	264	16	)	)	PUNCT
ejpam-3322	264	17	)	)	PUNCT
ejpam-3322	264	18	(	(	PUNCT
ejpam-3322	264	19	γ	γ	NOUN
ejpam-3322	264	20	)	)	PUNCT
ejpam-3322	264	21	,	,	PUNCT
ejpam-3322	264	22	(	(	PUNCT
ejpam-3322	264	23	14	14	NUM
ejpam-3322	264	24	)	)	PUNCT
ejpam-3322	264	25	where	where	SCONJ
ejpam-3322	264	26	β′′	β′′	NOUN
ejpam-3322	264	27	=	=	SYM
ejpam-3322	264	28	α′(β1)⊗	α′(β1)⊗	PROPN
ejpam-3322	264	29	β2	β2	PROPN
ejpam-3322	264	30	.	.	PUNCT
ejpam-3322	265	1	but	but	CCONJ
ejpam-3322	265	2	,	,	PUNCT
ejpam-3322	265	3	from	from	ADP
ejpam-3322	265	4	the	the	DET
ejpam-3322	265	5	definition	definition	NOUN
ejpam-3322	265	6	of	of	ADP
ejpam-3322	265	7	the	the	DET
ejpam-3322	265	8	coevaluation	coevaluation	NOUN
ejpam-3322	265	9	map	map	NOUN
ejpam-3322	265	10	,	,	PUNCT
ejpam-3322	265	11	we	we	PRON
ejpam-3322	265	12	know	know	VERB
ejpam-3322	265	13	that	that	SCONJ
ejpam-3322	265	14	coev(1	coev(1	ADV
ejpam-3322	265	15	)	)	PUNCT
ejpam-3322	266	1	=	=	PUNCT
ejpam-3322	266	2	∑	∑	PUNCT
ejpam-3322	266	3	ξ∈	ξ∈	NOUN
ejpam-3322	266	4	basis	basis	NOUN
ejpam-3322	266	5	of	of	ADP
ejpam-3322	266	6	v	v	ADP
ejpam-3322	266	7	ξ	ξ	PROPN
ejpam-3322	266	8	/̄	/̄	PUNCT
ejpam-3322	266	9	τ	τ	PROPN
ejpam-3322	266	10	(	(	PUNCT
ejpam-3322	266	11	〈	〈	PROPN
ejpam-3322	266	12	ξ〉l	ξ〉l	PROPN
ejpam-3322	266	13	,	,	PUNCT
ejpam-3322	266	14	〈	〈	PROPN
ejpam-3322	266	15	ξ	ξ	PROPN
ejpam-3322	266	16	〉	〉	NOUN
ejpam-3322	266	17	)	)	PUNCT
ejpam-3322	266	18	−1	−1	NOUN
ejpam-3322	267	1	⊗	⊗	PROPN
ejpam-3322	267	2	ξ̂	ξ̂	NOUN
ejpam-3322	267	3	,	,	PUNCT
ejpam-3322	267	4	.	.	PUNCT
ejpam-3322	268	1	so	so	ADV
ejpam-3322	268	2	we	we	PRON
ejpam-3322	268	3	can	can	AUX
ejpam-3322	268	4	put	put	VERB
ejpam-3322	268	5	β	β	X
ejpam-3322	268	6	=	=	SYM
ejpam-3322	268	7	ξ	ξ	X
ejpam-3322	268	8	/̄	/̄	PUNCT
ejpam-3322	268	9	τ	τ	PROPN
ejpam-3322	268	10	(	(	PUNCT
ejpam-3322	268	11	〈	〈	PROPN
ejpam-3322	268	12	ξ〉l	ξ〉l	PROPN
ejpam-3322	268	13	,	,	PUNCT
ejpam-3322	268	14	〈	〈	PROPN
ejpam-3322	268	15	ξ	ξ	PROPN
ejpam-3322	268	16	〉	〉	NOUN
ejpam-3322	268	17	)	)	PUNCT
ejpam-3322	268	18	−1	−1	NOUN
ejpam-3322	268	19	and	and	CCONJ
ejpam-3322	268	20	γ	γ	X
ejpam-3322	268	21	=	=	SYM
ejpam-3322	268	22	ξ̂	ξ̂	NOUN
ejpam-3322	268	23	,	,	PUNCT
ejpam-3322	268	24	that	that	PRON
ejpam-3322	268	25	imply	imply	VERB
ejpam-3322	268	26	that	that	SCONJ
ejpam-3322	268	27	〈	〈	PROPN
ejpam-3322	268	28	β	β	NOUN
ejpam-3322	268	29	〉	〉	NOUN
ejpam-3322	269	1	=	=	SYM
ejpam-3322	269	2	〈	〈	PROPN
ejpam-3322	269	3	ξ〉/	ξ〉/	PROPN
ejpam-3322	269	4	τ	τ	X
ejpam-3322	269	5	(	(	PUNCT
ejpam-3322	269	6	〈	〈	PROPN
ejpam-3322	269	7	ξ〉l	ξ〉l	PROPN
ejpam-3322	269	8	,	,	PUNCT
ejpam-3322	269	9	〈	〈	PROPN
ejpam-3322	269	10	ξ	ξ	PROPN
ejpam-3322	269	11	〉	〉	NOUN
ejpam-3322	269	12	)	)	PUNCT
ejpam-3322	269	13	−1	−1	NOUN
ejpam-3322	269	14	and	and	CCONJ
ejpam-3322	269	15	〈	〈	PROPN
ejpam-3322	269	16	γ	γ	PROPN
ejpam-3322	269	17	〉	〉	NOUN
ejpam-3322	269	18	=	=	SYM
ejpam-3322	269	19	〈	〈	PROPN
ejpam-3322	269	20	ξ̂	ξ̂	NOUN
ejpam-3322	269	21	〉	〉	NOUN
ejpam-3322	269	22	=	=	SYM
ejpam-3322	269	23	〈	〈	PROPN
ejpam-3322	269	24	ξ〉l	ξ〉l	PROPN
ejpam-3322	269	25	.	.	PUNCT
ejpam-3322	270	1	thus	thus	ADV
ejpam-3322	270	2	,	,	PUNCT
ejpam-3322	270	3	if	if	SCONJ
ejpam-3322	270	4	we	we	PRON
ejpam-3322	270	5	apply	apply	VERB
ejpam-3322	270	6	the	the	DET
ejpam-3322	270	7	coproduct	coproduct	NOUN
ejpam-3322	270	8	on	on	ADP
ejpam-3322	270	9	β	β	NOUN
ejpam-3322	270	10	,	,	PUNCT
ejpam-3322	270	11	we	we	PRON
ejpam-3322	270	12	get	get	VERB
ejpam-3322	270	13	∆c(β	∆c(β	ADJ
ejpam-3322	270	14	)	)	PUNCT
ejpam-3322	270	15	=	=	SYM
ejpam-3322	270	16	∆c(ξ/	∆c(ξ/	PROPN
ejpam-3322	270	17	τ	τ	X
ejpam-3322	270	18	(	(	PUNCT
ejpam-3322	270	19	〈	〈	PROPN
ejpam-3322	270	20	ξ〉l	ξ〉l	PROPN
ejpam-3322	270	21	,	,	PUNCT
ejpam-3322	270	22	〈	〈	PROPN
ejpam-3322	270	23	ξ	ξ	PROPN
ejpam-3322	270	24	〉	〉	NOUN
ejpam-3322	270	25	)	)	PUNCT
ejpam-3322	270	26	−1	−1	NOUN
ejpam-3322	270	27	)	)	PUNCT
ejpam-3322	270	28	=	=	SYM
ejpam-3322	271	1	ξ1/̄τ(〈ξ1〉l	ξ1/̄τ(〈ξ1〉l	PROPN
ejpam-3322	271	2	,	,	PUNCT
ejpam-3322	271	3	〈	〈	PROPN
ejpam-3322	271	4	ξ1〉)−1	ξ1〉)−1	X
ejpam-3322	271	5	⊗	⊗	PROPN
ejpam-3322	271	6	ξ2/̄τ(ξl2	ξ2/̄τ(ξl2	PROPN
ejpam-3322	271	7	,	,	PUNCT
ejpam-3322	271	8	ξ2)−1	ξ2)−1	NOUN
ejpam-3322	271	9	.	.	PUNCT
ejpam-3322	272	1	consequently	consequently	ADV
ejpam-3322	272	2	,	,	PUNCT
ejpam-3322	272	3	we	we	PRON
ejpam-3322	272	4	can	can	AUX
ejpam-3322	272	5	write	write	VERB
ejpam-3322	272	6	β1	β1	PROPN
ejpam-3322	272	7	=	=	PRON
ejpam-3322	272	8	ξ1/	ξ1/	CCONJ
ejpam-3322	272	9	τ	τ	PROPN
ejpam-3322	272	10	(	(	PUNCT
ejpam-3322	272	11	〈	〈	PROPN
ejpam-3322	272	12	ξ1〉l	ξ1〉l	PROPN
ejpam-3322	272	13	,	,	PUNCT
ejpam-3322	272	14	〈	〈	PROPN
ejpam-3322	272	15	ξ1	ξ1	NOUN
ejpam-3322	272	16	〉	〉	PROPN
ejpam-3322	272	17	)	)	PUNCT
ejpam-3322	272	18	−1	−1	NOUN
ejpam-3322	272	19	and	and	CCONJ
ejpam-3322	272	20	β2	β2	NOUN
ejpam-3322	272	21	=	=	SYM
ejpam-3322	272	22	ξ2/̄τ(〈ξ2〉l	ξ2/̄τ(〈ξ2〉l	ADJ
ejpam-3322	272	23	,	,	PUNCT
ejpam-3322	272	24	〈	〈	NOUN
ejpam-3322	272	25	ξ2〉)−1	ξ2〉)−1	NOUN
ejpam-3322	272	26	,	,	PUNCT
ejpam-3322	272	27	with	with	ADP
ejpam-3322	272	28	〈	〈	PROPN
ejpam-3322	272	29	β1	β1	VERB
ejpam-3322	272	30	〉	〉	NOUN
ejpam-3322	272	31	=	=	SYM
ejpam-3322	272	32	〈	〈	PROPN
ejpam-3322	272	33	ξ1	ξ1	PROPN
ejpam-3322	272	34	〉	〉	PROPN
ejpam-3322	272	35	c	c	AUX
ejpam-3322	273	1	τ(〈ξ1〉l	τ(〈ξ1〉l	ADJ
ejpam-3322	273	2	,	,	PUNCT
ejpam-3322	273	3	〈	〈	PROPN
ejpam-3322	273	4	ξ1〉)−1	ξ1〉)−1	X
ejpam-3322	273	5	and	and	CCONJ
ejpam-3322	273	6	〈	〈	PROPN
ejpam-3322	273	7	β2	β2	NOUN
ejpam-3322	273	8	〉	〉	NOUN
ejpam-3322	273	9	=	=	SYM
ejpam-3322	273	10	〈	〈	PROPN
ejpam-3322	273	11	ξ2	ξ2	NOUN
ejpam-3322	273	12	〉	〉	PROPN
ejpam-3322	273	13	c	c	NOUN
ejpam-3322	273	14	τ(〈ξ2〉l	τ(〈ξ2〉l	PROPN
ejpam-3322	273	15	,	,	PUNCT
ejpam-3322	273	16	〈	〈	NOUN
ejpam-3322	273	17	ξ2〉)−1	ξ2〉)−1	NOUN
ejpam-3322	273	18	.	.	PUNCT
ejpam-3322	274	1	now	now	ADV
ejpam-3322	274	2	,	,	PUNCT
ejpam-3322	274	3	let	let	VERB
ejpam-3322	274	4	ξ	ξ	X
ejpam-3322	274	5	=	=	SYM
ejpam-3322	274	6	δt⊗	δt⊗	PROPN
ejpam-3322	274	7	v	v	NOUN
ejpam-3322	274	8	,	,	PUNCT
ejpam-3322	274	9	γ	γ	X
ejpam-3322	274	10	=	=	SYM
ejpam-3322	274	11	t⊗	t⊗	PROPN
ejpam-3322	274	12	δv	δv	ADV
ejpam-3322	274	13	,	,	PUNCT
ejpam-3322	274	14	ξ1	ξ1	NOUN
ejpam-3322	274	15	=	=	PUNCT
ejpam-3322	274	16	δt1	δt1	VERB
ejpam-3322	274	17	⊗	⊗	NUM
ejpam-3322	274	18	v1	v1	NOUN
ejpam-3322	274	19	and	and	CCONJ
ejpam-3322	274	20	ξ2	ξ2	NOUN
ejpam-3322	274	21	=	=	PUNCT
ejpam-3322	274	22	δt2	δt2	VERB
ejpam-3322	274	23	⊗	⊗	PROPN
ejpam-3322	274	24	v2	v2	PROPN
ejpam-3322	274	25	,	,	PUNCT
ejpam-3322	274	26	with	with	ADP
ejpam-3322	274	27	a	a	DET
ejpam-3322	274	28	=	=	SYM
ejpam-3322	274	29	〈	〈	PROPN
ejpam-3322	274	30	ξ	ξ	PROPN
ejpam-3322	274	31	〉	〉	NOUN
ejpam-3322	274	32	=	=	SYM
ejpam-3322	274	33	〈	〈	PROPN
ejpam-3322	274	34	δt⊗	δt⊗	PROPN
ejpam-3322	274	35	v	v	ADP
ejpam-3322	274	36	〉	〉	PROPN
ejpam-3322	274	37	,	,	PUNCT
ejpam-3322	274	38	al	al	PROPN
ejpam-3322	274	39	=	=	SYM
ejpam-3322	274	40	〈	〈	PROPN
ejpam-3322	274	41	γ	γ	PROPN
ejpam-3322	274	42	〉	〉	NOUN
ejpam-3322	275	1	=	=	SYM
ejpam-3322	275	2	〈	〈	PROPN
ejpam-3322	275	3	t⊗	t⊗	PROPN
ejpam-3322	275	4	δv	δv	PROPN
ejpam-3322	275	5	〉	〉	PROPN
ejpam-3322	275	6	,	,	PUNCT
ejpam-3322	275	7	a1	a1	NOUN
ejpam-3322	275	8	=	=	SYM
ejpam-3322	275	9	〈	〈	PROPN
ejpam-3322	275	10	ξ1	ξ1	NOUN
ejpam-3322	275	11	〉	〉	NUM
ejpam-3322	275	12	=	=	PUNCT
ejpam-3322	275	13	〈	〈	NOUN
ejpam-3322	275	14	δt1	δt1	NOUN
ejpam-3322	275	15	⊗	⊗	PROPN
ejpam-3322	275	16	v1	v1	PROPN
ejpam-3322	275	17	〉	〉	PROPN
ejpam-3322	275	18	and	and	CCONJ
ejpam-3322	275	19	a2	a2	PROPN
ejpam-3322	275	20	=	=	SYM
ejpam-3322	276	1	〈	〈	PROPN
ejpam-3322	276	2	ξ2	ξ2	NOUN
ejpam-3322	276	3	〉	〉	NOUN
ejpam-3322	276	4	=	=	PUNCT
ejpam-3322	277	1	〈	〈	NOUN
ejpam-3322	277	2	δt2	δt2	VERB
ejpam-3322	277	3	⊗	⊗	PROPN
ejpam-3322	277	4	v2	v2	PROPN
ejpam-3322	277	5	〉	〉	PROPN
ejpam-3322	277	6	.	.	PUNCT
ejpam-3322	278	1	b.	b.	PROPN
ejpam-3322	278	2	al	al	PROPN
ejpam-3322	278	3	-	-	PUNCT
ejpam-3322	278	4	harbi	harbi	PROPN
ejpam-3322	278	5	,	,	PUNCT
ejpam-3322	278	6	w.	w.	PROPN
ejpam-3322	278	7	m.	m.	PROPN
ejpam-3322	278	8	fakieh	fakieh	PROPN
ejpam-3322	278	9	,	,	PUNCT
ejpam-3322	278	10	m.	m.	NOUN
ejpam-3322	278	11	m.	m.	PROPN
ejpam-3322	278	12	al	al	PROPN
ejpam-3322	278	13	-	-	PUNCT
ejpam-3322	278	14	shomrani	shomrani	PROPN
ejpam-3322	278	15	/	/	SYM
ejpam-3322	278	16	eur	eur	NOUN
ejpam-3322	278	17	.	.	PUNCT
ejpam-3322	279	1	j.	j.	PROPN
ejpam-3322	279	2	pure	pure	PROPN
ejpam-3322	279	3	appl	appl	PROPN
ejpam-3322	279	4	.	.	PROPN
ejpam-3322	279	5	math	math	PROPN
ejpam-3322	279	6	,	,	PUNCT
ejpam-3322	279	7	11	11	NUM
ejpam-3322	279	8	(	(	PUNCT
ejpam-3322	279	9	4	4	NUM
ejpam-3322	279	10	)	)	PUNCT
ejpam-3322	279	11	(	(	PUNCT
ejpam-3322	279	12	2018	2018	NUM
ejpam-3322	279	13	)	)	PUNCT
ejpam-3322	279	14	,	,	PUNCT
ejpam-3322	279	15	1027	1027	NUM
ejpam-3322	279	16	-	-	SYM
ejpam-3322	279	17	1045	1045	NUM
ejpam-3322	279	18	1037	1037	NUM
ejpam-3322	279	19	as	as	ADP
ejpam-3322	279	20	τ(〈ξ1〉l	τ(〈ξ1〉l	ADJ
ejpam-3322	279	21	,	,	PUNCT
ejpam-3322	279	22	〈	〈	PROPN
ejpam-3322	279	23	ξ1〉)−1	ξ1〉)−1	X
ejpam-3322	279	24	=	=	X
ejpam-3322	279	25	e−1	e−1	PROPN
ejpam-3322	279	26	=	=	SYM
ejpam-3322	279	27	e	e	PROPN
ejpam-3322	279	28	and	and	CCONJ
ejpam-3322	279	29	τ(〈ξ2〉l	τ(〈ξ2〉l	PROPN
ejpam-3322	279	30	,	,	PUNCT
ejpam-3322	279	31	〈	〈	NOUN
ejpam-3322	279	32	ξ2〉)−1	ξ2〉)−1	NOUN
ejpam-3322	279	33	=	=	PUNCT
ejpam-3322	279	34	e−1	e−1	NOUN
ejpam-3322	279	35	=	=	SYM
ejpam-3322	279	36	e	e	NOUN
ejpam-3322	280	1	,	,	PUNCT
ejpam-3322	280	2	it	it	PRON
ejpam-3322	280	3	follows	follow	VERB
ejpam-3322	280	4	that	that	SCONJ
ejpam-3322	280	5	β1	β1	NOUN
ejpam-3322	280	6	=	=	PUNCT
ejpam-3322	280	7	ξ1/̄e	ξ1/̄e	NOUN
ejpam-3322	280	8	=	=	SYM
ejpam-3322	280	9	ξ1	ξ1	NOUN
ejpam-3322	280	10	and	and	CCONJ
ejpam-3322	280	11	β2	β2	NOUN
ejpam-3322	280	12	=	=	SYM
ejpam-3322	280	13	ξ2/̄e	ξ2/̄e	ADJ
ejpam-3322	280	14	=	=	SYM
ejpam-3322	280	15	ξ2	ξ2	PROPN
ejpam-3322	280	16	,	,	PUNCT
ejpam-3322	280	17	which	which	PRON
ejpam-3322	280	18	means	mean	VERB
ejpam-3322	280	19	that	that	SCONJ
ejpam-3322	280	20	β′′	β′′	NOUN
ejpam-3322	280	21	=	=	SYM
ejpam-3322	280	22	α′(δt1	α′(δt1	NOUN
ejpam-3322	281	1	⊗	⊗	NUM
ejpam-3322	281	2	v1)⊗	v1)⊗	INTJ
ejpam-3322	281	3	(	(	PUNCT
ejpam-3322	281	4	δt2	δt2	PROPN
ejpam-3322	281	5	⊗	⊗	PROPN
ejpam-3322	281	6	v2	v2	PROPN
ejpam-3322	281	7	)	)	PUNCT
ejpam-3322	281	8	.	.	PUNCT
ejpam-3322	282	1	if	if	SCONJ
ejpam-3322	282	2	we	we	PRON
ejpam-3322	282	3	put	put	VERB
ejpam-3322	282	4	α′	α′	NUM
ejpam-3322	282	5	=	=	PUNCT
ejpam-3322	282	6	t1⊗δv1	t1⊗δv1	X
ejpam-3322	282	7	in	in	ADP
ejpam-3322	282	8	the	the	DET
ejpam-3322	282	9	right	right	ADJ
ejpam-3322	282	10	hand	hand	NOUN
ejpam-3322	282	11	side	side	NOUN
ejpam-3322	282	12	of	of	ADP
ejpam-3322	282	13	the	the	DET
ejpam-3322	282	14	above	above	ADJ
ejpam-3322	282	15	equation	equation	NOUN
ejpam-3322	282	16	,	,	PUNCT
ejpam-3322	282	17	then	then	ADV
ejpam-3322	282	18	it	it	PRON
ejpam-3322	282	19	can	can	AUX
ejpam-3322	282	20	be	be	AUX
ejpam-3322	282	21	rewritten	rewrite	VERB
ejpam-3322	282	22	as	as	ADP
ejpam-3322	282	23	β′′	β′′	NOUN
ejpam-3322	282	24	=	=	SYM
ejpam-3322	282	25	ev	ev	X
ejpam-3322	282	26	(	(	PUNCT
ejpam-3322	282	27	(	(	PUNCT
ejpam-3322	282	28	t1	t1	PROPN
ejpam-3322	282	29	⊗	⊗	PROPN
ejpam-3322	282	30	δv1)⊗	δv1)⊗	PROPN
ejpam-3322	282	31	(	(	PUNCT
ejpam-3322	282	32	δt1	δt1	VERB
ejpam-3322	282	33	⊗	⊗	PROPN
ejpam-3322	282	34	v1	v1	NOUN
ejpam-3322	282	35	)	)	PUNCT
ejpam-3322	282	36	)	)	PUNCT
ejpam-3322	283	1	⊗	⊗	PROPN
ejpam-3322	283	2	(	(	PUNCT
ejpam-3322	283	3	δt2	δt2	VERB
ejpam-3322	283	4	⊗	⊗	PROPN
ejpam-3322	283	5	v2	v2	PROPN
ejpam-3322	283	6	)	)	PUNCT
ejpam-3322	283	7	=	=	PRON
ejpam-3322	283	8	δt1,t1δv1,v1(δt2	δt1,t1δv1,v1(δt2	VERB
ejpam-3322	283	9	⊗	⊗	NUM
ejpam-3322	283	10	v2	v2	PROPN
ejpam-3322	283	11	)	)	PUNCT
ejpam-3322	283	12	=	=	PUNCT
ejpam-3322	284	1	(	(	PUNCT
ejpam-3322	284	2	δt2	δt2	VERB
ejpam-3322	284	3	⊗	⊗	NUM
ejpam-3322	284	4	v2	v2	PROPN
ejpam-3322	284	5	)	)	PUNCT
ejpam-3322	284	6	.	.	PUNCT
ejpam-3322	285	1	also	also	ADV
ejpam-3322	285	2	,	,	PUNCT
ejpam-3322	285	3	if	if	SCONJ
ejpam-3322	285	4	we	we	PRON
ejpam-3322	285	5	put	put	VERB
ejpam-3322	285	6	q	q	NOUN
ejpam-3322	285	7	=	=	PUNCT
ejpam-3322	285	8	〈	〈	PROPN
ejpam-3322	285	9	β2〉l	β2〉l	PROPN
ejpam-3322	285	10	b	b	PROPN
ejpam-3322	285	11	τ(〈β2	τ(〈β2	PROPN
ejpam-3322	285	12	〉	〉	PROPN
ejpam-3322	285	13	,	,	PUNCT
ejpam-3322	285	14	〈	〈	PROPN
ejpam-3322	285	15	γ	γ	X
ejpam-3322	285	16	〉	〉	NUM
ejpam-3322	285	17	)	)	PUNCT
ejpam-3322	286	1	=	=	SYM
ejpam-3322	286	2	al2	al2	PROPN
ejpam-3322	286	3	b	b	PROPN
ejpam-3322	286	4	τ(a2	τ(a2	NOUN
ejpam-3322	286	5	,	,	PUNCT
ejpam-3322	286	6	a	a	DET
ejpam-3322	286	7	l	l	NOUN
ejpam-3322	286	8	)	)	PUNCT
ejpam-3322	286	9	,	,	PUNCT
ejpam-3322	286	10	then	then	ADV
ejpam-3322	286	11	β′′/̄q	β′′/̄q	PROPN
ejpam-3322	286	12	=	=	PUNCT
ejpam-3322	286	13	(	(	PUNCT
ejpam-3322	286	14	δt2	δt2	VERB
ejpam-3322	286	15	⊗	⊗	NUM
ejpam-3322	286	16	v2)/̄q	v2)/̄q	NOUN
ejpam-3322	286	17	=	=	SYM
ejpam-3322	286	18	(	(	PUNCT
ejpam-3322	286	19	δt2c(a2bq	δt2c(a2bq	NOUN
ejpam-3322	286	20	)	)	PUNCT
ejpam-3322	286	21	⊗	⊗	PROPN
ejpam-3322	286	22	(	(	PUNCT
ejpam-3322	286	23	a2	a2	PROPN
ejpam-3322	286	24	b	b	PROPN
ejpam-3322	286	25	q	q	NOUN
ejpam-3322	286	26	)	)	PUNCT
ejpam-3322	286	27	−1v2q	−1v2q	NOUN
ejpam-3322	286	28	)	)	PUNCT
ejpam-3322	286	29	.	.	PUNCT
ejpam-3322	287	1	now	now	ADV
ejpam-3322	287	2	we	we	PRON
ejpam-3322	287	3	substitute	substitute	VERB
ejpam-3322	287	4	these	these	DET
ejpam-3322	287	5	simplified	simplified	ADJ
ejpam-3322	287	6	parts	part	NOUN
ejpam-3322	287	7	in	in	ADP
ejpam-3322	287	8	equation	equation	NOUN
ejpam-3322	287	9	(	(	PUNCT
ejpam-3322	287	10	14	14	NUM
ejpam-3322	287	11	)	)	PUNCT
ejpam-3322	287	12	to	to	PART
ejpam-3322	287	13	get	get	VERB
ejpam-3322	287	14	µc∗(α⊗	µc∗(α⊗	NUM
ejpam-3322	287	15	α	α	NOUN
ejpam-3322	287	16	′	′	NOUN
ejpam-3322	287	17	)	)	PUNCT
ejpam-3322	288	1	=	=	SYM
ejpam-3322	288	2	α	α	PROPN
ejpam-3322	288	3	(	(	PUNCT
ejpam-3322	288	4	(	(	PUNCT
ejpam-3322	288	5	δt2c(a2bq	δt2c(a2bq	NOUN
ejpam-3322	288	6	)	)	PUNCT
ejpam-3322	288	7	⊗	⊗	PROPN
ejpam-3322	288	8	(	(	PUNCT
ejpam-3322	288	9	a2	a2	PROPN
ejpam-3322	288	10	b	b	PROPN
ejpam-3322	288	11	q	q	NOUN
ejpam-3322	288	12	)	)	PUNCT
ejpam-3322	288	13	−1v2q	−1v2q	NOUN
ejpam-3322	288	14	)	)	PUNCT
ejpam-3322	288	15	)	)	PUNCT
ejpam-3322	288	16	(	(	PUNCT
ejpam-3322	288	17	γ	γ	X
ejpam-3322	288	18	)	)	PUNCT
ejpam-3322	288	19	.	.	PUNCT
ejpam-3322	289	1	if	if	SCONJ
ejpam-3322	289	2	we	we	PRON
ejpam-3322	289	3	put	put	VERB
ejpam-3322	289	4	α	α	NOUN
ejpam-3322	289	5	=	=	SYM
ejpam-3322	289	6	t2	t2	PROPN
ejpam-3322	289	7	⊗	⊗	PROPN
ejpam-3322	289	8	δv2	δv2	NOUN
ejpam-3322	289	9	,	,	PUNCT
ejpam-3322	289	10	the	the	DET
ejpam-3322	289	11	above	above	ADJ
ejpam-3322	289	12	equation	equation	NOUN
ejpam-3322	289	13	becomes	become	VERB
ejpam-3322	289	14	µc∗(α⊗	µc∗(α⊗	NUM
ejpam-3322	289	15	α	α	NOUN
ejpam-3322	289	16	′	′	NUM
ejpam-3322	289	17	)	)	PUNCT
ejpam-3322	290	1	=	=	SYM
ejpam-3322	290	2	ev	ev	X
ejpam-3322	290	3	(	(	PUNCT
ejpam-3322	290	4	(	(	PUNCT
ejpam-3322	290	5	t2	t2	PROPN
ejpam-3322	290	6	⊗	⊗	PROPN
ejpam-3322	290	7	δv2)⊗	δv2)⊗	PROPN
ejpam-3322	290	8	(	(	PUNCT
ejpam-3322	290	9	δt2c(a2bq	δt2c(a2bq	NOUN
ejpam-3322	290	10	)	)	PUNCT
ejpam-3322	290	11	⊗	⊗	PROPN
ejpam-3322	290	12	(	(	PUNCT
ejpam-3322	290	13	a2	a2	PROPN
ejpam-3322	290	14	b	b	PROPN
ejpam-3322	290	15	q	q	NOUN
ejpam-3322	290	16	)	)	PUNCT
ejpam-3322	290	17	−1v2q	−1v2q	NOUN
ejpam-3322	290	18	)	)	PUNCT
ejpam-3322	290	19	)	)	PUNCT
ejpam-3322	290	20	(	(	PUNCT
ejpam-3322	290	21	γ	γ	X
ejpam-3322	290	22	)	)	PUNCT
ejpam-3322	290	23	=	=	SYM
ejpam-3322	290	24	δt2,t2c(a2bq)δv2,(a2bq)−1v2q)(γ	δt2,t2c(a2bq)δv2,(a2bq)−1v2q)(γ	NOUN
ejpam-3322	290	25	)	)	PUNCT
ejpam-3322	290	26	(	(	PUNCT
ejpam-3322	290	27	15	15	NUM
ejpam-3322	290	28	)	)	PUNCT
ejpam-3322	290	29	which	which	PRON
ejpam-3322	290	30	implies	imply	VERB
ejpam-3322	290	31	that	that	SCONJ
ejpam-3322	290	32	t2	t2	NOUN
ejpam-3322	290	33	=	=	SYM
ejpam-3322	290	34	t2	t2	PROPN
ejpam-3322	290	35	c	c	PROPN
ejpam-3322	290	36	(	(	PUNCT
ejpam-3322	290	37	a2	a2	PROPN
ejpam-3322	290	38	b	b	PROPN
ejpam-3322	290	39	q	q	NOUN
ejpam-3322	290	40	)	)	PUNCT
ejpam-3322	290	41	=	=	SYM
ejpam-3322	291	1	t2	t2	PROPN
ejpam-3322	291	2	c	c	PROPN
ejpam-3322	291	3	(	(	PUNCT
ejpam-3322	291	4	a2	a2	PROPN
ejpam-3322	291	5	b	b	PROPN
ejpam-3322	291	6	(	(	PUNCT
ejpam-3322	291	7	al2	al2	PROPN
ejpam-3322	291	8	b	b	PROPN
ejpam-3322	291	9	τ(a2	τ(a2	NOUN
ejpam-3322	291	10	,	,	PUNCT
ejpam-3322	291	11	a	a	DET
ejpam-3322	291	12	l	l	NOUN
ejpam-3322	291	13	)	)	PUNCT
ejpam-3322	291	14	)	)	PUNCT
ejpam-3322	291	15	)	)	PUNCT
ejpam-3322	291	16	,	,	PUNCT
ejpam-3322	291	17	v2	v2	NOUN
ejpam-3322	291	18	=	=	SYM
ejpam-3322	291	19	(	(	PUNCT
ejpam-3322	291	20	a2	a2	PROPN
ejpam-3322	291	21	b	b	PROPN
ejpam-3322	291	22	q	q	NOUN
ejpam-3322	291	23	)	)	PUNCT
ejpam-3322	291	24	−1v2q	−1v2q	NOUN
ejpam-3322	291	25	=	=	SYM
ejpam-3322	291	26	(	(	PUNCT
ejpam-3322	291	27	a2	a2	PROPN
ejpam-3322	291	28	b	b	PROPN
ejpam-3322	291	29	(	(	PUNCT
ejpam-3322	291	30	al2	al2	PROPN
ejpam-3322	291	31	b	b	PROPN
ejpam-3322	291	32	τ(a2	τ(a2	NOUN
ejpam-3322	291	33	,	,	PUNCT
ejpam-3322	291	34	a	a	DET
ejpam-3322	291	35	l	l	NOUN
ejpam-3322	291	36	)	)	PUNCT
ejpam-3322	291	37	)	)	PUNCT
ejpam-3322	291	38	−1	−1	NOUN
ejpam-3322	291	39	v2	v2	NOUN
ejpam-3322	291	40	(	(	PUNCT
ejpam-3322	291	41	al2	al2	PROPN
ejpam-3322	291	42	b	b	PROPN
ejpam-3322	291	43	τ(a2	τ(a2	NOUN
ejpam-3322	291	44	,	,	PUNCT
ejpam-3322	291	45	a	a	DET
ejpam-3322	291	46	l	l	NOUN
ejpam-3322	291	47	)	)	PUNCT
ejpam-3322	291	48	)	)	PUNCT
ejpam-3322	291	49	.	.	PUNCT
ejpam-3322	292	1	to	to	PART
ejpam-3322	292	2	have	have	VERB
ejpam-3322	292	3	these	these	DET
ejpam-3322	292	4	equations	equation	NOUN
ejpam-3322	292	5	satisfied	satisfy	VERB
ejpam-3322	292	6	we	we	PRON
ejpam-3322	292	7	should	should	AUX
ejpam-3322	292	8	have	have	VERB
ejpam-3322	292	9	τ(a2	τ(a2	NOUN
ejpam-3322	292	10	,	,	PUNCT
ejpam-3322	292	11	a	a	DET
ejpam-3322	292	12	l	l	NOUN
ejpam-3322	292	13	)	)	PUNCT
ejpam-3322	293	1	=	=	SYM
ejpam-3322	293	2	e.	e.	PROPN
ejpam-3322	293	3	hence	hence	ADV
ejpam-3322	293	4	,	,	PUNCT
ejpam-3322	293	5	al2	al2	PROPN
ejpam-3322	293	6	b	b	PROPN
ejpam-3322	293	7	τ(a2	τ(a2	NOUN
ejpam-3322	293	8	,	,	PUNCT
ejpam-3322	293	9	a	a	DET
ejpam-3322	293	10	l	l	NOUN
ejpam-3322	293	11	)	)	PUNCT
ejpam-3322	293	12	=	=	SYM
ejpam-3322	293	13	e	e	X
ejpam-3322	293	14	and	and	CCONJ
ejpam-3322	293	15	a2	a2	PROPN
ejpam-3322	293	16	b	b	PROPN
ejpam-3322	293	17	(	(	PUNCT
ejpam-3322	293	18	al2	al2	PROPN
ejpam-3322	293	19	b	b	PROPN
ejpam-3322	293	20	τ(a2	τ(a2	NOUN
ejpam-3322	293	21	,	,	PUNCT
ejpam-3322	293	22	a	a	DET
ejpam-3322	293	23	l	l	NOUN
ejpam-3322	293	24	)	)	PUNCT
ejpam-3322	293	25	)	)	PUNCT
ejpam-3322	294	1	=	=	PUNCT
ejpam-3322	294	2	e.	e.	PROPN
ejpam-3322	294	3	on	on	ADP
ejpam-3322	294	4	the	the	DET
ejpam-3322	294	5	other	other	ADJ
ejpam-3322	294	6	hand	hand	NOUN
ejpam-3322	294	7	,	,	PUNCT
ejpam-3322	294	8	we	we	PRON
ejpam-3322	294	9	know	know	VERB
ejpam-3322	294	10	that	that	SCONJ
ejpam-3322	294	11	δt	δt	VERB
ejpam-3322	294	12	⊗	⊗	PROPN
ejpam-3322	294	13	v	v	PROPN
ejpam-3322	294	14	=	=	PUNCT
ejpam-3322	295	1	(	(	PUNCT
ejpam-3322	295	2	δt1	δt1	PROPN
ejpam-3322	295	3	⊗	⊗	ADJ
ejpam-3322	295	4	v1)⊗	v1)⊗	NOUN
ejpam-3322	295	5	(	(	PUNCT
ejpam-3322	295	6	δt2	δt2	PROPN
ejpam-3322	295	7	⊗	⊗	PROPN
ejpam-3322	295	8	v2	v2	PROPN
ejpam-3322	295	9	)	)	PUNCT
ejpam-3322	295	10	=	=	SYM
ejpam-3322	295	11	δt2,t1cv1δt1cτ(a1,a2	δt2,t1cv1δt1cτ(a1,a2	NOUN
ejpam-3322	295	12	)	)	PUNCT
ejpam-3322	295	13	⊗	⊗	NOUN
ejpam-3322	295	14	τ(a1	τ(a1	NOUN
ejpam-3322	295	15	,	,	PUNCT
ejpam-3322	295	16	a2)−1v1v2	a2)−1v1v2	VERB
ejpam-3322	295	17	thus	thus	ADV
ejpam-3322	295	18	,	,	PUNCT
ejpam-3322	295	19	v	v	NOUN
ejpam-3322	295	20	=	=	PUNCT
ejpam-3322	295	21	τ(a1	τ(a1	NOUN
ejpam-3322	295	22	,	,	PUNCT
ejpam-3322	295	23	a2)−1v1v2	a2)−1v1v2	NOUN
ejpam-3322	295	24	and	and	CCONJ
ejpam-3322	295	25	t	t	PROPN
ejpam-3322	295	26	=	=	SYM
ejpam-3322	295	27	t1	t1	PROPN
ejpam-3322	295	28	c	c	NOUN
ejpam-3322	295	29	τ(a1	τ(a1	NOUN
ejpam-3322	295	30	,	,	PUNCT
ejpam-3322	295	31	a2	a2	PROPN
ejpam-3322	295	32	)	)	PUNCT
ejpam-3322	295	33	.	.	PUNCT
ejpam-3322	296	1	therefore	therefore	ADV
ejpam-3322	296	2	,	,	PUNCT
ejpam-3322	296	3	µc∗(α⊗	µc∗(α⊗	X
ejpam-3322	296	4	α	α	NOUN
ejpam-3322	296	5	′	′	NUM
ejpam-3322	296	6	)	)	PUNCT
ejpam-3322	297	1	=	=	PUNCT
ejpam-3322	297	2	δt1cv1,t2	δt1cv1,t2	NOUN
ejpam-3322	297	3	(	(	PUNCT
ejpam-3322	297	4	t1	t1	NOUN
ejpam-3322	297	5	c	c	NOUN
ejpam-3322	297	6	τ(a1	τ(a1	NOUN
ejpam-3322	297	7	,	,	PUNCT
ejpam-3322	297	8	a2	a2	PROPN
ejpam-3322	297	9	)	)	PUNCT
ejpam-3322	297	10	⊗	⊗	PROPN
ejpam-3322	297	11	δτ(a1,a2)−1v1v2	δτ(a1,a2)−1v1v2	X
ejpam-3322	297	12	)	)	PUNCT
ejpam-3322	297	13	.	.	PUNCT
ejpam-3322	298	1	to	to	PART
ejpam-3322	298	2	confirm	confirm	VERB
ejpam-3322	298	3	our	our	PRON
ejpam-3322	298	4	calculation	calculation	NOUN
ejpam-3322	298	5	we	we	PRON
ejpam-3322	298	6	show	show	VERB
ejpam-3322	298	7	t	t	PROPN
ejpam-3322	298	8	c	c	NOUN
ejpam-3322	298	9	v	v	NOUN
ejpam-3322	298	10	=	=	SYM
ejpam-3322	298	11	t	t	X
ejpam-3322	298	12	·	·	PUNCT
ejpam-3322	298	13	a	a	DET
ejpam-3322	298	14	knowing	knowing	NOUN
ejpam-3322	298	15	that	that	SCONJ
ejpam-3322	298	16	t1	t1	PROPN
ejpam-3322	298	17	c	c	NOUN
ejpam-3322	298	18	v1	v1	PROPN
ejpam-3322	298	19	=	=	SYM
ejpam-3322	298	20	t1	t1	PROPN
ejpam-3322	298	21	·	·	PUNCT
ejpam-3322	298	22	a1	a1	NOUN
ejpam-3322	298	23	,	,	PUNCT
ejpam-3322	298	24	t2	t2	NOUN
ejpam-3322	298	25	c	c	PROPN
ejpam-3322	298	26	v2	v2	NOUN
ejpam-3322	298	27	=	=	SYM
ejpam-3322	298	28	t2	t2	PROPN
ejpam-3322	298	29	·	·	PUNCT
ejpam-3322	298	30	a2	a2	PROPN
ejpam-3322	298	31	,	,	PUNCT
ejpam-3322	298	32	t1	t1	NOUN
ejpam-3322	298	33	c	c	NOUN
ejpam-3322	298	34	v1	v1	PROPN
ejpam-3322	298	35	=	=	SYM
ejpam-3322	298	36	t2	t2	NOUN
ejpam-3322	298	37	,	,	PUNCT
ejpam-3322	298	38	and	and	CCONJ
ejpam-3322	298	39	a	a	DET
ejpam-3322	298	40	=	=	PUNCT
ejpam-3322	298	41	a1	a1	NOUN
ejpam-3322	298	42	·	·	PUNCT
ejpam-3322	298	43	a2	a2	PROPN
ejpam-3322	298	44	.	.	PUNCT
ejpam-3322	299	1	we	we	PRON
ejpam-3322	299	2	start	start	VERB
ejpam-3322	299	3	with	with	ADP
ejpam-3322	299	4	the	the	DET
ejpam-3322	299	5	right	right	ADJ
ejpam-3322	299	6	hand	hand	NOUN
ejpam-3322	299	7	side	side	NOUN
ejpam-3322	299	8	as	as	SCONJ
ejpam-3322	299	9	follows	follow	VERB
ejpam-3322	299	10	:	:	PUNCT
ejpam-3322	299	11	t	t	PROPN
ejpam-3322	299	12	·	·	PUNCT
ejpam-3322	299	13	a	a	DET
ejpam-3322	299	14	=	=	SYM
ejpam-3322	299	15	t1	t1	NOUN
ejpam-3322	299	16	c	c	NOUN
ejpam-3322	299	17	τ(a1	τ(a1	NOUN
ejpam-3322	299	18	,	,	PUNCT
ejpam-3322	299	19	a2	a2	PROPN
ejpam-3322	299	20	)	)	PUNCT
ejpam-3322	299	21	·	·	PUNCT
ejpam-3322	300	1	(	(	PUNCT
ejpam-3322	300	2	a1	a1	PROPN
ejpam-3322	300	3	·	·	SYM
ejpam-3322	300	4	a2	a2	PROPN
ejpam-3322	300	5	)	)	PUNCT
ejpam-3322	300	6	=	=	PRON
ejpam-3322	300	7	(	(	PUNCT
ejpam-3322	300	8	t1	t1	NOUN
ejpam-3322	300	9	·	·	PUNCT
ejpam-3322	300	10	a1	a1	PROPN
ejpam-3322	300	11	)	)	PUNCT
ejpam-3322	300	12	·	·	PUNCT
ejpam-3322	300	13	a2	a2	PROPN
ejpam-3322	300	14	=	=	SYM
ejpam-3322	300	15	(	(	PUNCT
ejpam-3322	300	16	t1	t1	NOUN
ejpam-3322	300	17	c	c	PROPN
ejpam-3322	300	18	v1	v1	PROPN
ejpam-3322	300	19	)	)	PUNCT
ejpam-3322	300	20	·	·	PUNCT
ejpam-3322	300	21	a2	a2	PROPN
ejpam-3322	300	22	=	=	SYM
ejpam-3322	300	23	t2	t2	PROPN
ejpam-3322	300	24	·	·	PUNCT
ejpam-3322	300	25	a2	a2	PROPN
ejpam-3322	300	26	=	=	SYM
ejpam-3322	300	27	t2	t2	PROPN
ejpam-3322	300	28	c	c	PROPN
ejpam-3322	300	29	v2	v2	PROPN
ejpam-3322	300	30	.	.	PUNCT
ejpam-3322	301	1	on	on	ADP
ejpam-3322	301	2	the	the	DET
ejpam-3322	301	3	other	other	ADJ
ejpam-3322	301	4	hand	hand	NOUN
ejpam-3322	301	5	,	,	PUNCT
ejpam-3322	301	6	t	t	PROPN
ejpam-3322	301	7	c	c	PROPN
ejpam-3322	301	8	v	v	X
ejpam-3322	301	9	=	=	SYM
ejpam-3322	301	10	t1	t1	NOUN
ejpam-3322	301	11	c	c	NOUN
ejpam-3322	301	12	τ(a1	τ(a1	NOUN
ejpam-3322	301	13	,	,	PUNCT
ejpam-3322	301	14	a2	a2	PROPN
ejpam-3322	301	15	)	)	PUNCT
ejpam-3322	301	16	c	c	NOUN
ejpam-3322	301	17	τ(a1	τ(a1	NOUN
ejpam-3322	301	18	,	,	PUNCT
ejpam-3322	301	19	a2)−1	a2)−1	X
ejpam-3322	301	20	c	c	NOUN
ejpam-3322	301	21	v1v2	v1v2	PUNCT
ejpam-3322	302	1	=	=	SYM
ejpam-3322	302	2	t1	t1	NUM
ejpam-3322	302	3	c	c	NOUN
ejpam-3322	302	4	v1v2	v1v2	PUNCT
ejpam-3322	303	1	=	=	SYM
ejpam-3322	303	2	t1	t1	NOUN
ejpam-3322	303	3	c	c	NOUN
ejpam-3322	303	4	v1	v1	PROPN
ejpam-3322	303	5	c	c	NOUN
ejpam-3322	303	6	v2	v2	NOUN
ejpam-3322	303	7	=	=	SYM
ejpam-3322	303	8	t2	t2	PROPN
ejpam-3322	303	9	c	c	PROPN
ejpam-3322	303	10	v2	v2	PROPN
ejpam-3322	303	11	.	.	PUNCT
ejpam-3322	304	1	�	�	PROPN
ejpam-3322	304	2	b.	b.	PROPN
ejpam-3322	304	3	al	al	PROPN
ejpam-3322	304	4	-	-	PUNCT
ejpam-3322	304	5	harbi	harbi	PROPN
ejpam-3322	304	6	,	,	PUNCT
ejpam-3322	304	7	w.	w.	PROPN
ejpam-3322	304	8	m.	m.	PROPN
ejpam-3322	304	9	fakieh	fakieh	PROPN
ejpam-3322	304	10	,	,	PUNCT
ejpam-3322	304	11	m.	m.	NOUN
ejpam-3322	304	12	m.	m.	PROPN
ejpam-3322	304	13	al	al	PROPN
ejpam-3322	304	14	-	-	PUNCT
ejpam-3322	304	15	shomrani	shomrani	PROPN
ejpam-3322	304	16	/	/	SYM
ejpam-3322	304	17	eur	eur	NOUN
ejpam-3322	304	18	.	.	PUNCT
ejpam-3322	305	1	j.	j.	PROPN
ejpam-3322	305	2	pure	pure	PROPN
ejpam-3322	305	3	appl	appl	PROPN
ejpam-3322	305	4	.	.	PROPN
ejpam-3322	305	5	math	math	PROPN
ejpam-3322	305	6	,	,	PUNCT
ejpam-3322	305	7	11	11	NUM
ejpam-3322	305	8	(	(	PUNCT
ejpam-3322	305	9	4	4	NUM
ejpam-3322	305	10	)	)	PUNCT
ejpam-3322	305	11	(	(	PUNCT
ejpam-3322	305	12	2018	2018	NUM
ejpam-3322	305	13	)	)	PUNCT
ejpam-3322	305	14	,	,	PUNCT
ejpam-3322	305	15	1027	1027	NUM
ejpam-3322	305	16	-	-	SYM
ejpam-3322	305	17	1045	1045	NUM
ejpam-3322	305	18	1038	1038	NUM
ejpam-3322	305	19	proposition	proposition	NOUN
ejpam-3322	305	20	3.2	3.2	NUM
ejpam-3322	305	21	.	.	PUNCT
ejpam-3322	306	1	let	let	VERB
ejpam-3322	306	2	a	a	DET
ejpam-3322	306	3	be	be	AUX
ejpam-3322	306	4	an	an	DET
ejpam-3322	306	5	algebra	algebra	NOUN
ejpam-3322	306	6	in	in	ADP
ejpam-3322	306	7	the	the	DET
ejpam-3322	306	8	category	category	NOUN
ejpam-3322	306	9	c.	c.	NOUN
ejpam-3322	306	10	then	then	ADV
ejpam-3322	306	11	the	the	DET
ejpam-3322	306	12	counit	counit	VERB
ejpam-3322	306	13	εa∗	εa∗	NOUN
ejpam-3322	306	14	on	on	ADP
ejpam-3322	306	15	a∗	a∗	NOUN
ejpam-3322	306	16	for	for	ADP
ejpam-3322	306	17	any	any	DET
ejpam-3322	306	18	element	element	NOUN
ejpam-3322	306	19	α	α	NOUN
ejpam-3322	306	20	=	=	PUNCT
ejpam-3322	306	21	(	(	PUNCT
ejpam-3322	306	22	s⊗	s⊗	NOUN
ejpam-3322	306	23	δu	δu	NOUN
ejpam-3322	306	24	)	)	PUNCT
ejpam-3322	306	25	∈	∈	PROPN
ejpam-3322	306	26	a∗	a∗	NOUN
ejpam-3322	306	27	is	be	AUX
ejpam-3322	306	28	given	give	VERB
ejpam-3322	306	29	by	by	ADP
ejpam-3322	306	30	εa∗(s⊗	εa∗(s⊗	X
ejpam-3322	306	31	δu	δu	NOUN
ejpam-3322	306	32	)	)	PUNCT
ejpam-3322	306	33	=	=	SYM
ejpam-3322	307	1	δu	δu	X
ejpam-3322	307	2	,	,	PUNCT
ejpam-3322	307	3	e	e	NOUN
ejpam-3322	307	4	,	,	PUNCT
ejpam-3322	307	5	for	for	ADP
ejpam-3322	307	6	u	u	PROPN
ejpam-3322	307	7	∈	∈	PROPN
ejpam-3322	307	8	g	g	PROPN
ejpam-3322	307	9	and	and	CCONJ
ejpam-3322	307	10	s	s	VERB
ejpam-3322	307	11	∈m	∈m	NOUN
ejpam-3322	307	12	.	.	PUNCT
ejpam-3322	308	1	proof	proof	NOUN
ejpam-3322	308	2	.	.	PUNCT
ejpam-3322	309	1	from	from	ADP
ejpam-3322	309	2	proposition	proposition	NOUN
ejpam-3322	309	3	(	(	PUNCT
ejpam-3322	309	4	2.11	2.11	NUM
ejpam-3322	309	5	)	)	PUNCT
ejpam-3322	309	6	,	,	PUNCT
ejpam-3322	309	7	we	we	PRON
ejpam-3322	309	8	know	know	VERB
ejpam-3322	309	9	that	that	SCONJ
ejpam-3322	309	10	a∗	a∗	PROPN
ejpam-3322	309	11	@@	@@	SYM
ejpam-3322	309	12	�	�	PROPN
ejpam-3322	309	13	�	�	PROPN
ejpam-3322	309	14	�	�	PROPN
ejpam-3322	309	15	�	�	PROPN
ejpam-3322	309	16	�	�	PROPN
ejpam-3322	309	17	ηa=	ηa=	PROPN
ejpam-3322	309	18	�	�	PROPN
ejpam-3322	309	19	�	�	PROPN
ejpam-3322	309	20	�	�	PROPN
ejpam-3322	309	21	εa∗	εa∗	NOUN
ejpam-3322	309	22	a∗	a∗	ADJ
ejpam-3322	309	23	figure	figure	NOUN
ejpam-3322	309	24	5	5	NUM
ejpam-3322	309	25	:	:	PUNCT
ejpam-3322	309	26	definition	definition	NOUN
ejpam-3322	309	27	of	of	ADP
ejpam-3322	309	28	counit	counit	VERB
ejpam-3322	309	29	on	on	ADP
ejpam-3322	309	30	a∗.	a∗.	NOUN
ejpam-3322	309	31	we	we	PRON
ejpam-3322	309	32	follow	follow	VERB
ejpam-3322	309	33	figure	figure	NOUN
ejpam-3322	309	34	5	5	NUM
ejpam-3322	309	35	from	from	ADP
ejpam-3322	309	36	top	top	NOUN
ejpam-3322	309	37	to	to	ADP
ejpam-3322	309	38	bottom	bottom	NOUN
ejpam-3322	309	39	and	and	CCONJ
ejpam-3322	309	40	start	start	VERB
ejpam-3322	309	41	with	with	ADP
ejpam-3322	309	42	the	the	DET
ejpam-3322	309	43	following	following	NOUN
ejpam-3322	309	44	for	for	ADP
ejpam-3322	309	45	α	α	PROPN
ejpam-3322	309	46	∈	∈	PROPN
ejpam-3322	309	47	a∗	a∗	PROPN
ejpam-3322	309	48	and	and	CCONJ
ejpam-3322	309	49	k	k	PROPN
ejpam-3322	309	50	∈	∈	PROPN
ejpam-3322	310	1	k	k	NOUN
ejpam-3322	310	2	:	:	PUNCT
ejpam-3322	311	1	α	α	X
ejpam-3322	311	2	=	=	NOUN
ejpam-3322	311	3	α⊗	α⊗	PROPN
ejpam-3322	311	4	k.	k.	PROPN
ejpam-3322	311	5	(	(	PUNCT
ejpam-3322	311	6	16	16	NUM
ejpam-3322	311	7	)	)	PUNCT
ejpam-3322	311	8	knowing	know	VERB
ejpam-3322	311	9	that	that	SCONJ
ejpam-3322	311	10	ηa	ηa	INTJ
ejpam-3322	311	11	:	:	PUNCT
ejpam-3322	311	12	k	k	X
ejpam-3322	311	13	−→	−→	ADV
ejpam-3322	311	14	a	a	PRON
ejpam-3322	311	15	,	,	PUNCT
ejpam-3322	311	16	by	by	ADP
ejpam-3322	311	17	definition	definition	NOUN
ejpam-3322	311	18	(	(	PUNCT
ejpam-3322	311	19	2.1	2.1	NUM
ejpam-3322	311	20	)	)	PUNCT
ejpam-3322	311	21	,	,	PUNCT
ejpam-3322	311	22	we	we	PRON
ejpam-3322	311	23	apply	apply	VERB
ejpam-3322	311	24	the	the	DET
ejpam-3322	311	25	map	map	NOUN
ejpam-3322	311	26	(	(	PUNCT
ejpam-3322	311	27	ia∗	ia∗	ADJ
ejpam-3322	311	28	⊗	⊗	PROPN
ejpam-3322	311	29	ηa	ηa	ADP
ejpam-3322	311	30	)	)	PUNCT
ejpam-3322	311	31	on	on	ADP
ejpam-3322	311	32	equation	equation	NOUN
ejpam-3322	311	33	(	(	PUNCT
ejpam-3322	311	34	16	16	NUM
ejpam-3322	311	35	)	)	PUNCT
ejpam-3322	311	36	to	to	PART
ejpam-3322	311	37	get	get	VERB
ejpam-3322	311	38	(	(	PUNCT
ejpam-3322	311	39	ia∗	ia∗	ADJ
ejpam-3322	311	40	⊗	⊗	PROPN
ejpam-3322	311	41	ηa)(α⊗	ηa)(α⊗	PROPN
ejpam-3322	311	42	k	k	NOUN
ejpam-3322	311	43	)	)	PUNCT
ejpam-3322	311	44	=	=	SYM
ejpam-3322	311	45	ia∗(α)⊗	ia∗(α)⊗	NOUN
ejpam-3322	311	46	ηa(k	ηa(k	NUM
ejpam-3322	311	47	)	)	PUNCT
ejpam-3322	311	48	=	=	PUNCT
ejpam-3322	312	1	α⊗	α⊗	X
ejpam-3322	312	2	β	β	X
ejpam-3322	312	3	,	,	PUNCT
ejpam-3322	312	4	(	(	PUNCT
ejpam-3322	312	5	17	17	NUM
ejpam-3322	312	6	)	)	PUNCT
ejpam-3322	312	7	where	where	SCONJ
ejpam-3322	312	8	β	β	X
ejpam-3322	312	9	=	=	PUNCT
ejpam-3322	312	10	(	(	PUNCT
ejpam-3322	312	11	δs	δs	NOUN
ejpam-3322	312	12	⊗	⊗	PROPN
ejpam-3322	312	13	e	e	PROPN
ejpam-3322	312	14	)	)	PUNCT
ejpam-3322	312	15	∈	∈	PROPN
ejpam-3322	312	16	a	a	PRON
ejpam-3322	312	17	.	.	PUNCT
ejpam-3322	313	1	now	now	ADV
ejpam-3322	313	2	,	,	PUNCT
ejpam-3322	313	3	we	we	PRON
ejpam-3322	313	4	put	put	VERB
ejpam-3322	313	5	α	α	NOUN
ejpam-3322	313	6	=	=	PUNCT
ejpam-3322	314	1	(	(	PUNCT
ejpam-3322	314	2	s	s	PROPN
ejpam-3322	314	3	⊗	⊗	PROPN
ejpam-3322	314	4	δu	δu	NOUN
ejpam-3322	314	5	)	)	PUNCT
ejpam-3322	314	6	and	and	CCONJ
ejpam-3322	314	7	apply	apply	VERB
ejpam-3322	314	8	the	the	DET
ejpam-3322	314	9	evaluation	evaluation	NOUN
ejpam-3322	314	10	map	map	NOUN
ejpam-3322	314	11	on	on	ADP
ejpam-3322	314	12	the	the	DET
ejpam-3322	314	13	right	right	ADJ
ejpam-3322	314	14	hand	hand	NOUN
ejpam-3322	314	15	side	side	NOUN
ejpam-3322	314	16	of	of	ADP
ejpam-3322	314	17	equation	equation	NOUN
ejpam-3322	314	18	(	(	PUNCT
ejpam-3322	314	19	17	17	NUM
ejpam-3322	314	20	)	)	PUNCT
ejpam-3322	314	21	to	to	PART
ejpam-3322	314	22	have	have	VERB
ejpam-3322	314	23	ev(α⊗	ev(α⊗	PROPN
ejpam-3322	314	24	β	β	NOUN
ejpam-3322	314	25	)	)	PUNCT
ejpam-3322	315	1	=	=	SYM
ejpam-3322	315	2	ev((s⊗	ev((s⊗	X
ejpam-3322	315	3	δu)⊗	δu)⊗	PROPN
ejpam-3322	315	4	(	(	PUNCT
ejpam-3322	315	5	δs	δs	NOUN
ejpam-3322	315	6	⊗	⊗	PROPN
ejpam-3322	315	7	e	e	NOUN
ejpam-3322	315	8	)	)	PUNCT
ejpam-3322	315	9	)	)	PUNCT
ejpam-3322	316	1	=	=	SYM
ejpam-3322	317	1	δu	δu	X
ejpam-3322	317	2	,	,	PUNCT
ejpam-3322	317	3	eδs	eδs	NOUN
ejpam-3322	317	4	,	,	PUNCT
ejpam-3322	317	5	s	s	PART
ejpam-3322	317	6	=	=	SYM
ejpam-3322	317	7	δu	δu	X
ejpam-3322	317	8	,	,	PUNCT
ejpam-3322	317	9	e.	e.	PROPN
ejpam-3322	317	10	finally	finally	ADV
ejpam-3322	317	11	,	,	PUNCT
ejpam-3322	317	12	considering	consider	VERB
ejpam-3322	317	13	the	the	DET
ejpam-3322	317	14	left	left	ADJ
ejpam-3322	317	15	hand	hand	NOUN
ejpam-3322	317	16	side	side	NOUN
ejpam-3322	317	17	of	of	ADP
ejpam-3322	317	18	the	the	DET
ejpam-3322	317	19	equality	equality	NOUN
ejpam-3322	317	20	in	in	ADP
ejpam-3322	317	21	figure	figure	NOUN
ejpam-3322	317	22	5	5	NUM
ejpam-3322	317	23	gives	give	VERB
ejpam-3322	317	24	εa∗(s⊗	εa∗(s⊗	NOUN
ejpam-3322	317	25	δu	δu	NOUN
ejpam-3322	317	26	)	)	PUNCT
ejpam-3322	317	27	=	=	SYM
ejpam-3322	317	28	δu	δu	X
ejpam-3322	317	29	,	,	PUNCT
ejpam-3322	317	30	e.	e.	PROPN
ejpam-3322	317	31	�	�	PROPN
ejpam-3322	317	32	proposition	proposition	PROPN
ejpam-3322	317	33	3.3	3.3	NUM
ejpam-3322	317	34	.	.	PUNCT
ejpam-3322	318	1	let	let	VERB
ejpam-3322	318	2	c	c	PRON
ejpam-3322	318	3	be	be	AUX
ejpam-3322	318	4	a	a	DET
ejpam-3322	318	5	coalgebra	coalgebra	NOUN
ejpam-3322	318	6	in	in	ADP
ejpam-3322	318	7	the	the	DET
ejpam-3322	318	8	category	category	NOUN
ejpam-3322	318	9	c	c	NOUN
ejpam-3322	318	10	.	.	PUNCT
ejpam-3322	319	1	then	then	ADV
ejpam-3322	319	2	the	the	DET
ejpam-3322	319	3	unit	unit	NOUN
ejpam-3322	319	4	ηc∗	ηc∗	VERB
ejpam-3322	319	5	on	on	ADP
ejpam-3322	319	6	c∗	c∗	PROPN
ejpam-3322	319	7	can	can	AUX
ejpam-3322	319	8	be	be	AUX
ejpam-3322	319	9	given	give	VERB
ejpam-3322	319	10	by	by	ADP
ejpam-3322	319	11	ηc∗(1k	ηc∗(1k	NOUN
ejpam-3322	319	12	)	)	PUNCT
ejpam-3322	319	13	=	=	SYM
ejpam-3322	320	1	∑	∑	PUNCT
ejpam-3322	320	2	v∈g	v∈g	PROPN
ejpam-3322	320	3	e⊗	e⊗	PROPN
ejpam-3322	320	4	δv	δv	PROPN
ejpam-3322	320	5	,	,	PUNCT
ejpam-3322	320	6	where	where	SCONJ
ejpam-3322	320	7	1k	1k	PRON
ejpam-3322	320	8	is	be	AUX
ejpam-3322	320	9	the	the	DET
ejpam-3322	320	10	unity	unity	NOUN
ejpam-3322	320	11	of	of	ADP
ejpam-3322	320	12	k.	k.	PROPN
ejpam-3322	320	13	b.	b.	PROPN
ejpam-3322	321	1	al	al	PROPN
ejpam-3322	321	2	-	-	PUNCT
ejpam-3322	321	3	harbi	harbi	PROPN
ejpam-3322	321	4	,	,	PUNCT
ejpam-3322	321	5	w.	w.	PROPN
ejpam-3322	321	6	m.	m.	PROPN
ejpam-3322	321	7	fakieh	fakieh	PROPN
ejpam-3322	321	8	,	,	PUNCT
ejpam-3322	321	9	m.	m.	NOUN
ejpam-3322	321	10	m.	m.	PROPN
ejpam-3322	321	11	al	al	PROPN
ejpam-3322	321	12	-	-	PUNCT
ejpam-3322	321	13	shomrani	shomrani	PROPN
ejpam-3322	321	14	/	/	SYM
ejpam-3322	321	15	eur	eur	NOUN
ejpam-3322	321	16	.	.	PUNCT
ejpam-3322	322	1	j.	j.	PROPN
ejpam-3322	322	2	pure	pure	PROPN
ejpam-3322	322	3	appl	appl	PROPN
ejpam-3322	322	4	.	.	PROPN
ejpam-3322	322	5	math	math	PROPN
ejpam-3322	322	6	,	,	PUNCT
ejpam-3322	322	7	11	11	NUM
ejpam-3322	322	8	(	(	PUNCT
ejpam-3322	322	9	4	4	NUM
ejpam-3322	322	10	)	)	PUNCT
ejpam-3322	322	11	(	(	PUNCT
ejpam-3322	322	12	2018	2018	NUM
ejpam-3322	322	13	)	)	PUNCT
ejpam-3322	322	14	,	,	PUNCT
ejpam-3322	322	15	1027	1027	NUM
ejpam-3322	322	16	-	-	SYM
ejpam-3322	322	17	1045	1045	NUM
ejpam-3322	322	18	1039	1039	NUM
ejpam-3322	322	19	proof	proof	NOUN
ejpam-3322	322	20	.	.	PUNCT
ejpam-3322	323	1	from	from	ADP
ejpam-3322	323	2	proposition	proposition	NOUN
ejpam-3322	323	3	(	(	PUNCT
ejpam-3322	323	4	2.12	2.12	NUM
ejpam-3322	323	5	)	)	PUNCT
ejpam-3322	323	6	,	,	PUNCT
ejpam-3322	323	7	we	we	PRON
ejpam-3322	323	8	know	know	VERB
ejpam-3322	323	9	that	that	SCONJ
ejpam-3322	323	10	�	�	PROPN
ejpam-3322	323	11	�	�	PROPN
ejpam-3322	323	12	@@	@@	PROPN
ejpam-3322	323	13	c∗	c∗	PROPN
ejpam-3322	323	14	�	�	PROPN
ejpam-3322	323	15	�	�	PROPN
ejpam-3322	323	16	�	�	PROPN
ejpam-3322	323	17	εc	εc	ADP
ejpam-3322	323	18	=	=	PROPN
ejpam-3322	323	19	c∗	c∗	PROPN
ejpam-3322	323	20	�	�	PROPN
ejpam-3322	323	21	�	�	PROPN
ejpam-3322	323	22	�	�	PROPN
ejpam-3322	323	23	�	�	PROPN
ejpam-3322	323	24	ηc∗	ηc∗	PROPN
ejpam-3322	323	25	figure	figure	VERB
ejpam-3322	323	26	6	6	NUM
ejpam-3322	323	27	:	:	PUNCT
ejpam-3322	323	28	definition	definition	NOUN
ejpam-3322	323	29	of	of	ADP
ejpam-3322	323	30	unit	unit	NOUN
ejpam-3322	323	31	on	on	ADP
ejpam-3322	323	32	c∗.	c∗.	NOUN
ejpam-3322	323	33	we	we	PRON
ejpam-3322	323	34	follow	follow	VERB
ejpam-3322	323	35	figure	figure	NOUN
ejpam-3322	323	36	6	6	NUM
ejpam-3322	323	37	from	from	ADP
ejpam-3322	323	38	top	top	NOUN
ejpam-3322	323	39	to	to	ADP
ejpam-3322	323	40	bottom	bottom	NOUN
ejpam-3322	323	41	and	and	CCONJ
ejpam-3322	323	42	start	start	VERB
ejpam-3322	323	43	by	by	ADP
ejpam-3322	323	44	considering	consider	VERB
ejpam-3322	323	45	the	the	DET
ejpam-3322	323	46	following	following	NOUN
ejpam-3322	323	47	:	:	PUNCT
ejpam-3322	323	48	coev(1	coev(1	ADV
ejpam-3322	323	49	)	)	PUNCT
ejpam-3322	324	1	=	=	PUNCT
ejpam-3322	324	2	β	β	PROPN
ejpam-3322	324	3	⊗	⊗	PROPN
ejpam-3322	324	4	γ	γ	X
ejpam-3322	324	5	,	,	PUNCT
ejpam-3322	324	6	(	(	PUNCT
ejpam-3322	324	7	18	18	NUM
ejpam-3322	324	8	)	)	PUNCT
ejpam-3322	324	9	for	for	ADP
ejpam-3322	324	10	β	β	X
ejpam-3322	324	11	∈	∈	PROPN
ejpam-3322	324	12	c	c	PROPN
ejpam-3322	324	13	and	and	CCONJ
ejpam-3322	324	14	γ	γ	PROPN
ejpam-3322	324	15	∈	∈	PROPN
ejpam-3322	324	16	c∗	c∗	PROPN
ejpam-3322	324	17	,	,	PUNCT
ejpam-3322	324	18	which	which	PRON
ejpam-3322	324	19	implies	imply	VERB
ejpam-3322	324	20	〈	〈	PROPN
ejpam-3322	324	21	β	β	NOUN
ejpam-3322	324	22	〉	〉	NOUN
ejpam-3322	324	23	·	·	PUNCT
ejpam-3322	325	1	〈	〈	PROPN
ejpam-3322	325	2	γ	γ	X
ejpam-3322	325	3	〉	〉	PROPN
ejpam-3322	325	4	=	=	SYM
ejpam-3322	325	5	e.	e.	PROPN
ejpam-3322	325	6	but	but	CCONJ
ejpam-3322	325	7	,	,	PUNCT
ejpam-3322	325	8	from	from	ADP
ejpam-3322	325	9	the	the	DET
ejpam-3322	325	10	definition	definition	NOUN
ejpam-3322	325	11	of	of	ADP
ejpam-3322	325	12	the	the	DET
ejpam-3322	325	13	coevaluation	coevaluation	NOUN
ejpam-3322	325	14	map	map	NOUN
ejpam-3322	325	15	,	,	PUNCT
ejpam-3322	325	16	we	we	PRON
ejpam-3322	325	17	know	know	VERB
ejpam-3322	325	18	coev(1	coev(1	ADJ
ejpam-3322	325	19	)	)	PUNCT
ejpam-3322	326	1	=	=	PUNCT
ejpam-3322	326	2	∑	∑	PUNCT
ejpam-3322	326	3	ξ∈	ξ∈	NOUN
ejpam-3322	326	4	basis	basis	NOUN
ejpam-3322	326	5	of	of	ADP
ejpam-3322	326	6	v	v	ADP
ejpam-3322	326	7	ξ	ξ	PROPN
ejpam-3322	326	8	/̄	/̄	PUNCT
ejpam-3322	326	9	τ	τ	PROPN
ejpam-3322	326	10	(	(	PUNCT
ejpam-3322	326	11	〈	〈	PROPN
ejpam-3322	326	12	ξ〉l	ξ〉l	PROPN
ejpam-3322	326	13	,	,	PUNCT
ejpam-3322	326	14	〈	〈	PROPN
ejpam-3322	326	15	ξ	ξ	PROPN
ejpam-3322	326	16	〉	〉	NOUN
ejpam-3322	326	17	)	)	PUNCT
ejpam-3322	326	18	−1	−1	NOUN
ejpam-3322	327	1	⊗	⊗	PROPN
ejpam-3322	327	2	ξ̂.	ξ̂.	NOUN
ejpam-3322	327	3	we	we	PRON
ejpam-3322	327	4	let	let	VERB
ejpam-3322	327	5	β	β	X
ejpam-3322	327	6	=	=	SYM
ejpam-3322	327	7	ξ	ξ	X
ejpam-3322	327	8	/̄	/̄	PUNCT
ejpam-3322	327	9	τ	τ	PROPN
ejpam-3322	327	10	(	(	PUNCT
ejpam-3322	327	11	〈	〈	PROPN
ejpam-3322	327	12	ξ〉l	ξ〉l	PROPN
ejpam-3322	327	13	,	,	PUNCT
ejpam-3322	327	14	〈	〈	PROPN
ejpam-3322	327	15	ξ	ξ	PROPN
ejpam-3322	327	16	〉	〉	NOUN
ejpam-3322	327	17	)	)	PUNCT
ejpam-3322	327	18	−1	−1	NOUN
ejpam-3322	327	19	,	,	PUNCT
ejpam-3322	327	20	γ	γ	X
ejpam-3322	327	21	=	=	SYM
ejpam-3322	327	22	ξ̂	ξ̂	NOUN
ejpam-3322	327	23	and	and	CCONJ
ejpam-3322	327	24	w	w	PROPN
ejpam-3322	327	25	=	=	SYM
ejpam-3322	327	26	τ(〈ξ〉l	τ(〈ξ〉l	NOUN
ejpam-3322	327	27	,	,	PUNCT
ejpam-3322	327	28	〈	〈	PROPN
ejpam-3322	327	29	ξ〉)−1	ξ〉)−1	NOUN
ejpam-3322	327	30	.	.	PUNCT
ejpam-3322	328	1	if	if	SCONJ
ejpam-3322	328	2	ξ	ξ	X
ejpam-3322	328	3	=	=	SYM
ejpam-3322	328	4	δt	δt	PROPN
ejpam-3322	328	5	⊗	⊗	PROPN
ejpam-3322	328	6	v	v	PROPN
ejpam-3322	328	7	,	,	PUNCT
ejpam-3322	328	8	γ	γ	X
ejpam-3322	328	9	=	=	SYM
ejpam-3322	328	10	t⊗	t⊗	PROPN
ejpam-3322	328	11	δv	δv	PROPN
ejpam-3322	328	12	,	,	PUNCT
ejpam-3322	328	13	then	then	ADV
ejpam-3322	328	14	a	a	DET
ejpam-3322	328	15	=	=	SYM
ejpam-3322	328	16	〈	〈	PROPN
ejpam-3322	328	17	ξ	ξ	PROPN
ejpam-3322	328	18	〉	〉	NOUN
ejpam-3322	328	19	=	=	SYM
ejpam-3322	328	20	〈	〈	PROPN
ejpam-3322	328	21	δt	δt	X
ejpam-3322	328	22	⊗	⊗	PROPN
ejpam-3322	328	23	v	v	PROPN
ejpam-3322	328	24	〉	〉	PROPN
ejpam-3322	328	25	,	,	PUNCT
ejpam-3322	328	26	and	and	CCONJ
ejpam-3322	328	27	al	al	PROPN
ejpam-3322	328	28	=	=	SYM
ejpam-3322	328	29	〈	〈	PROPN
ejpam-3322	328	30	γ	γ	PROPN
ejpam-3322	328	31	〉	〉	NOUN
ejpam-3322	328	32	=	=	SYM
ejpam-3322	328	33	〈	〈	PROPN
ejpam-3322	328	34	t⊗	t⊗	NOUN
ejpam-3322	328	35	δv	δv	PROPN
ejpam-3322	328	36	〉	〉	PROPN
ejpam-3322	328	37	.	.	PUNCT
ejpam-3322	329	1	hence	hence	ADV
ejpam-3322	329	2	,	,	PUNCT
ejpam-3322	329	3	β	β	X
ejpam-3322	329	4	=	=	SYM
ejpam-3322	329	5	(	(	PUNCT
ejpam-3322	329	6	δt	δt	X
ejpam-3322	329	7	⊗	⊗	PROPN
ejpam-3322	329	8	v)/̄w	v)/̄w	ADV
ejpam-3322	329	9	=	=	SYM
ejpam-3322	329	10	δtc(abw	δtc(abw	X
ejpam-3322	329	11	)	)	PUNCT
ejpam-3322	330	1	⊗	⊗	NOUN
ejpam-3322	330	2	(	(	PUNCT
ejpam-3322	330	3	a	a	DET
ejpam-3322	330	4	b	b	X
ejpam-3322	330	5	w)−1vw	w)−1vw	NOUN
ejpam-3322	330	6	.	.	PUNCT
ejpam-3322	331	1	now	now	ADV
ejpam-3322	331	2	,	,	PUNCT
ejpam-3322	331	3	applying	apply	VERB
ejpam-3322	331	4	the	the	DET
ejpam-3322	331	5	map	map	NOUN
ejpam-3322	331	6	(	(	PUNCT
ejpam-3322	331	7	εc	εc	NOUN
ejpam-3322	331	8	⊗	⊗	PROPN
ejpam-3322	331	9	ic∗	ic∗	NOUN
ejpam-3322	331	10	)	)	PUNCT
ejpam-3322	331	11	on	on	ADP
ejpam-3322	331	12	equation	equation	NOUN
ejpam-3322	331	13	(	(	PUNCT
ejpam-3322	331	14	18	18	NUM
ejpam-3322	331	15	)	)	PUNCT
ejpam-3322	331	16	gives	give	VERB
ejpam-3322	331	17	εc(β)⊗	εc(β)⊗	PROPN
ejpam-3322	331	18	ic∗(γ	ic∗(γ	NOUN
ejpam-3322	331	19	)	)	PUNCT
ejpam-3322	331	20	=	=	PUNCT
ejpam-3322	332	1	∑	∑	PUNCT
ejpam-3322	332	2	v∈g	v∈g	NOUN
ejpam-3322	332	3	δtc(abw),e	δtc(abw),e	PUNCT
ejpam-3322	332	4	⊗	⊗	PROPN
ejpam-3322	332	5	(	(	PUNCT
ejpam-3322	332	6	t⊗	t⊗	PROPN
ejpam-3322	332	7	δv	δv	PROPN
ejpam-3322	332	8	)	)	PUNCT
ejpam-3322	332	9	=	=	PUNCT
ejpam-3322	332	10	∑	∑	PUNCT
ejpam-3322	332	11	v∈g	v∈g	NOUN
ejpam-3322	332	12	δtc(abw),e	δtc(abw),e	PUNCT
ejpam-3322	332	13	(	(	PUNCT
ejpam-3322	332	14	t⊗	t⊗	NOUN
ejpam-3322	332	15	δv	δv	NUM
ejpam-3322	332	16	)	)	PUNCT
ejpam-3322	332	17	.	.	PUNCT
ejpam-3322	333	1	(	(	PUNCT
ejpam-3322	333	2	19	19	NUM
ejpam-3322	333	3	)	)	PUNCT
ejpam-3322	333	4	to	to	PART
ejpam-3322	333	5	get	get	VERB
ejpam-3322	333	6	a	a	DET
ejpam-3322	333	7	nonzero	nonzero	NOUN
ejpam-3322	333	8	solution	solution	NOUN
ejpam-3322	333	9	we	we	PRON
ejpam-3322	333	10	should	should	AUX
ejpam-3322	333	11	have	have	VERB
ejpam-3322	333	12	t	t	PROPN
ejpam-3322	333	13	c	c	PROPN
ejpam-3322	333	14	(	(	PUNCT
ejpam-3322	333	15	a	a	DET
ejpam-3322	333	16	b	b	NOUN
ejpam-3322	333	17	w	w	NOUN
ejpam-3322	333	18	)	)	PUNCT
ejpam-3322	333	19	=	=	PUNCT
ejpam-3322	334	1	e⇒	e⇒	PROPN
ejpam-3322	334	2	t	t	PROPN
ejpam-3322	334	3	c	c	PROPN
ejpam-3322	334	4	(	(	PUNCT
ejpam-3322	334	5	a	a	DET
ejpam-3322	334	6	b	b	PROPN
ejpam-3322	334	7	w	w	NOUN
ejpam-3322	334	8	)	)	PUNCT
ejpam-3322	334	9	c	c	NOUN
ejpam-3322	334	10	(	(	PUNCT
ejpam-3322	334	11	a	a	DET
ejpam-3322	334	12	b	b	NOUN
ejpam-3322	334	13	w)−1	w)−1	NOUN
ejpam-3322	334	14	=	=	SYM
ejpam-3322	334	15	e	e	X
ejpam-3322	334	16	c	c	X
ejpam-3322	334	17	(	(	PUNCT
ejpam-3322	334	18	a	a	PRON
ejpam-3322	334	19	b	b	NOUN
ejpam-3322	334	20	w)−1	w)−1	NOUN
ejpam-3322	334	21	⇒	⇒	NOUN
ejpam-3322	334	22	t	t	PROPN
ejpam-3322	334	23	=	=	SYM
ejpam-3322	334	24	e	e	NOUN
ejpam-3322	334	25	which	which	PRON
ejpam-3322	334	26	leads	lead	VERB
ejpam-3322	334	27	to	to	ADP
ejpam-3322	334	28	a	a	DET
ejpam-3322	334	29	=	=	SYM
ejpam-3322	334	30	〈	〈	PROPN
ejpam-3322	334	31	δt	δt	X
ejpam-3322	334	32	⊗	⊗	PROPN
ejpam-3322	334	33	v	v	PROPN
ejpam-3322	334	34	〉	〉	NOUN
ejpam-3322	334	35	=	=	SYM
ejpam-3322	334	36	〈	〈	PROPN
ejpam-3322	334	37	δe	δe	NOUN
ejpam-3322	334	38	⊗	⊗	PROPN
ejpam-3322	334	39	v	v	PROPN
ejpam-3322	334	40	〉	〉	NOUN
ejpam-3322	334	41	=	=	SYM
ejpam-3322	334	42	e.	e.	PROPN
ejpam-3322	335	1	thus	thus	ADV
ejpam-3322	335	2	,	,	PUNCT
ejpam-3322	335	3	equation	equation	NOUN
ejpam-3322	335	4	(	(	PUNCT
ejpam-3322	335	5	19	19	NUM
ejpam-3322	335	6	)	)	PUNCT
ejpam-3322	335	7	can	can	AUX
ejpam-3322	335	8	be	be	AUX
ejpam-3322	335	9	rewritten	rewrite	VERB
ejpam-3322	335	10	as	as	ADP
ejpam-3322	335	11	εc(β)⊗	εc(β)⊗	NOUN
ejpam-3322	335	12	ic∗(γ	ic∗(γ	NOUN
ejpam-3322	335	13	)	)	PUNCT
ejpam-3322	335	14	=	=	PUNCT
ejpam-3322	336	1	∑	∑	PUNCT
ejpam-3322	336	2	v∈g	v∈g	PROPN
ejpam-3322	336	3	e⊗	e⊗	PROPN
ejpam-3322	336	4	δv	δv	PROPN
ejpam-3322	336	5	.	.	PUNCT
ejpam-3322	337	1	finally	finally	ADV
ejpam-3322	337	2	,	,	PUNCT
ejpam-3322	337	3	considering	consider	VERB
ejpam-3322	337	4	the	the	DET
ejpam-3322	337	5	left	left	ADJ
ejpam-3322	337	6	hand	hand	NOUN
ejpam-3322	337	7	side	side	NOUN
ejpam-3322	337	8	of	of	ADP
ejpam-3322	337	9	the	the	DET
ejpam-3322	337	10	equality	equality	NOUN
ejpam-3322	337	11	in	in	ADP
ejpam-3322	337	12	figure	figure	NOUN
ejpam-3322	337	13	6	6	NUM
ejpam-3322	337	14	gives	give	VERB
ejpam-3322	337	15	ηc∗(1k	ηc∗(1k	NOUN
ejpam-3322	337	16	)	)	PUNCT
ejpam-3322	337	17	=	=	SYM
ejpam-3322	338	1	∑	∑	PUNCT
ejpam-3322	338	2	v∈g	v∈g	PROPN
ejpam-3322	338	3	e⊗	e⊗	PROPN
ejpam-3322	338	4	δv	δv	PROPN
ejpam-3322	338	5	.	.	PUNCT
ejpam-3322	338	6	�	�	PROPN
ejpam-3322	338	7	b.	b.	PROPN
ejpam-3322	338	8	al	al	PROPN
ejpam-3322	338	9	-	-	PUNCT
ejpam-3322	338	10	harbi	harbi	PROPN
ejpam-3322	338	11	,	,	PUNCT
ejpam-3322	338	12	w.	w.	PROPN
ejpam-3322	338	13	m.	m.	PROPN
ejpam-3322	338	14	fakieh	fakieh	PROPN
ejpam-3322	338	15	,	,	PUNCT
ejpam-3322	338	16	m.	m.	NOUN
ejpam-3322	338	17	m.	m.	PROPN
ejpam-3322	338	18	al	al	PROPN
ejpam-3322	338	19	-	-	PUNCT
ejpam-3322	338	20	shomrani	shomrani	PROPN
ejpam-3322	338	21	/	/	SYM
ejpam-3322	338	22	eur	eur	NOUN
ejpam-3322	338	23	.	.	PUNCT
ejpam-3322	339	1	j.	j.	PROPN
ejpam-3322	339	2	pure	pure	PROPN
ejpam-3322	339	3	appl	appl	PROPN
ejpam-3322	339	4	.	.	PROPN
ejpam-3322	339	5	math	math	PROPN
ejpam-3322	339	6	,	,	PUNCT
ejpam-3322	339	7	11	11	NUM
ejpam-3322	339	8	(	(	PUNCT
ejpam-3322	339	9	4	4	NUM
ejpam-3322	339	10	)	)	PUNCT
ejpam-3322	339	11	(	(	PUNCT
ejpam-3322	339	12	2018	2018	NUM
ejpam-3322	339	13	)	)	PUNCT
ejpam-3322	339	14	,	,	PUNCT
ejpam-3322	339	15	1027	1027	NUM
ejpam-3322	339	16	-	-	SYM
ejpam-3322	339	17	1045	1045	NUM
ejpam-3322	339	18	1040	1040	NUM
ejpam-3322	339	19	in	in	ADP
ejpam-3322	339	20	the	the	DET
ejpam-3322	339	21	next	next	ADJ
ejpam-3322	339	22	propositions	proposition	NOUN
ejpam-3322	339	23	we	we	PRON
ejpam-3322	339	24	will	will	AUX
ejpam-3322	339	25	check	check	VERB
ejpam-3322	339	26	the	the	DET
ejpam-3322	339	27	unit	unit	NOUN
ejpam-3322	339	28	property	property	NOUN
ejpam-3322	339	29	and	and	CCONJ
ejpam-3322	339	30	the	the	DET
ejpam-3322	339	31	counit	counit	VERB
ejpam-3322	339	32	property	property	NOUN
ejpam-3322	339	33	for	for	ADP
ejpam-3322	339	34	ηc∗	ηc∗	PRON
ejpam-3322	339	35	and	and	CCONJ
ejpam-3322	339	36	εa∗	εa∗	NOUN
ejpam-3322	339	37	respectively	respectively	ADV
ejpam-3322	339	38	.	.	PUNCT
ejpam-3322	340	1	proposition	proposition	NOUN
ejpam-3322	340	2	3.4	3.4	NUM
ejpam-3322	340	3	.	.	PUNCT
ejpam-3322	341	1	let	let	VERB
ejpam-3322	341	2	a	a	DET
ejpam-3322	341	3	be	be	AUX
ejpam-3322	341	4	an	an	DET
ejpam-3322	341	5	algebra	algebra	NOUN
ejpam-3322	341	6	in	in	ADP
ejpam-3322	341	7	the	the	DET
ejpam-3322	341	8	category	category	NOUN
ejpam-3322	341	9	c.	c.	NOUN
ejpam-3322	341	10	then	then	ADV
ejpam-3322	341	11	the	the	DET
ejpam-3322	341	12	counit	counit	VERB
ejpam-3322	341	13	property	property	NOUN
ejpam-3322	341	14	for	for	ADP
ejpam-3322	341	15	the	the	DET
ejpam-3322	341	16	counit	counit	VERB
ejpam-3322	341	17	on	on	ADP
ejpam-3322	341	18	a∗	a∗	PROPN
ejpam-3322	341	19	is	be	AUX
ejpam-3322	341	20	satisfied	satisfied	ADJ
ejpam-3322	341	21	,	,	PUNCT
ejpam-3322	341	22	i.e.	i.e.	X
ejpam-3322	341	23	(	(	PUNCT
ejpam-3322	341	24	εa∗	εa∗	PROPN
ejpam-3322	341	25	⊗	⊗	PROPN
ejpam-3322	341	26	ia∗)∆a∗(t⊗	ia∗)∆a∗(t⊗	PROPN
ejpam-3322	341	27	δv	δv	CCONJ
ejpam-3322	341	28	)	)	PUNCT
ejpam-3322	341	29	=	=	PUNCT
ejpam-3322	342	1	(	(	PUNCT
ejpam-3322	342	2	ia∗	ia∗	ADJ
ejpam-3322	342	3	⊗	⊗	PROPN
ejpam-3322	342	4	εa∗)∆a∗(t⊗	εa∗)∆a∗(t⊗	PROPN
ejpam-3322	342	5	δv	δv	CCONJ
ejpam-3322	342	6	)	)	PUNCT
ejpam-3322	342	7	for	for	ADP
ejpam-3322	342	8	any	any	DET
ejpam-3322	342	9	element	element	NOUN
ejpam-3322	342	10	γ	γ	X
ejpam-3322	342	11	=	=	SYM
ejpam-3322	342	12	(	(	PUNCT
ejpam-3322	342	13	t⊗	t⊗	PROPN
ejpam-3322	342	14	δv	δv	CCONJ
ejpam-3322	342	15	)	)	PUNCT
ejpam-3322	342	16	∈	∈	PROPN
ejpam-3322	342	17	a∗	a∗	NOUN
ejpam-3322	342	18	with	with	ADP
ejpam-3322	342	19	v	v	NUM
ejpam-3322	342	20	∈	∈	PROPN
ejpam-3322	342	21	g	g	NOUN
ejpam-3322	342	22	,	,	PUNCT
ejpam-3322	342	23	t	t	PROPN
ejpam-3322	342	24	∈m	∈m	NOUN
ejpam-3322	342	25	.	.	PUNCT
ejpam-3322	342	26	�	�	PROPN
ejpam-3322	342	27	�	�	PROPN
ejpam-3322	342	28	@@	@@	PROPN
ejpam-3322	342	29	∗	∗	PROPN
ejpam-3322	342	30	�	�	PROPN
ejpam-3322	342	31	�	�	PROPN
ejpam-3322	342	32	�	�	PROPN
ejpam-3322	342	33	εa∗	εa∗	NOUN
ejpam-3322	342	34	=	=	NOUN
ejpam-3322	342	35	=	=	SYM
ejpam-3322	342	36	�	�	PROPN
ejpam-3322	342	37	�	�	PROPN
ejpam-3322	342	38	@@	@@	PROPN
ejpam-3322	342	39	∗	∗	PROPN
ejpam-3322	342	40	�	�	PROPN
ejpam-3322	342	41	�	�	PROPN
ejpam-3322	342	42	�	�	PROPN
ejpam-3322	342	43	εa∗	εa∗	NOUN
ejpam-3322	342	44	a∗	a∗	PROPN
ejpam-3322	342	45	a∗	a∗	PROPN
ejpam-3322	342	46	a∗	a∗	PROPN
ejpam-3322	342	47	a∗	a∗	PROPN
ejpam-3322	342	48	a∗	a∗	PROPN
ejpam-3322	342	49	a∗	a∗	PROPN
ejpam-3322	342	50	figure	figure	NOUN
ejpam-3322	342	51	7	7	NUM
ejpam-3322	342	52	:	:	PUNCT
ejpam-3322	342	53	counit	counit	VERB
ejpam-3322	342	54	property	property	NOUN
ejpam-3322	342	55	on	on	ADP
ejpam-3322	342	56	a∗.	a∗.	NOUN
ejpam-3322	342	57	proof	proof	NOUN
ejpam-3322	342	58	.	.	PUNCT
ejpam-3322	343	1	as	as	SCONJ
ejpam-3322	343	2	a	a	PRON
ejpam-3322	343	3	is	be	AUX
ejpam-3322	343	4	an	an	DET
ejpam-3322	343	5	algebra	algebra	NOUN
ejpam-3322	343	6	in	in	ADP
ejpam-3322	343	7	the	the	DET
ejpam-3322	343	8	category	category	NOUN
ejpam-3322	343	9	c	c	NOUN
ejpam-3322	343	10	,	,	PUNCT
ejpam-3322	343	11	it	it	PRON
ejpam-3322	343	12	has	have	VERB
ejpam-3322	343	13	a	a	DET
ejpam-3322	343	14	unit	unit	NOUN
ejpam-3322	343	15	map	map	NOUN
ejpam-3322	343	16	ηa	ηa	INTJ
ejpam-3322	343	17	:	:	PUNCT
ejpam-3322	344	1	k	k	X
ejpam-3322	344	2	−→	−→	VERB
ejpam-3322	344	3	a	a	DET
ejpam-3322	344	4	satisfying	satisfy	VERB
ejpam-3322	344	5	µa(ia	µa(ia	PROPN
ejpam-3322	344	6	⊗	⊗	PROPN
ejpam-3322	344	7	ηa)(β	ηa)(β	NOUN
ejpam-3322	344	8	⊗	⊗	PROPN
ejpam-3322	344	9	k	k	NOUN
ejpam-3322	344	10	)	)	PUNCT
ejpam-3322	344	11	=	=	SYM
ejpam-3322	344	12	kβ	kβ	NOUN
ejpam-3322	344	13	=	=	PUNCT
ejpam-3322	344	14	µa(ηa	µa(ηa	PROPN
ejpam-3322	344	15	⊗	⊗	ADJ
ejpam-3322	344	16	ia)(k	ia)(k	PROPN
ejpam-3322	344	17	⊗	⊗	NUM
ejpam-3322	344	18	β	β	NOUN
ejpam-3322	344	19	)	)	PUNCT
ejpam-3322	344	20	.	.	PUNCT
ejpam-3322	345	1	we	we	PRON
ejpam-3322	345	2	consider	consider	VERB
ejpam-3322	345	3	the	the	DET
ejpam-3322	345	4	dual	dual	ADJ
ejpam-3322	345	5	map	map	NOUN
ejpam-3322	345	6	η∗a	η∗a	NOUN
ejpam-3322	345	7	:	:	PUNCT
ejpam-3322	345	8	a∗	a∗	PROPN
ejpam-3322	345	9	−→	−→	NOUN
ejpam-3322	345	10	k∗	k∗	NOUN
ejpam-3322	345	11	=	=	PROPN
ejpam-3322	345	12	k	k	PROPN
ejpam-3322	345	13	and	and	CCONJ
ejpam-3322	345	14	let	let	VERB
ejpam-3322	345	15	εa∗	εa∗	NOUN
ejpam-3322	345	16	:	:	PUNCT
ejpam-3322	345	17	a∗	a∗	PROPN
ejpam-3322	345	18	−→	−→	PROPN
ejpam-3322	345	19	k	k	PROPN
ejpam-3322	345	20	denote	denote	VERB
ejpam-3322	345	21	the	the	DET
ejpam-3322	345	22	restriction	restriction	NOUN
ejpam-3322	345	23	of	of	ADP
ejpam-3322	345	24	η∗a	η∗a	NUM
ejpam-3322	345	25	to	to	ADP
ejpam-3322	345	26	a∗.	a∗.	NOUN
ejpam-3322	345	27	now	now	ADV
ejpam-3322	345	28	,	,	PUNCT
ejpam-3322	345	29	for	for	ADP
ejpam-3322	345	30	γ	γ	X
ejpam-3322	345	31	=	=	SYM
ejpam-3322	345	32	(	(	PUNCT
ejpam-3322	345	33	t⊗	t⊗	PROPN
ejpam-3322	345	34	δv	δv	CCONJ
ejpam-3322	345	35	)	)	PUNCT
ejpam-3322	345	36	∈	∈	PROPN
ejpam-3322	345	37	a∗	a∗	NOUN
ejpam-3322	345	38	,	,	PUNCT
ejpam-3322	346	1	k	k	PROPN
ejpam-3322	346	2	∈	∈	PROPN
ejpam-3322	346	3	k	k	NOUN
ejpam-3322	346	4	,	,	PUNCT
ejpam-3322	346	5	we	we	PRON
ejpam-3322	346	6	have	have	VERB
ejpam-3322	346	7	εa∗(γ)(k	εa∗(γ)(k	NOUN
ejpam-3322	346	8	)	)	PUNCT
ejpam-3322	347	1	=	=	SYM
ejpam-3322	347	2	γ	γ	X
ejpam-3322	347	3	(	(	PUNCT
ejpam-3322	347	4	ηa(k	ηa(k	PROPN
ejpam-3322	347	5	)	)	PUNCT
ejpam-3322	347	6	)	)	PUNCT
ejpam-3322	348	1	=	=	SYM
ejpam-3322	348	2	γ	γ	X
ejpam-3322	348	3	(	(	PUNCT
ejpam-3322	348	4	ηa(1k)k	ηa(1k)k	ADV
ejpam-3322	348	5	)	)	PUNCT
ejpam-3322	348	6	=	=	PUNCT
ejpam-3322	348	7	γ(1a)(k	γ(1a)(k	NOUN
ejpam-3322	348	8	)	)	PUNCT
ejpam-3322	348	9	.	.	PUNCT
ejpam-3322	349	1	(	(	PUNCT
ejpam-3322	349	2	20	20	NUM
ejpam-3322	349	3	)	)	PUNCT
ejpam-3322	349	4	hence	hence	ADV
ejpam-3322	349	5	,	,	PUNCT
ejpam-3322	349	6	εa∗(γ	εa∗(γ	NOUN
ejpam-3322	349	7	)	)	PUNCT
ejpam-3322	349	8	=	=	SYM
ejpam-3322	349	9	γ(1a	γ(1a	PROPN
ejpam-3322	349	10	)	)	PUNCT
ejpam-3322	349	11	.	.	PUNCT
ejpam-3322	350	1	next	next	ADV
ejpam-3322	350	2	,	,	PUNCT
ejpam-3322	350	3	let	let	VERB
ejpam-3322	350	4	µ∗a	µ∗a	NUM
ejpam-3322	350	5	:	:	PUNCT
ejpam-3322	350	6	a∗	a∗	ADJ
ejpam-3322	350	7	−→	−→	NOUN
ejpam-3322	350	8	(	(	PUNCT
ejpam-3322	350	9	a⊗a)∗	a⊗a)∗	PROPN
ejpam-3322	350	10	be	be	AUX
ejpam-3322	350	11	the	the	DET
ejpam-3322	350	12	transpose	transpose	NOUN
ejpam-3322	350	13	of	of	ADP
ejpam-3322	350	14	the	the	DET
ejpam-3322	350	15	multiplication	multiplication	NOUN
ejpam-3322	350	16	map	map	NOUN
ejpam-3322	350	17	µa	µa	ADP
ejpam-3322	350	18	defined	define	VERB
ejpam-3322	350	19	as	as	ADP
ejpam-3322	350	20	µ∗a(γ)(β1	µ∗a(γ)(β1	ADP
ejpam-3322	350	21	⊗	⊗	PROPN
ejpam-3322	350	22	β2	β2	PROPN
ejpam-3322	350	23	)	)	PUNCT
ejpam-3322	350	24	=	=	SYM
ejpam-3322	350	25	γ(µa(β1	γ(µa(β1	PROPN
ejpam-3322	350	26	⊗	⊗	PROPN
ejpam-3322	350	27	β2	β2	PROPN
ejpam-3322	350	28	)	)	PUNCT
ejpam-3322	350	29	)	)	PUNCT
ejpam-3322	350	30	=	=	PUNCT
ejpam-3322	351	1	γ(β1.β2	γ(β1.β2	PROPN
ejpam-3322	351	2	)	)	PUNCT
ejpam-3322	351	3	.	.	PUNCT
ejpam-3322	352	1	(	(	PUNCT
ejpam-3322	352	2	21	21	NUM
ejpam-3322	352	3	)	)	PUNCT
ejpam-3322	352	4	it	it	PRON
ejpam-3322	352	5	is	be	AUX
ejpam-3322	352	6	known	know	VERB
ejpam-3322	352	7	that	that	SCONJ
ejpam-3322	352	8	µ∗a(a∗	µ∗a(a∗	PRON
ejpam-3322	352	9	)	)	PUNCT
ejpam-3322	352	10	⊆	⊆	X
ejpam-3322	352	11	a∗⊗a∗	a∗⊗a∗	PROPN
ejpam-3322	353	1	[	[	X
ejpam-3322	353	2	11	11	NUM
ejpam-3322	353	3	]	]	PUNCT
ejpam-3322	353	4	.	.	PUNCT
ejpam-3322	354	1	let	let	VERB
ejpam-3322	354	2	∆a∗	∆a∗	NOUN
ejpam-3322	354	3	denote	denote	VERB
ejpam-3322	354	4	the	the	DET
ejpam-3322	354	5	restriction	restriction	NOUN
ejpam-3322	354	6	of	of	ADP
ejpam-3322	354	7	µ∗a	µ∗a	PUNCT
ejpam-3322	354	8	toa∗.	toa∗.	NOUN
ejpam-3322	354	9	then	then	ADV
ejpam-3322	354	10	∆a∗	∆a∗	ADV
ejpam-3322	354	11	:	:	PUNCT
ejpam-3322	354	12	a∗	a∗	ADJ
ejpam-3322	354	13	−→	−→	ADJ
ejpam-3322	354	14	a∗	a∗	PROPN
ejpam-3322	354	15	⊗a∗	⊗a∗	PROPN
ejpam-3322	354	16	is	be	AUX
ejpam-3322	354	17	a	a	DET
ejpam-3322	354	18	k	k	ADJ
ejpam-3322	354	19	-	-	PUNCT
ejpam-3322	354	20	linear	linear	ADJ
ejpam-3322	354	21	map	map	NOUN
ejpam-3322	354	22	defined	define	VERB
ejpam-3322	354	23	as	as	ADP
ejpam-3322	354	24	∆a∗(γ	∆a∗(γ	PROPN
ejpam-3322	354	25	)	)	PUNCT
ejpam-3322	354	26	=	=	PUNCT
ejpam-3322	354	27	µ∗a(γ	µ∗a(γ	NUM
ejpam-3322	354	28	)	)	PUNCT
ejpam-3322	354	29	,	,	PUNCT
ejpam-3322	354	30	for	for	ADP
ejpam-3322	354	31	γ	γ	PROPN
ejpam-3322	354	32	∈	∈	PROPN
ejpam-3322	354	33	a∗.	a∗.	NOUN
ejpam-3322	354	34	(	(	PUNCT
ejpam-3322	354	35	22	22	NUM
ejpam-3322	354	36	)	)	PUNCT
ejpam-3322	354	37	b.	b.	PROPN
ejpam-3322	355	1	al	al	PROPN
ejpam-3322	355	2	-	-	PUNCT
ejpam-3322	355	3	harbi	harbi	PROPN
ejpam-3322	355	4	,	,	PUNCT
ejpam-3322	355	5	w.	w.	PROPN
ejpam-3322	355	6	m.	m.	PROPN
ejpam-3322	355	7	fakieh	fakieh	PROPN
ejpam-3322	355	8	,	,	PUNCT
ejpam-3322	355	9	m.	m.	NOUN
ejpam-3322	355	10	m.	m.	PROPN
ejpam-3322	355	11	al	al	PROPN
ejpam-3322	355	12	-	-	PUNCT
ejpam-3322	355	13	shomrani	shomrani	PROPN
ejpam-3322	355	14	/	/	SYM
ejpam-3322	355	15	eur	eur	NOUN
ejpam-3322	355	16	.	.	PUNCT
ejpam-3322	356	1	j.	j.	PROPN
ejpam-3322	356	2	pure	pure	PROPN
ejpam-3322	356	3	appl	appl	PROPN
ejpam-3322	356	4	.	.	PROPN
ejpam-3322	356	5	math	math	PROPN
ejpam-3322	356	6	,	,	PUNCT
ejpam-3322	356	7	11	11	NUM
ejpam-3322	356	8	(	(	PUNCT
ejpam-3322	356	9	4	4	NUM
ejpam-3322	356	10	)	)	PUNCT
ejpam-3322	356	11	(	(	PUNCT
ejpam-3322	356	12	2018	2018	NUM
ejpam-3322	356	13	)	)	PUNCT
ejpam-3322	356	14	,	,	PUNCT
ejpam-3322	356	15	1027	1027	NUM
ejpam-3322	356	16	-	-	SYM
ejpam-3322	356	17	1045	1045	NUM
ejpam-3322	356	18	1041	1041	NUM
ejpam-3322	356	19	thus	thus	ADV
ejpam-3322	356	20	,	,	PUNCT
ejpam-3322	356	21	for	for	ADP
ejpam-3322	356	22	γ	γ	X
ejpam-3322	356	23	=	=	SYM
ejpam-3322	356	24	(	(	PUNCT
ejpam-3322	356	25	t⊗	t⊗	PROPN
ejpam-3322	356	26	δv	δv	CCONJ
ejpam-3322	356	27	)	)	PUNCT
ejpam-3322	356	28	∈	∈	PROPN
ejpam-3322	356	29	a∗	a∗	NOUN
ejpam-3322	356	30	,	,	PUNCT
ejpam-3322	356	31	β	β	X
ejpam-3322	356	32	=	=	SYM
ejpam-3322	356	33	(	(	PUNCT
ejpam-3322	356	34	δs	δs	PROPN
ejpam-3322	356	35	⊗	⊗	PROPN
ejpam-3322	356	36	u	u	NOUN
ejpam-3322	356	37	)	)	PUNCT
ejpam-3322	356	38	∈	∈	PROPN
ejpam-3322	356	39	a	a	PRON
ejpam-3322	356	40	and	and	CCONJ
ejpam-3322	356	41	k	k	PROPN
ejpam-3322	356	42	∈	∈	PROPN
ejpam-3322	357	1	k	k	NOUN
ejpam-3322	357	2	,	,	PUNCT
ejpam-3322	357	3	we	we	PRON
ejpam-3322	357	4	have	have	AUX
ejpam-3322	357	5	(	(	PUNCT
ejpam-3322	357	6	εa∗	εa∗	PROPN
ejpam-3322	357	7	⊗	⊗	PROPN
ejpam-3322	357	8	ia∗)∆a∗(γ)(k	ia∗)∆a∗(γ)(k	PROPN
ejpam-3322	357	9	⊗	⊗	NOUN
ejpam-3322	357	10	β	β	X
ejpam-3322	357	11	)	)	PUNCT
ejpam-3322	357	12	=	=	SYM
ejpam-3322	357	13	(	(	PUNCT
ejpam-3322	357	14	η∗a	η∗a	NUM
ejpam-3322	357	15	⊗	⊗	PROPN
ejpam-3322	357	16	i∗a)µ∗a(γ)(k	i∗a)µ∗a(γ)(k	PROPN
ejpam-3322	357	17	⊗	⊗	NUM
ejpam-3322	357	18	β	β	X
ejpam-3322	357	19	)	)	PUNCT
ejpam-3322	357	20	=	=	PUNCT
ejpam-3322	358	1	µ∗a(γ)(ηa	µ∗a(γ)(ηa	PROPN
ejpam-3322	358	2	⊗	⊗	ADJ
ejpam-3322	358	3	ia)(k	ia)(k	PROPN
ejpam-3322	358	4	⊗	⊗	NUM
ejpam-3322	358	5	β	β	X
ejpam-3322	358	6	)	)	PUNCT
ejpam-3322	358	7	=	=	SYM
ejpam-3322	358	8	γ	γ	X
ejpam-3322	358	9	(	(	PUNCT
ejpam-3322	358	10	µa(ηa(k)⊗	µa(ηa(k)⊗	NOUN
ejpam-3322	358	11	β	β	NOUN
ejpam-3322	358	12	)	)	PUNCT
ejpam-3322	358	13	)	)	PUNCT
ejpam-3322	359	1	=	=	SYM
ejpam-3322	359	2	γ	γ	X
ejpam-3322	359	3	(	(	PUNCT
ejpam-3322	359	4	µa	µa	X
ejpam-3322	359	5	(	(	PUNCT
ejpam-3322	359	6	(	(	PUNCT
ejpam-3322	359	7	δt	δt	NOUN
ejpam-3322	359	8	⊗	⊗	PROPN
ejpam-3322	359	9	e)⊗	e)⊗	PROPN
ejpam-3322	359	10	(	(	PUNCT
ejpam-3322	359	11	δs	δs	NOUN
ejpam-3322	359	12	⊗	⊗	PROPN
ejpam-3322	359	13	u	u	NOUN
ejpam-3322	359	14	)	)	PUNCT
ejpam-3322	359	15	)	)	PUNCT
ejpam-3322	359	16	)	)	PUNCT
ejpam-3322	360	1	=	=	SYM
ejpam-3322	360	2	γ	γ	X
ejpam-3322	360	3	(	(	PUNCT
ejpam-3322	360	4	δs	δs	NOUN
ejpam-3322	360	5	,	,	PUNCT
ejpam-3322	360	6	tceδtcτ(a	tceδtcτ(a	NOUN
ejpam-3322	360	7	,	,	PUNCT
ejpam-3322	360	8	b	b	NOUN
ejpam-3322	360	9	)	)	PUNCT
ejpam-3322	360	10	⊗	⊗	NUM
ejpam-3322	360	11	τ(a	τ(a	NOUN
ejpam-3322	360	12	,	,	PUNCT
ejpam-3322	360	13	b)−1eu	b)−1eu	NOUN
ejpam-3322	360	14	)	)	PUNCT
ejpam-3322	361	1	=	=	SYM
ejpam-3322	361	2	γ	γ	X
ejpam-3322	361	3	(	(	PUNCT
ejpam-3322	361	4	δs	δs	NOUN
ejpam-3322	361	5	,	,	PUNCT
ejpam-3322	361	6	tδtcτ(e	tδtcτ(e	NOUN
ejpam-3322	361	7	,	,	PUNCT
ejpam-3322	361	8	b	b	NOUN
ejpam-3322	361	9	)	)	PUNCT
ejpam-3322	361	10	⊗	⊗	PROPN
ejpam-3322	361	11	τ(e	τ(e	PROPN
ejpam-3322	361	12	,	,	PUNCT
ejpam-3322	361	13	b)−1eu	b)−1eu	NOUN
ejpam-3322	361	14	)	)	PUNCT
ejpam-3322	361	15	=	=	PUNCT
ejpam-3322	362	1	γ(δs	γ(δs	PROPN
ejpam-3322	362	2	⊗	⊗	NUM
ejpam-3322	362	3	u	u	NOUN
ejpam-3322	362	4	)	)	PUNCT
ejpam-3322	362	5	=	=	SYM
ejpam-3322	362	6	γ(β	γ(β	PROPN
ejpam-3322	362	7	)	)	PUNCT
ejpam-3322	362	8	=	=	SYM
ejpam-3322	362	9	γ	γ	X
ejpam-3322	362	10	(	(	PUNCT
ejpam-3322	362	11	µa(β	µa(β	ADP
ejpam-3322	362	12	⊗	⊗	PROPN
ejpam-3322	362	13	ηa(k	ηa(k	PROPN
ejpam-3322	362	14	)	)	PUNCT
ejpam-3322	362	15	)	)	PUNCT
ejpam-3322	362	16	)	)	PUNCT
ejpam-3322	363	1	=	=	SYM
ejpam-3322	364	1	µ∗a(γ)(ia	µ∗a(γ)(ia	PROPN
ejpam-3322	364	2	⊗	⊗	PROPN
ejpam-3322	364	3	ηa)(β	ηa)(β	PROPN
ejpam-3322	364	4	⊗	⊗	PROPN
ejpam-3322	364	5	k	k	NOUN
ejpam-3322	364	6	)	)	PUNCT
ejpam-3322	364	7	=	=	SYM
ejpam-3322	364	8	(	(	PUNCT
ejpam-3322	364	9	i∗a	i∗a	PROPN
ejpam-3322	364	10	⊗	⊗	PROPN
ejpam-3322	364	11	η∗a)µ∗a(γ)(β	η∗a)µ∗a(γ)(β	PROPN
ejpam-3322	364	12	⊗	⊗	NUM
ejpam-3322	364	13	k	k	NOUN
ejpam-3322	364	14	)	)	PUNCT
ejpam-3322	364	15	=	=	PUNCT
ejpam-3322	365	1	(	(	PUNCT
ejpam-3322	365	2	ia∗	ia∗	ADJ
ejpam-3322	365	3	⊗	⊗	PROPN
ejpam-3322	365	4	εa∗)∆a∗(γ)(β	εa∗)∆a∗(γ)(β	PROPN
ejpam-3322	365	5	⊗	⊗	PROPN
ejpam-3322	365	6	k	k	NOUN
ejpam-3322	365	7	)	)	PUNCT
ejpam-3322	365	8	,	,	PUNCT
ejpam-3322	365	9	where	where	SCONJ
ejpam-3322	365	10	a	a	DET
ejpam-3322	365	11	=	=	SYM
ejpam-3322	365	12	〈	〈	PROPN
ejpam-3322	365	13	δt	δt	X
ejpam-3322	365	14	⊗	⊗	PROPN
ejpam-3322	365	15	e	e	PROPN
ejpam-3322	365	16	〉	〉	NOUN
ejpam-3322	365	17	=	=	SYM
ejpam-3322	365	18	e	e	PROPN
ejpam-3322	365	19	and	and	CCONJ
ejpam-3322	365	20	b	b	X
ejpam-3322	365	21	=	=	SYM
ejpam-3322	365	22	〈	〈	PROPN
ejpam-3322	365	23	δs	δs	NOUN
ejpam-3322	365	24	⊗	⊗	PROPN
ejpam-3322	365	25	u	u	PROPN
ejpam-3322	365	26	〉	〉	PROPN
ejpam-3322	365	27	.	.	PUNCT
ejpam-3322	366	1	we	we	PRON
ejpam-3322	366	2	have	have	AUX
ejpam-3322	366	3	used	use	VERB
ejpam-3322	366	4	the	the	DET
ejpam-3322	366	5	following	following	ADJ
ejpam-3322	366	6	calculations	calculation	NOUN
ejpam-3322	366	7	:	:	PUNCT
ejpam-3322	366	8	τ(a	τ(a	NOUN
ejpam-3322	366	9	,	,	PUNCT
ejpam-3322	366	10	b	b	NOUN
ejpam-3322	366	11	)	)	PUNCT
ejpam-3322	366	12	=	=	SYM
ejpam-3322	366	13	τ(e	τ(e	PROPN
ejpam-3322	366	14	,	,	PUNCT
ejpam-3322	366	15	b	b	X
ejpam-3322	366	16	)	)	PUNCT
ejpam-3322	366	17	=	=	SYM
ejpam-3322	366	18	e	e	NOUN
ejpam-3322	366	19	,	,	PUNCT
ejpam-3322	366	20	τ(a	τ(a	X
ejpam-3322	366	21	,	,	PUNCT
ejpam-3322	366	22	b)−1	b)−1	NOUN
ejpam-3322	366	23	=	=	SYM
ejpam-3322	366	24	τ(e	τ(e	PROPN
ejpam-3322	366	25	,	,	PUNCT
ejpam-3322	366	26	b)−1	b)−1	NOUN
ejpam-3322	366	27	=	=	SYM
ejpam-3322	366	28	e−1	e−1	PROPN
ejpam-3322	366	29	=	=	SYM
ejpam-3322	366	30	e	e	PROPN
ejpam-3322	366	31	,	,	PUNCT
ejpam-3322	366	32	t	t	PROPN
ejpam-3322	366	33	c	c	NOUN
ejpam-3322	366	34	τ(a	τ(a	NOUN
ejpam-3322	366	35	,	,	PUNCT
ejpam-3322	366	36	b	b	NOUN
ejpam-3322	366	37	)	)	PUNCT
ejpam-3322	366	38	=	=	SYM
ejpam-3322	366	39	t	t	NOUN
ejpam-3322	366	40	c	c	NOUN
ejpam-3322	366	41	e	e	PROPN
ejpam-3322	366	42	=	=	PROPN
ejpam-3322	366	43	t	t	PROPN
ejpam-3322	366	44	,	,	PUNCT
ejpam-3322	366	45	τ(a	τ(a	NOUN
ejpam-3322	366	46	,	,	PUNCT
ejpam-3322	366	47	b)−1eu	b)−1eu	NOUN
ejpam-3322	366	48	=	=	SYM
ejpam-3322	366	49	u	u	PROPN
ejpam-3322	366	50	and	and	CCONJ
ejpam-3322	366	51	t	t	PROPN
ejpam-3322	366	52	=	=	PUNCT
ejpam-3322	366	53	s.	s.	PROPN
ejpam-3322	366	54	therefore	therefore	ADV
ejpam-3322	366	55	,	,	PUNCT
ejpam-3322	366	56	εa∗	εa∗	PROPN
ejpam-3322	366	57	satisfies	satisfy	VERB
ejpam-3322	366	58	the	the	DET
ejpam-3322	366	59	counit	counit	VERB
ejpam-3322	366	60	property	property	NOUN
ejpam-3322	366	61	as	as	SCONJ
ejpam-3322	366	62	claimed	claim	VERB
ejpam-3322	366	63	.	.	PUNCT
ejpam-3322	367	1	�	�	PROPN
ejpam-3322	367	2	proposition	proposition	NOUN
ejpam-3322	367	3	3.5	3.5	NUM
ejpam-3322	367	4	.	.	PUNCT
ejpam-3322	368	1	let	let	VERB
ejpam-3322	368	2	c	c	PRON
ejpam-3322	368	3	be	be	AUX
ejpam-3322	368	4	a	a	DET
ejpam-3322	368	5	coalgebra	coalgebra	NOUN
ejpam-3322	368	6	in	in	ADP
ejpam-3322	368	7	category	category	NOUN
ejpam-3322	368	8	c.	c.	NOUN
ejpam-3322	368	9	then	then	ADV
ejpam-3322	368	10	the	the	DET
ejpam-3322	368	11	unit	unit	NOUN
ejpam-3322	368	12	property	property	NOUN
ejpam-3322	368	13	on	on	ADP
ejpam-3322	368	14	c∗	c∗	PROPN
ejpam-3322	368	15	is	be	AUX
ejpam-3322	368	16	satisfied	satisfied	ADJ
ejpam-3322	368	17	,	,	PUNCT
ejpam-3322	368	18	i.e.	i.e.	X
ejpam-3322	368	19	µc∗(ic∗	µc∗(ic∗	PUNCT
ejpam-3322	368	20	⊗	⊗	PROPN
ejpam-3322	368	21	ηc∗	ηc∗	NOUN
ejpam-3322	368	22	)	)	PUNCT
ejpam-3322	368	23	(	(	PUNCT
ejpam-3322	368	24	γ	γ	PROPN
ejpam-3322	368	25	⊗	⊗	PROPN
ejpam-3322	368	26	k	k	PROPN
ejpam-3322	368	27	)	)	PUNCT
ejpam-3322	369	1	=	=	SYM
ejpam-3322	370	1	µc∗(ηc∗	µc∗(ηc∗	PROPN
ejpam-3322	370	2	⊗	⊗	PROPN
ejpam-3322	370	3	ic∗	ic∗	NOUN
ejpam-3322	370	4	)	)	PUNCT
ejpam-3322	370	5	(	(	PUNCT
ejpam-3322	370	6	k	k	PROPN
ejpam-3322	370	7	⊗	⊗	PROPN
ejpam-3322	370	8	γ	γ	PROPN
ejpam-3322	370	9	)	)	PUNCT
ejpam-3322	370	10	for	for	ADP
ejpam-3322	370	11	any	any	DET
ejpam-3322	370	12	element	element	NOUN
ejpam-3322	370	13	γ	γ	X
ejpam-3322	370	14	=	=	SYM
ejpam-3322	370	15	(	(	PUNCT
ejpam-3322	370	16	t⊗	t⊗	PROPN
ejpam-3322	370	17	δv	δv	CCONJ
ejpam-3322	370	18	)	)	PUNCT
ejpam-3322	370	19	∈	∈	PROPN
ejpam-3322	370	20	c∗	c∗	NOUN
ejpam-3322	370	21	with	with	ADP
ejpam-3322	370	22	v	v	NUM
ejpam-3322	370	23	∈	∈	PROPN
ejpam-3322	370	24	g	g	NOUN
ejpam-3322	370	25	,	,	PUNCT
ejpam-3322	370	26	t	t	NOUN
ejpam-3322	370	27	∈m	∈m	NOUN
ejpam-3322	370	28	,	,	PUNCT
ejpam-3322	370	29	and	and	CCONJ
ejpam-3322	370	30	k	k	PROPN
ejpam-3322	370	31	∈	∈	PROPN
ejpam-3322	370	32	k.	k.	PROPN
ejpam-3322	370	33	c∗	c∗	PROPN
ejpam-3322	370	34	@@	@@	SYM
ejpam-3322	370	35	�	�	PROPN
ejpam-3322	370	36	�	�	PROPN
ejpam-3322	370	37	�	�	PROPN
ejpam-3322	370	38	�	�	PROPN
ejpam-3322	370	39	�	�	PROPN
ejpam-3322	370	40	�	�	PROPN
ejpam-3322	370	41	ηc∗	ηc∗	PROPN
ejpam-3322	370	42	∗	∗	NOUN
ejpam-3322	370	43	=	=	PUNCT
ejpam-3322	371	1	=	=	SYM
ejpam-3322	371	2	c∗	c∗	PROPN
ejpam-3322	371	3	@@	@@	X
ejpam-3322	371	4	�	�	PROPN
ejpam-3322	371	5	�	�	PROPN
ejpam-3322	371	6	�	�	PROPN
ejpam-3322	371	7	�	�	PROPN
ejpam-3322	371	8	�	�	PROPN
ejpam-3322	371	9	�	�	PROPN
ejpam-3322	371	10	ηc∗	ηc∗	PROPN
ejpam-3322	371	11	∗	∗	PROPN
ejpam-3322	371	12	c∗	c∗	PROPN
ejpam-3322	371	13	c∗	c∗	PROPN
ejpam-3322	371	14	c∗	c∗	PROPN
ejpam-3322	371	15	c∗	c∗	PROPN
ejpam-3322	371	16	figure	figure	NOUN
ejpam-3322	371	17	8	8	NUM
ejpam-3322	371	18	:	:	PUNCT
ejpam-3322	371	19	unit	unit	NOUN
ejpam-3322	371	20	property	property	NOUN
ejpam-3322	371	21	on	on	ADP
ejpam-3322	371	22	c∗.	c∗.	X
ejpam-3322	371	23	b.	b.	PROPN
ejpam-3322	371	24	al	al	PROPN
ejpam-3322	371	25	-	-	PUNCT
ejpam-3322	371	26	harbi	harbi	PROPN
ejpam-3322	371	27	,	,	PUNCT
ejpam-3322	371	28	w.	w.	PROPN
ejpam-3322	371	29	m.	m.	PROPN
ejpam-3322	371	30	fakieh	fakieh	PROPN
ejpam-3322	371	31	,	,	PUNCT
ejpam-3322	371	32	m.	m.	NOUN
ejpam-3322	371	33	m.	m.	PROPN
ejpam-3322	371	34	al	al	PROPN
ejpam-3322	371	35	-	-	PUNCT
ejpam-3322	371	36	shomrani	shomrani	PROPN
ejpam-3322	371	37	/	/	SYM
ejpam-3322	371	38	eur	eur	NOUN
ejpam-3322	371	39	.	.	PUNCT
ejpam-3322	372	1	j.	j.	PROPN
ejpam-3322	372	2	pure	pure	PROPN
ejpam-3322	372	3	appl	appl	PROPN
ejpam-3322	372	4	.	.	PROPN
ejpam-3322	372	5	math	math	PROPN
ejpam-3322	372	6	,	,	PUNCT
ejpam-3322	372	7	11	11	NUM
ejpam-3322	372	8	(	(	PUNCT
ejpam-3322	372	9	4	4	NUM
ejpam-3322	372	10	)	)	PUNCT
ejpam-3322	372	11	(	(	PUNCT
ejpam-3322	372	12	2018	2018	NUM
ejpam-3322	372	13	)	)	PUNCT
ejpam-3322	372	14	,	,	PUNCT
ejpam-3322	372	15	1027	1027	NUM
ejpam-3322	372	16	-	-	SYM
ejpam-3322	372	17	1045	1045	NUM
ejpam-3322	372	18	1042	1042	NUM
ejpam-3322	372	19	proof	proof	NOUN
ejpam-3322	372	20	.	.	PUNCT
ejpam-3322	373	1	as	as	SCONJ
ejpam-3322	373	2	c	c	PROPN
ejpam-3322	373	3	is	be	AUX
ejpam-3322	373	4	a	a	DET
ejpam-3322	373	5	coalgebra	coalgebra	NOUN
ejpam-3322	373	6	in	in	ADP
ejpam-3322	373	7	the	the	DET
ejpam-3322	373	8	category	category	NOUN
ejpam-3322	373	9	c	c	NOUN
ejpam-3322	373	10	,	,	PUNCT
ejpam-3322	373	11	it	it	PRON
ejpam-3322	373	12	has	have	VERB
ejpam-3322	373	13	a	a	DET
ejpam-3322	373	14	counit	counit	VERB
ejpam-3322	373	15	map	map	NOUN
ejpam-3322	373	16	εc	εc	ADP
ejpam-3322	373	17	:	:	PUNCT
ejpam-3322	374	1	c	c	AUX
ejpam-3322	374	2	−→	−→	NOUN
ejpam-3322	374	3	k	k	X
ejpam-3322	374	4	satisfying	satisfy	VERB
ejpam-3322	374	5	the	the	DET
ejpam-3322	374	6	counit	counit	VERB
ejpam-3322	374	7	property	property	NOUN
ejpam-3322	374	8	,	,	PUNCT
ejpam-3322	374	9	i.e∑	i.e∑	X
ejpam-3322	374	10	(	(	PUNCT
ejpam-3322	374	11	β	β	NOUN
ejpam-3322	374	12	)	)	PUNCT
ejpam-3322	374	13	εc(β(1))β(2	εc(β(1))β(2	NOUN
ejpam-3322	374	14	)	)	PUNCT
ejpam-3322	374	15	=	=	SYM
ejpam-3322	374	16	β	β	X
ejpam-3322	374	17	=	=	PUNCT
ejpam-3322	374	18	∑	∑	PUNCT
ejpam-3322	374	19	(	(	PUNCT
ejpam-3322	374	20	β	β	NOUN
ejpam-3322	374	21	)	)	PUNCT
ejpam-3322	374	22	εc(β(2))β(1	εc(β(2))β(1	NOUN
ejpam-3322	374	23	)	)	PUNCT
ejpam-3322	374	24	.	.	PUNCT
ejpam-3322	375	1	the	the	DET
ejpam-3322	375	2	transpose	transpose	NOUN
ejpam-3322	375	3	of	of	ADP
ejpam-3322	375	4	the	the	DET
ejpam-3322	375	5	counit	counit	VERB
ejpam-3322	375	6	map	map	NOUN
ejpam-3322	375	7	of	of	ADP
ejpam-3322	375	8	c	c	PROPN
ejpam-3322	375	9	is	be	AUX
ejpam-3322	375	10	ε∗c	ε∗c	PROPN
ejpam-3322	375	11	:	:	PUNCT
ejpam-3322	375	12	k∗	k∗	VERB
ejpam-3322	375	13	−→	−→	PROPN
ejpam-3322	375	14	c∗	c∗	PROPN
ejpam-3322	375	15	which	which	PRON
ejpam-3322	375	16	is	be	AUX
ejpam-3322	375	17	defined	define	VERB
ejpam-3322	375	18	by	by	ADP
ejpam-3322	375	19	ε∗c(γ)(β	ε∗c(γ)(β	NOUN
ejpam-3322	375	20	)	)	PUNCT
ejpam-3322	375	21	=	=	SYM
ejpam-3322	375	22	γ	γ	X
ejpam-3322	375	23	(	(	PUNCT
ejpam-3322	375	24	εc(β	εc(β	X
ejpam-3322	375	25	)	)	PUNCT
ejpam-3322	375	26	)	)	PUNCT
ejpam-3322	375	27	,	,	PUNCT
ejpam-3322	375	28	for	for	ADP
ejpam-3322	375	29	γ	γ	PROPN
ejpam-3322	375	30	∈	∈	PROPN
ejpam-3322	375	31	k∗	k∗	PROPN
ejpam-3322	375	32	,	,	PUNCT
ejpam-3322	375	33	β	β	PROPN
ejpam-3322	375	34	∈	∈	PROPN
ejpam-3322	375	35	c.	c.	NOUN
ejpam-3322	375	36	if	if	SCONJ
ejpam-3322	375	37	we	we	PRON
ejpam-3322	375	38	identify	identify	VERB
ejpam-3322	375	39	k	k	PROPN
ejpam-3322	375	40	with	with	ADP
ejpam-3322	375	41	k∗	k∗	PROPN
ejpam-3322	375	42	,	,	PUNCT
ejpam-3322	375	43	we	we	PRON
ejpam-3322	375	44	get	get	VERB
ejpam-3322	375	45	ε∗c	ε∗c	NOUN
ejpam-3322	375	46	:	:	PUNCT
ejpam-3322	375	47	k	k	PROPN
ejpam-3322	375	48	−→	−→	PROPN
ejpam-3322	375	49	c∗	c∗	PROPN
ejpam-3322	375	50	defined	define	VERB
ejpam-3322	375	51	as	as	ADP
ejpam-3322	375	52	ε∗c(k)(β	ε∗c(k)(β	NOUN
ejpam-3322	375	53	)	)	PUNCT
ejpam-3322	376	1	=	=	SYM
ejpam-3322	376	2	k	k	X
ejpam-3322	376	3	(	(	PUNCT
ejpam-3322	376	4	εc(β	εc(β	X
ejpam-3322	376	5	)	)	PUNCT
ejpam-3322	376	6	)	)	PUNCT
ejpam-3322	377	1	=	=	SYM
ejpam-3322	377	2	kεc(β	kεc(β	PROPN
ejpam-3322	377	3	)	)	PUNCT
ejpam-3322	377	4	,	,	PUNCT
ejpam-3322	377	5	(	(	PUNCT
ejpam-3322	377	6	23	23	NUM
ejpam-3322	377	7	)	)	PUNCT
ejpam-3322	377	8	for	for	ADP
ejpam-3322	377	9	k	k	PROPN
ejpam-3322	377	10	∈	∈	PROPN
ejpam-3322	377	11	k	k	PROPN
ejpam-3322	377	12	,	,	PUNCT
ejpam-3322	377	13	β	β	X
ejpam-3322	377	14	∈	∈	PROPN
ejpam-3322	377	15	a.	a.	NOUN
ejpam-3322	377	16	now	now	ADV
ejpam-3322	377	17	,	,	PUNCT
ejpam-3322	377	18	we	we	PRON
ejpam-3322	377	19	use	use	VERB
ejpam-3322	377	20	the	the	DET
ejpam-3322	377	21	same	same	ADJ
ejpam-3322	377	22	techniques	technique	NOUN
ejpam-3322	377	23	as	as	ADP
ejpam-3322	377	24	in	in	ADP
ejpam-3322	377	25	the	the	DET
ejpam-3322	377	26	proof	proof	NOUN
ejpam-3322	377	27	of	of	ADP
ejpam-3322	377	28	the	the	DET
ejpam-3322	377	29	previous	previous	ADJ
ejpam-3322	377	30	proposition	proposition	NOUN
ejpam-3322	377	31	to	to	PART
ejpam-3322	377	32	have	have	AUX
ejpam-3322	377	33	ηc∗	ηc∗	NOUN
ejpam-3322	377	34	=	=	SYM
ejpam-3322	377	35	ε∗c	ε∗c	NOUN
ejpam-3322	377	36	and	and	CCONJ
ejpam-3322	377	37	µc∗	µc∗	ADJ
ejpam-3322	377	38	=	=	NOUN
ejpam-3322	377	39	∆∗c	∆∗c	NOUN
ejpam-3322	377	40	.	.	PUNCT
ejpam-3322	378	1	we	we	PRON
ejpam-3322	378	2	define	define	VERB
ejpam-3322	378	3	the	the	DET
ejpam-3322	378	4	following	follow	VERB
ejpam-3322	378	5	maps	map	NOUN
ejpam-3322	378	6	:	:	PUNCT
ejpam-3322	378	7	ic∗	ic∗	NOUN
ejpam-3322	378	8	⊗	⊗	PROPN
ejpam-3322	378	9	ηc∗	ηc∗	PROPN
ejpam-3322	378	10	:	:	PUNCT
ejpam-3322	378	11	c∗	c∗	ADJ
ejpam-3322	378	12	⊗k	⊗k	NOUN
ejpam-3322	378	13	−→	−→	ADJ
ejpam-3322	378	14	c∗	c∗	PROPN
ejpam-3322	378	15	⊗c∗	⊗c∗	NOUN
ejpam-3322	378	16	by	by	ADP
ejpam-3322	378	17	γ	γ	PROPN
ejpam-3322	378	18	⊗	⊗	PROPN
ejpam-3322	378	19	k	k	PROPN
ejpam-3322	378	20	7−→	7−→	PROPN
ejpam-3322	378	21	γ	γ	PROPN
ejpam-3322	378	22	⊗	⊗	PROPN
ejpam-3322	378	23	ηc∗(k	ηc∗(k	PROPN
ejpam-3322	378	24	)	)	PUNCT
ejpam-3322	378	25	,	,	PUNCT
ejpam-3322	378	26	and	and	CCONJ
ejpam-3322	378	27	ηc∗	ηc∗	PROPN
ejpam-3322	378	28	⊗	⊗	PROPN
ejpam-3322	378	29	ic∗	ic∗	PROPN
ejpam-3322	378	30	:	:	PUNCT
ejpam-3322	378	31	k	k	PROPN
ejpam-3322	378	32	⊗	⊗	PROPN
ejpam-3322	378	33	c∗	c∗	PROPN
ejpam-3322	378	34	−→	−→	PROPN
ejpam-3322	378	35	c∗	c∗	PROPN
ejpam-3322	378	36	⊗	⊗	PROPN
ejpam-3322	378	37	c∗	c∗	PROPN
ejpam-3322	378	38	by	by	ADP
ejpam-3322	378	39	k	k	PROPN
ejpam-3322	378	40	⊗	⊗	PROPN
ejpam-3322	378	41	γ	γ	PROPN
ejpam-3322	378	42	7−→	7−→	PROPN
ejpam-3322	378	43	ηc∗(k)⊗	ηc∗(k)⊗	VERB
ejpam-3322	378	44	γ	γ	PROPN
ejpam-3322	378	45	.	.	PROPN
ejpam-3322	378	46	next	next	ADV
ejpam-3322	378	47	,	,	PUNCT
ejpam-3322	378	48	it	it	PRON
ejpam-3322	378	49	is	be	AUX
ejpam-3322	378	50	known	know	VERB
ejpam-3322	378	51	that	that	SCONJ
ejpam-3322	378	52	the	the	DET
ejpam-3322	378	53	transpose	transpose	NOUN
ejpam-3322	378	54	of	of	ADP
ejpam-3322	378	55	∆c	∆c	PROPN
ejpam-3322	378	56	is	be	AUX
ejpam-3322	378	57	a	a	DET
ejpam-3322	378	58	k	k	ADJ
ejpam-3322	378	59	-	-	PUNCT
ejpam-3322	378	60	linear	linear	ADJ
ejpam-3322	378	61	map	map	NOUN
ejpam-3322	378	62	∆∗c	∆∗c	NOUN
ejpam-3322	378	63	:	:	PUNCT
ejpam-3322	378	64	(	(	PUNCT
ejpam-3322	378	65	c	c	NOUN
ejpam-3322	378	66	⊗c)∗	⊗c)∗	PROPN
ejpam-3322	378	67	−→	−→	ADJ
ejpam-3322	378	68	c∗	c∗	NOUN
ejpam-3322	378	69	,	,	PUNCT
ejpam-3322	378	70	defined	define	VERB
ejpam-3322	378	71	by	by	ADP
ejpam-3322	378	72	∆∗c(ψ)(β	∆∗c(ψ)(β	NOUN
ejpam-3322	378	73	)	)	PUNCT
ejpam-3322	378	74	=	=	PUNCT
ejpam-3322	378	75	ψ(∆c(β	ψ(∆c(β	NOUN
ejpam-3322	378	76	)	)	PUNCT
ejpam-3322	378	77	)	)	PUNCT
ejpam-3322	378	78	,	,	PUNCT
ejpam-3322	378	79	(	(	PUNCT
ejpam-3322	378	80	24	24	NUM
ejpam-3322	378	81	)	)	PUNCT
ejpam-3322	378	82	for	for	ADP
ejpam-3322	378	83	ψ	ψ	X
ejpam-3322	378	84	∈	∈	PROPN
ejpam-3322	378	85	(	(	PUNCT
ejpam-3322	378	86	c	c	PROPN
ejpam-3322	378	87	⊗	⊗	PROPN
ejpam-3322	378	88	c)∗	c)∗	PROPN
ejpam-3322	378	89	,	,	PUNCT
ejpam-3322	378	90	β	β	PROPN
ejpam-3322	378	91	∈	∈	PROPN
ejpam-3322	378	92	c.	c.	NOUN
ejpam-3322	378	93	also	also	ADV
ejpam-3322	378	94	,	,	PUNCT
ejpam-3322	378	95	by	by	ADP
ejpam-3322	378	96	corollary	corollary	ADJ
ejpam-3322	378	97	2.4	2.4	NUM
ejpam-3322	378	98	,	,	PUNCT
ejpam-3322	378	99	we	we	PRON
ejpam-3322	378	100	have	have	VERB
ejpam-3322	378	101	c∗	c∗	PROPN
ejpam-3322	378	102	⊗	⊗	PROPN
ejpam-3322	378	103	c∗	c∗	PROPN
ejpam-3322	378	104	⊆	⊆	NUM
ejpam-3322	378	105	(	(	PUNCT
ejpam-3322	378	106	c	c	PROPN
ejpam-3322	378	107	⊗	⊗	PROPN
ejpam-3322	378	108	c)∗.	c)∗.	PROPN
ejpam-3322	378	109	hence	hence	ADV
ejpam-3322	378	110	,	,	PUNCT
ejpam-3322	378	111	∆∗c	∆∗c	NOUN
ejpam-3322	378	112	leads	lead	VERB
ejpam-3322	378	113	to	to	ADP
ejpam-3322	378	114	a	a	DET
ejpam-3322	378	115	k	k	ADJ
ejpam-3322	378	116	-	-	PUNCT
ejpam-3322	378	117	linear	linear	ADJ
ejpam-3322	378	118	map	map	NOUN
ejpam-3322	378	119	µc∗	µc∗	PUNCT
ejpam-3322	378	120	:	:	PUNCT
ejpam-3322	378	121	c∗	c∗	PROPN
ejpam-3322	378	122	⊗	⊗	PROPN
ejpam-3322	378	123	c∗	c∗	PROPN
ejpam-3322	378	124	−→	−→	PROPN
ejpam-3322	378	125	c∗	c∗	NOUN
ejpam-3322	378	126	,	,	PUNCT
ejpam-3322	378	127	defined	define	VERB
ejpam-3322	378	128	by	by	ADP
ejpam-3322	378	129	µc∗(γ1	µc∗(γ1	NOUN
ejpam-3322	378	130	⊗	⊗	ADJ
ejpam-3322	378	131	γ2)(β	γ2)(β	NOUN
ejpam-3322	378	132	)	)	PUNCT
ejpam-3322	378	133	=	=	PRON
ejpam-3322	378	134	∆∗c(γ1	∆∗c(γ1	VERB
ejpam-3322	378	135	⊗	⊗	NUM
ejpam-3322	378	136	γ2)(β	γ2)(β	NOUN
ejpam-3322	378	137	)	)	PUNCT
ejpam-3322	379	1	=	=	SYM
ejpam-3322	379	2	(	(	PUNCT
ejpam-3322	379	3	γ1	γ1	PROPN
ejpam-3322	379	4	⊗	⊗	PROPN
ejpam-3322	379	5	γ2)(∆c(β	γ2)(∆c(β	PROPN
ejpam-3322	379	6	)	)	PUNCT
ejpam-3322	379	7	)	)	PUNCT
ejpam-3322	380	1	=	=	PUNCT
ejpam-3322	380	2	∑	∑	PUNCT
ejpam-3322	380	3	(	(	PUNCT
ejpam-3322	380	4	β	β	NOUN
ejpam-3322	380	5	)	)	PUNCT
ejpam-3322	380	6	γ1(β1)⊗	γ1(β1)⊗	NOUN
ejpam-3322	380	7	γ2(β2	γ2(β2	PROPN
ejpam-3322	380	8	)	)	PUNCT
ejpam-3322	380	9	.	.	PUNCT
ejpam-3322	381	1	(	(	PUNCT
ejpam-3322	381	2	25	25	NUM
ejpam-3322	381	3	)	)	PUNCT
ejpam-3322	381	4	thus	thus	ADV
ejpam-3322	381	5	,	,	PUNCT
ejpam-3322	381	6	if	if	SCONJ
ejpam-3322	381	7	we	we	PRON
ejpam-3322	381	8	put	put	VERB
ejpam-3322	381	9	γ	γ	NOUN
ejpam-3322	381	10	=	=	SYM
ejpam-3322	381	11	(	(	PUNCT
ejpam-3322	381	12	t⊗δv	t⊗δv	NOUN
ejpam-3322	381	13	)	)	PUNCT
ejpam-3322	381	14	,	,	PUNCT
ejpam-3322	381	15	β	β	X
ejpam-3322	381	16	=	=	SYM
ejpam-3322	381	17	(	(	PUNCT
ejpam-3322	381	18	δs⊗u	δs⊗u	NUM
ejpam-3322	381	19	)	)	PUNCT
ejpam-3322	381	20	,	,	PUNCT
ejpam-3322	381	21	β1	β1	PROPN
ejpam-3322	381	22	=	=	SYM
ejpam-3322	381	23	(	(	PUNCT
ejpam-3322	381	24	δs1⊗u1	δs1⊗u1	NOUN
ejpam-3322	381	25	)	)	PUNCT
ejpam-3322	381	26	and	and	CCONJ
ejpam-3322	381	27	β2	β2	NOUN
ejpam-3322	381	28	=	=	SYM
ejpam-3322	381	29	(	(	PUNCT
ejpam-3322	381	30	δs2⊗u2	δs2⊗u2	NUM
ejpam-3322	381	31	)	)	PUNCT
ejpam-3322	381	32	with	with	ADP
ejpam-3322	381	33	β	β	X
ejpam-3322	381	34	=	=	SYM
ejpam-3322	381	35	b.	b.	PROPN
ejpam-3322	381	36	al	al	PROPN
ejpam-3322	381	37	-	-	PUNCT
ejpam-3322	381	38	harbi	harbi	PROPN
ejpam-3322	381	39	,	,	PUNCT
ejpam-3322	381	40	w.	w.	PROPN
ejpam-3322	381	41	m.	m.	PROPN
ejpam-3322	381	42	fakieh	fakieh	PROPN
ejpam-3322	381	43	,	,	PUNCT
ejpam-3322	381	44	m.	m.	NOUN
ejpam-3322	381	45	m.	m.	PROPN
ejpam-3322	381	46	al	al	PROPN
ejpam-3322	381	47	-	-	PUNCT
ejpam-3322	381	48	shomrani	shomrani	PROPN
ejpam-3322	381	49	/	/	SYM
ejpam-3322	381	50	eur	eur	NOUN
ejpam-3322	381	51	.	.	PUNCT
ejpam-3322	382	1	j.	j.	PROPN
ejpam-3322	382	2	pure	pure	PROPN
ejpam-3322	382	3	appl	appl	PROPN
ejpam-3322	382	4	.	.	PROPN
ejpam-3322	382	5	math	math	PROPN
ejpam-3322	382	6	,	,	PUNCT
ejpam-3322	382	7	11	11	NUM
ejpam-3322	382	8	(	(	PUNCT
ejpam-3322	382	9	4	4	NUM
ejpam-3322	382	10	)	)	PUNCT
ejpam-3322	382	11	(	(	PUNCT
ejpam-3322	382	12	2018	2018	NUM
ejpam-3322	382	13	)	)	PUNCT
ejpam-3322	382	14	,	,	PUNCT
ejpam-3322	382	15	1027	1027	NUM
ejpam-3322	382	16	-	-	SYM
ejpam-3322	382	17	1045	1045	NUM
ejpam-3322	382	18	1043	1043	NUM
ejpam-3322	382	19	β1	β1	PROPN
ejpam-3322	382	20	⊗	⊗	PROPN
ejpam-3322	382	21	β2	β2	PROPN
ejpam-3322	382	22	and	and	CCONJ
ejpam-3322	382	23	〈	〈	PROPN
ejpam-3322	382	24	β	β	NOUN
ejpam-3322	382	25	〉	〉	NOUN
ejpam-3322	382	26	=	=	SYM
ejpam-3322	382	27	〈	〈	PROPN
ejpam-3322	382	28	β1	β1	PROPN
ejpam-3322	382	29	〉	〉	PROPN
ejpam-3322	382	30	·	·	PUNCT
ejpam-3322	383	1	〈	〈	PROPN
ejpam-3322	383	2	β2	β2	PROPN
ejpam-3322	383	3	〉	〉	PROPN
ejpam-3322	383	4	,	,	PUNCT
ejpam-3322	383	5	for	for	ADP
ejpam-3322	383	6	k	k	PROPN
ejpam-3322	383	7	∈	∈	PROPN
ejpam-3322	383	8	k	k	PROPN
ejpam-3322	383	9	,	,	PUNCT
ejpam-3322	383	10	β	β	X
ejpam-3322	383	11	,	,	PUNCT
ejpam-3322	383	12	β1	β1	PROPN
ejpam-3322	383	13	,	,	PUNCT
ejpam-3322	383	14	β2	β2	NOUN
ejpam-3322	383	15	∈	∈	PROPN
ejpam-3322	383	16	c	c	PROPN
ejpam-3322	383	17	and	and	CCONJ
ejpam-3322	383	18	γ	γ	PROPN
ejpam-3322	383	19	∈	∈	PROPN
ejpam-3322	383	20	c∗	c∗	NOUN
ejpam-3322	383	21	,	,	PUNCT
ejpam-3322	383	22	we	we	PRON
ejpam-3322	383	23	get	get	VERB
ejpam-3322	383	24	µc∗(ic∗	µc∗(ic∗	PUNCT
ejpam-3322	383	25	⊗	⊗	ADJ
ejpam-3322	383	26	ηc∗)(γ	ηc∗)(γ	NOUN
ejpam-3322	383	27	⊗	⊗	PROPN
ejpam-3322	383	28	k)(β	k)(β	PROPN
ejpam-3322	383	29	)	)	PUNCT
ejpam-3322	383	30	=	=	SYM
ejpam-3322	383	31	∆∗c	∆∗c	NOUN
ejpam-3322	383	32	(	(	PUNCT
ejpam-3322	383	33	γ	γ	PROPN
ejpam-3322	383	34	⊗	⊗	PROPN
ejpam-3322	383	35	ε∗c(k	ε∗c(k	PROPN
ejpam-3322	383	36	)	)	PUNCT
ejpam-3322	383	37	)	)	PUNCT
ejpam-3322	383	38	(	(	PUNCT
ejpam-3322	383	39	β	β	X
ejpam-3322	383	40	)	)	PUNCT
ejpam-3322	383	41	=	=	SYM
ejpam-3322	383	42	(	(	PUNCT
ejpam-3322	383	43	γ	γ	PROPN
ejpam-3322	383	44	⊗	⊗	PROPN
ejpam-3322	383	45	ε∗c(k	ε∗c(k	PROPN
ejpam-3322	383	46	)	)	PUNCT
ejpam-3322	383	47	)	)	PUNCT
ejpam-3322	384	1	(	(	PUNCT
ejpam-3322	384	2	∆c(β	∆c(β	ADJ
ejpam-3322	384	3	)	)	PUNCT
ejpam-3322	384	4	)	)	PUNCT
ejpam-3322	385	1	=	=	PUNCT
ejpam-3322	385	2	(	(	PUNCT
ejpam-3322	385	3	γ	γ	PROPN
ejpam-3322	385	4	⊗	⊗	PROPN
ejpam-3322	385	5	ε∗c(k	ε∗c(k	PROPN
ejpam-3322	385	6	)	)	PUNCT
ejpam-3322	385	7	)	)	PUNCT
ejpam-3322	386	1	(	(	PUNCT
ejpam-3322	386	2	β1	β1	PROPN
ejpam-3322	386	3	⊗	⊗	PROPN
ejpam-3322	386	4	β2	β2	PROPN
ejpam-3322	386	5	)	)	PUNCT
ejpam-3322	386	6	=	=	PUNCT
ejpam-3322	386	7	∑	∑	PUNCT
ejpam-3322	386	8	(	(	PUNCT
ejpam-3322	386	9	β	β	NOUN
ejpam-3322	386	10	)	)	PUNCT
ejpam-3322	386	11	γ(β1)⊗	γ(β1)⊗	PROPN
ejpam-3322	386	12	ε∗c(k)(β2	ε∗c(k)(β2	NOUN
ejpam-3322	386	13	)	)	PUNCT
ejpam-3322	387	1	=	=	PUNCT
ejpam-3322	387	2	∑	∑	PUNCT
ejpam-3322	387	3	(	(	PUNCT
ejpam-3322	387	4	β	β	NOUN
ejpam-3322	387	5	)	)	PUNCT
ejpam-3322	387	6	γ(β1)⊗	γ(β1)⊗	PROPN
ejpam-3322	388	1	k	k	PROPN
ejpam-3322	388	2	(	(	PUNCT
ejpam-3322	388	3	εc(β2	εc(β2	NOUN
ejpam-3322	388	4	)	)	PUNCT
ejpam-3322	388	5	)	)	PUNCT
ejpam-3322	389	1	=	=	PUNCT
ejpam-3322	389	2	∑	∑	PUNCT
ejpam-3322	389	3	(	(	PUNCT
ejpam-3322	389	4	β	β	NOUN
ejpam-3322	389	5	)	)	PUNCT
ejpam-3322	390	1	γ(β1)k	γ(β1)k	PROPN
ejpam-3322	390	2	(	(	PUNCT
ejpam-3322	390	3	εc(β2	εc(β2	NOUN
ejpam-3322	390	4	)	)	PUNCT
ejpam-3322	390	5	)	)	PUNCT
ejpam-3322	391	1	=	=	PUNCT
ejpam-3322	392	1	k	k	X
ejpam-3322	392	2	∑	∑	PUNCT
ejpam-3322	392	3	(	(	PUNCT
ejpam-3322	392	4	β	β	NOUN
ejpam-3322	392	5	)	)	PUNCT
ejpam-3322	392	6	γ(β1)εc(β2	γ(β1)εc(β2	NOUN
ejpam-3322	392	7	)	)	PUNCT
ejpam-3322	392	8	=	=	PUNCT
ejpam-3322	393	1	k	k	X
ejpam-3322	393	2	∑	∑	PUNCT
ejpam-3322	393	3	(	(	PUNCT
ejpam-3322	393	4	β	β	NOUN
ejpam-3322	393	5	)	)	PUNCT
ejpam-3322	393	6	γ(δs1	γ(δs1	NOUN
ejpam-3322	393	7	⊗	⊗	NOUN
ejpam-3322	393	8	u1)δs2,e	u1)δs2,e	PROPN
ejpam-3322	393	9	=	=	SYM
ejpam-3322	393	10	k	k	X
ejpam-3322	393	11	∑	∑	PUNCT
ejpam-3322	393	12	(	(	PUNCT
ejpam-3322	393	13	β	β	NOUN
ejpam-3322	393	14	)	)	PUNCT
ejpam-3322	393	15	δs2,eγ(δs1	δs2,eγ(δs1	NOUN
ejpam-3322	393	16	⊗	⊗	PROPN
ejpam-3322	393	17	u1	u1	NOUN
ejpam-3322	393	18	)	)	PUNCT
ejpam-3322	393	19	=	=	SYM
ejpam-3322	394	1	k	k	X
ejpam-3322	394	2	∑	∑	PUNCT
ejpam-3322	394	3	(	(	PUNCT
ejpam-3322	394	4	β	β	NOUN
ejpam-3322	394	5	)	)	PUNCT
ejpam-3322	394	6	εc(β2)γ(β1	εc(β2)γ(β1	NOUN
ejpam-3322	394	7	)	)	PUNCT
ejpam-3322	394	8	=	=	SYM
ejpam-3322	395	1	k	k	X
ejpam-3322	395	2	∑	∑	PUNCT
ejpam-3322	395	3	(	(	PUNCT
ejpam-3322	395	4	β	β	NOUN
ejpam-3322	395	5	)	)	PUNCT
ejpam-3322	395	6	γ	γ	PROPN
ejpam-3322	395	7	(	(	PUNCT
ejpam-3322	395	8	εc(β2)β1	εc(β2)β1	X
ejpam-3322	395	9	)	)	PUNCT
ejpam-3322	396	1	=	=	PUNCT
ejpam-3322	396	2	kγ	kγ	PROPN
ejpam-3322	396	3	(	(	PUNCT
ejpam-3322	396	4	∑	∑	PROPN
ejpam-3322	396	5	(	(	PUNCT
ejpam-3322	396	6	β	β	NOUN
ejpam-3322	396	7	)	)	PUNCT
ejpam-3322	396	8	εc(β2)β1	εc(β2)β1	NOUN
ejpam-3322	396	9	)	)	PUNCT
ejpam-3322	397	1	=	=	SYM
ejpam-3322	397	2	kγ(β	kγ(β	X
ejpam-3322	397	3	)	)	PUNCT
ejpam-3322	397	4	=	=	SYM
ejpam-3322	397	5	kγ	kγ	PROPN
ejpam-3322	397	6	(	(	PUNCT
ejpam-3322	397	7	∑	∑	PROPN
ejpam-3322	397	8	(	(	PUNCT
ejpam-3322	397	9	β	β	NOUN
ejpam-3322	397	10	)	)	PUNCT
ejpam-3322	397	11	β2εc(β1	β2εc(β1	PUNCT
ejpam-3322	397	12	)	)	PUNCT
ejpam-3322	397	13	)	)	PUNCT
ejpam-3322	398	1	=	=	PUNCT
ejpam-3322	399	1	k	k	X
ejpam-3322	399	2	∑	∑	PUNCT
ejpam-3322	399	3	(	(	PUNCT
ejpam-3322	399	4	β	β	NOUN
ejpam-3322	399	5	)	)	PUNCT
ejpam-3322	399	6	γ	γ	X
ejpam-3322	399	7	(	(	PUNCT
ejpam-3322	399	8	β2εc(β1	β2εc(β1	PUNCT
ejpam-3322	399	9	)	)	PUNCT
ejpam-3322	399	10	)	)	PUNCT
ejpam-3322	400	1	=	=	PUNCT
ejpam-3322	401	1	k	k	X
ejpam-3322	401	2	∑	∑	PUNCT
ejpam-3322	401	3	(	(	PUNCT
ejpam-3322	401	4	β	β	NOUN
ejpam-3322	401	5	)	)	PUNCT
ejpam-3322	401	6	γ(δs2	γ(δs2	PUNCT
ejpam-3322	402	1	⊗	⊗	PROPN
ejpam-3322	402	2	u2)δs1,e	u2)δs1,e	PROPN
ejpam-3322	403	1	=	=	SYM
ejpam-3322	403	2	k	k	PROPN
ejpam-3322	403	3	∑	∑	PUNCT
ejpam-3322	403	4	(	(	PUNCT
ejpam-3322	403	5	β	β	NOUN
ejpam-3322	403	6	)	)	PUNCT
ejpam-3322	403	7	δs1,eγ(δs2	δs1,eγ(δs2	PROPN
ejpam-3322	403	8	⊗	⊗	PROPN
ejpam-3322	403	9	u2	u2	PROPN
ejpam-3322	403	10	)	)	PUNCT
ejpam-3322	403	11	=	=	SYM
ejpam-3322	404	1	k	k	X
ejpam-3322	404	2	∑	∑	PUNCT
ejpam-3322	404	3	(	(	PUNCT
ejpam-3322	404	4	β	β	NOUN
ejpam-3322	404	5	)	)	PUNCT
ejpam-3322	404	6	εc(β1)γ(β2	εc(β1)γ(β2	NOUN
ejpam-3322	404	7	)	)	PUNCT
ejpam-3322	404	8	=	=	SYM
ejpam-3322	404	9	∑	∑	PUNCT
ejpam-3322	404	10	(	(	PUNCT
ejpam-3322	404	11	β	β	NOUN
ejpam-3322	404	12	)	)	PUNCT
ejpam-3322	404	13	k	k	PROPN
ejpam-3322	404	14	(	(	PUNCT
ejpam-3322	404	15	εc(β1	εc(β1	NOUN
ejpam-3322	404	16	)	)	PUNCT
ejpam-3322	404	17	)	)	PUNCT
ejpam-3322	404	18	γ(β2	γ(β2	NOUN
ejpam-3322	404	19	)	)	PUNCT
ejpam-3322	405	1	=	=	PUNCT
ejpam-3322	405	2	∑	∑	PUNCT
ejpam-3322	405	3	(	(	PUNCT
ejpam-3322	405	4	β	β	NOUN
ejpam-3322	405	5	)	)	PUNCT
ejpam-3322	405	6	ε∗c(k)(β1)γ(β2	ε∗c(k)(β1)γ(β2	NOUN
ejpam-3322	405	7	)	)	PUNCT
ejpam-3322	405	8	=	=	PUNCT
ejpam-3322	406	1	∑	∑	PUNCT
ejpam-3322	406	2	(	(	PUNCT
ejpam-3322	406	3	β	β	NOUN
ejpam-3322	406	4	)	)	PUNCT
ejpam-3322	406	5	k	k	PROPN
ejpam-3322	406	6	(	(	PUNCT
ejpam-3322	406	7	εc(β1	εc(β1	NUM
ejpam-3322	406	8	)	)	PUNCT
ejpam-3322	406	9	)	)	PUNCT
ejpam-3322	407	1	⊗	⊗	PROPN
ejpam-3322	407	2	γ(β2	γ(β2	NOUN
ejpam-3322	407	3	)	)	PUNCT
ejpam-3322	408	1	=	=	PUNCT
ejpam-3322	408	2	∑	∑	PUNCT
ejpam-3322	408	3	(	(	PUNCT
ejpam-3322	408	4	β	β	NOUN
ejpam-3322	408	5	)	)	PUNCT
ejpam-3322	408	6	ε∗c(k)(β1)⊗	ε∗c(k)(β1)⊗	PROPN
ejpam-3322	408	7	γ(β2	γ(β2	NOUN
ejpam-3322	408	8	)	)	PUNCT
ejpam-3322	409	1	=	=	PUNCT
ejpam-3322	409	2	∑	∑	PUNCT
ejpam-3322	409	3	(	(	PUNCT
ejpam-3322	409	4	β	β	NOUN
ejpam-3322	409	5	)	)	PUNCT
ejpam-3322	409	6	(	(	PUNCT
ejpam-3322	409	7	ε∗c(k)⊗	ε∗c(k)⊗	NOUN
ejpam-3322	409	8	γ)(β1	γ)(β1	PROPN
ejpam-3322	409	9	⊗	⊗	PROPN
ejpam-3322	409	10	β2	β2	PROPN
ejpam-3322	409	11	)	)	PUNCT
ejpam-3322	409	12	=	=	PUNCT
ejpam-3322	410	1	(	(	PUNCT
ejpam-3322	410	2	ε∗c(k)⊗	ε∗c(k)⊗	NOUN
ejpam-3322	410	3	γ	γ	X
ejpam-3322	410	4	)	)	PUNCT
ejpam-3322	410	5	∆c(β	∆c(β	PROPN
ejpam-3322	410	6	)	)	PUNCT
ejpam-3322	410	7	=	=	PUNCT
ejpam-3322	410	8	∆c∗	∆c∗	NOUN
ejpam-3322	410	9	(	(	PUNCT
ejpam-3322	410	10	ε∗c(k)⊗	ε∗c(k)⊗	NOUN
ejpam-3322	410	11	γ	γ	PROPN
ejpam-3322	410	12	)	)	PUNCT
ejpam-3322	410	13	(	(	PUNCT
ejpam-3322	410	14	β	β	X
ejpam-3322	410	15	)	)	PUNCT
ejpam-3322	410	16	=	=	SYM
ejpam-3322	410	17	∆c∗	∆c∗	PROPN
ejpam-3322	410	18	(	(	PUNCT
ejpam-3322	410	19	ε∗c	ε∗c	PROPN
ejpam-3322	410	20	⊗	⊗	PROPN
ejpam-3322	410	21	ic∗	ic∗	NOUN
ejpam-3322	410	22	)	)	PUNCT
ejpam-3322	410	23	(	(	PUNCT
ejpam-3322	410	24	k	k	PROPN
ejpam-3322	410	25	⊗	⊗	PROPN
ejpam-3322	410	26	γ)(β	γ)(β	PROPN
ejpam-3322	410	27	)	)	PUNCT
ejpam-3322	411	1	=	=	PRON
ejpam-3322	411	2	µc∗	µc∗	PROPN
ejpam-3322	411	3	(	(	PUNCT
ejpam-3322	411	4	ηc∗	ηc∗	PROPN
ejpam-3322	411	5	⊗	⊗	PROPN
ejpam-3322	411	6	ic∗	ic∗	PROPN
ejpam-3322	411	7	)	)	PUNCT
ejpam-3322	411	8	(	(	PUNCT
ejpam-3322	411	9	k	k	PROPN
ejpam-3322	411	10	⊗	⊗	PROPN
ejpam-3322	411	11	γ)(β	γ)(β	NOUN
ejpam-3322	411	12	)	)	PUNCT
ejpam-3322	411	13	.	.	PUNCT
ejpam-3322	412	1	in	in	ADP
ejpam-3322	412	2	the	the	DET
ejpam-3322	412	3	above	above	ADJ
ejpam-3322	412	4	calculations	calculation	NOUN
ejpam-3322	412	5	we	we	PRON
ejpam-3322	412	6	have	have	AUX
ejpam-3322	412	7	used	use	VERB
ejpam-3322	412	8	equations	equation	NOUN
ejpam-3322	412	9	(	(	PUNCT
ejpam-3322	412	10	23	23	NUM
ejpam-3322	412	11	)	)	PUNCT
ejpam-3322	412	12	,	,	PUNCT
ejpam-3322	412	13	(	(	PUNCT
ejpam-3322	412	14	24	24	NUM
ejpam-3322	412	15	)	)	PUNCT
ejpam-3322	412	16	and	and	CCONJ
ejpam-3322	412	17	(	(	PUNCT
ejpam-3322	412	18	25	25	NUM
ejpam-3322	412	19	)	)	PUNCT
ejpam-3322	412	20	,	,	PUNCT
ejpam-3322	412	21	the	the	DET
ejpam-3322	412	22	facts	fact	NOUN
ejpam-3322	412	23	that	that	SCONJ
ejpam-3322	413	1	k	k	PROPN
ejpam-3322	413	2	(	(	PUNCT
ejpam-3322	413	3	εc(β2	εc(β2	NOUN
ejpam-3322	413	4	)	)	PUNCT
ejpam-3322	413	5	)	)	PUNCT
ejpam-3322	414	1	∈	∈	PROPN
ejpam-3322	414	2	k	k	PROPN
ejpam-3322	414	3	and	and	CCONJ
ejpam-3322	414	4	c	c	PROPN
ejpam-3322	414	5	⊗	⊗	PROPN
ejpam-3322	414	6	k	k	PROPN
ejpam-3322	414	7	∼=	∼=	PROPN
ejpam-3322	414	8	c	c	NOUN
ejpam-3322	414	9	,	,	PUNCT
ejpam-3322	414	10	proposition	proposition	NOUN
ejpam-3322	414	11	2.9	2.9	NUM
ejpam-3322	414	12	and	and	CCONJ
ejpam-3322	414	13	definition	definition	NOUN
ejpam-3322	414	14	2.2	2.2	NUM
ejpam-3322	414	15	.	.	PUNCT
ejpam-3322	415	1	therefore	therefore	ADV
ejpam-3322	415	2	,	,	PUNCT
ejpam-3322	415	3	ηc∗	ηc∗	PROPN
ejpam-3322	415	4	satisfies	satisfy	VERB
ejpam-3322	415	5	the	the	DET
ejpam-3322	415	6	unit	unit	NOUN
ejpam-3322	415	7	property	property	NOUN
ejpam-3322	415	8	as	as	SCONJ
ejpam-3322	415	9	required	require	VERB
ejpam-3322	415	10	.	.	PUNCT
ejpam-3322	416	1	�	�	PROPN
ejpam-3322	416	2	example	example	NOUN
ejpam-3322	416	3	1	1	X
ejpam-3322	416	4	.	.	PUNCT
ejpam-3322	417	1	let	let	VERB
ejpam-3322	417	2	x	x	PRON
ejpam-3322	417	3	be	be	AUX
ejpam-3322	417	4	the	the	DET
ejpam-3322	417	5	dihedral	dihedral	ADJ
ejpam-3322	417	6	group	group	NOUN
ejpam-3322	417	7	d6	d6	NOUN
ejpam-3322	417	8	=	=	SYM
ejpam-3322	417	9	〈	〈	PROPN
ejpam-3322	417	10	x	x	X
ejpam-3322	417	11	,	,	PUNCT
ejpam-3322	417	12	y	y	PROPN
ejpam-3322	417	13	:	:	PUNCT
ejpam-3322	417	14	x6	x6	PROPN
ejpam-3322	417	15	=	=	SYM
ejpam-3322	417	16	y2	y2	NOUN
ejpam-3322	418	1	=	=	SYM
ejpam-3322	418	2	1	1	NUM
ejpam-3322	418	3	,	,	PUNCT
ejpam-3322	418	4	xy	xy	NOUN
ejpam-3322	418	5	=	=	PUNCT
ejpam-3322	419	1	yx5	yx5	NOUN
ejpam-3322	419	2	〉	〉	NOUN
ejpam-3322	419	3	and	and	CCONJ
ejpam-3322	419	4	let	let	VERB
ejpam-3322	419	5	g	g	PROPN
ejpam-3322	419	6	be	be	AUX
ejpam-3322	419	7	the	the	DET
ejpam-3322	419	8	non	non	ADJ
ejpam-3322	419	9	-	-	ADJ
ejpam-3322	419	10	normal	normal	ADJ
ejpam-3322	419	11	subgroup	subgroup	NOUN
ejpam-3322	419	12	{	{	PUNCT
ejpam-3322	419	13	1	1	NUM
ejpam-3322	419	14	,	,	PUNCT
ejpam-3322	419	15	x3	x3	ADJ
ejpam-3322	419	16	,	,	PUNCT
ejpam-3322	419	17	y	y	NOUN
ejpam-3322	419	18	,	,	PUNCT
ejpam-3322	419	19	x3y	x3y	NUM
ejpam-3322	419	20	}	}	PUNCT
ejpam-3322	419	21	.	.	PUNCT
ejpam-3322	420	1	if	if	SCONJ
ejpam-3322	420	2	we	we	PRON
ejpam-3322	420	3	choose	choose	VERB
ejpam-3322	420	4	m	m	VERB
ejpam-3322	420	5	=	=	PUNCT
ejpam-3322	420	6	{	{	PUNCT
ejpam-3322	420	7	1	1	NUM
ejpam-3322	420	8	,	,	PUNCT
ejpam-3322	420	9	x	x	NOUN
ejpam-3322	420	10	,	,	PUNCT
ejpam-3322	420	11	x5	x5	PROPN
ejpam-3322	420	12	}	}	PUNCT
ejpam-3322	420	13	to	to	PART
ejpam-3322	420	14	be	be	AUX
ejpam-3322	420	15	the	the	DET
ejpam-3322	420	16	set	set	NOUN
ejpam-3322	420	17	of	of	ADP
ejpam-3322	420	18	left	left	ADJ
ejpam-3322	420	19	coset	coset	NOUN
ejpam-3322	420	20	representatives	representative	NOUN
ejpam-3322	420	21	,	,	PUNCT
ejpam-3322	420	22	then	then	ADV
ejpam-3322	420	23	the	the	DET
ejpam-3322	420	24	·	·	PROPN
ejpam-3322	420	25	,	,	PUNCT
ejpam-3322	420	26	τ	τ	PROPN
ejpam-3322	420	27	,	,	PUNCT
ejpam-3322	420	28	the	the	DET
ejpam-3322	420	29	action	action	NOUN
ejpam-3322	420	30	b	b	PROPN
ejpam-3322	420	31	and	and	CCONJ
ejpam-3322	420	32	the	the	DET
ejpam-3322	420	33	coaction	coaction	NOUN
ejpam-3322	420	34	c	c	NOUN
ejpam-3322	420	35	,	,	PUNCT
ejpam-3322	420	36	are	be	AUX
ejpam-3322	420	37	given	give	VERB
ejpam-3322	420	38	by	by	ADP
ejpam-3322	420	39	the	the	DET
ejpam-3322	420	40	following	following	ADJ
ejpam-3322	420	41	tables	table	NOUN
ejpam-3322	420	42	:	:	PUNCT
ejpam-3322	420	43	·	·	PUNCT
ejpam-3322	420	44	1	1	NUM
ejpam-3322	420	45	x	x	SYM
ejpam-3322	420	46	x5	x5	NOUN
ejpam-3322	420	47	1	1	NUM
ejpam-3322	420	48	1	1	NUM
ejpam-3322	420	49	x	x	SYM
ejpam-3322	420	50	x5	x5	NOUN
ejpam-3322	420	51	x	x	SYM
ejpam-3322	420	52	x	x	SYM
ejpam-3322	420	53	x5	x5	NOUN
ejpam-3322	420	54	1	1	NUM
ejpam-3322	420	55	x5	x5	NOUN
ejpam-3322	420	56	x5	x5	PROPN
ejpam-3322	420	57	1	1	NUM
ejpam-3322	420	58	x	x	SYM
ejpam-3322	420	59	τ	τ	PROPN
ejpam-3322	420	60	1	1	NUM
ejpam-3322	420	61	x	x	SYM
ejpam-3322	420	62	x5	x5	NOUN
ejpam-3322	420	63	1	1	NUM
ejpam-3322	420	64	1	1	NUM
ejpam-3322	420	65	1	1	NUM
ejpam-3322	420	66	1	1	NUM
ejpam-3322	420	67	x	x	SYM
ejpam-3322	420	68	1	1	NUM
ejpam-3322	420	69	x3	x3	ADJ
ejpam-3322	420	70	1	1	NUM
ejpam-3322	420	71	x5	x5	NOUN
ejpam-3322	420	72	1	1	NUM
ejpam-3322	420	73	1	1	NUM
ejpam-3322	420	74	x3	x3	PROPN
ejpam-3322	420	75	b.	b.	PROPN
ejpam-3322	421	1	al	al	PROPN
ejpam-3322	421	2	-	-	PUNCT
ejpam-3322	421	3	harbi	harbi	PROPN
ejpam-3322	421	4	,	,	PUNCT
ejpam-3322	421	5	w.	w.	PROPN
ejpam-3322	421	6	m.	m.	PROPN
ejpam-3322	421	7	fakieh	fakieh	PROPN
ejpam-3322	421	8	,	,	PUNCT
ejpam-3322	421	9	m.	m.	NOUN
ejpam-3322	421	10	m.	m.	PROPN
ejpam-3322	421	11	al	al	PROPN
ejpam-3322	421	12	-	-	PUNCT
ejpam-3322	421	13	shomrani	shomrani	PROPN
ejpam-3322	421	14	/	/	SYM
ejpam-3322	421	15	eur	eur	NOUN
ejpam-3322	421	16	.	.	PUNCT
ejpam-3322	422	1	j.	j.	PROPN
ejpam-3322	422	2	pure	pure	PROPN
ejpam-3322	422	3	appl	appl	PROPN
ejpam-3322	422	4	.	.	PROPN
ejpam-3322	422	5	math	math	PROPN
ejpam-3322	422	6	,	,	PUNCT
ejpam-3322	422	7	11	11	NUM
ejpam-3322	422	8	(	(	PUNCT
ejpam-3322	422	9	4	4	NUM
ejpam-3322	422	10	)	)	PUNCT
ejpam-3322	422	11	(	(	PUNCT
ejpam-3322	422	12	2018	2018	NUM
ejpam-3322	422	13	)	)	PUNCT
ejpam-3322	422	14	,	,	PUNCT
ejpam-3322	422	15	1027	1027	NUM
ejpam-3322	422	16	-	-	SYM
ejpam-3322	422	17	1045	1045	NUM
ejpam-3322	422	18	1044	1044	NUM
ejpam-3322	422	19	s	s	PROPN
ejpam-3322	422	20	b	b	SYM
ejpam-3322	422	21	u	u	NOUN
ejpam-3322	422	22	1	1	NUM
ejpam-3322	422	23	x3	x3	PROPN
ejpam-3322	422	24	y	y	PROPN
ejpam-3322	422	25	x3y	x3y	NUM
ejpam-3322	422	26	1	1	NUM
ejpam-3322	422	27	1	1	NUM
ejpam-3322	422	28	x3	x3	NOUN
ejpam-3322	422	29	y	y	PROPN
ejpam-3322	422	30	x3y	x3y	PROPN
ejpam-3322	422	31	x	x	SYM
ejpam-3322	422	32	1	1	NUM
ejpam-3322	422	33	x3	x3	PROPN
ejpam-3322	422	34	y	y	PROPN
ejpam-3322	422	35	x3y	x3y	PROPN
ejpam-3322	422	36	x5	x5	PROPN
ejpam-3322	422	37	1	1	NUM
ejpam-3322	422	38	x3	x3	PROPN
ejpam-3322	422	39	y	y	PROPN
ejpam-3322	422	40	x3y	x3y	PROPN
ejpam-3322	422	41	s	s	PART
ejpam-3322	422	42	c	c	NOUN
ejpam-3322	422	43	u	u	NOUN
ejpam-3322	422	44	1	1	NUM
ejpam-3322	422	45	x3	x3	PROPN
ejpam-3322	422	46	y	y	PROPN
ejpam-3322	422	47	x3y	x3y	NUM
ejpam-3322	423	1	1	1	NUM
ejpam-3322	423	2	1	1	NUM
ejpam-3322	423	3	1	1	NUM
ejpam-3322	423	4	1	1	NUM
ejpam-3322	423	5	1	1	NUM
ejpam-3322	423	6	x	x	SYM
ejpam-3322	423	7	x	x	SYM
ejpam-3322	423	8	x	x	SYM
ejpam-3322	423	9	x5	x5	NUM
ejpam-3322	423	10	x5	x5	PROPN
ejpam-3322	423	11	x5	x5	PROPN
ejpam-3322	423	12	x5	x5	PROPN
ejpam-3322	423	13	x5	x5	NOUN
ejpam-3322	423	14	x	x	SYM
ejpam-3322	423	15	x	x	NOUN
ejpam-3322	423	16	we	we	PRON
ejpam-3322	423	17	take	take	VERB
ejpam-3322	423	18	our	our	PRON
ejpam-3322	423	19	field	field	NOUN
ejpam-3322	423	20	to	to	PART
ejpam-3322	423	21	be	be	AUX
ejpam-3322	423	22	the	the	DET
ejpam-3322	423	23	binary	binary	ADJ
ejpam-3322	423	24	field	field	NOUN
ejpam-3322	423	25	f	f	PROPN
ejpam-3322	423	26	=	=	PUNCT
ejpam-3322	423	27	{	{	PUNCT
ejpam-3322	423	28	0	0	NUM
ejpam-3322	423	29	,	,	PUNCT
ejpam-3322	423	30	1	1	NUM
ejpam-3322	423	31	}	}	PUNCT
ejpam-3322	423	32	.	.	PUNCT
ejpam-3322	424	1	we	we	PRON
ejpam-3322	424	2	check	check	VERB
ejpam-3322	424	3	multiplication	multiplication	NOUN
ejpam-3322	424	4	µc∗	µc∗	PUNCT
ejpam-3322	424	5	in	in	ADP
ejpam-3322	424	6	proposition	proposition	NOUN
ejpam-3322	424	7	3.1	3.1	NUM
ejpam-3322	424	8	.	.	PUNCT
ejpam-3322	425	1	for	for	ADP
ejpam-3322	425	2	two	two	NUM
ejpam-3322	425	3	elements	element	NOUN
ejpam-3322	425	4	α′	α′	NUM
ejpam-3322	425	5	=	=	SYM
ejpam-3322	425	6	(	(	PUNCT
ejpam-3322	425	7	t1	t1	PROPN
ejpam-3322	425	8	⊗	⊗	PROPN
ejpam-3322	425	9	δv1	δv1	PROPN
ejpam-3322	425	10	)	)	PUNCT
ejpam-3322	425	11	and	and	CCONJ
ejpam-3322	425	12	α	α	X
ejpam-3322	425	13	=	=	SYM
ejpam-3322	425	14	(	(	PUNCT
ejpam-3322	425	15	t2	t2	PROPN
ejpam-3322	425	16	⊗	⊗	PROPN
ejpam-3322	425	17	δv2	δv2	PROPN
ejpam-3322	425	18	)	)	PUNCT
ejpam-3322	425	19	in	in	ADP
ejpam-3322	425	20	c∗	c∗	PROPN
ejpam-3322	425	21	with	with	ADP
ejpam-3322	425	22	v1	v1	NOUN
ejpam-3322	425	23	,	,	PUNCT
ejpam-3322	425	24	v2	v2	PROPN
ejpam-3322	425	25	∈	∈	PROPN
ejpam-3322	425	26	g	g	NOUN
ejpam-3322	425	27	,	,	PUNCT
ejpam-3322	425	28	t1	t1	PROPN
ejpam-3322	425	29	,	,	PUNCT
ejpam-3322	425	30	t2	t2	PROPN
ejpam-3322	425	31	∈	∈	PROPN
ejpam-3322	425	32	m	m	INTJ
ejpam-3322	425	33	,	,	PUNCT
ejpam-3322	425	34	if	if	SCONJ
ejpam-3322	425	35	we	we	PRON
ejpam-3322	425	36	put	put	VERB
ejpam-3322	425	37	t1	t1	NOUN
ejpam-3322	425	38	=	=	SYM
ejpam-3322	425	39	x	x	NOUN
ejpam-3322	425	40	,	,	PUNCT
ejpam-3322	425	41	t2	t2	NOUN
ejpam-3322	425	42	=	=	SYM
ejpam-3322	425	43	x5	x5	PROPN
ejpam-3322	425	44	in	in	ADP
ejpam-3322	425	45	m	m	PROPN
ejpam-3322	425	46	,	,	PUNCT
ejpam-3322	425	47	v1	v1	PROPN
ejpam-3322	425	48	=	=	SYM
ejpam-3322	425	49	y	y	PROPN
ejpam-3322	425	50	,	,	PUNCT
ejpam-3322	425	51	v2	v2	X
ejpam-3322	425	52	=	=	SYM
ejpam-3322	425	53	x3	x3	ADJ
ejpam-3322	425	54	in	in	ADP
ejpam-3322	425	55	g	g	PROPN
ejpam-3322	425	56	,	,	PUNCT
ejpam-3322	425	57	then	then	ADV
ejpam-3322	425	58	α	α	NOUN
ejpam-3322	425	59	=	=	PUNCT
ejpam-3322	425	60	(	(	PUNCT
ejpam-3322	425	61	x5	x5	PROPN
ejpam-3322	425	62	⊗	⊗	PROPN
ejpam-3322	425	63	δx3	δx3	PROPN
ejpam-3322	425	64	)	)	PUNCT
ejpam-3322	425	65	,	,	PUNCT
ejpam-3322	425	66	α′	α′	NUM
ejpam-3322	425	67	=	=	PUNCT
ejpam-3322	425	68	(	(	PUNCT
ejpam-3322	425	69	x	x	PROPN
ejpam-3322	425	70	⊗	⊗	PROPN
ejpam-3322	425	71	δy	δy	PROPN
ejpam-3322	425	72	)	)	PUNCT
ejpam-3322	425	73	,	,	PUNCT
ejpam-3322	425	74	a2	a2	PROPN
ejpam-3322	425	75	=	=	PUNCT
ejpam-3322	426	1	〈	〈	PROPN
ejpam-3322	426	2	δt2	δt2	VERB
ejpam-3322	426	3	⊗	⊗	PROPN
ejpam-3322	426	4	v2	v2	PROPN
ejpam-3322	426	5	〉	〉	PROPN
ejpam-3322	426	6	,	,	PUNCT
ejpam-3322	426	7	a1	a1	NOUN
ejpam-3322	426	8	=	=	SYM
ejpam-3322	426	9	〈	〈	NOUN
ejpam-3322	426	10	δt1	δt1	NOUN
ejpam-3322	426	11	⊗	⊗	PROPN
ejpam-3322	426	12	v1	v1	PROPN
ejpam-3322	426	13	〉	〉	PROPN
ejpam-3322	426	14	,	,	PUNCT
ejpam-3322	426	15	and	and	CCONJ
ejpam-3322	426	16	a	a	DET
ejpam-3322	426	17	=	=	PUNCT
ejpam-3322	426	18	a1	a1	NOUN
ejpam-3322	426	19	·	·	PUNCT
ejpam-3322	426	20	a2	a2	PROPN
ejpam-3322	426	21	.	.	PUNCT
ejpam-3322	427	1	we	we	PRON
ejpam-3322	427	2	start	start	VERB
ejpam-3322	427	3	by	by	ADP
ejpam-3322	427	4	calculating	calculate	VERB
ejpam-3322	427	5	the	the	DET
ejpam-3322	427	6	following	following	NOUN
ejpam-3322	427	7	:	:	PUNCT
ejpam-3322	427	8	t2	t2	PROPN
ejpam-3322	427	9	·	·	PUNCT
ejpam-3322	427	10	a2	a2	PROPN
ejpam-3322	427	11	=	=	SYM
ejpam-3322	427	12	t2	t2	PROPN
ejpam-3322	427	13	c	c	PROPN
ejpam-3322	427	14	v2	v2	PROPN
ejpam-3322	427	15	,	,	PUNCT
ejpam-3322	427	16	x5	x5	PROPN
ejpam-3322	427	17	·	·	PUNCT
ejpam-3322	427	18	a2	a2	PROPN
ejpam-3322	427	19	=	=	SYM
ejpam-3322	427	20	x5	x5	PROPN
ejpam-3322	427	21	c	c	NOUN
ejpam-3322	428	1	x3	x3	PROPN
ejpam-3322	428	2	⇒	⇒	PROPN
ejpam-3322	428	3	x5	x5	PROPN
ejpam-3322	428	4	·	·	PUNCT
ejpam-3322	428	5	a2	a2	PROPN
ejpam-3322	428	6	=	=	SYM
ejpam-3322	428	7	x5	x5	PROPN
ejpam-3322	428	8	⇒	⇒	NOUN
ejpam-3322	428	9	a2	a2	PROPN
ejpam-3322	428	10	=	=	SYM
ejpam-3322	428	11	1	1	NUM
ejpam-3322	428	12	,	,	PUNCT
ejpam-3322	428	13	and	and	CCONJ
ejpam-3322	428	14	t1	t1	NOUN
ejpam-3322	428	15	·	·	PUNCT
ejpam-3322	428	16	a1	a1	NOUN
ejpam-3322	428	17	=	=	NOUN
ejpam-3322	428	18	t1	t1	PROPN
ejpam-3322	428	19	c	c	NOUN
ejpam-3322	428	20	v1	v1	PROPN
ejpam-3322	428	21	,	,	PUNCT
ejpam-3322	428	22	x	x	X
ejpam-3322	428	23	·	·	PUNCT
ejpam-3322	428	24	a1	a1	NOUN
ejpam-3322	428	25	=	=	NOUN
ejpam-3322	428	26	x	x	SYM
ejpam-3322	428	27	c	c	X
ejpam-3322	428	28	y	y	PROPN
ejpam-3322	428	29	⇒	⇒	VERB
ejpam-3322	428	30	x	x	PUNCT
ejpam-3322	428	31	·	·	PUNCT
ejpam-3322	428	32	a1	a1	NOUN
ejpam-3322	428	33	=	=	SYM
ejpam-3322	428	34	x5	x5	PROPN
ejpam-3322	428	35	⇒	⇒	NOUN
ejpam-3322	428	36	a1	a1	NOUN
ejpam-3322	428	37	=	=	PUNCT
ejpam-3322	428	38	x.	x.	NOUN
ejpam-3322	428	39	also	also	ADV
ejpam-3322	428	40	,	,	PUNCT
ejpam-3322	428	41	a	a	DET
ejpam-3322	428	42	=	=	PUNCT
ejpam-3322	428	43	a1	a1	NOUN
ejpam-3322	428	44	·	·	PUNCT
ejpam-3322	428	45	a2	a2	PROPN
ejpam-3322	428	46	⇒	⇒	VERB
ejpam-3322	428	47	a	a	DET
ejpam-3322	428	48	=	=	X
ejpam-3322	428	49	x	x	SYM
ejpam-3322	428	50	·	·	PUNCT
ejpam-3322	428	51	1	1	NUM
ejpam-3322	428	52	=	=	SYM
ejpam-3322	428	53	x	x	X
ejpam-3322	428	54	⇒	⇒	PROPN
ejpam-3322	428	55	al	al	PROPN
ejpam-3322	428	56	=	=	PROPN
ejpam-3322	428	57	x5	x5	PROPN
ejpam-3322	428	58	.	.	PUNCT
ejpam-3322	429	1	the	the	DET
ejpam-3322	429	2	following	follow	VERB
ejpam-3322	429	3	calculations	calculation	NOUN
ejpam-3322	429	4	are	be	AUX
ejpam-3322	429	5	needed	need	VERB
ejpam-3322	429	6	as	as	ADV
ejpam-3322	429	7	well	well	ADV
ejpam-3322	429	8	:	:	PUNCT
ejpam-3322	429	9	t1	t1	NOUN
ejpam-3322	429	10	c	c	NOUN
ejpam-3322	429	11	τ(a1	τ(a1	NOUN
ejpam-3322	429	12	,	,	PUNCT
ejpam-3322	429	13	a2	a2	NOUN
ejpam-3322	429	14	)	)	PUNCT
ejpam-3322	429	15	=	=	PUNCT
ejpam-3322	430	1	x	x	SYM
ejpam-3322	430	2	c	c	NOUN
ejpam-3322	430	3	τ(x	τ(x	PROPN
ejpam-3322	430	4	,	,	PUNCT
ejpam-3322	430	5	1	1	NUM
ejpam-3322	430	6	)	)	PUNCT
ejpam-3322	430	7	=	=	PUNCT
ejpam-3322	430	8	x	x	PUNCT
ejpam-3322	430	9	c	c	NOUN
ejpam-3322	430	10	1	1	NUM
ejpam-3322	430	11	=	=	SYM
ejpam-3322	430	12	x	x	NOUN
ejpam-3322	430	13	,	,	PUNCT
ejpam-3322	430	14	τ(a1	τ(a1	NOUN
ejpam-3322	430	15	,	,	PUNCT
ejpam-3322	430	16	a2)−1	a2)−1	X
ejpam-3322	430	17	v1	v1	VERB
ejpam-3322	430	18	v2	v2	NOUN
ejpam-3322	430	19	=	=	SYM
ejpam-3322	430	20	τ(x	τ(x	NOUN
ejpam-3322	430	21	,	,	PUNCT
ejpam-3322	430	22	1)−1	1)−1	NUM
ejpam-3322	430	23	v1	v1	NOUN
ejpam-3322	430	24	v2	v2	NOUN
ejpam-3322	430	25	=	=	SYM
ejpam-3322	430	26	1	1	NUM
ejpam-3322	430	27	y	y	NOUN
ejpam-3322	430	28	x3	x3	NOUN
ejpam-3322	430	29	=	=	PUNCT
ejpam-3322	430	30	x3y	x3y	ADJ
ejpam-3322	430	31	,	,	PUNCT
ejpam-3322	430	32	and	and	CCONJ
ejpam-3322	430	33	t1	t1	NOUN
ejpam-3322	431	1	c	c	NOUN
ejpam-3322	431	2	v1	v1	PROPN
ejpam-3322	431	3	=	=	PUNCT
ejpam-3322	431	4	x	x	PUNCT
ejpam-3322	431	5	c	c	NOUN
ejpam-3322	431	6	y	y	PROPN
ejpam-3322	431	7	=	=	SYM
ejpam-3322	431	8	x5	x5	PROPN
ejpam-3322	431	9	,	,	PUNCT
ejpam-3322	431	10	and	and	CCONJ
ejpam-3322	431	11	t2	t2	PROPN
ejpam-3322	431	12	=	=	SYM
ejpam-3322	431	13	x5	x5	PROPN
ejpam-3322	431	14	.	.	PUNCT
ejpam-3322	432	1	now	now	ADV
ejpam-3322	432	2	,	,	PUNCT
ejpam-3322	432	3	we	we	PRON
ejpam-3322	432	4	substitute	substitute	VERB
ejpam-3322	432	5	in	in	ADP
ejpam-3322	432	6	the	the	DET
ejpam-3322	432	7	formula	formula	NOUN
ejpam-3322	432	8	of	of	ADP
ejpam-3322	432	9	µc∗	µc∗	NOUN
ejpam-3322	432	10	as	as	SCONJ
ejpam-3322	432	11	follows	follow	VERB
ejpam-3322	432	12	:	:	PUNCT
ejpam-3322	432	13	µc∗(α⊗	µc∗(α⊗	X
ejpam-3322	432	14	α	α	NOUN
ejpam-3322	432	15	′	′	NUM
ejpam-3322	432	16	)	)	PUNCT
ejpam-3322	433	1	=	=	PUNCT
ejpam-3322	433	2	δt1cv1,t2	δt1cv1,t2	NOUN
ejpam-3322	433	3	(	(	PUNCT
ejpam-3322	433	4	t1	t1	NOUN
ejpam-3322	433	5	c	c	NOUN
ejpam-3322	433	6	τ(a1	τ(a1	NOUN
ejpam-3322	433	7	,	,	PUNCT
ejpam-3322	433	8	a2	a2	PROPN
ejpam-3322	433	9	)	)	PUNCT
ejpam-3322	433	10	⊗	⊗	PROPN
ejpam-3322	433	11	δτ(a1,a2)−1v1v2	δτ(a1,a2)−1v1v2	X
ejpam-3322	433	12	)	)	PUNCT
ejpam-3322	433	13	,	,	PUNCT
ejpam-3322	433	14	references	reference	NOUN
ejpam-3322	433	15	1045	1045	NUM
ejpam-3322	433	16	µc∗	µc∗	PUNCT
ejpam-3322	433	17	(	(	PUNCT
ejpam-3322	433	18	(	(	PUNCT
ejpam-3322	433	19	x5	x5	PROPN
ejpam-3322	433	20	⊗	⊗	PROPN
ejpam-3322	433	21	δx3)⊗	δx3)⊗	PROPN
ejpam-3322	433	22	(	(	PUNCT
ejpam-3322	433	23	x⊗	x⊗	PROPN
ejpam-3322	433	24	δy	δy	PROPN
ejpam-3322	433	25	)	)	PUNCT
ejpam-3322	433	26	)	)	PUNCT
ejpam-3322	434	1	=	=	NOUN
ejpam-3322	434	2	δx5,x5	δx5,x5	NOUN
ejpam-3322	434	3	(	(	PUNCT
ejpam-3322	434	4	x⊗	x⊗	PROPN
ejpam-3322	434	5	δx3y	δx3y	PROPN
ejpam-3322	434	6	)	)	PUNCT
ejpam-3322	434	7	=	=	PRON
ejpam-3322	434	8	x⊗	x⊗	PROPN
ejpam-3322	434	9	δx3y	δx3y	PROPN
ejpam-3322	434	10	∈	∈	PROPN
ejpam-3322	434	11	c∗.	c∗.	NOUN
ejpam-3322	434	12	next	next	ADV
ejpam-3322	434	13	,	,	PUNCT
ejpam-3322	434	14	we	we	PRON
ejpam-3322	434	15	check	check	VERB
ejpam-3322	434	16	the	the	DET
ejpam-3322	434	17	counit	counit	VERB
ejpam-3322	434	18	εa∗	εa∗	NOUN
ejpam-3322	434	19	in	in	ADP
ejpam-3322	434	20	proposition	proposition	NOUN
ejpam-3322	434	21	3.2	3.2	NUM
ejpam-3322	434	22	,	,	PUNCT
ejpam-3322	434	23	for	for	ADP
ejpam-3322	434	24	any	any	DET
ejpam-3322	434	25	element	element	NOUN
ejpam-3322	434	26	α	α	NOUN
ejpam-3322	434	27	=	=	PUNCT
ejpam-3322	434	28	(	(	PUNCT
ejpam-3322	434	29	s	s	PROPN
ejpam-3322	434	30	⊗	⊗	PROPN
ejpam-3322	434	31	δu	δu	NOUN
ejpam-3322	434	32	)	)	PUNCT
ejpam-3322	434	33	∈	∈	PROPN
ejpam-3322	434	34	a∗	a∗	NOUN
ejpam-3322	434	35	with	with	ADP
ejpam-3322	434	36	s	s	NOUN
ejpam-3322	434	37	∈m	∈m	NOUN
ejpam-3322	434	38	and	and	CCONJ
ejpam-3322	434	39	u	u	NOUN
ejpam-3322	434	40	∈	∈	PROPN
ejpam-3322	434	41	g	g	NOUN
ejpam-3322	434	42	as	as	SCONJ
ejpam-3322	434	43	follows	follow	VERB
ejpam-3322	434	44	:	:	PUNCT
ejpam-3322	434	45	choose	choose	VERB
ejpam-3322	434	46	s	s	NOUN
ejpam-3322	434	47	=	=	PUNCT
ejpam-3322	434	48	x.	x.	NOUN
ejpam-3322	434	49	if	if	SCONJ
ejpam-3322	434	50	u	u	PROPN
ejpam-3322	434	51	=	=	SYM
ejpam-3322	434	52	e	e	NOUN
ejpam-3322	434	53	=	=	SYM
ejpam-3322	434	54	1	1	NUM
ejpam-3322	434	55	,	,	PUNCT
ejpam-3322	434	56	then	then	ADV
ejpam-3322	434	57	εa∗(x⊗	εa∗(x⊗	NUM
ejpam-3322	434	58	δ1	δ1	NOUN
ejpam-3322	434	59	)	)	PUNCT
ejpam-3322	434	60	=	=	PUNCT
ejpam-3322	434	61	δ1,1	δ1,1	NOUN
ejpam-3322	434	62	=	=	SYM
ejpam-3322	434	63	1	1	NUM
ejpam-3322	434	64	∈	∈	PROPN
ejpam-3322	434	65	f.	f.	NOUN
ejpam-3322	434	66	if	if	SCONJ
ejpam-3322	434	67	u	u	PROPN
ejpam-3322	434	68	6=	6=	PROPN
ejpam-3322	434	69	e	e	PROPN
ejpam-3322	434	70	,	,	PUNCT
ejpam-3322	434	71	for	for	ADP
ejpam-3322	434	72	example	example	NOUN
ejpam-3322	434	73	u	u	X
ejpam-3322	434	74	=	=	PROPN
ejpam-3322	434	75	y	y	PROPN
ejpam-3322	434	76	,	,	PUNCT
ejpam-3322	434	77	then	then	ADV
ejpam-3322	434	78	εa∗(x⊗	εa∗(x⊗	NUM
ejpam-3322	434	79	δy	δy	NOUN
ejpam-3322	434	80	)	)	PUNCT
ejpam-3322	434	81	=	=	NOUN
ejpam-3322	434	82	δy,1	δy,1	NOUN
ejpam-3322	434	83	=	=	SYM
ejpam-3322	434	84	0	0	NUM
ejpam-3322	435	1	∈	∈	PROPN
ejpam-3322	435	2	f.	f.	NOUN
ejpam-3322	435	3	finally	finally	ADV
ejpam-3322	435	4	,	,	PUNCT
ejpam-3322	435	5	we	we	PRON
ejpam-3322	435	6	check	check	VERB
ejpam-3322	435	7	the	the	DET
ejpam-3322	435	8	unit	unit	NOUN
ejpam-3322	435	9	ηc∗	ηc∗	VERB
ejpam-3322	435	10	in	in	ADP
ejpam-3322	435	11	proposition	proposition	NOUN
ejpam-3322	435	12	3.3	3.3	NUM
ejpam-3322	435	13	,	,	PUNCT
ejpam-3322	435	14	for	for	ADP
ejpam-3322	435	15	1	1	NUM
ejpam-3322	435	16	∈	∈	PROPN
ejpam-3322	435	17	f.	f.	NOUN
ejpam-3322	435	18	if	if	SCONJ
ejpam-3322	435	19	we	we	PRON
ejpam-3322	435	20	let	let	VERB
ejpam-3322	435	21	t	t	NOUN
ejpam-3322	435	22	=	=	SYM
ejpam-3322	435	23	1	1	NUM
ejpam-3322	435	24	∈	∈	PROPN
ejpam-3322	435	25	m	m	NOUN
ejpam-3322	435	26	,	,	PUNCT
ejpam-3322	435	27	v	v	X
ejpam-3322	436	1	=	=	SYM
ejpam-3322	436	2	y	y	PROPN
ejpam-3322	436	3	∈	∈	PROPN
ejpam-3322	436	4	g	g	NOUN
ejpam-3322	436	5	,	,	PUNCT
ejpam-3322	436	6	then	then	ADV
ejpam-3322	436	7	ηc∗(1	ηc∗(1	NOUN
ejpam-3322	436	8	)	)	PUNCT
ejpam-3322	436	9	=	=	SYM
ejpam-3322	437	1	1⊗	1⊗	NUM
ejpam-3322	437	2	δy	δy	NOUN
ejpam-3322	437	3	.	.	PUNCT
ejpam-3322	438	1	references	reference	NOUN
ejpam-3322	439	1	[	[	X
ejpam-3322	439	2	1	1	NUM
ejpam-3322	439	3	]	]	X
ejpam-3322	439	4	m	m	VERB
ejpam-3322	439	5	m	m	VERB
ejpam-3322	439	6	al	al	PROPN
ejpam-3322	439	7	-	-	PUNCT
ejpam-3322	439	8	shomrani	shomrani	PROPN
ejpam-3322	439	9	.	.	PUNCT
ejpam-3322	440	1	algebras	algebras	PROPN
ejpam-3322	440	2	and	and	CCONJ
ejpam-3322	440	3	their	their	PRON
ejpam-3322	440	4	dual	dual	ADJ
ejpam-3322	440	5	in	in	ADP
ejpam-3322	440	6	rigid	rigid	ADJ
ejpam-3322	440	7	tensor	tensor	NOUN
ejpam-3322	440	8	categories	category	NOUN
ejpam-3322	440	9	.	.	PUNCT
ejpam-3322	441	1	int	int	NOUN
ejpam-3322	441	2	.	.	PUNCT
ejpam-3322	442	1	math	math	NOUN
ejpam-3322	442	2	.	.	PUNCT
ejpam-3322	443	1	forum	forum	PROPN
ejpam-3322	443	2	,	,	PUNCT
ejpam-3322	443	3	1(9	1(9	PROPN
ejpam-3322	443	4	-	-	SYM
ejpam-3322	443	5	12):525	12):525	NUM
ejpam-3322	443	6	550	550	NUM
ejpam-3322	443	7	,	,	PUNCT
ejpam-3322	443	8	2006	2006	NUM
ejpam-3322	443	9	.	.	PUNCT
ejpam-3322	444	1	[	[	X
ejpam-3322	444	2	2	2	NUM
ejpam-3322	444	3	]	]	X
ejpam-3322	444	4	m	m	VERB
ejpam-3322	444	5	m	m	VERB
ejpam-3322	444	6	al	al	PROPN
ejpam-3322	444	7	-	-	PUNCT
ejpam-3322	444	8	shomrani	shomrani	PROPN
ejpam-3322	444	9	and	and	CCONJ
ejpam-3322	444	10	e	e	PROPN
ejpam-3322	444	11	j	j	PROPN
ejpam-3322	444	12	beggs	beggs	PROPN
ejpam-3322	444	13	.	.	PUNCT
ejpam-3322	445	1	making	make	VERB
ejpam-3322	445	2	nontrivially	nontrivially	ADV
ejpam-3322	445	3	associated	associate	VERB
ejpam-3322	445	4	modular	modular	ADJ
ejpam-3322	445	5	categories	category	NOUN
ejpam-3322	445	6	from	from	ADP
ejpam-3322	445	7	finite	finite	ADJ
ejpam-3322	445	8	groups	group	NOUN
ejpam-3322	445	9	.	.	PUNCT
ejpam-3322	446	1	international	international	ADJ
ejpam-3322	446	2	journal	journal	PROPN
ejpam-3322	446	3	of	of	ADP
ejpam-3322	446	4	mathematics	mathematics	PROPN
ejpam-3322	446	5	and	and	CCONJ
ejpam-3322	446	6	mathematical	mathematical	ADJ
ejpam-3322	446	7	sciences	science	NOUN
ejpam-3322	446	8	,	,	PUNCT
ejpam-3322	446	9	2004(42):2231	2004(42):2231	NUM
ejpam-3322	446	10	-	-	SYM
ejpam-3322	446	11	2264	2264	NUM
ejpam-3322	446	12	,	,	PUNCT
ejpam-3322	446	13	2004	2004	NUM
ejpam-3322	446	14	.	.	PUNCT
ejpam-3322	447	1	[	[	X
ejpam-3322	447	2	3	3	NUM
ejpam-3322	447	3	]	]	X
ejpam-3322	447	4	e	e	PROPN
ejpam-3322	447	5	j	j	PROPN
ejpam-3322	447	6	beggs	beggs	PROPN
ejpam-3322	447	7	,	,	PUNCT
ejpam-3322	447	8	j	j	PROPN
ejpam-3322	447	9	d	d	X
ejpam-3322	447	10	gould	gould	PROPN
ejpam-3322	447	11	and	and	CCONJ
ejpam-3322	447	12	s	s	PROPN
ejpam-3322	447	13	majid	majid	PROPN
ejpam-3322	447	14	.	.	PUNCT
ejpam-3322	448	1	finite	finite	PROPN
ejpam-3322	448	2	group	group	NOUN
ejpam-3322	448	3	factorizations	factorization	VERB
ejpam-3322	448	4	and	and	CCONJ
ejpam-3322	448	5	braiding	braid	VERB
ejpam-3322	448	6	.	.	PUNCT
ejpam-3322	449	1	j.	j.	PROPN
ejpam-3322	449	2	algebra	algebra	PROPN
ejpam-3322	449	3	,	,	PUNCT
ejpam-3322	449	4	181(1):112	181(1):112	NUM
ejpam-3322	449	5	-151	-151	PROPN
ejpam-3322	449	6	,	,	PUNCT
ejpam-3322	449	7	1996	1996	NUM
ejpam-3322	449	8	.	.	PUNCT
ejpam-3322	450	1	[	[	X
ejpam-3322	450	2	4	4	NUM
ejpam-3322	450	3	]	]	X
ejpam-3322	450	4	e	e	PROPN
ejpam-3322	450	5	j	j	PROPN
ejpam-3322	450	6	beggs	beggs	PROPN
ejpam-3322	450	7	.	.	PUNCT
ejpam-3322	451	1	making	make	VERB
ejpam-3322	451	2	non	non	ADJ
ejpam-3322	451	3	-	-	ADJ
ejpam-3322	451	4	trivially	trivially	ADV
ejpam-3322	451	5	associated	associated	ADJ
ejpam-3322	451	6	tensor	tensor	NOUN
ejpam-3322	451	7	categories	category	NOUN
ejpam-3322	451	8	from	from	ADP
ejpam-3322	451	9	left	left	ADJ
ejpam-3322	451	10	coset	coset	NOUN
ejpam-3322	451	11	representatives	representative	NOUN
ejpam-3322	451	12	.	.	PUNCT
ejpam-3322	452	1	journal	journal	NOUN
ejpam-3322	452	2	of	of	ADP
ejpam-3322	452	3	pure	pure	ADJ
ejpam-3322	452	4	and	and	CCONJ
ejpam-3322	452	5	applied	applied	ADJ
ejpam-3322	452	6	algebra	algebra	NOUN
ejpam-3322	452	7	,	,	PUNCT
ejpam-3322	452	8	177(1):5	177(1):5	NUM
ejpam-3322	452	9	41	41	NUM
ejpam-3322	452	10	,	,	PUNCT
ejpam-3322	452	11	2003	2003	NUM
ejpam-3322	452	12	.	.	PUNCT
ejpam-3322	453	1	[	[	X
ejpam-3322	453	2	5	5	NUM
ejpam-3322	453	3	]	]	PUNCT
ejpam-3322	453	4	e	e	PROPN
ejpam-3322	453	5	j	j	PROPN
ejpam-3322	453	6	beggs	beggs	PROPN
ejpam-3322	453	7	and	and	CCONJ
ejpam-3322	453	8	s	s	PROPN
ejpam-3322	453	9	majid	majid	PROPN
ejpam-3322	453	10	.	.	PUNCT
ejpam-3322	454	1	quasitriangular	quasitriangular	ADJ
ejpam-3322	454	2	and	and	CCONJ
ejpam-3322	454	3	differential	differential	ADJ
ejpam-3322	454	4	structures	structure	NOUN
ejpam-3322	454	5	on	on	ADP
ejpam-3322	454	6	bicrossproduct	bicrossproduct	NOUN
ejpam-3322	454	7	hopf	hopf	PROPN
ejpam-3322	454	8	algebras	algebra	VERB
ejpam-3322	454	9	.	.	PUNCT
ejpam-3322	455	1	j.	j.	PROPN
ejpam-3322	455	2	algebra	algebra	PROPN
ejpam-3322	455	3	,	,	PUNCT
ejpam-3322	455	4	219(2):682–727	219(2):682–727	NUM
ejpam-3322	455	5	,	,	PUNCT
ejpam-3322	455	6	1999	1999	NUM
ejpam-3322	455	7	.	.	PUNCT
ejpam-3322	456	1	[	[	X
ejpam-3322	456	2	6	6	NUM
ejpam-3322	456	3	]	]	PUNCT
ejpam-3322	456	4	d	d	NOUN
ejpam-3322	456	5	i	i	PRON
ejpam-3322	456	6	gurevich	gurevich	VERB
ejpam-3322	456	7	and	and	CCONJ
ejpam-3322	456	8	s	s	PROPN
ejpam-3322	456	9	majid	majid	PROPN
ejpam-3322	456	10	.	.	PUNCT
ejpam-3322	457	1	braided	braid	VERB
ejpam-3322	457	2	groups	group	NOUN
ejpam-3322	457	3	of	of	ADP
ejpam-3322	457	4	hopf	hopf	PROPN
ejpam-3322	457	5	algebras	algebras	PROPN
ejpam-3322	457	6	obtained	obtain	VERB
ejpam-3322	457	7	by	by	ADP
ejpam-3322	457	8	twisting	twisting	NOUN
ejpam-3322	457	9	.	.	PUNCT
ejpam-3322	458	1	pacific	pacific	PROPN
ejpam-3322	458	2	j.	j.	PROPN
ejpam-3322	458	3	math	math	PROPN
ejpam-3322	458	4	,	,	PUNCT
ejpam-3322	458	5	162(1):27–44	162(1):27–44	NUM
ejpam-3322	458	6	,	,	PUNCT
ejpam-3322	458	7	1994	1994	NUM
ejpam-3322	458	8	.	.	PUNCT
ejpam-3322	459	1	[	[	X
ejpam-3322	459	2	7	7	NUM
ejpam-3322	459	3	]	]	X
ejpam-3322	459	4	s	s	PART
ejpam-3322	459	5	majid	majid	PROPN
ejpam-3322	459	6	.	.	PUNCT
ejpam-3322	460	1	foundations	foundation	NOUN
ejpam-3322	460	2	of	of	ADP
ejpam-3322	460	3	quantum	quantum	NOUN
ejpam-3322	460	4	group	group	NOUN
ejpam-3322	460	5	theory	theory	NOUN
ejpam-3322	460	6	.	.	PUNCT
ejpam-3322	461	1	cambridge	cambridge	PROPN
ejpam-3322	461	2	university	university	PROPN
ejpam-3322	461	3	press	press	PROPN
ejpam-3322	461	4	,	,	PUNCT
ejpam-3322	461	5	cambridge	cambridge	PROPN
ejpam-3322	461	6	,	,	PUNCT
ejpam-3322	461	7	uk	uk	PROPN
ejpam-3322	461	8	,	,	PUNCT
ejpam-3322	461	9	1995	1995	NUM
ejpam-3322	461	10	.	.	PUNCT
ejpam-3322	462	1	[	[	X
ejpam-3322	462	2	8	8	NUM
ejpam-3322	462	3	]	]	X
ejpam-3322	462	4	s	s	PART
ejpam-3322	462	5	majid	majid	PROPN
ejpam-3322	462	6	.	.	PUNCT
ejpam-3322	462	7	quantum	quantum	NOUN
ejpam-3322	462	8	groups	group	NOUN
ejpam-3322	462	9	primer	primer	PROPN
ejpam-3322	462	10	.	.	PROPN
ejpam-3322	463	1	cambridge	cambridge	PROPN
ejpam-3322	463	2	university	university	PROPN
ejpam-3322	463	3	press	press	PROPN
ejpam-3322	463	4	,	,	PUNCT
ejpam-3322	463	5	cambridge	cambridge	PROPN
ejpam-3322	463	6	,	,	PUNCT
ejpam-3322	463	7	uk	uk	PROPN
ejpam-3322	463	8	,	,	PUNCT
ejpam-3322	463	9	2002	2002	NUM
ejpam-3322	463	10	.	.	PUNCT
ejpam-3322	464	1	[	[	X
ejpam-3322	464	2	9	9	NUM
ejpam-3322	464	3	]	]	SYM
ejpam-3322	464	4	m	m	NOUN
ejpam-3322	464	5	sweedler	sweedler	NOUN
ejpam-3322	464	6	.	.	PUNCT
ejpam-3322	465	1	hopf	hopf	PROPN
ejpam-3322	465	2	algebras	algebras	PROPN
ejpam-3322	465	3	.	.	PUNCT
ejpam-3322	465	4	w.	w.	PROPN
ejpam-3322	465	5	a.	a.	PROPN
ejpam-3322	465	6	benjamin	benjamin	PROPN
ejpam-3322	465	7	,	,	PUNCT
ejpam-3322	465	8	new	new	PROPN
ejpam-3322	465	9	york	york	PROPN
ejpam-3322	465	10	,	,	PUNCT
ejpam-3322	465	11	usa	usa	PROPN
ejpam-3322	465	12	,	,	PUNCT
ejpam-3322	465	13	1969	1969	NUM
ejpam-3322	465	14	.	.	PUNCT
ejpam-3322	466	1	[	[	X
ejpam-3322	466	2	10	10	NUM
ejpam-3322	466	3	]	]	X
ejpam-3322	466	4	m	m	PROPN
ejpam-3322	466	5	takeuchi	takeuchi	PROPN
ejpam-3322	466	6	.	.	PUNCT
ejpam-3322	467	1	finite	finite	PROPN
ejpam-3322	467	2	hopf	hopf	PROPN
ejpam-3322	467	3	algebras	algebras	PROPN
ejpam-3322	467	4	in	in	ADP
ejpam-3322	467	5	braided	braid	VERB
ejpam-3322	467	6	tensor	tensor	NOUN
ejpam-3322	467	7	categories	category	NOUN
ejpam-3322	467	8	.	.	PUNCT
ejpam-3322	468	1	j.	j.	PROPN
ejpam-3322	468	2	pure	pure	PROPN
ejpam-3322	468	3	appl	appl	PROPN
ejpam-3322	468	4	.	.	PUNCT
ejpam-3322	469	1	algebra	algebra	NOUN
ejpam-3322	469	2	,	,	PUNCT
ejpam-3322	469	3	138:59–82	138:59–82	NUM
ejpam-3322	469	4	,	,	PUNCT
ejpam-3322	469	5	1999	1999	NUM
ejpam-3322	469	6	.	.	PUNCT
ejpam-3322	470	1	[	[	X
ejpam-3322	470	2	11	11	NUM
ejpam-3322	470	3	]	]	X
ejpam-3322	470	4	r	r	NOUN
ejpam-3322	470	5	g	g	NOUN
ejpam-3322	470	6	underwood	underwood	NOUN
ejpam-3322	470	7	.	.	PUNCT
ejpam-3322	471	1	fundamentals	fundamental	NOUN
ejpam-3322	471	2	of	of	ADP
ejpam-3322	471	3	hopf	hopf	ADJ
ejpam-3322	471	4	algebras	algebra	NOUN
ejpam-3322	471	5	.	.	PUNCT
ejpam-3322	472	1	springer	springer	PROPN
ejpam-3322	472	2	international	international	ADJ
ejpam-3322	472	3	publishing	publishing	PROPN
ejpam-3322	472	4	,	,	PUNCT
ejpam-3322	472	5	switzerland	switzerland	PROPN
ejpam-3322	472	6	,	,	PUNCT
ejpam-3322	472	7	2015	2015	NUM
ejpam-3322	472	8	.	.	PUNCT