id	sid	tid	token	lemma	pos
ejpam-7055	1	1	european	european	PROPN
ejpam-7055	1	2	journal	journal	PROPN
ejpam-7055	1	3	of	of	ADP
ejpam-7055	1	4	pure	pure	ADJ
ejpam-7055	1	5	and	and	CCONJ
ejpam-7055	1	6	applied	applied	ADJ
ejpam-7055	1	7	mathematics	mathematic	NOUN
ejpam-7055	1	8	2025	2025	NUM
ejpam-7055	1	9	,	,	PUNCT
ejpam-7055	1	10	vol	vol	NOUN
ejpam-7055	1	11	.	.	PROPN
ejpam-7055	1	12	18	18	NUM
ejpam-7055	1	13	,	,	PUNCT
ejpam-7055	1	14	issue	issue	NOUN
ejpam-7055	1	15	4	4	NUM
ejpam-7055	1	16	,	,	PUNCT
ejpam-7055	1	17	article	article	NOUN
ejpam-7055	1	18	number	number	NOUN
ejpam-7055	1	19	7055	7055	NUM
ejpam-7055	1	20	issn	issn	PROPN
ejpam-7055	1	21	1307	1307	NUM
ejpam-7055	1	22	-	-	SYM
ejpam-7055	1	23	5543	5543	NUM
ejpam-7055	1	24	–	–	PUNCT
ejpam-7055	1	25	ejpam.com	ejpam.com	X
ejpam-7055	1	26	published	publish	VERB
ejpam-7055	1	27	by	by	ADP
ejpam-7055	1	28	new	new	PROPN
ejpam-7055	1	29	york	york	PROPN
ejpam-7055	1	30	business	business	PROPN
ejpam-7055	1	31	global	global	PROPN
ejpam-7055	1	32	exploring	explore	VERB
ejpam-7055	1	33	categorical	categorical	ADJ
ejpam-7055	1	34	perspectives	perspective	NOUN
ejpam-7055	1	35	on	on	ADP
ejpam-7055	1	36	soft	soft	ADJ
ejpam-7055	1	37	bck	bck	NOUN
ejpam-7055	1	38	/	/	SYM
ejpam-7055	1	39	bci	bci	NOUN
ejpam-7055	1	40	-	-	PUNCT
ejpam-7055	1	41	algebras	algebras	PROPN
ejpam-7055	1	42	g.	g.	PROPN
ejpam-7055	1	43	muhiuddin1,∗	muhiuddin1,∗	PROPN
ejpam-7055	1	44	,	,	PUNCT
ejpam-7055	1	45	mohamed	mohamed	PROPN
ejpam-7055	1	46	e.	e.	PROPN
ejpam-7055	1	47	elnair1,2	elnair1,2	PROPN
ejpam-7055	1	48	,	,	PUNCT
ejpam-7055	1	49	ahmed	ahmed	PROPN
ejpam-7055	1	50	a.	a.	PROPN
ejpam-7055	1	51	khidir1	khidir1	PROPN
ejpam-7055	1	52	,	,	PUNCT
ejpam-7055	1	53	mohammed	mohammed	PROPN
ejpam-7055	1	54	hassan1	hassan1	PROPN
ejpam-7055	1	55	1	1	NUM
ejpam-7055	1	56	department	department	NOUN
ejpam-7055	1	57	of	of	ADP
ejpam-7055	1	58	mathematics	mathematic	NOUN
ejpam-7055	1	59	,	,	PUNCT
ejpam-7055	1	60	faculty	faculty	NOUN
ejpam-7055	1	61	of	of	ADP
ejpam-7055	1	62	science	science	NOUN
ejpam-7055	1	63	,	,	PUNCT
ejpam-7055	1	64	university	university	NOUN
ejpam-7055	1	65	of	of	ADP
ejpam-7055	1	66	tabuk	tabuk	PROPN
ejpam-7055	1	67	,	,	PUNCT
ejpam-7055	1	68	p.o	p.o	PROPN
ejpam-7055	1	69	.	.	PROPN
ejpam-7055	1	70	box	box	PROPN
ejpam-7055	1	71	741	741	NUM
ejpam-7055	1	72	,	,	PUNCT
ejpam-7055	1	73	tabuk	tabuk	NOUN
ejpam-7055	1	74	71491	71491	NUM
ejpam-7055	1	75	,	,	PUNCT
ejpam-7055	1	76	saudi	saudi	PROPN
ejpam-7055	1	77	arabia	arabia	PROPN
ejpam-7055	1	78	2	2	NUM
ejpam-7055	1	79	department	department	NOUN
ejpam-7055	1	80	of	of	ADP
ejpam-7055	1	81	mathematics	mathematics	PROPN
ejpam-7055	1	82	and	and	CCONJ
ejpam-7055	1	83	physics	physics	PROPN
ejpam-7055	1	84	,	,	PUNCT
ejpam-7055	1	85	gezira	gezira	PROPN
ejpam-7055	1	86	university	university	PROPN
ejpam-7055	1	87	,	,	PUNCT
ejpam-7055	1	88	p.	p.	PROPN
ejpam-7055	1	89	o.	o.	PROPN
ejpam-7055	1	90	box	box	PROPN
ejpam-7055	1	91	20	20	NUM
ejpam-7055	1	92	,	,	PUNCT
ejpam-7055	1	93	sudan	sudan	PROPN
ejpam-7055	1	94	abstract	abstract	NOUN
ejpam-7055	1	95	.	.	PUNCT
ejpam-7055	2	1	in	in	ADP
ejpam-7055	2	2	this	this	DET
ejpam-7055	2	3	manuscript	manuscript	NOUN
ejpam-7055	2	4	,	,	PUNCT
ejpam-7055	2	5	we	we	PRON
ejpam-7055	2	6	present	present	VERB
ejpam-7055	2	7	new	new	ADJ
ejpam-7055	2	8	ideas	idea	NOUN
ejpam-7055	2	9	concerning	concern	VERB
ejpam-7055	2	10	the	the	DET
ejpam-7055	2	11	domain	domain	NOUN
ejpam-7055	2	12	of	of	ADP
ejpam-7055	2	13	soft	soft	ADJ
ejpam-7055	2	14	bck	bck	NOUN
ejpam-7055	2	15	/	/	SYM
ejpam-7055	2	16	bcialgebras	bcialgebra	NOUN
ejpam-7055	2	17	and	and	CCONJ
ejpam-7055	2	18	outline	outline	VERB
ejpam-7055	2	19	specific	specific	ADJ
ejpam-7055	2	20	categorical	categorical	ADJ
ejpam-7055	2	21	frameworks	framework	NOUN
ejpam-7055	2	22	,	,	PUNCT
ejpam-7055	2	23	including	include	VERB
ejpam-7055	2	24	equalizers	equalizer	NOUN
ejpam-7055	2	25	and	and	CCONJ
ejpam-7055	2	26	finite	finite	ADJ
ejpam-7055	2	27	products	product	NOUN
ejpam-7055	2	28	.	.	PUNCT
ejpam-7055	3	1	additionally	additionally	ADV
ejpam-7055	3	2	,	,	PUNCT
ejpam-7055	3	3	we	we	PRON
ejpam-7055	3	4	demonstrate	demonstrate	VERB
ejpam-7055	3	5	that	that	SCONJ
ejpam-7055	3	6	the	the	DET
ejpam-7055	3	7	category	category	NOUN
ejpam-7055	3	8	of	of	ADP
ejpam-7055	3	9	soft	soft	ADJ
ejpam-7055	3	10	bck	bck	NOUN
ejpam-7055	3	11	/	/	SYM
ejpam-7055	3	12	bci	bci	NOUN
ejpam-7055	3	13	-	-	PUNCT
ejpam-7055	3	14	algebras	algebras	PROPN
ejpam-7055	3	15	conforms	conform	VERB
ejpam-7055	3	16	to	to	ADP
ejpam-7055	3	17	a	a	DET
ejpam-7055	3	18	topological	topological	ADJ
ejpam-7055	3	19	construct	construct	NOUN
ejpam-7055	3	20	.	.	PUNCT
ejpam-7055	4	1	moreover	moreover	ADV
ejpam-7055	4	2	,	,	PUNCT
ejpam-7055	4	3	we	we	PRON
ejpam-7055	4	4	establish	establish	VERB
ejpam-7055	4	5	that	that	SCONJ
ejpam-7055	4	6	the	the	DET
ejpam-7055	4	7	category	category	NOUN
ejpam-7055	4	8	of	of	ADP
ejpam-7055	4	9	soft	soft	ADJ
ejpam-7055	4	10	bck	bck	NOUN
ejpam-7055	4	11	/	/	SYM
ejpam-7055	4	12	bci	bci	NOUN
ejpam-7055	4	13	-	-	PUNCT
ejpam-7055	4	14	algebras	algebras	PROPN
ejpam-7055	4	15	features	feature	VERB
ejpam-7055	4	16	distinctive	distinctive	ADJ
ejpam-7055	4	17	elements	element	NOUN
ejpam-7055	4	18	such	such	ADJ
ejpam-7055	4	19	as	as	ADP
ejpam-7055	4	20	terminal	terminal	ADJ
ejpam-7055	4	21	objects	object	NOUN
ejpam-7055	4	22	,	,	PUNCT
ejpam-7055	4	23	initial	initial	ADJ
ejpam-7055	4	24	objects	object	NOUN
ejpam-7055	4	25	,	,	PUNCT
ejpam-7055	4	26	and	and	CCONJ
ejpam-7055	4	27	zero	zero	NUM
ejpam-7055	4	28	objects	object	NOUN
ejpam-7055	4	29	.	.	PUNCT
ejpam-7055	5	1	2020	2020	NUM
ejpam-7055	5	2	mathematics	mathematic	NOUN
ejpam-7055	5	3	subject	subject	NOUN
ejpam-7055	5	4	classifications	classification	NOUN
ejpam-7055	5	5	:	:	PUNCT
ejpam-7055	5	6	18a20	18a20	NUM
ejpam-7055	5	7	,	,	PUNCT
ejpam-7055	5	8	18d05	18d05	NUM
ejpam-7055	5	9	,	,	PUNCT
ejpam-7055	5	10	06f35	06f35	ADJ
ejpam-7055	5	11	key	key	ADJ
ejpam-7055	5	12	words	word	NOUN
ejpam-7055	5	13	and	and	CCONJ
ejpam-7055	5	14	phrases	phrase	NOUN
ejpam-7055	5	15	:	:	PUNCT
ejpam-7055	5	16	bck	bck	VERB
ejpam-7055	5	17	/	/	SYM
ejpam-7055	5	18	bci	bci	NOUN
ejpam-7055	5	19	-	-	NOUN
ejpam-7055	5	20	algebra	algebra	ADJ
ejpam-7055	5	21	,	,	PUNCT
ejpam-7055	5	22	soft	soft	ADJ
ejpam-7055	5	23	bck	bck	NOUN
ejpam-7055	5	24	/	/	SYM
ejpam-7055	5	25	bci	bci	NOUN
ejpam-7055	5	26	-	-	NOUN
ejpam-7055	5	27	algebra	algebra	NOUN
ejpam-7055	5	28	,	,	PUNCT
ejpam-7055	5	29	category	category	NOUN
ejpam-7055	5	30	of	of	ADP
ejpam-7055	5	31	soft	soft	ADJ
ejpam-7055	5	32	bck	bck	NOUN
ejpam-7055	5	33	/	/	SYM
ejpam-7055	5	34	bcialgebra	bcialgebra	NOUN
ejpam-7055	5	35	,	,	PUNCT
ejpam-7055	5	36	soft	soft	ADJ
ejpam-7055	5	37	bck	bck	NOUN
ejpam-7055	5	38	/	/	SYM
ejpam-7055	5	39	bci	bci	NOUN
ejpam-7055	5	40	-	-	ADJ
ejpam-7055	5	41	homomorphism	homomorphism	NOUN
ejpam-7055	5	42	1	1	NUM
ejpam-7055	5	43	.	.	X
ejpam-7055	5	44	introduction	introduction	NOUN
ejpam-7055	5	45	imai	imai	PROPN
ejpam-7055	5	46	and	and	CCONJ
ejpam-7055	5	47	iséki	iséki	NOUN
ejpam-7055	5	48	introduced	introduce	VERB
ejpam-7055	5	49	two	two	NUM
ejpam-7055	5	50	classes	class	NOUN
ejpam-7055	5	51	of	of	ADP
ejpam-7055	5	52	abstract	abstract	ADJ
ejpam-7055	5	53	algebras	algebra	NOUN
ejpam-7055	5	54	:	:	PUNCT
ejpam-7055	5	55	bck	bck	VERB
ejpam-7055	5	56	-	-	PUNCT
ejpam-7055	5	57	algebras	algebras	PROPN
ejpam-7055	5	58	and	and	CCONJ
ejpam-7055	5	59	bcialgebras	bcialgebra	NOUN
ejpam-7055	5	60	[	[	X
ejpam-7055	5	61	1	1	NUM
ejpam-7055	5	62	,	,	PUNCT
ejpam-7055	5	63	2	2	NUM
ejpam-7055	5	64	]	]	PUNCT
ejpam-7055	5	65	.	.	PUNCT
ejpam-7055	6	1	it	it	PRON
ejpam-7055	6	2	is	be	AUX
ejpam-7055	6	3	established	establish	VERB
ejpam-7055	6	4	that	that	SCONJ
ejpam-7055	6	5	the	the	DET
ejpam-7055	6	6	category	category	NOUN
ejpam-7055	6	7	of	of	ADP
ejpam-7055	6	8	bck	bck	PROPN
ejpam-7055	6	9	-	-	PUNCT
ejpam-7055	6	10	algebras	algebras	PROPN
ejpam-7055	6	11	is	be	AUX
ejpam-7055	6	12	a	a	DET
ejpam-7055	6	13	proper	proper	ADJ
ejpam-7055	6	14	subset	subset	NOUN
ejpam-7055	6	15	of	of	ADP
ejpam-7055	6	16	the	the	DET
ejpam-7055	6	17	category	category	NOUN
ejpam-7055	6	18	of	of	ADP
ejpam-7055	6	19	bci	bci	NOUN
ejpam-7055	6	20	-	-	PUNCT
ejpam-7055	6	21	algebras	algebra	NOUN
ejpam-7055	6	22	.	.	PUNCT
ejpam-7055	7	1	in	in	ADP
ejpam-7055	7	2	the	the	DET
ejpam-7055	7	3	realm	realm	NOUN
ejpam-7055	7	4	of	of	ADP
ejpam-7055	7	5	fuzzy	fuzzy	ADJ
ejpam-7055	7	6	set	set	NOUN
ejpam-7055	7	7	theory	theory	NOUN
ejpam-7055	7	8	[	[	X
ejpam-7055	7	9	3	3	NUM
ejpam-7055	7	10	,	,	PUNCT
ejpam-7055	7	11	4	4	NUM
ejpam-7055	7	12	]	]	PUNCT
ejpam-7055	7	13	,	,	PUNCT
ejpam-7055	7	14	molodtsov	molodtsov	NOUN
ejpam-7055	7	15	[	[	X
ejpam-7055	7	16	5	5	NUM
ejpam-7055	7	17	]	]	PUNCT
ejpam-7055	7	18	proposed	propose	VERB
ejpam-7055	7	19	the	the	DET
ejpam-7055	7	20	concept	concept	NOUN
ejpam-7055	7	21	of	of	ADP
ejpam-7055	7	22	soft	soft	ADJ
ejpam-7055	7	23	sets	set	NOUN
ejpam-7055	7	24	as	as	ADP
ejpam-7055	7	25	a	a	DET
ejpam-7055	7	26	novel	novel	ADJ
ejpam-7055	7	27	mathematical	mathematical	ADJ
ejpam-7055	7	28	approach	approach	NOUN
ejpam-7055	7	29	to	to	PART
ejpam-7055	7	30	address	address	VERB
ejpam-7055	7	31	uncertainties	uncertainty	NOUN
ejpam-7055	7	32	without	without	ADP
ejpam-7055	7	33	the	the	DET
ejpam-7055	7	34	presence	presence	NOUN
ejpam-7055	7	35	of	of	ADP
ejpam-7055	7	36	errors	error	NOUN
ejpam-7055	7	37	found	find	VERB
ejpam-7055	7	38	in	in	ADP
ejpam-7055	7	39	existing	exist	VERB
ejpam-7055	7	40	theories	theory	NOUN
ejpam-7055	7	41	.	.	PUNCT
ejpam-7055	8	1	subsequently	subsequently	ADV
ejpam-7055	8	2	,	,	PUNCT
ejpam-7055	8	3	maji	maji	PROPN
ejpam-7055	8	4	et	et	PROPN
ejpam-7055	8	5	al	al	PROPN
ejpam-7055	8	6	.	.	PUNCT
ejpam-7055	9	1	[	[	X
ejpam-7055	9	2	6	6	NUM
ejpam-7055	9	3	,	,	PUNCT
ejpam-7055	9	4	7	7	NUM
ejpam-7055	9	5	]	]	PUNCT
ejpam-7055	9	6	introduced	introduce	VERB
ejpam-7055	9	7	fuzzy	fuzzy	ADJ
ejpam-7055	9	8	soft	soft	ADJ
ejpam-7055	9	9	sets	set	NOUN
ejpam-7055	9	10	.	.	PUNCT
ejpam-7055	10	1	ali	ali	PROPN
ejpam-7055	10	2	et	et	PROPN
ejpam-7055	10	3	al	al	PROPN
ejpam-7055	10	4	.	.	PUNCT
ejpam-7055	11	1	[	[	X
ejpam-7055	11	2	8	8	NUM
ejpam-7055	11	3	]	]	PUNCT
ejpam-7055	11	4	explored	explore	VERB
ejpam-7055	11	5	new	new	ADJ
ejpam-7055	11	6	operations	operation	NOUN
ejpam-7055	11	7	on	on	ADP
ejpam-7055	11	8	soft	soft	ADJ
ejpam-7055	11	9	sets	set	NOUN
ejpam-7055	11	10	,	,	PUNCT
ejpam-7055	11	11	while	while	SCONJ
ejpam-7055	11	12	ongoing	ongoing	ADJ
ejpam-7055	11	13	research	research	NOUN
ejpam-7055	11	14	continues	continue	VERB
ejpam-7055	11	15	to	to	PART
ejpam-7055	11	16	advance	advance	VERB
ejpam-7055	11	17	soft	soft	ADJ
ejpam-7055	11	18	set	set	NOUN
ejpam-7055	11	19	theory	theory	NOUN
ejpam-7055	11	20	.	.	PUNCT
ejpam-7055	12	1	in	in	ADP
ejpam-7055	12	2	[	[	X
ejpam-7055	12	3	9	9	NUM
ejpam-7055	12	4	]	]	PUNCT
ejpam-7055	12	5	,	,	PUNCT
ejpam-7055	12	6	the	the	DET
ejpam-7055	12	7	application	application	NOUN
ejpam-7055	12	8	of	of	ADP
ejpam-7055	12	9	soft	soft	ADJ
ejpam-7055	12	10	set	set	NOUN
ejpam-7055	12	11	theory	theory	NOUN
ejpam-7055	12	12	is	be	AUX
ejpam-7055	12	13	extended	extend	VERB
ejpam-7055	12	14	to	to	ADP
ejpam-7055	12	15	various	various	ADJ
ejpam-7055	12	16	concepts	concept	NOUN
ejpam-7055	12	17	including	include	VERB
ejpam-7055	12	18	(	(	PUNCT
ejpam-7055	12	19	i	i	NOUN
ejpam-7055	12	20	)	)	PUNCT
ejpam-7055	12	21	filters	filter	NOUN
ejpam-7055	12	22	in	in	ADP
ejpam-7055	12	23	r0	r0	NOUN
ejpam-7055	12	24	-	-	PUNCT
ejpam-7055	12	25	algebras	algebras	X
ejpam-7055	12	26	;	;	PUNCT
ejpam-7055	12	27	(	(	PUNCT
ejpam-7055	12	28	ii	ii	NOUN
ejpam-7055	12	29	)	)	PUNCT
ejpam-7055	12	30	positive	positive	ADJ
ejpam-7055	12	31	implicative	implicative	ADJ
ejpam-7055	12	32	ideals	ideal	NOUN
ejpam-7055	12	33	of	of	ADP
ejpam-7055	12	34	bck	bck	NOUN
ejpam-7055	12	35	-	-	PUNCT
ejpam-7055	12	36	algebras	algebras	NOUN
ejpam-7055	13	1	[	[	X
ejpam-7055	13	2	10	10	NUM
ejpam-7055	13	3	]	]	PUNCT
ejpam-7055	13	4	;	;	PUNCT
ejpam-7055	13	5	(	(	PUNCT
ejpam-7055	13	6	iii	iii	NOUN
ejpam-7055	13	7	)	)	PUNCT
ejpam-7055	13	8	decision	decision	NOUN
ejpam-7055	13	9	-	-	PUNCT
ejpam-7055	13	10	making	make	VERB
ejpam-7055	13	11	problems	problem	NOUN
ejpam-7055	13	12	using	use	VERB
ejpam-7055	13	13	fuzzy	fuzzy	ADJ
ejpam-7055	13	14	soft	soft	ADJ
ejpam-7055	13	15	sets	set	NOUN
ejpam-7055	13	16	[	[	X
ejpam-7055	13	17	11	11	NUM
ejpam-7055	13	18	]	]	NUM
ejpam-7055	13	19	;	;	PUNCT
ejpam-7055	13	20	(	(	PUNCT
ejpam-7055	13	21	iv	iv	X
ejpam-7055	13	22	)	)	PUNCT
ejpam-7055	13	23	fuzzy	fuzzy	ADJ
ejpam-7055	13	24	soft	soft	ADJ
ejpam-7055	13	25	groups	group	NOUN
ejpam-7055	14	1	[	[	X
ejpam-7055	14	2	12	12	NUM
ejpam-7055	14	3	]	]	PUNCT
ejpam-7055	14	4	;	;	PUNCT
ejpam-7055	14	5	(	(	PUNCT
ejpam-7055	14	6	v	v	NOUN
ejpam-7055	14	7	)	)	PUNCT
ejpam-7055	14	8	fuzzy	fuzzy	ADJ
ejpam-7055	14	9	soft	soft	ADJ
ejpam-7055	14	10	sets	set	NOUN
ejpam-7055	14	11	in	in	ADP
ejpam-7055	14	12	bck	bck	PROPN
ejpam-7055	14	13	/	/	SYM
ejpam-7055	14	14	bci	bci	NOUN
ejpam-7055	14	15	-	-	PUNCT
ejpam-7055	14	16	algebras	algebras	X
ejpam-7055	15	1	[	[	X
ejpam-7055	15	2	13	13	NUM
ejpam-7055	15	3	]	]	SYM
ejpam-7055	15	4	;	;	PUNCT
ejpam-7055	15	5	(	(	PUNCT
ejpam-7055	15	6	vi	vi	X
ejpam-7055	15	7	)	)	PUNCT
ejpam-7055	15	8	normal	normal	ADJ
ejpam-7055	15	9	unisoft	unisoft	ADJ
ejpam-7055	15	10	filters	filter	NOUN
ejpam-7055	15	11	in	in	ADP
ejpam-7055	15	12	r0	r0	NOUN
ejpam-7055	15	13	-	-	PUNCT
ejpam-7055	15	14	algebras	algebras	PROPN
ejpam-7055	16	1	[	[	X
ejpam-7055	16	2	14	14	NUM
ejpam-7055	16	3	]	]	PUNCT
ejpam-7055	16	4	.	.	PUNCT
ejpam-7055	17	1	additionally	additionally	ADV
ejpam-7055	17	2	,	,	PUNCT
ejpam-7055	17	3	muhiuddin	muhiuddin	VERB
ejpam-7055	17	4	et	et	PROPN
ejpam-7055	17	5	al	al	PROPN
ejpam-7055	17	6	.	.	PROPN
ejpam-7055	17	7	studied	study	VERB
ejpam-7055	17	8	the	the	DET
ejpam-7055	17	9	application	application	NOUN
ejpam-7055	17	10	of	of	ADP
ejpam-7055	17	11	soft	soft	ADJ
ejpam-7055	17	12	set	set	NOUN
ejpam-7055	17	13	theory	theory	NOUN
ejpam-7055	17	14	in	in	ADP
ejpam-7055	17	15	areas	area	NOUN
ejpam-7055	17	16	such	such	ADJ
ejpam-7055	17	17	as	as	ADP
ejpam-7055	17	18	filter	filter	NOUN
ejpam-7055	17	19	theory	theory	NOUN
ejpam-7055	17	20	in	in	ADP
ejpam-7055	17	21	mtl	mtl	PROPN
ejpam-7055	17	22	-	-	PUNCT
ejpam-7055	17	23	algebras	algebras	X
ejpam-7055	18	1	[	[	X
ejpam-7055	18	2	15	15	NUM
ejpam-7055	18	3	]	]	X
ejpam-7055	18	4	,	,	PUNCT
ejpam-7055	18	5	unisoft	unisoft	ADJ
ejpam-7055	18	6	filters	filter	NOUN
ejpam-7055	18	7	in	in	ADP
ejpam-7055	18	8	r0	r0	NOUN
ejpam-7055	18	9	-	-	PUNCT
ejpam-7055	18	10	algebras	algebras	PROPN
ejpam-7055	19	1	[	[	X
ejpam-7055	19	2	16	16	NUM
ejpam-7055	19	3	]	]	PUNCT
ejpam-7055	19	4	,	,	PUNCT
ejpam-7055	19	5	cubic	cubic	ADJ
ejpam-7055	19	6	soft	soft	ADJ
ejpam-7055	19	7	∗corresponding	∗corresponde	VERB
ejpam-7055	19	8	author	author	NOUN
ejpam-7055	19	9	.	.	PUNCT
ejpam-7055	20	1	doi	doi	NOUN
ejpam-7055	20	2	:	:	PUNCT
ejpam-7055	20	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7055	https://doi.org/10.29020/nybg.ejpam.v18i4.7055	NOUN
ejpam-7055	20	4	email	email	NOUN
ejpam-7055	20	5	addresses	address	NOUN
ejpam-7055	20	6	:	:	PUNCT
ejpam-7055	20	7	chishtygm@gmail.com	chishtygm@gmail.com	X
ejpam-7055	20	8	,	,	PUNCT
ejpam-7055	20	9	gmuhiuddin@ut.edu.sa	gmuhiuddin@ut.edu.sa	PROPN
ejpam-7055	20	10	(	(	PUNCT
ejpam-7055	20	11	g.	g.	PROPN
ejpam-7055	20	12	muhiuddin	muhiuddin	PROPN
ejpam-7055	20	13	)	)	PUNCT
ejpam-7055	20	14	,	,	PUNCT
ejpam-7055	20	15	abomunzir124@gmail.com	abomunzir124@gmail.com	X
ejpam-7055	20	16	(	(	PUNCT
ejpam-7055	20	17	m.	m.	PROPN
ejpam-7055	20	18	e.	e.	PROPN
ejpam-7055	20	19	elnair	elnair	PROPN
ejpam-7055	20	20	)	)	PUNCT
ejpam-7055	20	21	,	,	PUNCT
ejpam-7055	20	22	akhidir@ut.edu.sa	akhidir@ut.edu.sa	PROPN
ejpam-7055	20	23	(	(	PUNCT
ejpam-7055	20	24	a.	a.	NOUN
ejpam-7055	20	25	a.	a.	NOUN
ejpam-7055	20	26	khidir	khidir	PROPN
ejpam-7055	20	27	)	)	PUNCT
ejpam-7055	20	28	,	,	PUNCT
ejpam-7055	20	29	m.salih@ut.edu.sa	m.salih@ut.edu.sa	PROPN
ejpam-7055	20	30	(	(	PUNCT
ejpam-7055	20	31	m.	m.	NOUN
ejpam-7055	20	32	hassan	hassan	PROPN
ejpam-7055	20	33	)	)	PUNCT
ejpam-7055	20	34	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7055	21	1	1	1	NUM
ejpam-7055	21	2	copyright	copyright	NOUN
ejpam-7055	21	3	:	:	PUNCT
ejpam-7055	21	4	©	©	PROPN
ejpam-7055	21	5	2025	2025	NUM
ejpam-7055	21	6	the	the	DET
ejpam-7055	21	7	author(s	author(s	NOUN
ejpam-7055	21	8	)	)	PUNCT
ejpam-7055	21	9	.	.	PUNCT
ejpam-7055	22	1	(	(	PUNCT
ejpam-7055	22	2	cc	cc	NOUN
ejpam-7055	22	3	by	by	ADP
ejpam-7055	22	4	-	-	PUNCT
ejpam-7055	22	5	nc	nc	PROPN
ejpam-7055	22	6	4.0	4.0	NUM
ejpam-7055	22	7	)	)	PUNCT
ejpam-7055	23	1	g.	g.	PROPN
ejpam-7055	23	2	muhiuddin	muhiuddin	PROPN
ejpam-7055	23	3	et	et	PROPN
ejpam-7055	23	4	al	al	PROPN
ejpam-7055	23	5	.	.	PUNCT
ejpam-7055	23	6	/	/	SYM
ejpam-7055	23	7	eur	eur	PROPN
ejpam-7055	23	8	.	.	PUNCT
ejpam-7055	24	1	j.	j.	PROPN
ejpam-7055	24	2	pure	pure	PROPN
ejpam-7055	24	3	appl	appl	PROPN
ejpam-7055	24	4	.	.	PROPN
ejpam-7055	24	5	math	math	PROPN
ejpam-7055	24	6	,	,	PUNCT
ejpam-7055	24	7	18	18	NUM
ejpam-7055	24	8	(	(	PUNCT
ejpam-7055	24	9	4	4	NUM
ejpam-7055	24	10	)	)	PUNCT
ejpam-7055	24	11	(	(	PUNCT
ejpam-7055	24	12	2025	2025	NUM
ejpam-7055	24	13	)	)	PUNCT
ejpam-7055	24	14	,	,	PUNCT
ejpam-7055	24	15	7055	7055	NUM
ejpam-7055	24	16	2	2	NUM
ejpam-7055	24	17	of	of	ADP
ejpam-7055	24	18	13	13	NUM
ejpam-7055	24	19	bck	bck	NOUN
ejpam-7055	24	20	/	/	SYM
ejpam-7055	24	21	bci	bci	NOUN
ejpam-7055	24	22	-	-	PUNCT
ejpam-7055	24	23	algebras	algebras	PUNCT
ejpam-7055	25	1	[	[	X
ejpam-7055	25	2	17	17	NUM
ejpam-7055	25	3	,	,	PUNCT
ejpam-7055	25	4	18	18	NUM
ejpam-7055	25	5	]	]	PUNCT
ejpam-7055	25	6	,	,	PUNCT
ejpam-7055	25	7	and	and	CCONJ
ejpam-7055	25	8	soft	soft	ADJ
ejpam-7055	25	9	ordered	order	VERB
ejpam-7055	25	10	semigroups	semigroup	NOUN
ejpam-7055	25	11	[	[	X
ejpam-7055	25	12	19	19	NUM
ejpam-7055	25	13	]	]	PUNCT
ejpam-7055	25	14	.	.	PUNCT
ejpam-7055	26	1	moreover	moreover	ADV
ejpam-7055	26	2	,	,	PUNCT
ejpam-7055	26	3	category	category	NOUN
ejpam-7055	26	4	theory	theory	NOUN
ejpam-7055	26	5	is	be	AUX
ejpam-7055	26	6	broadly	broadly	ADV
ejpam-7055	26	7	defined	define	VERB
ejpam-7055	26	8	as	as	ADP
ejpam-7055	26	9	a	a	DET
ejpam-7055	26	10	general	general	ADJ
ejpam-7055	26	11	mathematical	mathematical	ADJ
ejpam-7055	26	12	theory	theory	NOUN
ejpam-7055	26	13	of	of	ADP
ejpam-7055	26	14	structures	structure	NOUN
ejpam-7055	26	15	and	and	CCONJ
ejpam-7055	26	16	systems	system	NOUN
ejpam-7055	26	17	of	of	ADP
ejpam-7055	26	18	structures	structure	NOUN
ejpam-7055	26	19	.	.	PUNCT
ejpam-7055	27	1	for	for	ADP
ejpam-7055	27	2	detailed	detailed	ADJ
ejpam-7055	27	3	insights	insight	NOUN
ejpam-7055	27	4	into	into	ADP
ejpam-7055	27	5	categorical	categorical	ADJ
ejpam-7055	27	6	concepts	concept	NOUN
ejpam-7055	27	7	,	,	PUNCT
ejpam-7055	27	8	readers	reader	NOUN
ejpam-7055	27	9	are	be	AUX
ejpam-7055	27	10	directed	direct	VERB
ejpam-7055	27	11	to	to	ADP
ejpam-7055	27	12	[	[	X
ejpam-7055	27	13	20–24	20–24	NUM
ejpam-7055	27	14	]	]	PUNCT
ejpam-7055	27	15	.	.	PUNCT
ejpam-7055	28	1	in	in	ADP
ejpam-7055	28	2	recent	recent	ADJ
ejpam-7055	28	3	years	year	NOUN
ejpam-7055	28	4	,	,	PUNCT
ejpam-7055	28	5	researchers	researcher	NOUN
ejpam-7055	28	6	have	have	AUX
ejpam-7055	28	7	merged	merge	VERB
ejpam-7055	28	8	category	category	NOUN
ejpam-7055	28	9	theory	theory	NOUN
ejpam-7055	28	10	with	with	ADP
ejpam-7055	28	11	soft	soft	ADJ
ejpam-7055	28	12	set	set	NOUN
ejpam-7055	28	13	theory	theory	NOUN
ejpam-7055	28	14	to	to	PART
ejpam-7055	28	15	establish	establish	VERB
ejpam-7055	28	16	the	the	DET
ejpam-7055	28	17	category	category	NOUN
ejpam-7055	28	18	of	of	ADP
ejpam-7055	28	19	soft	soft	ADJ
ejpam-7055	28	20	sets	set	NOUN
ejpam-7055	28	21	across	across	ADP
ejpam-7055	28	22	various	various	ADJ
ejpam-7055	28	23	domains	domain	NOUN
ejpam-7055	28	24	.	.	PUNCT
ejpam-7055	29	1	notable	notable	ADJ
ejpam-7055	29	2	contributions	contribution	NOUN
ejpam-7055	29	3	include	include	VERB
ejpam-7055	29	4	:	:	PUNCT
ejpam-7055	29	5	•	•	NOUN
ejpam-7055	29	6	in	in	ADP
ejpam-7055	29	7	2013	2013	NUM
ejpam-7055	29	8	,	,	PUNCT
ejpam-7055	29	9	zahiri	zahiri	X
ejpam-7055	30	1	[	[	X
ejpam-7055	30	2	25	25	NUM
ejpam-7055	30	3	]	]	PUNCT
ejpam-7055	30	4	introduced	introduce	VERB
ejpam-7055	30	5	the	the	DET
ejpam-7055	30	6	concept	concept	NOUN
ejpam-7055	30	7	of	of	ADP
ejpam-7055	30	8	the	the	DET
ejpam-7055	30	9	“	"	PUNCT
ejpam-7055	30	10	category	category	NOUN
ejpam-7055	30	11	of	of	ADP
ejpam-7055	30	12	soft	soft	ADJ
ejpam-7055	30	13	sets	set	NOUN
ejpam-7055	30	14	.	.	PUNCT
ejpam-7055	30	15	”	"	PUNCT
ejpam-7055	31	1	•	•	NOUN
ejpam-7055	31	2	in	in	ADP
ejpam-7055	31	3	the	the	DET
ejpam-7055	31	4	same	same	ADJ
ejpam-7055	31	5	year	year	NOUN
ejpam-7055	31	6	,	,	PUNCT
ejpam-7055	31	7	sardar	sardar	PROPN
ejpam-7055	31	8	and	and	CCONJ
ejpam-7055	31	9	gupta	gupta	PROPN
ejpam-7055	32	1	[	[	X
ejpam-7055	32	2	26	26	NUM
ejpam-7055	32	3	]	]	PUNCT
ejpam-7055	32	4	constructed	construct	VERB
ejpam-7055	32	5	a	a	DET
ejpam-7055	32	6	soft	soft	ADJ
ejpam-7055	32	7	category	category	NOUN
ejpam-7055	32	8	and	and	CCONJ
ejpam-7055	32	9	investigated	investigate	VERB
ejpam-7055	32	10	several	several	ADJ
ejpam-7055	32	11	intriguing	intriguing	ADJ
ejpam-7055	32	12	properties	property	NOUN
ejpam-7055	32	13	.	.	PUNCT
ejpam-7055	33	1	•	•	NUM
ejpam-7055	33	2	in	in	ADP
ejpam-7055	33	3	2014	2014	NUM
ejpam-7055	33	4	,	,	PUNCT
ejpam-7055	33	5	zhou	zhou	PROPN
ejpam-7055	33	6	et	et	PROPN
ejpam-7055	33	7	al	al	PROPN
ejpam-7055	33	8	.	.	PUNCT
ejpam-7055	34	1	[	[	X
ejpam-7055	34	2	27	27	NUM
ejpam-7055	34	3	]	]	PUNCT
ejpam-7055	34	4	delved	delve	VERB
ejpam-7055	34	5	into	into	ADP
ejpam-7055	34	6	the	the	DET
ejpam-7055	34	7	categorical	categorical	ADJ
ejpam-7055	34	8	properties	property	NOUN
ejpam-7055	34	9	of	of	ADP
ejpam-7055	34	10	soft	soft	ADJ
ejpam-7055	34	11	sets	set	NOUN
ejpam-7055	34	12	.	.	PUNCT
ejpam-7055	35	1	•	•	NUM
ejpam-7055	35	2	borzooei	borzooei	PROPN
ejpam-7055	35	3	et	et	PROPN
ejpam-7055	35	4	al	al	PROPN
ejpam-7055	35	5	.	.	PUNCT
ejpam-7055	36	1	[	[	X
ejpam-7055	36	2	28	28	NUM
ejpam-7055	36	3	]	]	PUNCT
ejpam-7055	36	4	explored	explore	VERB
ejpam-7055	36	5	key	key	ADJ
ejpam-7055	36	6	concepts	concept	NOUN
ejpam-7055	36	7	related	relate	VERB
ejpam-7055	36	8	to	to	ADP
ejpam-7055	36	9	the	the	DET
ejpam-7055	36	10	category	category	NOUN
ejpam-7055	36	11	of	of	ADP
ejpam-7055	36	12	soft	soft	ADJ
ejpam-7055	36	13	sets	set	NOUN
ejpam-7055	36	14	in	in	ADP
ejpam-7055	36	15	2015	2015	NUM
ejpam-7055	36	16	.	.	PUNCT
ejpam-7055	37	1	•	•	NOUN
ejpam-7055	37	2	in	in	ADP
ejpam-7055	37	3	2016	2016	NUM
ejpam-7055	37	4	,	,	PUNCT
ejpam-7055	37	5	öztunç	öztunç	NOUN
ejpam-7055	37	6	[	[	X
ejpam-7055	37	7	29	29	NUM
ejpam-7055	37	8	]	]	PUNCT
ejpam-7055	37	9	examined	examine	VERB
ejpam-7055	37	10	specific	specific	ADJ
ejpam-7055	37	11	properties	property	NOUN
ejpam-7055	37	12	of	of	ADP
ejpam-7055	37	13	soft	soft	ADJ
ejpam-7055	37	14	categories	category	NOUN
ejpam-7055	37	15	.	.	PUNCT
ejpam-7055	38	1	•	•	NUM
ejpam-7055	38	2	shirmohammadi	shirmohammadi	NOUN
ejpam-7055	38	3	and	and	CCONJ
ejpam-7055	38	4	rasouli	rasouli	NOUN
ejpam-7055	38	5	[	[	X
ejpam-7055	38	6	30	30	NUM
ejpam-7055	38	7	]	]	PUNCT
ejpam-7055	38	8	presented	present	VERB
ejpam-7055	38	9	a	a	DET
ejpam-7055	38	10	categorical	categorical	ADJ
ejpam-7055	38	11	approach	approach	NOUN
ejpam-7055	38	12	to	to	ADP
ejpam-7055	38	13	soft	soft	ADJ
ejpam-7055	38	14	s	s	NOUN
ejpam-7055	38	15	-	-	PUNCT
ejpam-7055	38	16	acts	act	NOUN
ejpam-7055	38	17	in	in	ADP
ejpam-7055	38	18	2017	2017	NUM
ejpam-7055	38	19	.	.	PUNCT
ejpam-7055	39	1	•	•	NOUN
ejpam-7055	39	2	in	in	ADP
ejpam-7055	39	3	2022	2022	NUM
ejpam-7055	39	4	,	,	PUNCT
ejpam-7055	39	5	sharma	sharma	PROPN
ejpam-7055	39	6	et	et	PROPN
ejpam-7055	39	7	al	al	PROPN
ejpam-7055	39	8	.	.	PUNCT
ejpam-7055	40	1	[	[	X
ejpam-7055	40	2	31	31	NUM
ejpam-7055	40	3	]	]	PUNCT
ejpam-7055	40	4	introduced	introduce	VERB
ejpam-7055	40	5	the	the	DET
ejpam-7055	40	6	notion	notion	NOUN
ejpam-7055	40	7	of	of	ADP
ejpam-7055	40	8	the	the	DET
ejpam-7055	40	9	category	category	NOUN
ejpam-7055	40	10	of	of	ADP
ejpam-7055	40	11	intuitionistic	intuitionistic	ADJ
ejpam-7055	40	12	fuzzy	fuzzy	ADJ
ejpam-7055	40	13	modules	module	NOUN
ejpam-7055	40	14	.	.	PUNCT
ejpam-7055	41	1	2	2	X
ejpam-7055	41	2	.	.	X
ejpam-7055	41	3	purpose	purpose	NOUN
ejpam-7055	41	4	for	for	ADP
ejpam-7055	41	5	conducting	conduct	VERB
ejpam-7055	41	6	this	this	DET
ejpam-7055	41	7	research	research	NOUN
ejpam-7055	41	8	the	the	DET
ejpam-7055	41	9	study	study	NOUN
ejpam-7055	41	10	of	of	ADP
ejpam-7055	41	11	soft	soft	ADJ
ejpam-7055	41	12	bck	bck	NOUN
ejpam-7055	41	13	/	/	SYM
ejpam-7055	41	14	bci	bci	NOUN
ejpam-7055	41	15	-	-	PUNCT
ejpam-7055	41	16	algebras	algebras	PROPN
ejpam-7055	41	17	represents	represent	VERB
ejpam-7055	41	18	a	a	DET
ejpam-7055	41	19	fascinating	fascinating	ADJ
ejpam-7055	41	20	area	area	NOUN
ejpam-7055	41	21	of	of	ADP
ejpam-7055	41	22	research	research	NOUN
ejpam-7055	41	23	that	that	PRON
ejpam-7055	41	24	offers	offer	VERB
ejpam-7055	41	25	intriguing	intriguing	ADJ
ejpam-7055	41	26	insights	insight	NOUN
ejpam-7055	41	27	into	into	ADP
ejpam-7055	41	28	algebraic	algebraic	ADJ
ejpam-7055	41	29	systems	system	NOUN
ejpam-7055	41	30	.	.	PUNCT
ejpam-7055	42	1	by	by	ADP
ejpam-7055	42	2	investigating	investigate	VERB
ejpam-7055	42	3	and	and	CCONJ
ejpam-7055	42	4	elucidating	elucidate	VERB
ejpam-7055	42	5	the	the	DET
ejpam-7055	42	6	categorical	categorical	ADJ
ejpam-7055	42	7	structures	structure	NOUN
ejpam-7055	42	8	and	and	CCONJ
ejpam-7055	42	9	properties	property	NOUN
ejpam-7055	42	10	within	within	ADP
ejpam-7055	42	11	this	this	DET
ejpam-7055	42	12	domain	domain	NOUN
ejpam-7055	42	13	,	,	PUNCT
ejpam-7055	42	14	we	we	PRON
ejpam-7055	42	15	aim	aim	VERB
ejpam-7055	42	16	to	to	PART
ejpam-7055	42	17	expand	expand	VERB
ejpam-7055	42	18	the	the	DET
ejpam-7055	42	19	theoretical	theoretical	ADJ
ejpam-7055	42	20	foundations	foundation	NOUN
ejpam-7055	42	21	of	of	ADP
ejpam-7055	42	22	soft	soft	ADJ
ejpam-7055	42	23	bck	bck	NOUN
ejpam-7055	42	24	/	/	SYM
ejpam-7055	42	25	bci	bci	NOUN
ejpam-7055	42	26	-	-	PUNCT
ejpam-7055	42	27	algebras	algebras	X
ejpam-7055	42	28	.	.	PUNCT
ejpam-7055	43	1	our	our	PRON
ejpam-7055	43	2	exploration	exploration	NOUN
ejpam-7055	43	3	of	of	ADP
ejpam-7055	43	4	concepts	concept	NOUN
ejpam-7055	43	5	such	such	ADJ
ejpam-7055	43	6	as	as	ADP
ejpam-7055	43	7	equalizers	equalizer	NOUN
ejpam-7055	43	8	and	and	CCONJ
ejpam-7055	43	9	finite	finite	ADJ
ejpam-7055	43	10	products	product	NOUN
ejpam-7055	43	11	sheds	shed	VERB
ejpam-7055	43	12	light	light	NOUN
ejpam-7055	43	13	on	on	ADP
ejpam-7055	43	14	the	the	DET
ejpam-7055	43	15	organizational	organizational	ADJ
ejpam-7055	43	16	principles	principle	NOUN
ejpam-7055	43	17	governing	govern	VERB
ejpam-7055	43	18	these	these	DET
ejpam-7055	43	19	algebraic	algebraic	ADJ
ejpam-7055	43	20	systems	system	NOUN
ejpam-7055	43	21	.	.	PUNCT
ejpam-7055	44	1	furthermore	furthermore	ADV
ejpam-7055	44	2	,	,	PUNCT
ejpam-7055	44	3	our	our	PRON
ejpam-7055	44	4	discovery	discovery	NOUN
ejpam-7055	44	5	of	of	ADP
ejpam-7055	44	6	terminal	terminal	NOUN
ejpam-7055	44	7	,	,	PUNCT
ejpam-7055	44	8	initial	initial	ADJ
ejpam-7055	44	9	,	,	PUNCT
ejpam-7055	44	10	and	and	CCONJ
ejpam-7055	44	11	zero	zero	NUM
ejpam-7055	44	12	objects	object	NOUN
ejpam-7055	44	13	in	in	ADP
ejpam-7055	44	14	the	the	DET
ejpam-7055	44	15	category	category	NOUN
ejpam-7055	44	16	of	of	ADP
ejpam-7055	44	17	soft	soft	ADJ
ejpam-7055	44	18	bck	bck	NOUN
ejpam-7055	44	19	/	/	SYM
ejpam-7055	44	20	bci	bci	NOUN
ejpam-7055	44	21	-	-	PUNCT
ejpam-7055	44	22	algebras	algebras	PROPN
ejpam-7055	44	23	reveals	reveal	VERB
ejpam-7055	44	24	unique	unique	ADJ
ejpam-7055	44	25	elements	element	NOUN
ejpam-7055	44	26	that	that	PRON
ejpam-7055	44	27	contribute	contribute	VERB
ejpam-7055	44	28	to	to	ADP
ejpam-7055	44	29	a	a	DET
ejpam-7055	44	30	deeper	deep	ADJ
ejpam-7055	44	31	understanding	understanding	NOUN
ejpam-7055	44	32	of	of	ADP
ejpam-7055	44	33	their	their	PRON
ejpam-7055	44	34	structural	structural	ADJ
ejpam-7055	44	35	nuances	nuance	NOUN
ejpam-7055	44	36	.	.	PUNCT
ejpam-7055	45	1	through	through	ADP
ejpam-7055	45	2	this	this	DET
ejpam-7055	45	3	work	work	NOUN
ejpam-7055	45	4	,	,	PUNCT
ejpam-7055	45	5	we	we	PRON
ejpam-7055	45	6	not	not	PART
ejpam-7055	45	7	only	only	ADV
ejpam-7055	45	8	enhance	enhance	VERB
ejpam-7055	45	9	our	our	PRON
ejpam-7055	45	10	knowledge	knowledge	NOUN
ejpam-7055	45	11	of	of	ADP
ejpam-7055	45	12	categorical	categorical	ADJ
ejpam-7055	45	13	properties	property	NOUN
ejpam-7055	45	14	but	but	CCONJ
ejpam-7055	45	15	also	also	ADV
ejpam-7055	45	16	pave	pave	VERB
ejpam-7055	45	17	the	the	DET
ejpam-7055	45	18	way	way	NOUN
ejpam-7055	45	19	for	for	ADP
ejpam-7055	45	20	future	future	ADJ
ejpam-7055	45	21	research	research	NOUN
ejpam-7055	45	22	and	and	CCONJ
ejpam-7055	45	23	applications	application	NOUN
ejpam-7055	45	24	in	in	ADP
ejpam-7055	45	25	the	the	DET
ejpam-7055	45	26	realm	realm	NOUN
ejpam-7055	45	27	of	of	ADP
ejpam-7055	45	28	algebraic	algebraic	ADJ
ejpam-7055	45	29	structures	structure	NOUN
ejpam-7055	45	30	and	and	CCONJ
ejpam-7055	45	31	categorical	categorical	ADJ
ejpam-7055	45	32	theory	theory	NOUN
ejpam-7055	45	33	.	.	PUNCT
ejpam-7055	46	1	3	3	X
ejpam-7055	46	2	.	.	NOUN
ejpam-7055	46	3	targets	target	NOUN
ejpam-7055	46	4	of	of	ADP
ejpam-7055	46	5	the	the	DET
ejpam-7055	46	6	planned	plan	VERB
ejpam-7055	46	7	technique	technique	NOUN
ejpam-7055	46	8	•	•	ADP
ejpam-7055	46	9	to	to	PART
ejpam-7055	46	10	develop	develop	VERB
ejpam-7055	46	11	a	a	DET
ejpam-7055	46	12	systematic	systematic	ADJ
ejpam-7055	46	13	framework	framework	NOUN
ejpam-7055	46	14	for	for	ADP
ejpam-7055	46	15	analyzing	analyze	VERB
ejpam-7055	46	16	soft	soft	ADJ
ejpam-7055	46	17	bck	bck	NOUN
ejpam-7055	46	18	/	/	SYM
ejpam-7055	46	19	bci	bci	NOUN
ejpam-7055	46	20	-	-	PUNCT
ejpam-7055	46	21	algebras	algebras	PRON
ejpam-7055	46	22	and	and	CCONJ
ejpam-7055	46	23	exploring	explore	VERB
ejpam-7055	46	24	their	their	PRON
ejpam-7055	46	25	categorical	categorical	ADJ
ejpam-7055	46	26	structures	structure	NOUN
ejpam-7055	46	27	.	.	PUNCT
ejpam-7055	47	1	•	•	VERB
ejpam-7055	47	2	to	to	PART
ejpam-7055	47	3	investigate	investigate	VERB
ejpam-7055	47	4	the	the	DET
ejpam-7055	47	5	presence	presence	NOUN
ejpam-7055	47	6	of	of	ADP
ejpam-7055	47	7	equalizers	equalizer	NOUN
ejpam-7055	47	8	and	and	CCONJ
ejpam-7055	47	9	finite	finite	ADJ
ejpam-7055	47	10	products	product	NOUN
ejpam-7055	47	11	within	within	ADP
ejpam-7055	47	12	the	the	DET
ejpam-7055	47	13	category	category	NOUN
ejpam-7055	47	14	of	of	ADP
ejpam-7055	47	15	soft	soft	ADJ
ejpam-7055	47	16	bck	bck	NOUN
ejpam-7055	47	17	/	/	SYM
ejpam-7055	47	18	bci	bci	NOUN
ejpam-7055	47	19	-	-	PUNCT
ejpam-7055	47	20	algebras	algebras	X
ejpam-7055	47	21	.	.	PUNCT
ejpam-7055	48	1	g.	g.	PROPN
ejpam-7055	48	2	muhiuddin	muhiuddin	PROPN
ejpam-7055	48	3	et	et	PROPN
ejpam-7055	48	4	al	al	PROPN
ejpam-7055	48	5	.	.	PUNCT
ejpam-7055	48	6	/	/	SYM
ejpam-7055	48	7	eur	eur	PROPN
ejpam-7055	48	8	.	.	PUNCT
ejpam-7055	49	1	j.	j.	PROPN
ejpam-7055	49	2	pure	pure	PROPN
ejpam-7055	49	3	appl	appl	PROPN
ejpam-7055	49	4	.	.	PROPN
ejpam-7055	49	5	math	math	PROPN
ejpam-7055	49	6	,	,	PUNCT
ejpam-7055	49	7	18	18	NUM
ejpam-7055	49	8	(	(	PUNCT
ejpam-7055	49	9	4	4	NUM
ejpam-7055	49	10	)	)	PUNCT
ejpam-7055	49	11	(	(	PUNCT
ejpam-7055	49	12	2025	2025	NUM
ejpam-7055	49	13	)	)	PUNCT
ejpam-7055	49	14	,	,	PUNCT
ejpam-7055	49	15	7055	7055	NUM
ejpam-7055	49	16	3	3	NUM
ejpam-7055	49	17	of	of	ADP
ejpam-7055	49	18	13	13	NUM
ejpam-7055	49	19	•	•	NOUN
ejpam-7055	49	20	to	to	PART
ejpam-7055	49	21	demonstrate	demonstrate	VERB
ejpam-7055	49	22	the	the	DET
ejpam-7055	49	23	adherence	adherence	NOUN
ejpam-7055	49	24	of	of	ADP
ejpam-7055	49	25	the	the	DET
ejpam-7055	49	26	category	category	NOUN
ejpam-7055	49	27	of	of	ADP
ejpam-7055	49	28	soft	soft	ADJ
ejpam-7055	49	29	bck	bck	NOUN
ejpam-7055	49	30	/	/	SYM
ejpam-7055	49	31	bci	bci	NOUN
ejpam-7055	49	32	-	-	PUNCT
ejpam-7055	49	33	algebras	algebras	PROPN
ejpam-7055	49	34	to	to	ADP
ejpam-7055	49	35	a	a	DET
ejpam-7055	49	36	topological	topological	ADJ
ejpam-7055	49	37	construct	construct	NOUN
ejpam-7055	49	38	.	.	PUNCT
ejpam-7055	50	1	•	•	ADP
ejpam-7055	50	2	to	to	PART
ejpam-7055	50	3	identify	identify	VERB
ejpam-7055	50	4	and	and	CCONJ
ejpam-7055	50	5	characterize	characterize	VERB
ejpam-7055	50	6	special	special	ADJ
ejpam-7055	50	7	objects	object	NOUN
ejpam-7055	50	8	such	such	ADJ
ejpam-7055	50	9	as	as	ADP
ejpam-7055	50	10	terminal	terminal	ADJ
ejpam-7055	50	11	objects	object	NOUN
ejpam-7055	50	12	,	,	PUNCT
ejpam-7055	50	13	initial	initial	ADJ
ejpam-7055	50	14	objects	object	NOUN
ejpam-7055	50	15	,	,	PUNCT
ejpam-7055	50	16	and	and	CCONJ
ejpam-7055	50	17	zero	zero	NUM
ejpam-7055	50	18	objects	object	NOUN
ejpam-7055	50	19	in	in	ADP
ejpam-7055	50	20	the	the	DET
ejpam-7055	50	21	category	category	NOUN
ejpam-7055	50	22	of	of	ADP
ejpam-7055	50	23	soft	soft	ADJ
ejpam-7055	50	24	bck	bck	NOUN
ejpam-7055	50	25	/	/	SYM
ejpam-7055	50	26	bci	bci	NOUN
ejpam-7055	50	27	-	-	PUNCT
ejpam-7055	50	28	algebras	algebra	NOUN
ejpam-7055	50	29	.	.	PUNCT
ejpam-7055	50	30	•	•	NUM
ejpam-7055	50	31	to	to	PART
ejpam-7055	50	32	contribute	contribute	VERB
ejpam-7055	50	33	to	to	ADP
ejpam-7055	50	34	a	a	DET
ejpam-7055	50	35	deeper	deep	ADJ
ejpam-7055	50	36	understanding	understanding	NOUN
ejpam-7055	50	37	of	of	ADP
ejpam-7055	50	38	the	the	DET
ejpam-7055	50	39	categorical	categorical	ADJ
ejpam-7055	50	40	properties	property	NOUN
ejpam-7055	50	41	and	and	CCONJ
ejpam-7055	50	42	structural	structural	ADJ
ejpam-7055	50	43	nuances	nuance	NOUN
ejpam-7055	50	44	inherent	inherent	ADJ
ejpam-7055	50	45	in	in	ADP
ejpam-7055	50	46	soft	soft	ADJ
ejpam-7055	50	47	bck	bck	NOUN
ejpam-7055	50	48	/	/	SYM
ejpam-7055	50	49	bci	bci	NOUN
ejpam-7055	50	50	-	-	PUNCT
ejpam-7055	50	51	algebras	algebra	NOUN
ejpam-7055	50	52	.	.	PUNCT
ejpam-7055	51	1	•	•	NUM
ejpam-7055	51	2	to	to	PART
ejpam-7055	51	3	lay	lay	VERB
ejpam-7055	51	4	the	the	DET
ejpam-7055	51	5	groundwork	groundwork	NOUN
ejpam-7055	51	6	for	for	ADP
ejpam-7055	51	7	further	further	ADJ
ejpam-7055	51	8	exploration	exploration	NOUN
ejpam-7055	51	9	and	and	CCONJ
ejpam-7055	51	10	applications	application	NOUN
ejpam-7055	51	11	of	of	ADP
ejpam-7055	51	12	the	the	DET
ejpam-7055	51	13	proposed	propose	VERB
ejpam-7055	51	14	method	method	NOUN
ejpam-7055	51	15	in	in	ADP
ejpam-7055	51	16	the	the	DET
ejpam-7055	51	17	broader	broad	ADJ
ejpam-7055	51	18	context	context	NOUN
ejpam-7055	51	19	of	of	ADP
ejpam-7055	51	20	algebraic	algebraic	ADJ
ejpam-7055	51	21	structures	structure	NOUN
ejpam-7055	51	22	and	and	CCONJ
ejpam-7055	51	23	categorical	categorical	ADJ
ejpam-7055	51	24	theory	theory	NOUN
ejpam-7055	51	25	.	.	PUNCT
ejpam-7055	52	1	this	this	DET
ejpam-7055	52	2	paper	paper	NOUN
ejpam-7055	52	3	is	be	AUX
ejpam-7055	52	4	structured	structure	VERB
ejpam-7055	52	5	as	as	SCONJ
ejpam-7055	52	6	follows	follow	VERB
ejpam-7055	52	7	:	:	PUNCT
ejpam-7055	52	8	section	section	NOUN
ejpam-7055	52	9	2	2	NUM
ejpam-7055	52	10	presents	present	VERB
ejpam-7055	52	11	fundamental	fundamental	ADJ
ejpam-7055	52	12	notions	notion	NOUN
ejpam-7055	52	13	of	of	ADP
ejpam-7055	52	14	bck	bck	PROPN
ejpam-7055	52	15	/	/	SYM
ejpam-7055	52	16	bcialgebras	bcialgebra	NOUN
ejpam-7055	52	17	and	and	CCONJ
ejpam-7055	52	18	soft	soft	ADJ
ejpam-7055	52	19	bck	bck	NOUN
ejpam-7055	52	20	/	/	SYM
ejpam-7055	52	21	bci	bci	NOUN
ejpam-7055	52	22	-	-	PUNCT
ejpam-7055	52	23	algebras	algebras	PROPN
ejpam-7055	52	24	.	.	PUNCT
ejpam-7055	53	1	section	section	NOUN
ejpam-7055	53	2	3	3	NUM
ejpam-7055	53	3	entails	entail	VERB
ejpam-7055	53	4	the	the	DET
ejpam-7055	53	5	construction	construction	NOUN
ejpam-7055	53	6	of	of	ADP
ejpam-7055	53	7	the	the	DET
ejpam-7055	53	8	soft	soft	ADJ
ejpam-7055	53	9	bck	bck	NOUN
ejpam-7055	53	10	/	/	SYM
ejpam-7055	53	11	bci	bci	NOUN
ejpam-7055	53	12	-	-	PUNCT
ejpam-7055	53	13	algebras	algebras	ADJ
ejpam-7055	53	14	category	category	NOUN
ejpam-7055	53	15	and	and	CCONJ
ejpam-7055	53	16	various	various	ADJ
ejpam-7055	53	17	category	category	NOUN
ejpam-7055	53	18	-	-	PUNCT
ejpam-7055	53	19	related	relate	VERB
ejpam-7055	53	20	concepts	concept	NOUN
ejpam-7055	53	21	.	.	PUNCT
ejpam-7055	54	1	finally	finally	ADV
ejpam-7055	54	2	,	,	PUNCT
ejpam-7055	54	3	in	in	ADP
ejpam-7055	54	4	section	section	NOUN
ejpam-7055	54	5	4	4	NUM
ejpam-7055	54	6	,	,	PUNCT
ejpam-7055	54	7	we	we	PRON
ejpam-7055	54	8	explore	explore	VERB
ejpam-7055	54	9	the	the	DET
ejpam-7055	54	10	special	special	ADJ
ejpam-7055	54	11	objects	object	NOUN
ejpam-7055	54	12	within	within	ADP
ejpam-7055	54	13	the	the	DET
ejpam-7055	54	14	category	category	NOUN
ejpam-7055	54	15	of	of	ADP
ejpam-7055	54	16	soft	soft	ADJ
ejpam-7055	54	17	bck	bck	NOUN
ejpam-7055	54	18	-	-	PUNCT
ejpam-7055	54	19	algebras	algebras	NOUN
ejpam-7055	54	20	.	.	PUNCT
ejpam-7055	55	1	4	4	X
ejpam-7055	55	2	.	.	X
ejpam-7055	55	3	preliminaries	preliminary	NOUN
ejpam-7055	55	4	k.	k.	PROPN
ejpam-7055	55	5	iséki	iséki	PROPN
ejpam-7055	55	6	introduced	introduce	VERB
ejpam-7055	55	7	the	the	DET
ejpam-7055	55	8	significant	significant	ADJ
ejpam-7055	55	9	class	class	NOUN
ejpam-7055	55	10	of	of	ADP
ejpam-7055	55	11	logical	logical	ADJ
ejpam-7055	55	12	algebras	algebra	NOUN
ejpam-7055	55	13	known	know	VERB
ejpam-7055	55	14	as	as	ADP
ejpam-7055	55	15	bck	bck	NOUN
ejpam-7055	55	16	/	/	SYM
ejpam-7055	55	17	bcialgebras	bcialgebra	NOUN
ejpam-7055	55	18	,	,	PUNCT
ejpam-7055	55	19	described	describe	VERB
ejpam-7055	55	20	as	as	ADP
ejpam-7055	55	21	the	the	DET
ejpam-7055	55	22	most	most	ADV
ejpam-7055	55	23	important	important	ADJ
ejpam-7055	55	24	class	class	NOUN
ejpam-7055	55	25	of	of	ADP
ejpam-7055	55	26	logical	logical	ADJ
ejpam-7055	55	27	algebras	algebra	NOUN
ejpam-7055	56	1	[	[	X
ejpam-7055	56	2	1	1	NUM
ejpam-7055	56	3	,	,	PUNCT
ejpam-7055	56	4	2	2	NUM
ejpam-7055	56	5	]	]	PUNCT
ejpam-7055	56	6	.	.	PUNCT
ejpam-7055	57	1	a	a	DET
ejpam-7055	57	2	nonempty	nonempty	NOUN
ejpam-7055	57	3	subset	subset	VERB
ejpam-7055	57	4	t	t	PROPN
ejpam-7055	57	5	is	be	AUX
ejpam-7055	57	6	referred	refer	VERB
ejpam-7055	57	7	to	to	ADP
ejpam-7055	57	8	as	as	ADP
ejpam-7055	57	9	a	a	DET
ejpam-7055	57	10	bck	bck	NOUN
ejpam-7055	57	11	/	/	SYM
ejpam-7055	57	12	bci	bci	NOUN
ejpam-7055	57	13	-	-	PUNCT
ejpam-7055	57	14	subalgebra	subalgebra	NOUN
ejpam-7055	57	15	of	of	ADP
ejpam-7055	57	16	x̃	x̃	PROPN
ejpam-7055	57	17	if	if	SCONJ
ejpam-7055	57	18	ϖ∗ϱ	ϖ∗ϱ	PROPN
ejpam-7055	57	19	∈	∈	PROPN
ejpam-7055	57	20	t	t	PROPN
ejpam-7055	57	21	for	for	ADP
ejpam-7055	57	22	all	all	DET
ejpam-7055	57	23	ϖ	ϖ	NOUN
ejpam-7055	57	24	,	,	PUNCT
ejpam-7055	57	25	ϱ	ϱ	PROPN
ejpam-7055	57	26	∈	∈	PROPN
ejpam-7055	57	27	t	t	NOUN
ejpam-7055	57	28	where	where	SCONJ
ejpam-7055	57	29	x̃	x̃	PROPN
ejpam-7055	57	30	is	be	AUX
ejpam-7055	57	31	a	a	DET
ejpam-7055	57	32	bck	bck	VERB
ejpam-7055	57	33	/	/	SYM
ejpam-7055	57	34	bci	bci	NOUN
ejpam-7055	57	35	-	-	NOUN
ejpam-7055	57	36	algebra	algebra	NOUN
ejpam-7055	57	37	.	.	PUNCT
ejpam-7055	58	1	please	please	INTJ
ejpam-7055	58	2	consult	consult	VERB
ejpam-7055	58	3	[	[	X
ejpam-7055	58	4	32	32	NUM
ejpam-7055	58	5	]	]	PUNCT
ejpam-7055	58	6	,	,	PUNCT
ejpam-7055	58	7	for	for	ADP
ejpam-7055	58	8	further	further	ADJ
ejpam-7055	58	9	details	detail	NOUN
ejpam-7055	58	10	regarding	regard	VERB
ejpam-7055	58	11	bck	bck	PROPN
ejpam-7055	58	12	/	/	SYM
ejpam-7055	58	13	bcialgebras	bcialgebras	NOUN
ejpam-7055	58	14	.	.	PUNCT
ejpam-7055	59	1	a	a	DET
ejpam-7055	59	2	“	"	PUNCT
ejpam-7055	59	3	fuzzy	fuzzy	ADJ
ejpam-7055	59	4	set	set	NOUN
ejpam-7055	59	5	”	"	PUNCT
ejpam-7055	59	6	µ	µ	NOUN
ejpam-7055	59	7	in	in	ADP
ejpam-7055	59	8	a	a	DET
ejpam-7055	59	9	“	"	PUNCT
ejpam-7055	59	10	bck	bck	PROPN
ejpam-7055	59	11	/	/	SYM
ejpam-7055	59	12	bci	bci	NOUN
ejpam-7055	59	13	-	-	PUNCT
ejpam-7055	59	14	algebra	algebra	NOUN
ejpam-7055	59	15	”	"	PUNCT
ejpam-7055	59	16	x̃	x̃	PROPN
ejpam-7055	59	17	is	be	AUX
ejpam-7055	59	18	termed	term	VERB
ejpam-7055	59	19	a	a	DET
ejpam-7055	59	20	”	"	PUNCT
ejpam-7055	59	21	fuzzy	fuzzy	ADJ
ejpam-7055	59	22	bck	bck	NOUN
ejpam-7055	59	23	/	/	SYM
ejpam-7055	59	24	bci	bci	NOUN
ejpam-7055	59	25	-	-	PUNCT
ejpam-7055	59	26	algebra	algebra	NOUN
ejpam-7055	59	27	”	"	PUNCT
ejpam-7055	59	28	if	if	SCONJ
ejpam-7055	59	29	it	it	PRON
ejpam-7055	59	30	satisfies	satisfy	VERB
ejpam-7055	59	31	the	the	DET
ejpam-7055	59	32	condition	condition	NOUN
ejpam-7055	59	33	:	:	PUNCT
ejpam-7055	59	34	(	(	PUNCT
ejpam-7055	59	35	∀ϖ	∀ϖ	ADJ
ejpam-7055	59	36	,	,	PUNCT
ejpam-7055	59	37	ϱ	ϱ	ADP
ejpam-7055	59	38	∈	∈	PROPN
ejpam-7055	59	39	x̃	x̃	PROPN
ejpam-7055	59	40	)	)	PUNCT
ejpam-7055	60	1	“	"	PUNCT
ejpam-7055	60	2	(	(	PUNCT
ejpam-7055	60	3	µ(ϖ	µ(ϖ	NOUN
ejpam-7055	60	4	∗	∗	VERB
ejpam-7055	60	5	ϱ	ϱ	ADP
ejpam-7055	60	6	)	)	PUNCT
ejpam-7055	60	7	≥	≥	NOUN
ejpam-7055	60	8	min{µ(ϖ	min{µ(ϖ	PROPN
ejpam-7055	60	9	)	)	PUNCT
ejpam-7055	60	10	,	,	PUNCT
ejpam-7055	60	11	µ(ϱ	µ(ϱ	PROPN
ejpam-7055	60	12	)	)	PUNCT
ejpam-7055	60	13	}	}	PUNCT
ejpam-7055	60	14	)	)	PUNCT
ejpam-7055	60	15	”	"	PUNCT
ejpam-7055	60	16	.	.	PUNCT
ejpam-7055	61	1	molodtsov	molodtsov	PROPN
ejpam-7055	61	2	defined	define	VERB
ejpam-7055	61	3	a	a	DET
ejpam-7055	61	4	soft	soft	ADJ
ejpam-7055	61	5	set	set	NOUN
ejpam-7055	61	6	as	as	SCONJ
ejpam-7055	61	7	follows	follow	VERB
ejpam-7055	61	8	:	:	PUNCT
ejpam-7055	61	9	consider	consider	VERB
ejpam-7055	61	10	an	an	DET
ejpam-7055	61	11	initial	initial	ADJ
ejpam-7055	61	12	universe	universe	NOUN
ejpam-7055	61	13	set	set	VERB
ejpam-7055	61	14	u	u	NOUN
ejpam-7055	61	15	and	and	CCONJ
ejpam-7055	61	16	a	a	DET
ejpam-7055	61	17	set	set	NOUN
ejpam-7055	61	18	of	of	ADP
ejpam-7055	61	19	parameters	parameter	NOUN
ejpam-7055	61	20	e	e	NOUN
ejpam-7055	61	21	,	,	PUNCT
ejpam-7055	61	22	where	where	SCONJ
ejpam-7055	61	23	p(u	p(u	NOUN
ejpam-7055	61	24	)	)	PUNCT
ejpam-7055	61	25	denotes	denote	VERB
ejpam-7055	61	26	the	the	DET
ejpam-7055	61	27	power	power	NOUN
ejpam-7055	61	28	set	set	NOUN
ejpam-7055	61	29	of	of	ADP
ejpam-7055	61	30	u	u	PROPN
ejpam-7055	61	31	and	and	CCONJ
ejpam-7055	62	1	ω	ω	PROPN
ejpam-7055	62	2	⊂	⊂	PROPN
ejpam-7055	62	3	e.	e.	PROPN
ejpam-7055	62	4	definition	definition	NOUN
ejpam-7055	62	5	1	1	NUM
ejpam-7055	62	6	(	(	PUNCT
ejpam-7055	62	7	[	[	X
ejpam-7055	62	8	5	5	NUM
ejpam-7055	62	9	]	]	NUM
ejpam-7055	62	10	)	)	PUNCT
ejpam-7055	62	11	.	.	PUNCT
ejpam-7055	63	1	a	a	DET
ejpam-7055	63	2	pair	pair	NOUN
ejpam-7055	63	3	(	(	PUNCT
ejpam-7055	63	4	ζ	ζ	NOUN
ejpam-7055	63	5	,	,	PUNCT
ejpam-7055	63	6	ω	ω	NOUN
ejpam-7055	63	7	)	)	PUNCT
ejpam-7055	63	8	is	be	AUX
ejpam-7055	63	9	termed	term	VERB
ejpam-7055	63	10	a	a	DET
ejpam-7055	63	11	soft	soft	ADJ
ejpam-7055	63	12	set	set	NOUN
ejpam-7055	63	13	over	over	ADP
ejpam-7055	63	14	u	u	NOUN
ejpam-7055	63	15	,	,	PUNCT
ejpam-7055	63	16	where	where	SCONJ
ejpam-7055	63	17	ζ	ζ	NOUN
ejpam-7055	63	18	is	be	AUX
ejpam-7055	63	19	a	a	DET
ejpam-7055	63	20	function	function	NOUN
ejpam-7055	63	21	defined	define	VERB
ejpam-7055	63	22	by	by	ADP
ejpam-7055	63	23	ζ	ζ	NOUN
ejpam-7055	63	24	:	:	PUNCT
ejpam-7055	63	25	ω	ω	PROPN
ejpam-7055	63	26	→	→	SYM
ejpam-7055	63	27	p(u	p(u	NOUN
ejpam-7055	63	28	)	)	PUNCT
ejpam-7055	63	29	.	.	PUNCT
ejpam-7055	64	1	for	for	ADP
ejpam-7055	64	2	further	further	ADJ
ejpam-7055	64	3	insights	insight	NOUN
ejpam-7055	64	4	,	,	PUNCT
ejpam-7055	64	5	molodtsov	molodtsov	PROPN
ejpam-7055	64	6	presented	present	VERB
ejpam-7055	64	7	“	"	PUNCT
ejpam-7055	64	8	many	many	ADJ
ejpam-7055	64	9	examples	example	NOUN
ejpam-7055	64	10	”	"	PUNCT
ejpam-7055	64	11	in	in	ADP
ejpam-7055	64	12	[	[	X
ejpam-7055	64	13	5	5	NUM
ejpam-7055	64	14	]	]	PUNCT
ejpam-7055	64	15	.	.	PUNCT
ejpam-7055	65	1	definition	definition	NOUN
ejpam-7055	65	2	2	2	NUM
ejpam-7055	65	3	.	.	PUNCT
ejpam-7055	66	1	[	[	X
ejpam-7055	66	2	33	33	NUM
ejpam-7055	66	3	]	]	PUNCT
ejpam-7055	66	4	let	let	VERB
ejpam-7055	66	5	x̃	x̃	PROPN
ejpam-7055	66	6	be	be	AUX
ejpam-7055	66	7	a	a	DET
ejpam-7055	66	8	bck	bck	VERB
ejpam-7055	66	9	/	/	SYM
ejpam-7055	66	10	bci	bci	NOUN
ejpam-7055	66	11	-	-	NOUN
ejpam-7055	66	12	algebra	algebra	NOUN
ejpam-7055	66	13	.	.	PUNCT
ejpam-7055	67	1	let	let	VERB
ejpam-7055	67	2	(	(	PUNCT
ejpam-7055	67	3	ζ	ζ	NOUN
ejpam-7055	67	4	,	,	PUNCT
ejpam-7055	67	5	ω	ω	NOUN
ejpam-7055	67	6	)	)	PUNCT
ejpam-7055	67	7	be	be	AUX
ejpam-7055	67	8	called	call	VERB
ejpam-7055	67	9	a	a	DET
ejpam-7055	67	10	soft	soft	ADJ
ejpam-7055	67	11	bck	bck	NOUN
ejpam-7055	67	12	/	/	SYM
ejpam-7055	67	13	bcialgebra	bcialgebra	NOUN
ejpam-7055	67	14	over	over	ADP
ejpam-7055	67	15	x̃	x̃	PROPN
ejpam-7055	67	16	if	if	SCONJ
ejpam-7055	67	17	ζ(ϖ	ζ(ϖ	NOUN
ejpam-7055	67	18	)	)	PUNCT
ejpam-7055	67	19	is	be	AUX
ejpam-7055	67	20	a	a	DET
ejpam-7055	67	21	bck	bck	VERB
ejpam-7055	67	22	/	/	SYM
ejpam-7055	67	23	bci	bci	PROPN
ejpam-7055	67	24	sub	sub	NOUN
ejpam-7055	67	25	-	-	NOUN
ejpam-7055	67	26	algebra	algebra	NOUN
ejpam-7055	67	27	over	over	ADP
ejpam-7055	67	28	x̃	x̃	PROPN
ejpam-7055	67	29	,	,	PUNCT
ejpam-7055	67	30	∀ϖ	∀ϖ	PROPN
ejpam-7055	67	31	∈	∈	PROPN
ejpam-7055	67	32	ω	ω	NOUN
ejpam-7055	67	33	.	.	PUNCT
ejpam-7055	68	1	ζ	ζ	NOUN
ejpam-7055	68	2	:	:	PUNCT
ejpam-7055	68	3	ω	ω	PROPN
ejpam-7055	68	4	→	→	SYM
ejpam-7055	68	5	p	p	X
ejpam-7055	68	6	(	(	PUNCT
ejpam-7055	68	7	ϖ	ϖ	NOUN
ejpam-7055	68	8	)	)	PUNCT
ejpam-7055	68	9	and	and	CCONJ
ejpam-7055	68	10	ϖ	ϖ	PRON
ejpam-7055	68	11	7→	7→	NUM
ejpam-7055	68	12	ζ(ϖ	ζ(ϖ	NOUN
ejpam-7055	68	13	)	)	PUNCT
ejpam-7055	68	14	,	,	PUNCT
ejpam-7055	68	15	therefore	therefore	ADV
ejpam-7055	68	16	ζ(ϖ	ζ(ϖ	NOUN
ejpam-7055	68	17	)	)	PUNCT
ejpam-7055	68	18	is	be	AUX
ejpam-7055	68	19	bck	bck	PROPN
ejpam-7055	68	20	/	/	SYM
ejpam-7055	68	21	bci	bci	PROPN
ejpam-7055	68	22	sub	sub	NOUN
ejpam-7055	68	23	-	-	NOUN
ejpam-7055	68	24	algebra	algebra	ADJ
ejpam-7055	68	25	.	.	PUNCT
ejpam-7055	69	1	example	example	NOUN
ejpam-7055	70	1	1	1	NUM
ejpam-7055	70	2	.	.	PUNCT
ejpam-7055	71	1	[	[	X
ejpam-7055	71	2	33	33	NUM
ejpam-7055	71	3	]	]	PUNCT
ejpam-7055	71	4	let	let	VERB
ejpam-7055	71	5	“	"	PUNCT
ejpam-7055	71	6	x̃	x̃	PROPN
ejpam-7055	71	7	=	=	PUNCT
ejpam-7055	71	8	{	{	PUNCT
ejpam-7055	71	9	0	0	NUM
ejpam-7055	71	10	,	,	PUNCT
ejpam-7055	71	11	α	α	X
ejpam-7055	71	12	,	,	PUNCT
ejpam-7055	71	13	β	β	X
ejpam-7055	71	14	,	,	PUNCT
ejpam-7055	71	15	γ	γ	PROPN
ejpam-7055	71	16	,	,	PUNCT
ejpam-7055	71	17	δ	δ	PROPN
ejpam-7055	71	18	}	}	PUNCT
ejpam-7055	71	19	be	be	AUX
ejpam-7055	71	20	a	a	DET
ejpam-7055	71	21	bck	bck	NOUN
ejpam-7055	71	22	-	-	PUNCT
ejpam-7055	71	23	algebra	algebra	NOUN
ejpam-7055	71	24	with	with	ADP
ejpam-7055	71	25	the	the	DET
ejpam-7055	71	26	following	follow	VERB
ejpam-7055	71	27	cayley	cayley	ADJ
ejpam-7055	71	28	table	table	NOUN
ejpam-7055	71	29	”	"	PUNCT
ejpam-7055	71	30	:	:	PUNCT
ejpam-7055	71	31	let	let	VERB
ejpam-7055	71	32	(	(	PUNCT
ejpam-7055	71	33	ζ	ζ	NOUN
ejpam-7055	71	34	,	,	PUNCT
ejpam-7055	71	35	ω	ω	NOUN
ejpam-7055	71	36	)	)	PUNCT
ejpam-7055	71	37	be	be	AUX
ejpam-7055	71	38	soft	soft	ADJ
ejpam-7055	71	39	set	set	NOUN
ejpam-7055	71	40	over	over	ADP
ejpam-7055	71	41	x̃	x̃	PROPN
ejpam-7055	71	42	where	where	SCONJ
ejpam-7055	71	43	ω	ω	PROPN
ejpam-7055	71	44	=	=	SYM
ejpam-7055	71	45	x̃	x̃	PROPN
ejpam-7055	71	46	and	and	CCONJ
ejpam-7055	71	47	ζ	ζ	NOUN
ejpam-7055	71	48	:	:	PUNCT
ejpam-7055	71	49	ω	ω	PROPN
ejpam-7055	71	50	→	→	SYM
ejpam-7055	71	51	p	p	X
ejpam-7055	71	52	(	(	PUNCT
ejpam-7055	71	53	x̃	x̃	PROPN
ejpam-7055	71	54	)	)	PUNCT
ejpam-7055	71	55	is	be	AUX
ejpam-7055	71	56	a	a	DET
ejpam-7055	71	57	set	set	NOUN
ejpam-7055	71	58	-	-	PUNCT
ejpam-7055	71	59	valued	value	VERB
ejpam-7055	71	60	function	function	NOUN
ejpam-7055	71	61	defined	define	VERB
ejpam-7055	71	62	by	by	ADP
ejpam-7055	71	63	,	,	PUNCT
ejpam-7055	71	64	“	"	PUNCT
ejpam-7055	71	65	ζ(ϖ	ζ(ϖ	NOUN
ejpam-7055	71	66	)	)	PUNCT
ejpam-7055	71	67	=	=	SYM
ejpam-7055	71	68	{	{	PUNCT
ejpam-7055	71	69	ϱ	ϱ	X
ejpam-7055	71	70	∈	∈	PROPN
ejpam-7055	71	71	x̃	x̃	PROPN
ejpam-7055	71	72	:	:	PUNCT
ejpam-7055	71	73	ϖrϱ	ϖrϱ	PROPN
ejpam-7055	71	74	⇔	⇔	PROPN
ejpam-7055	71	75	ϱ	ϱ	ADP
ejpam-7055	71	76	∈	∈	PROPN
ejpam-7055	71	77	ϖ−1i	ϖ−1i	NOUN
ejpam-7055	71	78	}	}	PUNCT
ejpam-7055	71	79	”	"	PUNCT
ejpam-7055	71	80	for	for	ADP
ejpam-7055	71	81	all	all	PRON
ejpam-7055	71	82	ϖ	ϖ	PROPN
ejpam-7055	71	83	∈	∈	PROPN
ejpam-7055	71	84	ω	ω	NOUN
ejpam-7055	71	85	“	"	PUNCT
ejpam-7055	71	86	where	where	SCONJ
ejpam-7055	71	87	i	i	PRON
ejpam-7055	71	88	=	=	PUNCT
ejpam-7055	71	89	{	{	PUNCT
ejpam-7055	71	90	0	0	NUM
ejpam-7055	71	91	,	,	PUNCT
ejpam-7055	71	92	α	α	NOUN
ejpam-7055	71	93	}	}	PUNCT
ejpam-7055	71	94	and	and	CCONJ
ejpam-7055	71	95	ϖ−1	ϖ−1	PROPN
ejpam-7055	71	96	=	=	PUNCT
ejpam-7055	71	97	{	{	PUNCT
ejpam-7055	71	98	ϱ	ϱ	X
ejpam-7055	71	99	∈	∈	PROPN
ejpam-7055	71	100	x̃	x̃	PROPN
ejpam-7055	71	101	:	:	PUNCT
ejpam-7055	71	102	ϖ	ϖ	PUNCT
ejpam-7055	71	103	∧	∧	NOUN
ejpam-7055	71	104	ϱ	ϱ	ADP
ejpam-7055	71	105	∈	∈	PROPN
ejpam-7055	71	106	i	i	NOUN
ejpam-7055	71	107	}	}	PUNCT
ejpam-7055	71	108	”	"	PUNCT
ejpam-7055	71	109	g.	g.	PROPN
ejpam-7055	71	110	muhiuddin	muhiuddin	PROPN
ejpam-7055	71	111	et	et	PROPN
ejpam-7055	71	112	al	al	PROPN
ejpam-7055	71	113	.	.	PUNCT
ejpam-7055	71	114	/	/	SYM
ejpam-7055	71	115	eur	eur	PROPN
ejpam-7055	71	116	.	.	PUNCT
ejpam-7055	72	1	j.	j.	PROPN
ejpam-7055	72	2	pure	pure	PROPN
ejpam-7055	72	3	appl	appl	PROPN
ejpam-7055	72	4	.	.	PROPN
ejpam-7055	72	5	math	math	PROPN
ejpam-7055	72	6	,	,	PUNCT
ejpam-7055	72	7	18	18	NUM
ejpam-7055	72	8	(	(	PUNCT
ejpam-7055	72	9	4	4	NUM
ejpam-7055	72	10	)	)	PUNCT
ejpam-7055	72	11	(	(	PUNCT
ejpam-7055	72	12	2025	2025	NUM
ejpam-7055	72	13	)	)	PUNCT
ejpam-7055	72	14	,	,	PUNCT
ejpam-7055	72	15	7055	7055	NUM
ejpam-7055	72	16	4	4	NUM
ejpam-7055	72	17	of	of	ADP
ejpam-7055	72	18	13	13	NUM
ejpam-7055	72	19	∗	∗	NOUN
ejpam-7055	72	20	0	0	NUM
ejpam-7055	73	1	α	α	NOUN
ejpam-7055	73	2	β	β	X
ejpam-7055	73	3	γ	γ	X
ejpam-7055	73	4	δ	δ	PROPN
ejpam-7055	73	5	0	0	NUM
ejpam-7055	73	6	0	0	NUM
ejpam-7055	73	7	0	0	NUM
ejpam-7055	73	8	0	0	NUM
ejpam-7055	73	9	0	0	NUM
ejpam-7055	73	10	0	0	NUM
ejpam-7055	74	1	α	α	NOUN
ejpam-7055	74	2	α	α	NOUN
ejpam-7055	74	3	0	0	PUNCT
ejpam-7055	75	1	α	α	NOUN
ejpam-7055	75	2	α	α	NOUN
ejpam-7055	75	3	α	α	NOUN
ejpam-7055	75	4	β	β	X
ejpam-7055	75	5	β	β	X
ejpam-7055	75	6	β	β	NOUN
ejpam-7055	75	7	0	0	PUNCT
ejpam-7055	75	8	β	β	X
ejpam-7055	75	9	β	β	X
ejpam-7055	75	10	γ	γ	X
ejpam-7055	75	11	γ	γ	X
ejpam-7055	75	12	γ	γ	X
ejpam-7055	75	13	γ	γ	X
ejpam-7055	75	14	0	0	NUM
ejpam-7055	75	15	γ	γ	PROPN
ejpam-7055	75	16	δ	δ	PROPN
ejpam-7055	75	17	δ	δ	PROPN
ejpam-7055	75	18	δ	δ	PROPN
ejpam-7055	75	19	δ	δ	PROPN
ejpam-7055	75	20	δ	δ	PROPN
ejpam-7055	75	21	0	0	NUM
ejpam-7055	76	1	we	we	PRON
ejpam-7055	76	2	have	have	VERB
ejpam-7055	76	3	ζ(0	ζ(0	NOUN
ejpam-7055	76	4	)	)	PUNCT
ejpam-7055	76	5	=	=	SYM
ejpam-7055	76	6	ζ(α	ζ(α	NOUN
ejpam-7055	76	7	)	)	PUNCT
ejpam-7055	77	1	=	=	SYM
ejpam-7055	77	2	x̃	x̃	PROPN
ejpam-7055	77	3	,	,	PUNCT
ejpam-7055	77	4	ζ(β	ζ(β	PROPN
ejpam-7055	77	5	)	)	PUNCT
ejpam-7055	77	6	=	=	PUNCT
ejpam-7055	77	7	{	{	PUNCT
ejpam-7055	77	8	0	0	NUM
ejpam-7055	77	9	,	,	PUNCT
ejpam-7055	77	10	α	α	X
ejpam-7055	77	11	,	,	PUNCT
ejpam-7055	77	12	β	β	X
ejpam-7055	77	13	,	,	PUNCT
ejpam-7055	77	14	δ	δ	PROPN
ejpam-7055	77	15	}	}	PUNCT
ejpam-7055	77	16	,	,	PUNCT
ejpam-7055	77	17	ζ(δ	ζ(δ	NUM
ejpam-7055	77	18	)	)	PUNCT
ejpam-7055	77	19	=	=	PRON
ejpam-7055	77	20	{	{	PUNCT
ejpam-7055	77	21	0	0	NUM
ejpam-7055	77	22	,	,	PUNCT
ejpam-7055	77	23	α	α	X
ejpam-7055	77	24	,	,	PUNCT
ejpam-7055	77	25	β	β	X
ejpam-7055	77	26	,	,	PUNCT
ejpam-7055	77	27	δ	δ	PROPN
ejpam-7055	77	28	}	}	PUNCT
ejpam-7055	77	29	and	and	CCONJ
ejpam-7055	77	30	ζ(δ	ζ(δ	NUM
ejpam-7055	77	31	)	)	PUNCT
ejpam-7055	77	32	=	=	PRON
ejpam-7055	77	33	{	{	PUNCT
ejpam-7055	77	34	0	0	NUM
ejpam-7055	77	35	,	,	PUNCT
ejpam-7055	77	36	α	α	X
ejpam-7055	77	37	,	,	PUNCT
ejpam-7055	77	38	β	β	X
ejpam-7055	77	39	,	,	PUNCT
ejpam-7055	77	40	δ	δ	PROPN
ejpam-7055	77	41	}	}	PUNCT
ejpam-7055	77	42	are	be	AUX
ejpam-7055	77	43	bck	bck	NOUN
ejpam-7055	77	44	-	-	PUNCT
ejpam-7055	77	45	subalgebras	subalgebras	PROPN
ejpam-7055	77	46	of	of	ADP
ejpam-7055	77	47	x̃	x̃	PROPN
ejpam-7055	77	48	.	.	PUNCT
ejpam-7055	78	1	“	"	PUNCT
ejpam-7055	78	2	therefore	therefore	ADV
ejpam-7055	78	3	(	(	PUNCT
ejpam-7055	78	4	ζ	ζ	NOUN
ejpam-7055	78	5	,	,	PUNCT
ejpam-7055	78	6	ω	ω	NOUN
ejpam-7055	78	7	)	)	PUNCT
ejpam-7055	78	8	is	be	AUX
ejpam-7055	78	9	a	a	DET
ejpam-7055	78	10	soft	soft	ADJ
ejpam-7055	78	11	bck	bck	NOUN
ejpam-7055	78	12	-	-	PUNCT
ejpam-7055	78	13	algebra	algebra	NOUN
ejpam-7055	78	14	over	over	ADP
ejpam-7055	78	15	x̃	x̃	PROPN
ejpam-7055	78	16	”	"	PUNCT
ejpam-7055	78	17	.	.	PUNCT
ejpam-7055	79	1	definition	definition	NOUN
ejpam-7055	79	2	3	3	NUM
ejpam-7055	79	3	.	.	PUNCT
ejpam-7055	80	1	[	[	X
ejpam-7055	80	2	33	33	NUM
ejpam-7055	80	3	]	]	PUNCT
ejpam-7055	80	4	let	let	VERB
ejpam-7055	80	5	“	"	PUNCT
ejpam-7055	80	6	(	(	PUNCT
ejpam-7055	80	7	ζ	ζ	NOUN
ejpam-7055	80	8	,	,	PUNCT
ejpam-7055	80	9	ω	ω	NOUN
ejpam-7055	80	10	)	)	PUNCT
ejpam-7055	80	11	and	and	CCONJ
ejpam-7055	80	12	(	(	PUNCT
ejpam-7055	80	13	ϕ,b	ϕ,b	NOUN
ejpam-7055	80	14	)	)	PUNCT
ejpam-7055	80	15	be	be	VERB
ejpam-7055	80	16	two	two	NUM
ejpam-7055	80	17	soft	soft	ADJ
ejpam-7055	80	18	bck	bck	NOUN
ejpam-7055	80	19	/	/	SYM
ejpam-7055	80	20	bci	bci	NOUN
ejpam-7055	80	21	-	-	PUNCT
ejpam-7055	80	22	algebras	algebra	NOUN
ejpam-7055	80	23	over	over	ADP
ejpam-7055	80	24	x̃	x̃	PROPN
ejpam-7055	80	25	”	"	PUNCT
ejpam-7055	80	26	.	.	PUNCT
ejpam-7055	81	1	then	then	ADV
ejpam-7055	81	2	the	the	DET
ejpam-7055	81	3	bck	bck	PROPN
ejpam-7055	81	4	/	/	SYM
ejpam-7055	81	5	bci	bci	NOUN
ejpam-7055	81	6	-	-	ADJ
ejpam-7055	81	7	homomorphism	homomorphism	NOUN
ejpam-7055	81	8	µ	µ	X
ejpam-7055	81	9	:	:	PUNCT
ejpam-7055	81	10	ω	ω	PROPN
ejpam-7055	81	11	→	→	SYM
ejpam-7055	81	12	b	b	PROPN
ejpam-7055	81	13	is	be	AUX
ejpam-7055	81	14	“	"	PUNCT
ejpam-7055	81	15	called	call	VERB
ejpam-7055	81	16	”	"	PUNCT
ejpam-7055	81	17	a	a	DET
ejpam-7055	81	18	soft	soft	ADJ
ejpam-7055	81	19	bck	bck	NOUN
ejpam-7055	81	20	/	/	SYM
ejpam-7055	81	21	bci	bci	NOUN
ejpam-7055	81	22	-	-	PUNCT
ejpam-7055	81	23	homomorphism	homomorphism	NOUN
ejpam-7055	81	24	”	"	PUNCT
ejpam-7055	81	25	if	if	SCONJ
ejpam-7055	81	26	ζ(α	ζ(α	NOUN
ejpam-7055	81	27	)	)	PUNCT
ejpam-7055	81	28	⊆	⊆	NUM
ejpam-7055	81	29	(	(	PUNCT
ejpam-7055	81	30	ϕ	ϕ	NOUN
ejpam-7055	81	31	◦	◦	NOUN
ejpam-7055	81	32	µ)(α	µ)(α	NOUN
ejpam-7055	81	33	)	)	PUNCT
ejpam-7055	81	34	,	,	PUNCT
ejpam-7055	81	35	∀α	∀α	VERB
ejpam-7055	81	36	∈	∈	PROPN
ejpam-7055	81	37	ω	ω	PROPN
ejpam-7055	81	38	.	.	PUNCT
ejpam-7055	81	39	figure	figure	NOUN
ejpam-7055	81	40	1	1	NUM
ejpam-7055	81	41	:	:	PUNCT
ejpam-7055	81	42	i.e.	i.e.	X
ejpam-7055	81	43	ζ(α	ζ(α	NOUN
ejpam-7055	81	44	)	)	PUNCT
ejpam-7055	82	1	⊆	⊆	NUM
ejpam-7055	82	2	(	(	PUNCT
ejpam-7055	82	3	ϕ	ϕ	NOUN
ejpam-7055	82	4	◦	◦	NOUN
ejpam-7055	82	5	µ)(α	µ)(α	NOUN
ejpam-7055	82	6	)	)	PUNCT
ejpam-7055	82	7	=	=	SYM
ejpam-7055	82	8	ϕ(µ(α	ϕ(µ(α	PROPN
ejpam-7055	82	9	)	)	PUNCT
ejpam-7055	82	10	,	,	PUNCT
ejpam-7055	82	11	∀α	∀α	VERB
ejpam-7055	82	12	∈	∈	PROPN
ejpam-7055	82	13	ω	ω	NOUN
ejpam-7055	82	14	.	.	PROPN
ejpam-7055	83	1	5	5	NUM
ejpam-7055	83	2	.	.	X
ejpam-7055	83	3	category	category	NOUN
ejpam-7055	83	4	of	of	ADP
ejpam-7055	83	5	soft	soft	ADJ
ejpam-7055	83	6	bci	bci	NOUN
ejpam-7055	83	7	/	/	SYM
ejpam-7055	83	8	bck	bck	NOUN
ejpam-7055	83	9	-	-	PUNCT
ejpam-7055	83	10	algebra	algebra	NOUN
ejpam-7055	83	11	definition	definition	NOUN
ejpam-7055	83	12	4	4	NUM
ejpam-7055	83	13	.	.	PUNCT
ejpam-7055	83	14	to	to	PART
ejpam-7055	83	15	form	form	VERB
ejpam-7055	83	16	a	a	DET
ejpam-7055	83	17	category	category	NOUN
ejpam-7055	83	18	,	,	PUNCT
ejpam-7055	83	19	we	we	PRON
ejpam-7055	83	20	need	need	VERB
ejpam-7055	83	21	a	a	DET
ejpam-7055	83	22	class	class	NOUN
ejpam-7055	83	23	of	of	ADP
ejpam-7055	83	24	objects	object	NOUN
ejpam-7055	83	25	:	:	PUNCT
ejpam-7055	83	26	“	"	PUNCT
ejpam-7055	83	27	soft	soft	ADJ
ejpam-7055	83	28	bck	bck	NOUN
ejpam-7055	83	29	/	/	SYM
ejpam-7055	83	30	bci	bci	NOUN
ejpam-7055	83	31	-	-	PUNCT
ejpam-7055	83	32	algebras	algebra	NOUN
ejpam-7055	83	33	and	and	CCONJ
ejpam-7055	83	34	a	a	DET
ejpam-7055	83	35	class	class	NOUN
ejpam-7055	83	36	of	of	ADP
ejpam-7055	83	37	morphisms	morphism	NOUN
ejpam-7055	83	38	:	:	PUNCT
ejpam-7055	83	39	soft	soft	ADJ
ejpam-7055	83	40	bckhomomorphisms	bckhomomorphism	NOUN
ejpam-7055	83	41	”	"	PUNCT
ejpam-7055	83	42	.	.	PUNCT
ejpam-7055	84	1	(	(	PUNCT
ejpam-7055	84	2	i	i	NOUN
ejpam-7055	84	3	)	)	PUNCT
ejpam-7055	84	4	composition	composition	NOUN
ejpam-7055	84	5	of	of	ADP
ejpam-7055	84	6	maps	map	NOUN
ejpam-7055	84	7	.	.	PUNCT
ejpam-7055	85	1	(	(	PUNCT
ejpam-7055	85	2	ii	ii	NOUN
ejpam-7055	85	3	)	)	PUNCT
ejpam-7055	85	4	identity	identity	NOUN
ejpam-7055	85	5	.	.	PUNCT
ejpam-7055	86	1	proposition	proposition	NOUN
ejpam-7055	86	2	1	1	NUM
ejpam-7055	86	3	.	.	PUNCT
ejpam-7055	87	1	(	(	PUNCT
ejpam-7055	87	2	composition	composition	NOUN
ejpam-7055	87	3	of	of	ADP
ejpam-7055	87	4	soft	soft	ADJ
ejpam-7055	87	5	-	-	PUNCT
ejpam-7055	87	6	bck	bck	NOUN
ejpam-7055	87	7	/	/	SYM
ejpam-7055	87	8	bci	bci	NOUN
ejpam-7055	87	9	-	-	PUNCT
ejpam-7055	87	10	homomorphisms	homomorphism	NOUN
ejpam-7055	87	11	is	be	AUX
ejpam-7055	87	12	again	again	ADV
ejpam-7055	87	13	a	a	DET
ejpam-7055	87	14	soft	soft	ADJ
ejpam-7055	87	15	bck	bck	NOUN
ejpam-7055	87	16	/	/	SYM
ejpam-7055	87	17	bcihomomorphism	bcihomomorphism	NOUN
ejpam-7055	87	18	)	)	PUNCT
ejpam-7055	87	19	.	.	PUNCT
ejpam-7055	88	1	let	let	VERB
ejpam-7055	88	2	(	(	PUNCT
ejpam-7055	88	3	ζ	ζ	NOUN
ejpam-7055	88	4	,	,	PUNCT
ejpam-7055	88	5	ω),(ϕ,b	ω),(ϕ,b	NUM
ejpam-7055	88	6	)	)	PUNCT
ejpam-7055	88	7	and	and	CCONJ
ejpam-7055	88	8	(	(	PUNCT
ejpam-7055	88	9	φ,ℵ	φ,ℵ	NOUN
ejpam-7055	88	10	)	)	PUNCT
ejpam-7055	88	11	be	be	VERB
ejpam-7055	88	12	any	any	DET
ejpam-7055	88	13	three	three	NUM
ejpam-7055	88	14	bck	bck	NOUN
ejpam-7055	88	15	/	/	SYM
ejpam-7055	88	16	bci	bci	NOUN
ejpam-7055	88	17	-	-	PUNCT
ejpam-7055	88	18	algebras	algebras	X
ejpam-7055	88	19	.	.	PUNCT
ejpam-7055	89	1	let	let	VERB
ejpam-7055	89	2	µ	µ	X
ejpam-7055	89	3	:	:	PUNCT
ejpam-7055	89	4	ω	ω	PROPN
ejpam-7055	89	5	→	→	SYM
ejpam-7055	89	6	b	b	PROPN
ejpam-7055	89	7	and	and	CCONJ
ejpam-7055	89	8	ℏ	ℏ	PROPN
ejpam-7055	89	9	:	:	PUNCT
ejpam-7055	89	10	b	b	X
ejpam-7055	89	11	→	→	SYM
ejpam-7055	89	12	ℵ	ℵ	X
ejpam-7055	89	13	be	be	VERB
ejpam-7055	89	14	two	two	NUM
ejpam-7055	89	15	soft	soft	ADJ
ejpam-7055	89	16	bck	bck	NOUN
ejpam-7055	89	17	/	/	SYM
ejpam-7055	89	18	bci	bci	NOUN
ejpam-7055	89	19	-	-	PUNCT
ejpam-7055	89	20	homomorphisms	homomorphism	NOUN
ejpam-7055	89	21	.	.	PUNCT
ejpam-7055	90	1	then	then	ADV
ejpam-7055	90	2	ℏ	ℏ	PROPN
ejpam-7055	90	3	◦	◦	NOUN
ejpam-7055	90	4	µ	µ	X
ejpam-7055	90	5	:	:	PUNCT
ejpam-7055	90	6	ω	ω	NOUN
ejpam-7055	90	7	→	→	SYM
ejpam-7055	90	8	ℵ	ℵ	NOUN
ejpam-7055	90	9	is	be	AUX
ejpam-7055	90	10	again	again	ADV
ejpam-7055	90	11	a	a	DET
ejpam-7055	90	12	“	"	PUNCT
ejpam-7055	90	13	soft	soft	ADJ
ejpam-7055	90	14	bck	bck	NOUN
ejpam-7055	90	15	/	/	SYM
ejpam-7055	90	16	bci	bci	NOUN
ejpam-7055	90	17	-	-	PUNCT
ejpam-7055	90	18	homomorphism	homomorphism	NOUN
ejpam-7055	90	19	”	"	PUNCT
ejpam-7055	90	20	.	.	PUNCT
ejpam-7055	91	1	proof	proof	NOUN
ejpam-7055	91	2	.	.	PUNCT
ejpam-7055	92	1	let	let	VERB
ejpam-7055	92	2	µ	µ	X
ejpam-7055	92	3	:	:	PUNCT
ejpam-7055	92	4	ω	ω	PROPN
ejpam-7055	92	5	→	→	SYM
ejpam-7055	92	6	b	b	PROPN
ejpam-7055	92	7	and	and	CCONJ
ejpam-7055	92	8	ℏ	ℏ	PROPN
ejpam-7055	92	9	:	:	PUNCT
ejpam-7055	92	10	b	b	X
ejpam-7055	92	11	→	→	SYM
ejpam-7055	92	12	ℵ	ℵ	X
ejpam-7055	92	13	be	be	VERB
ejpam-7055	92	14	two	two	NUM
ejpam-7055	92	15	soft	soft	ADJ
ejpam-7055	92	16	bck	bck	NOUN
ejpam-7055	92	17	/	/	SYM
ejpam-7055	92	18	bci	bci	NOUN
ejpam-7055	92	19	-	-	PUNCT
ejpam-7055	92	20	homomorphisms	homomorphism	NOUN
ejpam-7055	92	21	.	.	PUNCT
ejpam-7055	93	1	then	then	ADV
ejpam-7055	93	2	by	by	ADP
ejpam-7055	93	3	definition	definition	NOUN
ejpam-7055	93	4	,	,	PUNCT
ejpam-7055	93	5	we	we	PRON
ejpam-7055	93	6	have	have	VERB
ejpam-7055	93	7	,	,	PUNCT
ejpam-7055	93	8	ζ(α	ζ(α	PROPN
ejpam-7055	93	9	)	)	PUNCT
ejpam-7055	94	1	⊆	⊆	NUM
ejpam-7055	94	2	(	(	PUNCT
ejpam-7055	94	3	ϕ	ϕ	NOUN
ejpam-7055	94	4	◦	◦	NOUN
ejpam-7055	94	5	µ)(α	µ)(α	NOUN
ejpam-7055	94	6	)	)	PUNCT
ejpam-7055	94	7	,	,	PUNCT
ejpam-7055	94	8	∀α	∀α	VERB
ejpam-7055	94	9	∈	∈	PROPN
ejpam-7055	94	10	ω	ω	NOUN
ejpam-7055	94	11	and	and	CCONJ
ejpam-7055	94	12	ϕ(β	ϕ(β	PROPN
ejpam-7055	94	13	)	)	PUNCT
ejpam-7055	95	1	⊆	⊆	NUM
ejpam-7055	95	2	(	(	PUNCT
ejpam-7055	95	3	φ	φ	NUM
ejpam-7055	95	4	◦	◦	NOUN
ejpam-7055	95	5	ℏ)(β	ℏ)(β	NOUN
ejpam-7055	95	6	)	)	PUNCT
ejpam-7055	95	7	,	,	PUNCT
ejpam-7055	95	8	∀β	∀β	PROPN
ejpam-7055	95	9	∈	∈	PROPN
ejpam-7055	95	10	b.	b.	PROPN
ejpam-7055	95	11	g.	g.	PROPN
ejpam-7055	95	12	muhiuddin	muhiuddin	PROPN
ejpam-7055	95	13	et	et	PROPN
ejpam-7055	95	14	al	al	PROPN
ejpam-7055	95	15	.	.	PUNCT
ejpam-7055	95	16	/	/	SYM
ejpam-7055	95	17	eur	eur	PROPN
ejpam-7055	95	18	.	.	PUNCT
ejpam-7055	96	1	j.	j.	PROPN
ejpam-7055	96	2	pure	pure	PROPN
ejpam-7055	96	3	appl	appl	PROPN
ejpam-7055	96	4	.	.	PROPN
ejpam-7055	96	5	math	math	PROPN
ejpam-7055	96	6	,	,	PUNCT
ejpam-7055	96	7	18	18	NUM
ejpam-7055	96	8	(	(	PUNCT
ejpam-7055	96	9	4	4	NUM
ejpam-7055	96	10	)	)	PUNCT
ejpam-7055	96	11	(	(	PUNCT
ejpam-7055	96	12	2025	2025	NUM
ejpam-7055	96	13	)	)	PUNCT
ejpam-7055	96	14	,	,	PUNCT
ejpam-7055	96	15	7055	7055	NUM
ejpam-7055	96	16	5	5	NUM
ejpam-7055	96	17	of	of	ADP
ejpam-7055	96	18	13	13	NUM
ejpam-7055	96	19	figure	figure	NOUN
ejpam-7055	96	20	2	2	NUM
ejpam-7055	96	21	:	:	PUNCT
ejpam-7055	96	22	to	to	PART
ejpam-7055	96	23	show	show	VERB
ejpam-7055	96	24	that	that	SCONJ
ejpam-7055	96	25	ℏ	ℏ	PROPN
ejpam-7055	96	26	◦	◦	NOUN
ejpam-7055	96	27	µ	µ	PRON
ejpam-7055	96	28	is	be	AUX
ejpam-7055	96	29	a	a	DET
ejpam-7055	96	30	soft	soft	ADJ
ejpam-7055	96	31	bck	bck	NOUN
ejpam-7055	96	32	/	/	SYM
ejpam-7055	96	33	bci	bci	NOUN
ejpam-7055	96	34	-	-	PUNCT
ejpam-7055	96	35	homomorphism	homomorphism	NOUN
ejpam-7055	96	36	,	,	PUNCT
ejpam-7055	96	37	we	we	PRON
ejpam-7055	96	38	have	have	VERB
ejpam-7055	96	39	to	to	PART
ejpam-7055	96	40	prove	prove	VERB
ejpam-7055	96	41	“	"	PUNCT
ejpam-7055	96	42	ζ(α	ζ(α	PROPN
ejpam-7055	96	43	)	)	PUNCT
ejpam-7055	96	44	⊆	⊆	NUM
ejpam-7055	96	45	(	(	PUNCT
ejpam-7055	96	46	φ	φ	NUM
ejpam-7055	96	47	◦	◦	NOUN
ejpam-7055	96	48	(	(	PUNCT
ejpam-7055	96	49	ℏ	ℏ	NOUN
ejpam-7055	96	50	◦	◦	NOUN
ejpam-7055	96	51	µ)(α	µ)(α	NOUN
ejpam-7055	96	52	)	)	PUNCT
ejpam-7055	96	53	,	,	PUNCT
ejpam-7055	96	54	∀α	∀α	VERB
ejpam-7055	96	55	∈	∈	PROPN
ejpam-7055	96	56	ω	ω	NOUN
ejpam-7055	96	57	.	.	PUNCT
ejpam-7055	96	58	”	"	PUNCT
ejpam-7055	97	1	now	now	ADV
ejpam-7055	97	2	,	,	PUNCT
ejpam-7055	97	3	ζ(α	ζ(α	PROPN
ejpam-7055	97	4	)	)	PUNCT
ejpam-7055	97	5	⊆	⊆	NUM
ejpam-7055	97	6	(	(	PUNCT
ejpam-7055	97	7	ϕ	ϕ	NOUN
ejpam-7055	97	8	◦	◦	NOUN
ejpam-7055	97	9	µ)(α	µ)(α	NOUN
ejpam-7055	97	10	)	)	PUNCT
ejpam-7055	98	1	=	=	SYM
ejpam-7055	98	2	(	(	PUNCT
ejpam-7055	98	3	ϕ	ϕ	NOUN
ejpam-7055	98	4	◦	◦	NOUN
ejpam-7055	98	5	µ(α	µ(α	PROPN
ejpam-7055	98	6	)	)	PUNCT
ejpam-7055	98	7	)	)	PUNCT
ejpam-7055	99	1	=	=	PUNCT
ejpam-7055	99	2	(	(	PUNCT
ejpam-7055	99	3	ϕ(β))forsomeβ	ϕ(β))forsomeβ	PROPN
ejpam-7055	99	4	=	=	SYM
ejpam-7055	99	5	µ(α	µ(α	PROPN
ejpam-7055	99	6	)	)	PUNCT
ejpam-7055	99	7	∈	∈	PROPN
ejpam-7055	99	8	b.	b.	PROPN
ejpam-7055	100	1	⊆	⊆	NUM
ejpam-7055	100	2	ϕ(φ	ϕ(φ	PROPN
ejpam-7055	100	3	◦	◦	VERB
ejpam-7055	100	4	ℏ)(β	ℏ)(β	NOUN
ejpam-7055	100	5	)	)	PUNCT
ejpam-7055	100	6	=	=	SYM
ejpam-7055	100	7	φ(ℏ(β	φ(ℏ(β	PROPN
ejpam-7055	100	8	)	)	PUNCT
ejpam-7055	100	9	)	)	PUNCT
ejpam-7055	101	1	=	=	SYM
ejpam-7055	101	2	φ(ℏ	φ(ℏ	PROPN
ejpam-7055	102	1	◦	◦	NOUN
ejpam-7055	102	2	(	(	PUNCT
ejpam-7055	102	3	µ(α	µ(α	PROPN
ejpam-7055	102	4	)	)	PUNCT
ejpam-7055	102	5	)	)	PUNCT
ejpam-7055	102	6	)	)	PUNCT
ejpam-7055	103	1	=	=	PRON
ejpam-7055	103	2	φ((ℏ	φ((ℏ	NOUN
ejpam-7055	103	3	◦	◦	NOUN
ejpam-7055	103	4	µ)(α	µ)(α	NOUN
ejpam-7055	103	5	)	)	PUNCT
ejpam-7055	103	6	=	=	PUNCT
ejpam-7055	104	1	φ	φ	PROPN
ejpam-7055	104	2	◦	◦	NOUN
ejpam-7055	104	3	(	(	PUNCT
ejpam-7055	104	4	ℏ	ℏ	NOUN
ejpam-7055	104	5	◦	◦	NOUN
ejpam-7055	104	6	µ))(α	µ))(α	NOUN
ejpam-7055	104	7	)	)	PUNCT
ejpam-7055	104	8	consequently	consequently	ADV
ejpam-7055	104	9	,	,	PUNCT
ejpam-7055	104	10	“	"	PUNCT
ejpam-7055	104	11	ℏ	ℏ	X
ejpam-7055	104	12	◦	◦	NOUN
ejpam-7055	104	13	µ	µ	PRON
ejpam-7055	104	14	is	be	AUX
ejpam-7055	104	15	a	a	DET
ejpam-7055	104	16	soft	soft	ADJ
ejpam-7055	104	17	bck	bck	NOUN
ejpam-7055	104	18	/	/	SYM
ejpam-7055	104	19	bci	bci	NOUN
ejpam-7055	104	20	-	-	PUNCT
ejpam-7055	104	21	homomorphism	homomorphism	NOUN
ejpam-7055	104	22	”	"	PUNCT
ejpam-7055	104	23	.	.	PUNCT
ejpam-7055	105	1	definition	definition	NOUN
ejpam-7055	105	2	5	5	NUM
ejpam-7055	105	3	.	.	PUNCT
ejpam-7055	106	1	let	let	VERB
ejpam-7055	106	2	“	"	PUNCT
ejpam-7055	106	3	(	(	PUNCT
ejpam-7055	106	4	ζ	ζ	PROPN
ejpam-7055	106	5	,	,	PUNCT
ejpam-7055	106	6	ω	ω	NOUN
ejpam-7055	106	7	)	)	PUNCT
ejpam-7055	106	8	be	be	VERB
ejpam-7055	106	9	a	a	DET
ejpam-7055	106	10	soft	soft	ADJ
ejpam-7055	106	11	-	-	PUNCT
ejpam-7055	106	12	bck	bck	NOUN
ejpam-7055	106	13	-	-	PUNCT
ejpam-7055	106	14	algebra	algebra	NOUN
ejpam-7055	106	15	over	over	ADP
ejpam-7055	106	16	x̃	x̃	PROPN
ejpam-7055	106	17	”	"	PUNCT
ejpam-7055	106	18	.	.	PUNCT
ejpam-7055	107	1	then	then	ADV
ejpam-7055	107	2	the	the	DET
ejpam-7055	107	3	soft	soft	ADJ
ejpam-7055	107	4	identity	identity	NOUN
ejpam-7055	107	5	bck	bck	NOUN
ejpam-7055	107	6	/	/	SYM
ejpam-7055	107	7	bcihomomorphism	bcihomomorphism	NOUN
ejpam-7055	107	8	is	be	AUX
ejpam-7055	107	9	defined	define	VERB
ejpam-7055	107	10	as	as	ADP
ejpam-7055	107	11	ζ(α	ζ(α	NOUN
ejpam-7055	107	12	)	)	PUNCT
ejpam-7055	107	13	⊆	⊆	NUM
ejpam-7055	107	14	(	(	PUNCT
ejpam-7055	107	15	ζ	ζ	NOUN
ejpam-7055	107	16	◦	◦	NOUN
ejpam-7055	107	17	idω)(α	idω)(α	NOUN
ejpam-7055	107	18	)	)	PUNCT
ejpam-7055	107	19	.	.	PUNCT
ejpam-7055	108	1	this	this	PRON
ejpam-7055	108	2	implies	imply	VERB
ejpam-7055	108	3	that	that	SCONJ
ejpam-7055	108	4	the	the	DET
ejpam-7055	108	5	following	follow	VERB
ejpam-7055	108	6	diagram	diagram	NOUN
ejpam-7055	108	7	commutes	commute	NOUN
ejpam-7055	108	8	.	.	PUNCT
ejpam-7055	109	1	figure	figure	VERB
ejpam-7055	109	2	3	3	NUM
ejpam-7055	109	3	:	:	PUNCT
ejpam-7055	109	4	g.	g.	PROPN
ejpam-7055	109	5	muhiuddin	muhiuddin	PROPN
ejpam-7055	109	6	et	et	PROPN
ejpam-7055	109	7	al	al	PROPN
ejpam-7055	109	8	.	.	PUNCT
ejpam-7055	109	9	/	/	SYM
ejpam-7055	109	10	eur	eur	PROPN
ejpam-7055	109	11	.	.	PUNCT
ejpam-7055	110	1	j.	j.	PROPN
ejpam-7055	110	2	pure	pure	PROPN
ejpam-7055	110	3	appl	appl	PROPN
ejpam-7055	110	4	.	.	PROPN
ejpam-7055	110	5	math	math	PROPN
ejpam-7055	110	6	,	,	PUNCT
ejpam-7055	110	7	18	18	NUM
ejpam-7055	110	8	(	(	PUNCT
ejpam-7055	110	9	4	4	NUM
ejpam-7055	110	10	)	)	PUNCT
ejpam-7055	110	11	(	(	PUNCT
ejpam-7055	110	12	2025	2025	NUM
ejpam-7055	110	13	)	)	PUNCT
ejpam-7055	110	14	,	,	PUNCT
ejpam-7055	110	15	7055	7055	NUM
ejpam-7055	110	16	6	6	NUM
ejpam-7055	110	17	of	of	ADP
ejpam-7055	110	18	13	13	NUM
ejpam-7055	110	19	then	then	ADV
ejpam-7055	110	20	idω	idω	NOUN
ejpam-7055	110	21	is	be	AUX
ejpam-7055	110	22	a	a	DET
ejpam-7055	110	23	soft	soft	ADJ
ejpam-7055	110	24	identity	identity	NOUN
ejpam-7055	110	25	bck	bck	NOUN
ejpam-7055	110	26	/	/	SYM
ejpam-7055	110	27	bci	bci	NOUN
ejpam-7055	110	28	-	-	PUNCT
ejpam-7055	110	29	homomorphism	homomorphism	NOUN
ejpam-7055	110	30	.	.	PUNCT
ejpam-7055	111	1	moreover	moreover	ADV
ejpam-7055	111	2	,	,	PUNCT
ejpam-7055	111	3	idω	idω	NOUN
ejpam-7055	111	4	:	:	PUNCT
ejpam-7055	111	5	(	(	PUNCT
ejpam-7055	111	6	ζ	ζ	NOUN
ejpam-7055	111	7	,	,	PUNCT
ejpam-7055	111	8	ω	ω	NOUN
ejpam-7055	111	9	)	)	PUNCT
ejpam-7055	111	10	→	→	SYM
ejpam-7055	111	11	(	(	PUNCT
ejpam-7055	111	12	ζ	ζ	PROPN
ejpam-7055	111	13	,	,	PUNCT
ejpam-7055	111	14	ω	ω	NOUN
ejpam-7055	111	15	)	)	PUNCT
ejpam-7055	111	16	is	be	AUX
ejpam-7055	111	17	a	a	DET
ejpam-7055	111	18	soft	soft	ADJ
ejpam-7055	111	19	bck	bck	NOUN
ejpam-7055	111	20	/	/	SYM
ejpam-7055	111	21	bci	bci	NOUN
ejpam-7055	111	22	-	-	NOUN
ejpam-7055	111	23	homomorphism	homomorphism	NOUN
ejpam-7055	111	24	if	if	SCONJ
ejpam-7055	111	25	ζ(α	ζ(α	NOUN
ejpam-7055	111	26	)	)	PUNCT
ejpam-7055	111	27	⊆	⊆	NUM
ejpam-7055	111	28	(	(	PUNCT
ejpam-7055	111	29	ζ	ζ	NOUN
ejpam-7055	111	30	◦	◦	NOUN
ejpam-7055	111	31	idω)(a	idω)(a	NOUN
ejpam-7055	111	32	)	)	PUNCT
ejpam-7055	111	33	,	,	PUNCT
ejpam-7055	111	34	∀α	∀α	VERB
ejpam-7055	111	35	∈	∈	PROPN
ejpam-7055	111	36	ω	ω	NOUN
ejpam-7055	111	37	.	.	PUNCT
ejpam-7055	112	1	now	now	ADV
ejpam-7055	112	2	,	,	PUNCT
ejpam-7055	112	3	in	in	ADP
ejpam-7055	112	4	view	view	NOUN
ejpam-7055	112	5	of	of	ADP
ejpam-7055	112	6	the	the	DET
ejpam-7055	112	7	above	above	ADJ
ejpam-7055	112	8	discussion	discussion	NOUN
ejpam-7055	112	9	,	,	PUNCT
ejpam-7055	112	10	we	we	PRON
ejpam-7055	112	11	have	have	VERB
ejpam-7055	112	12	the	the	DET
ejpam-7055	112	13	following	following	NOUN
ejpam-7055	112	14	.	.	PUNCT
ejpam-7055	113	1	definition	definition	NOUN
ejpam-7055	113	2	6	6	NUM
ejpam-7055	113	3	.	.	PUNCT
ejpam-7055	114	1	the	the	DET
ejpam-7055	114	2	“	"	PUNCT
ejpam-7055	114	3	class	class	NOUN
ejpam-7055	114	4	of	of	ADP
ejpam-7055	114	5	all	all	DET
ejpam-7055	114	6	soft	soft	ADJ
ejpam-7055	114	7	bck	bck	NOUN
ejpam-7055	114	8	/	/	SYM
ejpam-7055	114	9	bci	bci	NOUN
ejpam-7055	114	10	-	-	PUNCT
ejpam-7055	114	11	algebras	algebras	PROPN
ejpam-7055	114	12	together	together	ADV
ejpam-7055	114	13	with	with	ADP
ejpam-7055	114	14	the	the	DET
ejpam-7055	114	15	class	class	NOUN
ejpam-7055	114	16	of	of	ADP
ejpam-7055	114	17	all	all	DET
ejpam-7055	114	18	soft	soft	ADJ
ejpam-7055	114	19	bck	bck	NOUN
ejpam-7055	114	20	/	/	SYM
ejpam-7055	114	21	bci	bci	NOUN
ejpam-7055	114	22	-	-	PUNCT
ejpam-7055	114	23	homomorphisms	homomorphism	NOUN
ejpam-7055	114	24	from	from	ADP
ejpam-7055	114	25	a	a	DET
ejpam-7055	114	26	category	category	NOUN
ejpam-7055	114	27	”	"	PUNCT
ejpam-7055	114	28	.	.	PUNCT
ejpam-7055	115	1	it	it	PRON
ejpam-7055	115	2	is	be	AUX
ejpam-7055	115	3	called	call	VERB
ejpam-7055	115	4	the	the	DET
ejpam-7055	115	5	“	"	PUNCT
ejpam-7055	115	6	category	category	NOUN
ejpam-7055	115	7	of	of	ADP
ejpam-7055	115	8	soft	soft	ADJ
ejpam-7055	115	9	bck	bck	NOUN
ejpam-7055	115	10	/	/	SYM
ejpam-7055	115	11	bcialgebra	bcialgebra	NOUN
ejpam-7055	115	12	and	and	CCONJ
ejpam-7055	115	13	is	be	AUX
ejpam-7055	115	14	denoted	denote	VERB
ejpam-7055	115	15	by	by	ADP
ejpam-7055	115	16	”	"	PUNCT
ejpam-7055	115	17	sbcki	sbcki	NOUN
ejpam-7055	115	18	.	.	PUNCT
ejpam-7055	116	1	next	next	ADV
ejpam-7055	116	2	,	,	PUNCT
ejpam-7055	116	3	we	we	PRON
ejpam-7055	116	4	prove	prove	VERB
ejpam-7055	116	5	the	the	DET
ejpam-7055	116	6	following	follow	VERB
ejpam-7055	116	7	results	result	NOUN
ejpam-7055	116	8	:	:	PUNCT
ejpam-7055	116	9	theorem	theorem	NOUN
ejpam-7055	116	10	1	1	NUM
ejpam-7055	116	11	.	.	PUNCT
ejpam-7055	117	1	the	the	DET
ejpam-7055	117	2	category	category	NOUN
ejpam-7055	117	3	sbcki	sbcki	NOUN
ejpam-7055	117	4	has	have	VERB
ejpam-7055	117	5	equilizers	equilizer	NOUN
ejpam-7055	117	6	.	.	PUNCT
ejpam-7055	118	1	proof	proof	NOUN
ejpam-7055	118	2	.	.	PUNCT
ejpam-7055	119	1	we	we	PRON
ejpam-7055	119	2	begin	begin	VERB
ejpam-7055	119	3	this	this	DET
ejpam-7055	119	4	proof	proof	NOUN
ejpam-7055	119	5	with	with	ADP
ejpam-7055	119	6	the	the	DET
ejpam-7055	119	7	following	follow	VERB
ejpam-7055	119	8	diagram	diagram	NOUN
ejpam-7055	119	9	figure	figure	NOUN
ejpam-7055	119	10	4	4	NUM
ejpam-7055	119	11	:	:	PUNCT
ejpam-7055	119	12	let	let	VERB
ejpam-7055	119	13	(	(	PUNCT
ejpam-7055	119	14	ζ	ζ	NOUN
ejpam-7055	119	15	,	,	PUNCT
ejpam-7055	119	16	ω	ω	NOUN
ejpam-7055	119	17	)	)	PUNCT
ejpam-7055	119	18	and	and	CCONJ
ejpam-7055	119	19	(	(	PUNCT
ejpam-7055	119	20	ϕ,b	ϕ,b	NOUN
ejpam-7055	119	21	)	)	PUNCT
ejpam-7055	119	22	be	be	VERB
ejpam-7055	119	23	two	two	NUM
ejpam-7055	119	24	soft	soft	ADJ
ejpam-7055	119	25	-	-	PUNCT
ejpam-7055	119	26	bck	bck	NOUN
ejpam-7055	119	27	/	/	SYM
ejpam-7055	119	28	bci	bci	NOUN
ejpam-7055	119	29	-	-	PUNCT
ejpam-7055	119	30	algebras	algebra	NOUN
ejpam-7055	119	31	in	in	ADP
ejpam-7055	119	32	sbcki	sbcki	NOUN
ejpam-7055	119	33	-objects	-object	NOUN
ejpam-7055	119	34	over	over	ADP
ejpam-7055	119	35	x̃	x̃	PROPN
ejpam-7055	119	36	.	.	PUNCT
ejpam-7055	120	1	again	again	ADV
ejpam-7055	120	2	,	,	PUNCT
ejpam-7055	120	3	let	let	VERB
ejpam-7055	120	4	µ	µ	NOUN
ejpam-7055	120	5	and	and	CCONJ
ejpam-7055	120	6	λ	λ	PROPN
ejpam-7055	120	7	be	be	AUX
ejpam-7055	120	8	two	two	NUM
ejpam-7055	120	9	sbcki−morphisms	sbcki−morphism	NOUN
ejpam-7055	120	10	from	from	ADP
ejpam-7055	120	11	(	(	PUNCT
ejpam-7055	120	12	ζ	ζ	PROPN
ejpam-7055	120	13	,	,	PUNCT
ejpam-7055	120	14	ω	ω	NOUN
ejpam-7055	120	15	)	)	PUNCT
ejpam-7055	120	16	to	to	ADP
ejpam-7055	120	17	(	(	PUNCT
ejpam-7055	120	18	ϕ,b	ϕ,b	NOUN
ejpam-7055	120	19	)	)	PUNCT
ejpam-7055	120	20	.	.	PUNCT
ejpam-7055	121	1	define	define	VERB
ejpam-7055	121	2	ℵ	ℵ	NOUN
ejpam-7055	121	3	=	=	SYM
ejpam-7055	121	4	{	{	PUNCT
ejpam-7055	121	5	α	α	NOUN
ejpam-7055	121	6	∈	∈	PROPN
ejpam-7055	121	7	ω	ω	NOUN
ejpam-7055	121	8	:	:	PUNCT
ejpam-7055	121	9	µ(α	µ(α	NUM
ejpam-7055	121	10	)	)	PUNCT
ejpam-7055	121	11	=	=	PUNCT
ejpam-7055	121	12	λ(α	λ(α	PROPN
ejpam-7055	121	13	)	)	PUNCT
ejpam-7055	121	14	}	}	PUNCT
ejpam-7055	121	15	,	,	PUNCT
ejpam-7055	121	16	u	u	NOUN
ejpam-7055	121	17	:	:	PUNCT
ejpam-7055	121	18	ℵ	ℵ	PROPN
ejpam-7055	121	19	→	→	SYM
ejpam-7055	121	20	ω	ω	NOUN
ejpam-7055	121	21	an	an	DET
ejpam-7055	121	22	embedding	embedding	NOUN
ejpam-7055	121	23	,	,	PUNCT
ejpam-7055	121	24	and	and	CCONJ
ejpam-7055	121	25	φ	φ	NUM
ejpam-7055	121	26	=	=	SYM
ejpam-7055	121	27	ζ	ζ	PROPN
ejpam-7055	121	28	◦	◦	NOUN
ejpam-7055	121	29	u.	u.	NOUN
ejpam-7055	121	30	from	from	ADP
ejpam-7055	121	31	assumption	assumption	NOUN
ejpam-7055	121	32	,	,	PUNCT
ejpam-7055	121	33	we	we	PRON
ejpam-7055	121	34	have	have	VERB
ejpam-7055	121	35	(	(	PUNCT
ejpam-7055	121	36	φ,ℵ	φ,ℵ	NOUN
ejpam-7055	121	37	)	)	PUNCT
ejpam-7055	121	38	is	be	AUX
ejpam-7055	121	39	a	a	DET
ejpam-7055	121	40	sbcki	sbcki	NOUN
ejpam-7055	121	41	−	−	NOUN
ejpam-7055	121	42	object	object	NOUN
ejpam-7055	121	43	,	,	PUNCT
ejpam-7055	121	44	µ	µ	X
ejpam-7055	121	45	◦	◦	NOUN
ejpam-7055	121	46	u	u	NOUN
ejpam-7055	121	47	=	=	SYM
ejpam-7055	121	48	λ	λ	X
ejpam-7055	121	49	◦	◦	NOUN
ejpam-7055	121	50	u	u	NOUN
ejpam-7055	121	51	and	and	CCONJ
ejpam-7055	121	52	φ(c	φ(c	NOUN
ejpam-7055	121	53	)	)	PUNCT
ejpam-7055	121	54	=	=	PRON
ejpam-7055	122	1	(	(	PUNCT
ejpam-7055	122	2	ζ	ζ	PROPN
ejpam-7055	122	3	◦	◦	NOUN
ejpam-7055	122	4	u)(c	u)(c	PROPN
ejpam-7055	122	5	)	)	PUNCT
ejpam-7055	122	6	,	,	PUNCT
ejpam-7055	122	7	for	for	ADP
ejpam-7055	122	8	all	all	DET
ejpam-7055	122	9	c	c	NOUN
ejpam-7055	122	10	∈	∈	PRON
ejpam-7055	122	11	ℵ.	ℵ.	NOUN
ejpam-7055	123	1	thus	thus	ADV
ejpam-7055	123	2	by	by	ADP
ejpam-7055	123	3	definition	definition	NOUN
ejpam-7055	123	4	,	,	PUNCT
ejpam-7055	123	5	u	u	NOUN
ejpam-7055	123	6	is	be	AUX
ejpam-7055	123	7	a	a	DET
ejpam-7055	123	8	sbcki	sbcki	NOUN
ejpam-7055	123	9	−morphism	−morphism	NOUN
ejpam-7055	123	10	.	.	PUNCT
ejpam-7055	124	1	we	we	PRON
ejpam-7055	124	2	will	will	AUX
ejpam-7055	124	3	demonstrate	demonstrate	VERB
ejpam-7055	124	4	that	that	SCONJ
ejpam-7055	124	5	(	(	PUNCT
ejpam-7055	124	6	(	(	PUNCT
ejpam-7055	124	7	φ,ℵ	φ,ℵ	NOUN
ejpam-7055	124	8	)	)	PUNCT
ejpam-7055	124	9	,	,	PUNCT
ejpam-7055	124	10	u	u	NOUN
ejpam-7055	124	11	)	)	PUNCT
ejpam-7055	124	12	functions	function	NOUN
ejpam-7055	124	13	as	as	ADP
ejpam-7055	124	14	the	the	DET
ejpam-7055	124	15	equilizer	equilizer	NOUN
ejpam-7055	124	16	between	between	ADP
ejpam-7055	124	17	µ	µ	PROPN
ejpam-7055	124	18	and	and	CCONJ
ejpam-7055	124	19	λ	λ	PROPN
ejpam-7055	124	20	.	.	PUNCT
ejpam-7055	125	1	let	let	AUX
ejpam-7055	125	2	(	(	PUNCT
ejpam-7055	125	3	k	k	X
ejpam-7055	125	4	,	,	PUNCT
ejpam-7055	125	5	x̃	x̃	PROPN
ejpam-7055	125	6	)	)	PUNCT
ejpam-7055	125	7	be	be	AUX
ejpam-7055	125	8	a	a	DET
ejpam-7055	125	9	sbcki	sbcki	NOUN
ejpam-7055	125	10	-object	-object	NOUN
ejpam-7055	125	11	and	and	CCONJ
ejpam-7055	125	12	suppose	suppose	VERB
ejpam-7055	125	13	v	v	PRON
ejpam-7055	125	14	is	be	AUX
ejpam-7055	125	15	a	a	DET
ejpam-7055	125	16	sbcki	sbcki	NOUN
ejpam-7055	125	17	-morphism	-morphism	NOUN
ejpam-7055	125	18	from	from	ADP
ejpam-7055	125	19	(	(	PUNCT
ejpam-7055	125	20	k	k	X
ejpam-7055	125	21	,	,	PUNCT
ejpam-7055	125	22	x̃	x̃	PROPN
ejpam-7055	125	23	)	)	PUNCT
ejpam-7055	125	24	to	to	ADP
ejpam-7055	125	25	(	(	PUNCT
ejpam-7055	125	26	ζ	ζ	PROPN
ejpam-7055	125	27	,	,	PUNCT
ejpam-7055	125	28	ω	ω	NOUN
ejpam-7055	125	29	)	)	PUNCT
ejpam-7055	125	30	such	such	ADJ
ejpam-7055	125	31	that	that	SCONJ
ejpam-7055	125	32	ℵ	ℵ	NOUN
ejpam-7055	125	33	=	=	SYM
ejpam-7055	125	34	{	{	PUNCT
ejpam-7055	125	35	α	α	NOUN
ejpam-7055	125	36	∈	∈	PROPN
ejpam-7055	125	37	ω	ω	NOUN
ejpam-7055	125	38	:	:	PUNCT
ejpam-7055	125	39	µ(α	µ(α	NUM
ejpam-7055	125	40	)	)	PUNCT
ejpam-7055	125	41	=	=	SYM
ejpam-7055	125	42	λ(α)},ℵ	λ(α)},ℵ	PROPN
ejpam-7055	125	43	6=	6=	ADP
ejpam-7055	125	44	∅.	∅.	NOUN
ejpam-7055	125	45	since	since	SCONJ
ejpam-7055	125	46	µ(0	µ(0	NOUN
ejpam-7055	125	47	)	)	PUNCT
ejpam-7055	125	48	=	=	SYM
ejpam-7055	126	1	λ(0	λ(0	NOUN
ejpam-7055	126	2	)	)	PUNCT
ejpam-7055	127	1	=	=	NOUN
ejpam-7055	127	2	⇒	⇒	NOUN
ejpam-7055	127	3	0	0	NUM
ejpam-7055	128	1	∈	∈	NOUN
ejpam-7055	128	2	ℵ.	ℵ.	NOUN
ejpam-7055	128	3	let	let	AUX
ejpam-7055	128	4	ϖ1	ϖ1	VERB
ejpam-7055	128	5	,	,	PUNCT
ejpam-7055	128	6	ϖ2	ϖ2	NOUN
ejpam-7055	128	7	∈	∈	PROPN
ejpam-7055	128	8	ℵ.	ℵ.	PROPN
ejpam-7055	128	9	then	then	ADV
ejpam-7055	128	10	µ(ϖ1	µ(ϖ1	VERB
ejpam-7055	128	11	)	)	PUNCT
ejpam-7055	128	12	=	=	SYM
ejpam-7055	128	13	λ(ϖ1	λ(ϖ1	NOUN
ejpam-7055	128	14	)	)	PUNCT
ejpam-7055	128	15	and	and	CCONJ
ejpam-7055	128	16	µ(ϖ2	µ(ϖ2	NOUN
ejpam-7055	128	17	)	)	PUNCT
ejpam-7055	128	18	=	=	SYM
ejpam-7055	129	1	λ(ϖ2	λ(ϖ2	NOUN
ejpam-7055	129	2	)	)	PUNCT
ejpam-7055	129	3	.	.	PUNCT
ejpam-7055	130	1	we	we	PRON
ejpam-7055	130	2	have	have	VERB
ejpam-7055	130	3	µ(ϖ1	µ(ϖ1	ADJ
ejpam-7055	130	4	∗ϖ2	∗ϖ2	NOUN
ejpam-7055	130	5	)	)	PUNCT
ejpam-7055	130	6	=	=	SYM
ejpam-7055	130	7	µ(ϖ1	µ(ϖ1	NOUN
ejpam-7055	130	8	)	)	PUNCT
ejpam-7055	130	9	∗	∗	NOUN
ejpam-7055	130	10	µ(ϖ2	µ(ϖ2	NOUN
ejpam-7055	130	11	)	)	PUNCT
ejpam-7055	130	12	=	=	SYM
ejpam-7055	130	13	λ(ϖ1	λ(ϖ1	ADJ
ejpam-7055	130	14	)	)	PUNCT
ejpam-7055	130	15	∗	∗	NOUN
ejpam-7055	130	16	λ(ϖ2	λ(ϖ2	NOUN
ejpam-7055	130	17	)	)	PUNCT
ejpam-7055	130	18	=	=	SYM
ejpam-7055	130	19	λ(ϖ1	λ(ϖ1	ADJ
ejpam-7055	130	20	∗ϖ2	∗ϖ2	NOUN
ejpam-7055	130	21	)	)	PUNCT
ejpam-7055	130	22	.	.	PUNCT
ejpam-7055	131	1	g.	g.	PROPN
ejpam-7055	131	2	muhiuddin	muhiuddin	PROPN
ejpam-7055	131	3	et	et	PROPN
ejpam-7055	131	4	al	al	PROPN
ejpam-7055	131	5	.	.	PUNCT
ejpam-7055	131	6	/	/	SYM
ejpam-7055	131	7	eur	eur	PROPN
ejpam-7055	131	8	.	.	PUNCT
ejpam-7055	132	1	j.	j.	PROPN
ejpam-7055	132	2	pure	pure	PROPN
ejpam-7055	132	3	appl	appl	PROPN
ejpam-7055	132	4	.	.	PROPN
ejpam-7055	132	5	math	math	PROPN
ejpam-7055	132	6	,	,	PUNCT
ejpam-7055	132	7	18	18	NUM
ejpam-7055	132	8	(	(	PUNCT
ejpam-7055	132	9	4	4	NUM
ejpam-7055	132	10	)	)	PUNCT
ejpam-7055	132	11	(	(	PUNCT
ejpam-7055	132	12	2025	2025	NUM
ejpam-7055	132	13	)	)	PUNCT
ejpam-7055	132	14	,	,	PUNCT
ejpam-7055	132	15	7055	7055	NUM
ejpam-7055	132	16	7	7	NUM
ejpam-7055	132	17	of	of	ADP
ejpam-7055	132	18	13	13	NUM
ejpam-7055	132	19	this	this	PRON
ejpam-7055	132	20	implies	imply	VERB
ejpam-7055	132	21	that	that	SCONJ
ejpam-7055	132	22	ϖ1	ϖ1	VERB
ejpam-7055	132	23	∗ϖ2	∗ϖ2	NOUN
ejpam-7055	132	24	∈	∈	PROPN
ejpam-7055	132	25	ℵ.	ℵ.	NOUN
ejpam-7055	133	1	this	this	PRON
ejpam-7055	133	2	show	show	VERB
ejpam-7055	133	3	that	that	SCONJ
ejpam-7055	133	4	ℵ	ℵ	NOUN
ejpam-7055	133	5	is	be	AUX
ejpam-7055	133	6	a	a	DET
ejpam-7055	133	7	subalgebra	subalgebra	NOUN
ejpam-7055	133	8	of	of	ADP
ejpam-7055	133	9	ω	ω	PROPN
ejpam-7055	133	10	.	.	PUNCT
ejpam-7055	134	1	now	now	ADV
ejpam-7055	134	2	,	,	PUNCT
ejpam-7055	134	3	define	define	VERB
ejpam-7055	134	4	a	a	DET
ejpam-7055	134	5	map	map	NOUN
ejpam-7055	134	6	η	η	NOUN
ejpam-7055	134	7	:	:	PUNCT
ejpam-7055	134	8	x̃	x̃	PROPN
ejpam-7055	134	9	→	→	SYM
ejpam-7055	134	10	ℵ	ℵ	PROPN
ejpam-7055	134	11	and	and	CCONJ
ejpam-7055	134	12	η	η	PROPN
ejpam-7055	134	13	=	=	PROPN
ejpam-7055	135	1	v.	v.	CCONJ
ejpam-7055	135	2	in	in	ADP
ejpam-7055	135	3	what	what	PRON
ejpam-7055	135	4	follows	follow	VERB
ejpam-7055	135	5	,	,	PUNCT
ejpam-7055	135	6	our	our	PRON
ejpam-7055	135	7	focus	focus	NOUN
ejpam-7055	135	8	is	be	AUX
ejpam-7055	135	9	to	to	PART
ejpam-7055	135	10	demonstrate	demonstrate	VERB
ejpam-7055	135	11	that	that	SCONJ
ejpam-7055	135	12	η	η	PROPN
ejpam-7055	135	13	is	be	AUX
ejpam-7055	135	14	a	a	DET
ejpam-7055	135	15	sbcki	sbcki	NOUN
ejpam-7055	135	16	-morphism	-morphism	NOUN
ejpam-7055	135	17	from	from	ADP
ejpam-7055	135	18	(	(	PUNCT
ejpam-7055	135	19	k	k	X
ejpam-7055	135	20	,	,	PUNCT
ejpam-7055	135	21	x̃	x̃	PROPN
ejpam-7055	135	22	)	)	PUNCT
ejpam-7055	135	23	to	to	ADP
ejpam-7055	135	24	(	(	PUNCT
ejpam-7055	135	25	ϕ,ℵ	ϕ,ℵ	NOUN
ejpam-7055	135	26	)	)	PUNCT
ejpam-7055	135	27	,	,	PUNCT
ejpam-7055	135	28	and	and	CCONJ
ejpam-7055	135	29	that	that	DET
ejpam-7055	135	30	v	v	NOUN
ejpam-7055	135	31	=	=	SYM
ejpam-7055	135	32	u	u	PROPN
ejpam-7055	135	33	◦	◦	PROPN
ejpam-7055	135	34	η	η	PROPN
ejpam-7055	135	35	.	.	PROPN
ejpam-7055	135	36	firstly	firstly	ADV
ejpam-7055	135	37	by	by	ADP
ejpam-7055	135	38	µ	µ	PROPN
ejpam-7055	135	39	◦	◦	NOUN
ejpam-7055	135	40	v	v	NOUN
ejpam-7055	135	41	=	=	SYM
ejpam-7055	135	42	λ	λ	X
ejpam-7055	135	43	◦	◦	NOUN
ejpam-7055	135	44	v	v	NOUN
ejpam-7055	135	45	,	,	PUNCT
ejpam-7055	135	46	we	we	PRON
ejpam-7055	135	47	get	get	VERB
ejpam-7055	135	48	µ(v(ϖ	µ(v(ϖ	NOUN
ejpam-7055	135	49	)	)	PUNCT
ejpam-7055	135	50	)	)	PUNCT
ejpam-7055	136	1	=	=	SYM
ejpam-7055	136	2	λ(v(ϖ	λ(v(ϖ	PROPN
ejpam-7055	136	3	)	)	PUNCT
ejpam-7055	136	4	)	)	PUNCT
ejpam-7055	136	5	,	,	PUNCT
ejpam-7055	137	1	∀ϖ	∀ϖ	ADJ
ejpam-7055	137	2	∈	∈	NOUN
ejpam-7055	137	3	x̃	x̃	PROPN
ejpam-7055	137	4	⇒	⇒	PROPN
ejpam-7055	137	5	v(ϖ	v(ϖ	PROPN
ejpam-7055	137	6	)	)	PUNCT
ejpam-7055	137	7	∈	∈	PROPN
ejpam-7055	137	8	ℵ.	ℵ.	PROPN
ejpam-7055	137	9	hence	hence	ADV
ejpam-7055	137	10	η	η	PROPN
ejpam-7055	137	11	=	=	PROPN
ejpam-7055	137	12	v	v	PROPN
ejpam-7055	137	13	is	be	AUX
ejpam-7055	137	14	well	well	ADV
ejpam-7055	137	15	defined	define	VERB
ejpam-7055	137	16	.	.	PUNCT
ejpam-7055	138	1	again	again	ADV
ejpam-7055	138	2	,	,	PUNCT
ejpam-7055	138	3	if	if	SCONJ
ejpam-7055	138	4	φ	φ	NUM
ejpam-7055	138	5	=	=	SYM
ejpam-7055	138	6	ζ	ζ	PROPN
ejpam-7055	138	7	◦	◦	NOUN
ejpam-7055	138	8	u	u	NOUN
ejpam-7055	138	9	,	,	PUNCT
ejpam-7055	138	10	η	η	PROPN
ejpam-7055	138	11	=	=	PROPN
ejpam-7055	138	12	v	v	PROPN
ejpam-7055	138	13	and	and	CCONJ
ejpam-7055	138	14	v	v	ADP
ejpam-7055	138	15	being	be	AUX
ejpam-7055	138	16	a	a	DET
ejpam-7055	138	17	sbcki	sbcki	NOUN
ejpam-7055	138	18	−morphism	−morphism	NOUN
ejpam-7055	138	19	,	,	PUNCT
ejpam-7055	138	20	then	then	ADV
ejpam-7055	138	21	form	form	VERB
ejpam-7055	138	22	figure	figure	NOUN
ejpam-7055	138	23	4	4	NUM
ejpam-7055	138	24	,	,	PUNCT
ejpam-7055	138	25	we	we	PRON
ejpam-7055	138	26	have	have	VERB
ejpam-7055	138	27	k(ϖ	k(ϖ	X
ejpam-7055	138	28	)	)	PUNCT
ejpam-7055	138	29	⊆	⊆	NUM
ejpam-7055	138	30	ζ(v(ϖ	ζ(v(ϖ	NOUN
ejpam-7055	138	31	)	)	PUNCT
ejpam-7055	138	32	)	)	PUNCT
ejpam-7055	139	1	=	=	SYM
ejpam-7055	139	2	ζ(u	ζ(u	ADP
ejpam-7055	139	3	◦	◦	NOUN
ejpam-7055	139	4	η(ϖ	η(ϖ	NUM
ejpam-7055	139	5	)	)	PUNCT
ejpam-7055	139	6	)	)	PUNCT
ejpam-7055	139	7	=	=	SYM
ejpam-7055	139	8	ζ(u(η(ϖ	ζ(u(η(ϖ	PROPN
ejpam-7055	139	9	)	)	PUNCT
ejpam-7055	139	10	)	)	PUNCT
ejpam-7055	139	11	)	)	PUNCT
ejpam-7055	140	1	=	=	PRON
ejpam-7055	140	2	(	(	PUNCT
ejpam-7055	140	3	ζ	ζ	NOUN
ejpam-7055	140	4	◦	◦	NOUN
ejpam-7055	140	5	u)(η(ϖ	u)(η(ϖ	PUNCT
ejpam-7055	140	6	)	)	PUNCT
ejpam-7055	140	7	)	)	PUNCT
ejpam-7055	140	8	=	=	SYM
ejpam-7055	140	9	φ(η(ϖ	φ(η(ϖ	NOUN
ejpam-7055	140	10	)	)	PUNCT
ejpam-7055	140	11	)	)	PUNCT
ejpam-7055	140	12	for	for	ADP
ejpam-7055	140	13	all	all	PRON
ejpam-7055	140	14	ϖ	ϖ	NOUN
ejpam-7055	140	15	∈	∈	NOUN
ejpam-7055	140	16	x̃	x̃	PROPN
ejpam-7055	141	1	=	=	AUX
ejpam-7055	141	2	⇒	⇒	PROPN
ejpam-7055	141	3	η	η	PROPN
ejpam-7055	141	4	is	be	AUX
ejpam-7055	141	5	a	a	DET
ejpam-7055	141	6	sbcki	sbcki	NOUN
ejpam-7055	141	7	−morphism	−morphism	NOUN
ejpam-7055	141	8	(	(	PUNCT
ejpam-7055	141	9	by	by	ADP
ejpam-7055	141	10	definition	definition	NOUN
ejpam-7055	141	11	)	)	PUNCT
ejpam-7055	141	12	.	.	PUNCT
ejpam-7055	142	1	finally	finally	ADV
ejpam-7055	142	2	from	from	ADP
ejpam-7055	142	3	assumption	assumption	NOUN
ejpam-7055	142	4	,	,	PUNCT
ejpam-7055	142	5	we	we	PRON
ejpam-7055	142	6	know	know	VERB
ejpam-7055	142	7	that	that	PRON
ejpam-7055	142	8	v	v	X
ejpam-7055	142	9	=	=	SYM
ejpam-7055	142	10	u	u	NOUN
ejpam-7055	142	11	◦	◦	PROPN
ejpam-7055	142	12	η	η	PROPN
ejpam-7055	142	13	and	and	CCONJ
ejpam-7055	142	14	η	η	PROPN
ejpam-7055	142	15	is	be	AUX
ejpam-7055	142	16	unique	unique	ADJ
ejpam-7055	142	17	.	.	PUNCT
ejpam-7055	143	1	consequently	consequently	ADV
ejpam-7055	143	2	(	(	PUNCT
ejpam-7055	143	3	φ,ℵ	φ,ℵ	NOUN
ejpam-7055	143	4	)	)	PUNCT
ejpam-7055	143	5	is	be	AUX
ejpam-7055	143	6	the	the	DET
ejpam-7055	143	7	equilizer	equilizer	NOUN
ejpam-7055	143	8	of	of	ADP
ejpam-7055	143	9	µ	µ	PROPN
ejpam-7055	143	10	and	and	CCONJ
ejpam-7055	143	11	λ	λ	PROPN
ejpam-7055	143	12	is	be	AUX
ejpam-7055	143	13	sbcki	sbcki	NOUN
ejpam-7055	143	14	.	.	PUNCT
ejpam-7055	144	1	proposition	proposition	NOUN
ejpam-7055	144	2	2	2	NUM
ejpam-7055	144	3	.	.	PUNCT
ejpam-7055	145	1	the	the	DET
ejpam-7055	145	2	category	category	NOUN
ejpam-7055	145	3	sbcki	sbcki	NOUN
ejpam-7055	145	4	has	have	VERB
ejpam-7055	145	5	a	a	DET
ejpam-7055	145	6	finite	finite	ADJ
ejpam-7055	145	7	product	product	NOUN
ejpam-7055	145	8	.	.	PUNCT
ejpam-7055	146	1	proof	proof	NOUN
ejpam-7055	146	2	.	.	PUNCT
ejpam-7055	147	1	let	let	VERB
ejpam-7055	147	2	(	(	PUNCT
ejpam-7055	147	3	ζ	ζ	NOUN
ejpam-7055	147	4	,	,	PUNCT
ejpam-7055	147	5	ω	ω	NOUN
ejpam-7055	147	6	)	)	PUNCT
ejpam-7055	147	7	and	and	CCONJ
ejpam-7055	147	8	(	(	PUNCT
ejpam-7055	147	9	ϕ,b	ϕ,b	NOUN
ejpam-7055	147	10	)	)	PUNCT
ejpam-7055	147	11	are	be	AUX
ejpam-7055	147	12	two	two	NUM
ejpam-7055	147	13	sbci	sbci	NOUN
ejpam-7055	147	14	−	−	NOUN
ejpam-7055	147	15	objects	object	NOUN
ejpam-7055	147	16	.	.	PUNCT
ejpam-7055	148	1	define	define	VERB
ejpam-7055	148	2	three	three	NUM
ejpam-7055	148	3	mappings	mapping	NOUN
ejpam-7055	148	4	figure	figure	NOUN
ejpam-7055	148	5	5	5	NUM
ejpam-7055	148	6	:	:	PUNCT
ejpam-7055	148	7	φ	φ	NUM
ejpam-7055	148	8	:	:	PUNCT
ejpam-7055	149	1	ω×b	ω×b	PUNCT
ejpam-7055	149	2	→	→	SYM
ejpam-7055	149	3	p	p	X
ejpam-7055	149	4	(	(	PUNCT
ejpam-7055	149	5	u	u	NOUN
ejpam-7055	149	6	)	)	PUNCT
ejpam-7055	149	7	(	(	PUNCT
ejpam-7055	149	8	α	α	X
ejpam-7055	149	9	,	,	PUNCT
ejpam-7055	149	10	β	β	NOUN
ejpam-7055	149	11	)	)	PUNCT
ejpam-7055	149	12	7→	7→	NUM
ejpam-7055	149	13	ζ(α	ζ(α	NOUN
ejpam-7055	149	14	)	)	PUNCT
ejpam-7055	149	15	∩	∩	ADJ
ejpam-7055	149	16	ϕ(β	ϕ(β	X
ejpam-7055	149	17	)	)	PUNCT
ejpam-7055	149	18	p1	p1	NOUN
ejpam-7055	149	19	:	:	PUNCT
ejpam-7055	149	20	ω×b	ω×b	PROPN
ejpam-7055	149	21	→	→	SYM
ejpam-7055	149	22	ω	ω	PROPN
ejpam-7055	149	23	(	(	PUNCT
ejpam-7055	149	24	α	α	X
ejpam-7055	149	25	,	,	PUNCT
ejpam-7055	149	26	β	β	NOUN
ejpam-7055	149	27	)	)	PUNCT
ejpam-7055	149	28	7→	7→	NUM
ejpam-7055	150	1	α	α	NOUN
ejpam-7055	150	2	⇒	⇒	PROPN
ejpam-7055	150	3	p1(α	p1(α	PROPN
ejpam-7055	150	4	,	,	PUNCT
ejpam-7055	150	5	β	β	X
ejpam-7055	150	6	)	)	PUNCT
ejpam-7055	150	7	=	=	SYM
ejpam-7055	151	1	α	α	NOUN
ejpam-7055	151	2	p2	p2	NOUN
ejpam-7055	151	3	:	:	PUNCT
ejpam-7055	151	4	ω×b	ω×b	PROPN
ejpam-7055	151	5	→	→	SYM
ejpam-7055	151	6	b	b	PROPN
ejpam-7055	151	7	(	(	PUNCT
ejpam-7055	151	8	α	α	NOUN
ejpam-7055	151	9	,	,	PUNCT
ejpam-7055	151	10	β	β	NOUN
ejpam-7055	151	11	)	)	PUNCT
ejpam-7055	151	12	7→	7→	NUM
ejpam-7055	151	13	β	β	ADP
ejpam-7055	151	14	foreach	foreach	NOUN
ejpam-7055	151	15	(	(	PUNCT
ejpam-7055	151	16	α	α	X
ejpam-7055	151	17	,	,	PUNCT
ejpam-7055	151	18	β	β	NOUN
ejpam-7055	151	19	)	)	PUNCT
ejpam-7055	151	20	∈	∈	PROPN
ejpam-7055	151	21	ω×b	ω×b	PROPN
ejpam-7055	151	22	.	.	PUNCT
ejpam-7055	152	1	φ(α	φ(α	PROPN
ejpam-7055	152	2	,	,	PUNCT
ejpam-7055	152	3	β	β	X
ejpam-7055	152	4	)	)	PUNCT
ejpam-7055	152	5	=	=	SYM
ejpam-7055	152	6	ζ(α	ζ(α	NOUN
ejpam-7055	152	7	)	)	PUNCT
ejpam-7055	152	8	∩	∩	NOUN
ejpam-7055	152	9	ϕ(β	ϕ(β	X
ejpam-7055	152	10	)	)	PUNCT
ejpam-7055	152	11	⊆	⊆	NUM
ejpam-7055	152	12	ζ(α	ζ(α	NOUN
ejpam-7055	152	13	)	)	PUNCT
ejpam-7055	152	14	=	=	SYM
ejpam-7055	152	15	ζ(p1((α	ζ(p1((α	PROPN
ejpam-7055	152	16	,	,	PUNCT
ejpam-7055	152	17	β	β	NOUN
ejpam-7055	152	18	)	)	PUNCT
ejpam-7055	152	19	)	)	PUNCT
ejpam-7055	152	20	.	.	PUNCT
ejpam-7055	153	1	this	this	PRON
ejpam-7055	153	2	implies	imply	VERB
ejpam-7055	153	3	that	that	SCONJ
ejpam-7055	153	4	p1	p1	NOUN
ejpam-7055	153	5	is	be	AUX
ejpam-7055	153	6	an	an	DET
ejpam-7055	153	7	sbcki	sbcki	NOUN
ejpam-7055	153	8	−morphism	−morphism	PROPN
ejpam-7055	153	9	.	.	PUNCT
ejpam-7055	154	1	by	by	ADP
ejpam-7055	154	2	the	the	DET
ejpam-7055	154	3	some	some	DET
ejpam-7055	154	4	argument	argument	NOUN
ejpam-7055	154	5	,	,	PUNCT
ejpam-7055	154	6	p2	p2	PROPN
ejpam-7055	154	7	is	be	AUX
ejpam-7055	154	8	a	a	DET
ejpam-7055	154	9	sbcki	sbcki	NOUN
ejpam-7055	154	10	−	−	NOUN
ejpam-7055	154	11	morphism	morphism	NOUN
ejpam-7055	154	12	.	.	PUNCT
ejpam-7055	155	1	again	again	ADV
ejpam-7055	155	2	for	for	ADP
ejpam-7055	155	3	each	each	DET
ejpam-7055	155	4	sbcki	sbcki	NOUN
ejpam-7055	155	5	−	−	NOUN
ejpam-7055	155	6	objects	object	NOUN
ejpam-7055	155	7	(	(	PUNCT
ejpam-7055	155	8	i	i	NOUN
ejpam-7055	155	9	,	,	PUNCT
ejpam-7055	155	10	d	d	PROPN
ejpam-7055	155	11	)	)	PUNCT
ejpam-7055	155	12	,	,	PUNCT
ejpam-7055	155	13	suppose	suppose	VERB
ejpam-7055	155	14	that	that	SCONJ
ejpam-7055	155	15	µ	µ	NOUN
ejpam-7055	155	16	and	and	CCONJ
ejpam-7055	155	17	λ	λ	PROPN
ejpam-7055	155	18	are	be	AUX
ejpam-7055	155	19	sbcki	sbcki	VERB
ejpam-7055	155	20	−	−	PROPN
ejpam-7055	155	21	morphism	morphism	NOUN
ejpam-7055	155	22	from	from	ADP
ejpam-7055	155	23	(	(	PUNCT
ejpam-7055	155	24	i	i	PRON
ejpam-7055	155	25	,	,	PUNCT
ejpam-7055	155	26	d	d	NOUN
ejpam-7055	155	27	)	)	PUNCT
ejpam-7055	155	28	→	→	SYM
ejpam-7055	155	29	(	(	PUNCT
ejpam-7055	155	30	ζ	ζ	PROPN
ejpam-7055	155	31	,	,	PUNCT
ejpam-7055	155	32	ω	ω	NOUN
ejpam-7055	155	33	)	)	PUNCT
ejpam-7055	155	34	and	and	CCONJ
ejpam-7055	155	35	(	(	PUNCT
ejpam-7055	155	36	ϕ,b	ϕ,b	NOUN
ejpam-7055	155	37	)	)	PUNCT
ejpam-7055	155	38	.	.	PUNCT
ejpam-7055	156	1	g.	g.	PROPN
ejpam-7055	156	2	muhiuddin	muhiuddin	PROPN
ejpam-7055	156	3	et	et	PROPN
ejpam-7055	156	4	al	al	PROPN
ejpam-7055	156	5	.	.	PUNCT
ejpam-7055	156	6	/	/	SYM
ejpam-7055	156	7	eur	eur	PROPN
ejpam-7055	156	8	.	.	PUNCT
ejpam-7055	157	1	j.	j.	PROPN
ejpam-7055	157	2	pure	pure	PROPN
ejpam-7055	157	3	appl	appl	PROPN
ejpam-7055	157	4	.	.	PROPN
ejpam-7055	157	5	math	math	PROPN
ejpam-7055	157	6	,	,	PUNCT
ejpam-7055	157	7	18	18	NUM
ejpam-7055	157	8	(	(	PUNCT
ejpam-7055	157	9	4	4	NUM
ejpam-7055	157	10	)	)	PUNCT
ejpam-7055	157	11	(	(	PUNCT
ejpam-7055	157	12	2025	2025	NUM
ejpam-7055	157	13	)	)	PUNCT
ejpam-7055	157	14	,	,	PUNCT
ejpam-7055	157	15	7055	7055	NUM
ejpam-7055	157	16	8	8	NUM
ejpam-7055	157	17	of	of	ADP
ejpam-7055	157	18	13	13	NUM
ejpam-7055	157	19	figure	figure	NOUN
ejpam-7055	157	20	6	6	NUM
ejpam-7055	157	21	:	:	PUNCT
ejpam-7055	157	22	then	then	ADV
ejpam-7055	157	23	i(δ	i(δ	PROPN
ejpam-7055	157	24	)	)	PUNCT
ejpam-7055	157	25	⊆	⊆	NUM
ejpam-7055	157	26	ζ(µ(δ	ζ(µ(δ	ADJ
ejpam-7055	157	27	)	)	PUNCT
ejpam-7055	157	28	)	)	PUNCT
ejpam-7055	157	29	and	and	CCONJ
ejpam-7055	157	30	i(δ	i(δ	PROPN
ejpam-7055	157	31	)	)	PUNCT
ejpam-7055	157	32	⊆	⊆	NUM
ejpam-7055	157	33	ϕ(λ(δ	ϕ(λ(δ	PROPN
ejpam-7055	157	34	)	)	PUNCT
ejpam-7055	157	35	)	)	PUNCT
ejpam-7055	157	36	,	,	PUNCT
ejpam-7055	157	37	∀δ	∀δ	PROPN
ejpam-7055	157	38	∈	∈	PROPN
ejpam-7055	157	39	d.	d.	PROPN
ejpam-7055	157	40	further	far	ADV
ejpam-7055	157	41	,	,	PUNCT
ejpam-7055	157	42	define	define	VERB
ejpam-7055	157	43	ℏ	ℏ	PROPN
ejpam-7055	157	44	:	:	PUNCT
ejpam-7055	157	45	d	d	X
ejpam-7055	157	46	→	→	SYM
ejpam-7055	157	47	ω×b	ω×b	PROPN
ejpam-7055	157	48	δ	δ	PROPN
ejpam-7055	157	49	7→	7→	PROPN
ejpam-7055	157	50	(	(	PUNCT
ejpam-7055	157	51	µ(δ	µ(δ	NOUN
ejpam-7055	157	52	)	)	PUNCT
ejpam-7055	157	53	,	,	PUNCT
ejpam-7055	157	54	λ(δ	λ(δ	PROPN
ejpam-7055	157	55	)	)	PUNCT
ejpam-7055	157	56	)	)	PUNCT
ejpam-7055	157	57	ℏ(δ	ℏ(δ	NOUN
ejpam-7055	157	58	)	)	PUNCT
ejpam-7055	157	59	=	=	SYM
ejpam-7055	157	60	(	(	PUNCT
ejpam-7055	157	61	µ(δ	µ(δ	ADV
ejpam-7055	157	62	)	)	PUNCT
ejpam-7055	157	63	,	,	PUNCT
ejpam-7055	157	64	λ(δ	λ(δ	PROPN
ejpam-7055	157	65	)	)	PUNCT
ejpam-7055	157	66	)	)	PUNCT
ejpam-7055	157	67	for	for	ADP
ejpam-7055	157	68	each	each	DET
ejpam-7055	157	69	δ	δ	PROPN
ejpam-7055	157	70	∈	∈	PROPN
ejpam-7055	158	1	d	d	PROPN
ejpam-7055	158	2	,	,	PUNCT
ejpam-7055	158	3	then	then	ADV
ejpam-7055	158	4	we	we	PRON
ejpam-7055	158	5	get	get	VERB
ejpam-7055	158	6	i(δ	i(δ	NOUN
ejpam-7055	158	7	)	)	PUNCT
ejpam-7055	158	8	⊆	⊆	NUM
ejpam-7055	158	9	ζ(µ(δ	ζ(µ(δ	ADJ
ejpam-7055	158	10	)	)	PUNCT
ejpam-7055	158	11	∩	∩	NOUN
ejpam-7055	158	12	ϕ(λ(δ	ϕ(λ(δ	PROPN
ejpam-7055	158	13	)	)	PUNCT
ejpam-7055	158	14	)	)	PUNCT
ejpam-7055	158	15	)	)	PUNCT
ejpam-7055	159	1	=	=	SYM
ejpam-7055	159	2	φ(µ(δ	φ(µ(δ	ADV
ejpam-7055	159	3	)	)	PUNCT
ejpam-7055	159	4	,	,	PUNCT
ejpam-7055	159	5	λ(δ	λ(δ	PROPN
ejpam-7055	159	6	)	)	PUNCT
ejpam-7055	159	7	)	)	PUNCT
ejpam-7055	159	8	=	=	PUNCT
ejpam-7055	159	9	φ(ℏ(δ	φ(ℏ(δ	NOUN
ejpam-7055	159	10	)	)	PUNCT
ejpam-7055	159	11	=	=	SYM
ejpam-7055	159	12	(	(	PUNCT
ejpam-7055	159	13	φ	φ	NUM
ejpam-7055	159	14	◦	◦	PROPN
ejpam-7055	159	15	ℏ)(δ	ℏ)(δ	PROPN
ejpam-7055	159	16	)	)	PUNCT
ejpam-7055	159	17	this	this	PRON
ejpam-7055	159	18	implies	imply	VERB
ejpam-7055	159	19	that	that	SCONJ
ejpam-7055	159	20	ℏ	ℏ	PROPN
ejpam-7055	159	21	is	be	AUX
ejpam-7055	159	22	a	a	DET
ejpam-7055	159	23	sbci	sbci	NOUN
ejpam-7055	159	24	−morphism	−morphism	NOUN
ejpam-7055	159	25	.	.	PUNCT
ejpam-7055	160	1	finallyforevery	finallyforevery	PROPN
ejpam-7055	160	2	δ	δ	PROPN
ejpam-7055	160	3	∈	∈	PROPN
ejpam-7055	161	1	d	d	X
ejpam-7055	161	2	,	,	PUNCT
ejpam-7055	161	3	we	we	PRON
ejpam-7055	161	4	get	get	VERB
ejpam-7055	161	5	(	(	PUNCT
ejpam-7055	161	6	p1	p1	VERB
ejpam-7055	161	7	◦	◦	NOUN
ejpam-7055	161	8	ℏ)(δ	ℏ)(δ	PROPN
ejpam-7055	161	9	)	)	PUNCT
ejpam-7055	161	10	=	=	SYM
ejpam-7055	161	11	p1(ℏ(δ	p1(ℏ(δ	NOUN
ejpam-7055	161	12	)	)	PUNCT
ejpam-7055	161	13	)	)	PUNCT
ejpam-7055	162	1	=	=	PUNCT
ejpam-7055	162	2	p1(µ(δ	p1(µ(δ	ADJ
ejpam-7055	162	3	)	)	PUNCT
ejpam-7055	162	4	,	,	PUNCT
ejpam-7055	162	5	λ(δ	λ(δ	PROPN
ejpam-7055	162	6	)	)	PUNCT
ejpam-7055	162	7	)	)	PUNCT
ejpam-7055	163	1	=	=	SYM
ejpam-7055	163	2	µ(δ	µ(δ	NOUN
ejpam-7055	163	3	)	)	PUNCT
ejpam-7055	163	4	therefore	therefore	ADV
ejpam-7055	163	5	,	,	PUNCT
ejpam-7055	163	6	p1	p1	PROPN
ejpam-7055	163	7	◦	◦	NOUN
ejpam-7055	163	8	ℏ	ℏ	NOUN
ejpam-7055	163	9	=	=	PUNCT
ejpam-7055	163	10	µ.	µ.	NOUN
ejpam-7055	163	11	similarity	similarity	NOUN
ejpam-7055	163	12	,	,	PUNCT
ejpam-7055	163	13	p2	p2	PROPN
ejpam-7055	163	14	◦	◦	NOUN
ejpam-7055	163	15	ℏ	ℏ	NOUN
ejpam-7055	163	16	=	=	SYM
ejpam-7055	163	17	λ	λ	PROPN
ejpam-7055	163	18	.	.	PUNCT
ejpam-7055	163	19	clearly	clearly	ADV
ejpam-7055	163	20	,	,	PUNCT
ejpam-7055	163	21	ℏ	ℏ	PROPN
ejpam-7055	163	22	is	be	AUX
ejpam-7055	163	23	unique	unique	ADJ
ejpam-7055	163	24	.	.	PUNCT
ejpam-7055	164	1	consequently	consequently	ADV
ejpam-7055	164	2	,	,	PUNCT
ejpam-7055	164	3	{	{	PUNCT
ejpam-7055	164	4	(	(	PUNCT
ejpam-7055	164	5	φ,ℵ	φ,ℵ	NOUN
ejpam-7055	164	6	)	)	PUNCT
ejpam-7055	164	7	,	,	PUNCT
ejpam-7055	164	8	p1	p1	NOUN
ejpam-7055	164	9	,	,	PUNCT
ejpam-7055	164	10	p2	p2	PROPN
ejpam-7055	164	11	}	}	PUNCT
ejpam-7055	164	12	is	be	AUX
ejpam-7055	164	13	a	a	DET
ejpam-7055	164	14	finite	finite	ADJ
ejpam-7055	164	15	product	product	NOUN
ejpam-7055	164	16	of	of	ADP
ejpam-7055	164	17	(	(	PUNCT
ejpam-7055	164	18	ζ	ζ	PROPN
ejpam-7055	164	19	,	,	PUNCT
ejpam-7055	164	20	ω	ω	NOUN
ejpam-7055	164	21	)	)	PUNCT
ejpam-7055	164	22	and	and	CCONJ
ejpam-7055	164	23	(	(	PUNCT
ejpam-7055	164	24	ϕ,b	ϕ,b	NOUN
ejpam-7055	164	25	)	)	PUNCT
ejpam-7055	164	26	.	.	PUNCT
ejpam-7055	165	1	proposition	proposition	NOUN
ejpam-7055	165	2	3	3	NUM
ejpam-7055	165	3	.	.	PUNCT
ejpam-7055	166	1	the	the	DET
ejpam-7055	166	2	category	category	NOUN
ejpam-7055	166	3	sbcki	sbcki	NOUN
ejpam-7055	166	4	is	be	AUX
ejpam-7055	166	5	a	a	DET
ejpam-7055	166	6	“	"	PUNCT
ejpam-7055	166	7	topological	topological	ADJ
ejpam-7055	166	8	construct	construct	NOUN
ejpam-7055	166	9	”	"	PUNCT
ejpam-7055	166	10	.	.	PUNCT
ejpam-7055	167	1	proof	proof	NOUN
ejpam-7055	167	2	.	.	PUNCT
ejpam-7055	168	1	let	let	VERB
ejpam-7055	168	2	{	{	PUNCT
ejpam-7055	168	3	(	(	PUNCT
ejpam-7055	168	4	ζi	ζi	PROPN
ejpam-7055	168	5	,	,	PUNCT
ejpam-7055	168	6	ωi)}i∈i	ωi)}i∈i	NOUN
ejpam-7055	168	7	be	be	VERB
ejpam-7055	168	8	a	a	DET
ejpam-7055	168	9	family	family	NOUN
ejpam-7055	168	10	of	of	ADP
ejpam-7055	168	11	sbcki	sbcki	NOUN
ejpam-7055	168	12	-objects	-object	NOUN
ejpam-7055	168	13	indexed	index	VERB
ejpam-7055	168	14	by	by	ADP
ejpam-7055	168	15	a	a	DET
ejpam-7055	168	16	class	class	NOUN
ejpam-7055	168	17	i	i	PROPN
ejpam-7055	168	18	,	,	PUNCT
ejpam-7055	168	19	and	and	CCONJ
ejpam-7055	168	20	let	let	VERB
ejpam-7055	168	21	{	{	PUNCT
ejpam-7055	168	22	(	(	PUNCT
ejpam-7055	168	23	ζi	ζi	PROPN
ejpam-7055	168	24	:	:	X
ejpam-7055	168	25	ω	ω	PROPN
ejpam-7055	168	26	→	→	SYM
ejpam-7055	168	27	ωi)}i∈i	ωi)}i∈i	NOUN
ejpam-7055	168	28	be	be	VERB
ejpam-7055	168	29	a	a	DET
ejpam-7055	168	30	family	family	NOUN
ejpam-7055	168	31	of	of	ADP
ejpam-7055	168	32	mappings	mapping	NOUN
ejpam-7055	168	33	.	.	PUNCT
ejpam-7055	169	1	we	we	PRON
ejpam-7055	169	2	define	define	VERB
ejpam-7055	169	3	asoftset.over.u	asoftset.over.u	NOUN
ejpam-7055	169	4	as	as	SCONJ
ejpam-7055	169	5	follows	follow	VERB
ejpam-7055	169	6	:	:	PUNCT
ejpam-7055	169	7	ζ	ζ	NOUN
ejpam-7055	169	8	:	:	PUNCT
ejpam-7055	169	9	ω	ω	PROPN
ejpam-7055	169	10	→	→	SYM
ejpam-7055	169	11	p	p	X
ejpam-7055	169	12	(	(	PUNCT
ejpam-7055	169	13	u	u	NOUN
ejpam-7055	169	14	)	)	PUNCT
ejpam-7055	169	15	α	α	PROPN
ejpam-7055	169	16	→	→	SYM
ejpam-7055	169	17	∩i∈i(ζi(µi(α	∩i∈i(ζi(µi(α	PROPN
ejpam-7055	169	18	)	)	PUNCT
ejpam-7055	169	19	)	)	PUNCT
ejpam-7055	169	20	)	)	PUNCT
ejpam-7055	169	21	.	.	PUNCT
ejpam-7055	170	1	then	then	ADV
ejpam-7055	170	2	,	,	PUNCT
ejpam-7055	170	3	(	(	PUNCT
ejpam-7055	170	4	ζ	ζ	NOUN
ejpam-7055	170	5	,	,	PUNCT
ejpam-7055	170	6	ω	ω	NOUN
ejpam-7055	170	7	)	)	PUNCT
ejpam-7055	170	8	∈	∈	PROPN
ejpam-7055	170	9	ob(sbcki	ob(sbcki	PROPN
ejpam-7055	170	10	)	)	PUNCT
ejpam-7055	170	11	.	.	PUNCT
ejpam-7055	171	1	it	it	PRON
ejpam-7055	171	2	suffices	suffice	VERB
ejpam-7055	171	3	to	to	PART
ejpam-7055	171	4	show	show	VERB
ejpam-7055	171	5	that	that	SCONJ
ejpam-7055	171	6	{	{	PUNCT
ejpam-7055	171	7	µi	µi	INTJ
ejpam-7055	171	8	:	:	PUNCT
ejpam-7055	171	9	(	(	PUNCT
ejpam-7055	171	10	ζ	ζ	NOUN
ejpam-7055	171	11	,	,	PUNCT
ejpam-7055	171	12	ω	ω	NOUN
ejpam-7055	171	13	)	)	PUNCT
ejpam-7055	171	14	→	→	SYM
ejpam-7055	171	15	(	(	PUNCT
ejpam-7055	171	16	ζi	ζi	NOUN
ejpam-7055	171	17	,	,	PUNCT
ejpam-7055	171	18	ωi)}i∈i	ωi)}i∈i	NOUN
ejpam-7055	171	19	is	be	AUX
ejpam-7055	171	20	the	the	DET
ejpam-7055	171	21	unique	unique	ADJ
ejpam-7055	171	22	sbcki	sbcki	NOUN
ejpam-7055	171	23	initial	initial	ADJ
ejpam-7055	171	24	lift	lift	NOUN
ejpam-7055	171	25	of	of	ADP
ejpam-7055	171	26	{	{	PUNCT
ejpam-7055	171	27	µi	µi	INTJ
ejpam-7055	171	28	:	:	PUNCT
ejpam-7055	171	29	ω	ω	PROPN
ejpam-7055	171	30	→	→	SYM
ejpam-7055	171	31	ωi}i∈i	ωi}i∈i	PROPN
ejpam-7055	171	32	.	.	PUNCT
ejpam-7055	172	1	now	now	ADV
ejpam-7055	172	2	,	,	PUNCT
ejpam-7055	172	3	to	to	PART
ejpam-7055	172	4	“	"	PUNCT
ejpam-7055	172	5	complete	complete	VERB
ejpam-7055	172	6	the	the	DET
ejpam-7055	172	7	proof	proof	NOUN
ejpam-7055	172	8	,	,	PUNCT
ejpam-7055	172	9	we	we	PRON
ejpam-7055	172	10	take	take	VERB
ejpam-7055	172	11	the	the	DET
ejpam-7055	172	12	following	follow	VERB
ejpam-7055	172	13	two	two	NUM
ejpam-7055	172	14	cases	case	NOUN
ejpam-7055	172	15	”	"	PUNCT
ejpam-7055	172	16	.	.	PUNCT
ejpam-7055	173	1	case	case	NOUN
ejpam-7055	173	2	1	1	NUM
ejpam-7055	173	3	:	:	PUNCT
ejpam-7055	173	4	we	we	PRON
ejpam-7055	173	5	show	show	VERB
ejpam-7055	173	6	that	that	SCONJ
ejpam-7055	173	7	{	{	PUNCT
ejpam-7055	173	8	µi	µi	INTJ
ejpam-7055	173	9	:	:	PUNCT
ejpam-7055	173	10	(	(	PUNCT
ejpam-7055	173	11	ζ	ζ	NOUN
ejpam-7055	173	12	,	,	PUNCT
ejpam-7055	173	13	ω	ω	NOUN
ejpam-7055	173	14	)	)	PUNCT
ejpam-7055	173	15	→	→	SYM
ejpam-7055	173	16	(	(	PUNCT
ejpam-7055	173	17	ζi	ζi	NOUN
ejpam-7055	173	18	,	,	PUNCT
ejpam-7055	173	19	ωi)}i∈i	ωi)}i∈i	NOUN
ejpam-7055	173	20	is	be	AUX
ejpam-7055	173	21	a	a	DET
ejpam-7055	173	22	sbcki	sbcki	NOUN
ejpam-7055	173	23	initial.lift.of	initial.lift.of	PROPN
ejpam-7055	173	24	{	{	PUNCT
ejpam-7055	173	25	µi	µi	PROPN
ejpam-7055	173	26	:	:	PUNCT
ejpam-7055	173	27	ω	ω	PROPN
ejpam-7055	173	28	→	→	SYM
ejpam-7055	173	29	ωi}i∈i	ωi}i∈i	PROPN
ejpam-7055	173	30	.	.	PUNCT
ejpam-7055	174	1	firstly	firstly	ADV
ejpam-7055	174	2	,	,	PUNCT
ejpam-7055	174	3	we	we	PRON
ejpam-7055	174	4	claim	claim	VERB
ejpam-7055	174	5	that	that	SCONJ
ejpam-7055	174	6	{	{	PUNCT
ejpam-7055	174	7	µi	µi	INTJ
ejpam-7055	174	8	:	:	PUNCT
ejpam-7055	174	9	(	(	PUNCT
ejpam-7055	174	10	ζ	ζ	NOUN
ejpam-7055	174	11	,	,	PUNCT
ejpam-7055	174	12	ω	ω	NOUN
ejpam-7055	174	13	)	)	PUNCT
ejpam-7055	174	14	→	→	SYM
ejpam-7055	174	15	(	(	PUNCT
ejpam-7055	174	16	ζi	ζi	PROPN
ejpam-7055	174	17	,	,	PUNCT
ejpam-7055	174	18	ωi	ωi	NOUN
ejpam-7055	174	19	)	)	PUNCT
ejpam-7055	174	20	}	}	PUNCT
ejpam-7055	174	21	is	be	AUX
ejpam-7055	174	22	a	a	DET
ejpam-7055	174	23	family	family	NOUN
ejpam-7055	174	24	of	of	ADP
ejpam-7055	174	25	sbcki	sbcki	NOUN
ejpam-7055	174	26	-morphisms	-morphism	NOUN
ejpam-7055	174	27	for	for	ADP
ejpam-7055	174	28	every	every	DET
ejpam-7055	174	29	i	i	PROPN
ejpam-7055	174	30	∈	∈	PROPN
ejpam-7055	174	31	i.	i.	NOUN
ejpam-7055	174	32	by	by	ADP
ejpam-7055	174	33	the	the	DET
ejpam-7055	174	34	assumption	assumption	NOUN
ejpam-7055	174	35	,	,	PUNCT
ejpam-7055	174	36	for	for	ADP
ejpam-7055	174	37	each	each	DET
ejpam-7055	174	38	α	α	PROPN
ejpam-7055	174	39	∈	∈	PROPN
ejpam-7055	174	40	ω	ω	NOUN
ejpam-7055	174	41	and	and	CCONJ
ejpam-7055	174	42	i	i	PRON
ejpam-7055	174	43	∈	∈	PROPN
ejpam-7055	174	44	i	i	PRON
ejpam-7055	174	45	,	,	PUNCT
ejpam-7055	174	46	one	one	NUM
ejpam-7055	174	47	yields	yield	NOUN
ejpam-7055	174	48	ζ(α	ζ(α	NOUN
ejpam-7055	174	49	)	)	PUNCT
ejpam-7055	175	1	=	=	SYM
ejpam-7055	175	2	∩i∈i(ζi(µi(α	∩i∈i(ζi(µi(α	PROPN
ejpam-7055	175	3	)	)	PUNCT
ejpam-7055	175	4	)	)	PUNCT
ejpam-7055	175	5	)	)	PUNCT
ejpam-7055	176	1	⊆	⊆	NUM
ejpam-7055	176	2	ζi(µi(α	ζi(µi(α	NUM
ejpam-7055	176	3	)	)	PUNCT
ejpam-7055	176	4	)	)	PUNCT
ejpam-7055	176	5	,	,	PUNCT
ejpam-7055	176	6	g.	g.	PROPN
ejpam-7055	176	7	muhiuddin	muhiuddin	PROPN
ejpam-7055	176	8	et	et	PROPN
ejpam-7055	176	9	al	al	PROPN
ejpam-7055	176	10	.	.	PUNCT
ejpam-7055	176	11	/	/	SYM
ejpam-7055	176	12	eur	eur	PROPN
ejpam-7055	176	13	.	.	PUNCT
ejpam-7055	177	1	j.	j.	PROPN
ejpam-7055	177	2	pure	pure	PROPN
ejpam-7055	177	3	appl	appl	PROPN
ejpam-7055	177	4	.	.	PROPN
ejpam-7055	177	5	math	math	PROPN
ejpam-7055	177	6	,	,	PUNCT
ejpam-7055	177	7	18	18	NUM
ejpam-7055	177	8	(	(	PUNCT
ejpam-7055	177	9	4	4	NUM
ejpam-7055	177	10	)	)	PUNCT
ejpam-7055	177	11	(	(	PUNCT
ejpam-7055	177	12	2025	2025	NUM
ejpam-7055	177	13	)	)	PUNCT
ejpam-7055	177	14	,	,	PUNCT
ejpam-7055	177	15	7055	7055	NUM
ejpam-7055	177	16	9	9	NUM
ejpam-7055	177	17	of	of	ADP
ejpam-7055	177	18	13	13	NUM
ejpam-7055	177	19	where	where	SCONJ
ejpam-7055	177	20	{	{	PUNCT
ejpam-7055	177	21	µi}i∈i	µi}i∈i	ADV
ejpam-7055	177	22	is	be	AUX
ejpam-7055	177	23	a	a	DET
ejpam-7055	177	24	family	family	NOUN
ejpam-7055	177	25	of	of	ADP
ejpam-7055	177	26	sbcki	sbcki	NOUN
ejpam-7055	177	27	-morphisms	-morphism	NOUN
ejpam-7055	177	28	,	,	PUNCT
ejpam-7055	177	29	furthermore	furthermore	ADV
ejpam-7055	177	30	,	,	PUNCT
ejpam-7055	177	31	suppose	suppose	VERB
ejpam-7055	177	32	that	that	SCONJ
ejpam-7055	177	33	ϕ,b	ϕ,b	PROPN
ejpam-7055	177	34	∈	∈	PROPN
ejpam-7055	177	35	ob(sbcki	ob(sbcki	PROPN
ejpam-7055	177	36	)	)	PUNCT
ejpam-7055	177	37	,	,	PUNCT
ejpam-7055	177	38	λ	λ	INTJ
ejpam-7055	177	39	:	:	PUNCT
ejpam-7055	177	40	b	b	X
ejpam-7055	177	41	→	→	SYM
ejpam-7055	177	42	ω	ω	PROPN
ejpam-7055	177	43	is	be	AUX
ejpam-7055	177	44	a	a	DET
ejpam-7055	177	45	mapping	mapping	NOUN
ejpam-7055	177	46	such	such	ADJ
ejpam-7055	177	47	that	that	PRON
ejpam-7055	177	48	λi	λi	ADP
ejpam-7055	177	49	=	=	X
ejpam-7055	177	50	µi	µi	PROPN
ejpam-7055	177	51	◦	◦	NOUN
ejpam-7055	177	52	λ	λ	PROPN
ejpam-7055	177	53	for	for	ADP
ejpam-7055	177	54	every	every	DET
ejpam-7055	177	55	i	i	PROPN
ejpam-7055	177	56	∈	∈	PROPN
ejpam-7055	177	57	i	i	PRON
ejpam-7055	177	58	,	,	PUNCT
ejpam-7055	177	59	and	and	CCONJ
ejpam-7055	177	60	λi	λi	ADP
ejpam-7055	177	61	:	:	PUNCT
ejpam-7055	177	62	(	(	PUNCT
ejpam-7055	177	63	ϕ,b	ϕ,b	NOUN
ejpam-7055	177	64	)	)	PUNCT
ejpam-7055	177	65	)	)	PUNCT
ejpam-7055	177	66	→	→	PUNCT
ejpam-7055	177	67	(	(	PUNCT
ejpam-7055	177	68	ζi	ζi	PROPN
ejpam-7055	177	69	,	,	PUNCT
ejpam-7055	177	70	ωi	ωi	NOUN
ejpam-7055	177	71	)	)	PUNCT
ejpam-7055	177	72	is	be	AUX
ejpam-7055	177	73	is	be	AUX
ejpam-7055	177	74	a	a	DET
ejpam-7055	177	75	family	family	NOUN
ejpam-7055	177	76	of	of	ADP
ejpam-7055	177	77	sbcki	sbcki	NOUN
ejpam-7055	177	78	-morphisms	-morphism	NOUN
ejpam-7055	177	79	.	.	PUNCT
ejpam-7055	178	1	then	then	ADV
ejpam-7055	178	2	,	,	PUNCT
ejpam-7055	178	3	we	we	PRON
ejpam-7055	178	4	can	can	AUX
ejpam-7055	178	5	infer	infer	VERB
ejpam-7055	178	6	that	that	PRON
ejpam-7055	178	7	ϕ(β	ϕ(β	PROPN
ejpam-7055	178	8	)	)	PUNCT
ejpam-7055	178	9	⊆	⊆	NUM
ejpam-7055	178	10	∩i∈i(ζi(λi)β	∩i∈i(ζi(λi)β	NUM
ejpam-7055	178	11	)	)	PUNCT
ejpam-7055	178	12	)	)	PUNCT
ejpam-7055	179	1	=	=	PUNCT
ejpam-7055	179	2	∩i∈i(ζi(µi	∩i∈i(ζi(µi	NOUN
ejpam-7055	179	3	◦	◦	NOUN
ejpam-7055	179	4	g)(β	g)(β	NOUN
ejpam-7055	179	5	)	)	PUNCT
ejpam-7055	179	6	)	)	PUNCT
ejpam-7055	180	1	=	=	SYM
ejpam-7055	180	2	∩i∈i(ζi(µi(g(β	∩i∈i(ζi(µi(g(β	ADJ
ejpam-7055	180	3	)	)	PUNCT
ejpam-7055	180	4	)	)	PUNCT
ejpam-7055	180	5	)	)	PUNCT
ejpam-7055	180	6	)	)	PUNCT
ejpam-7055	181	1	=	=	SYM
ejpam-7055	181	2	ζ(g(β	ζ(g(β	NOUN
ejpam-7055	181	3	)	)	PUNCT
ejpam-7055	181	4	)	)	PUNCT
ejpam-7055	181	5	therefore	therefore	ADV
ejpam-7055	181	6	,	,	PUNCT
ejpam-7055	181	7	λ	λ	PROPN
ejpam-7055	181	8	represents	represent	VERB
ejpam-7055	181	9	a	a	DET
ejpam-7055	181	10	sbcki	sbcki	NOUN
ejpam-7055	181	11	-morphism	-morphism	NOUN
ejpam-7055	181	12	from	from	ADP
ejpam-7055	181	13	ϕ,b	ϕ,b	PROPN
ejpam-7055	181	14	to	to	ADP
ejpam-7055	181	15	ζ	ζ	PROPN
ejpam-7055	181	16	,	,	PUNCT
ejpam-7055	181	17	ω	ω	NOUN
ejpam-7055	181	18	.	.	PUNCT
ejpam-7055	182	1	as	as	ADP
ejpam-7055	182	2	per	per	ADP
ejpam-7055	182	3	the	the	DET
ejpam-7055	182	4	definition	definition	NOUN
ejpam-7055	182	5	,	,	PUNCT
ejpam-7055	182	6	it	it	PRON
ejpam-7055	182	7	is	be	AUX
ejpam-7055	182	8	evident	evident	ADJ
ejpam-7055	182	9	that	that	SCONJ
ejpam-7055	182	10	the	the	DET
ejpam-7055	182	11	family	family	NOUN
ejpam-7055	182	12	{	{	PUNCT
ejpam-7055	182	13	µi	µi	INTJ
ejpam-7055	182	14	:	:	PUNCT
ejpam-7055	182	15	(	(	PUNCT
ejpam-7055	182	16	ζ	ζ	NOUN
ejpam-7055	182	17	,	,	PUNCT
ejpam-7055	182	18	ω	ω	NOUN
ejpam-7055	182	19	)	)	PUNCT
ejpam-7055	182	20	→	→	SYM
ejpam-7055	182	21	(	(	PUNCT
ejpam-7055	182	22	ζi	ζi	NOUN
ejpam-7055	182	23	,	,	PUNCT
ejpam-7055	182	24	ωi)}i∈i	ωi)}i∈i	NOUN
ejpam-7055	182	25	constitutes	constitute	VERB
ejpam-7055	182	26	a	a	DET
ejpam-7055	182	27	sbcki	sbcki	NOUN
ejpam-7055	182	28	initial	initial	ADJ
ejpam-7055	182	29	lift	lift	NOUN
ejpam-7055	182	30	of	of	ADP
ejpam-7055	182	31	{	{	PUNCT
ejpam-7055	182	32	µi	µi	INTJ
ejpam-7055	182	33	:	:	PUNCT
ejpam-7055	182	34	ω	ω	PROPN
ejpam-7055	182	35	→	→	SYM
ejpam-7055	182	36	ωi}i∈i	ωi}i∈i	PROPN
ejpam-7055	182	37	.	.	PUNCT
ejpam-7055	183	1	in	in	ADP
ejpam-7055	183	2	case	case	NOUN
ejpam-7055	183	3	2	2	NUM
ejpam-7055	183	4	,	,	PUNCT
ejpam-7055	183	5	we	we	PRON
ejpam-7055	183	6	address	address	VERB
ejpam-7055	183	7	the	the	DET
ejpam-7055	183	8	”	"	PUNCT
ejpam-7055	183	9	uniqueness	uniqueness	NOUN
ejpam-7055	183	10	of	of	ADP
ejpam-7055	183	11	the	the	DET
ejpam-7055	183	12	initial	initial	ADJ
ejpam-7055	183	13	lift	lift	NOUN
ejpam-7055	183	14	”	"	PUNCT
ejpam-7055	183	15	.	.	PUNCT
ejpam-7055	184	1	assuming	assume	VERB
ejpam-7055	184	2	that	that	SCONJ
ejpam-7055	184	3	{	{	PUNCT
ejpam-7055	184	4	µi	µi	INTJ
ejpam-7055	184	5	:	:	PUNCT
ejpam-7055	184	6	(	(	PUNCT
ejpam-7055	184	7	ζ̃,ω	ζ̃,ω	NOUN
ejpam-7055	184	8	)	)	PUNCT
ejpam-7055	184	9	→	→	SYM
ejpam-7055	184	10	(	(	PUNCT
ejpam-7055	184	11	ζi	ζi	PROPN
ejpam-7055	184	12	,	,	PUNCT
ejpam-7055	184	13	ωi)}i∈i	ωi)}i∈i	NOUN
ejpam-7055	184	14	also	also	ADV
ejpam-7055	184	15	stands	stand	VERB
ejpam-7055	184	16	as	as	ADP
ejpam-7055	184	17	a	a	DET
ejpam-7055	184	18	sbcki	sbcki	NOUN
ejpam-7055	184	19	initial	initial	ADJ
ejpam-7055	184	20	lift	lift	NOUN
ejpam-7055	184	21	of	of	ADP
ejpam-7055	184	22	{	{	PUNCT
ejpam-7055	184	23	µi	µi	INTJ
ejpam-7055	184	24	:	:	PUNCT
ejpam-7055	184	25	ω	ω	PROPN
ejpam-7055	184	26	→	→	SYM
ejpam-7055	184	27	ωi}i∈i	ωi}i∈i	PROPN
ejpam-7055	184	28	,	,	PUNCT
ejpam-7055	184	29	distinct	distinct	ADJ
ejpam-7055	184	30	from	from	ADP
ejpam-7055	184	31	{	{	PUNCT
ejpam-7055	184	32	µi	µi	INTJ
ejpam-7055	184	33	:	:	PUNCT
ejpam-7055	184	34	(	(	PUNCT
ejpam-7055	184	35	ζ	ζ	NOUN
ejpam-7055	184	36	,	,	PUNCT
ejpam-7055	184	37	ω	ω	NOUN
ejpam-7055	184	38	)	)	PUNCT
ejpam-7055	184	39	→	→	SYM
ejpam-7055	184	40	(	(	PUNCT
ejpam-7055	184	41	ζi	ζi	PROPN
ejpam-7055	184	42	,	,	PUNCT
ejpam-7055	184	43	ωi)}i∈i	ωi)}i∈i	NOUN
ejpam-7055	184	44	,	,	PUNCT
ejpam-7055	184	45	then	then	ADV
ejpam-7055	184	46	{	{	PUNCT
ejpam-7055	184	47	µi	µi	INTJ
ejpam-7055	184	48	:	:	PUNCT
ejpam-7055	184	49	(	(	PUNCT
ejpam-7055	184	50	ζ̃,ω	ζ̃,ω	NOUN
ejpam-7055	184	51	)	)	PUNCT
ejpam-7055	184	52	→	→	SYM
ejpam-7055	184	53	(	(	PUNCT
ejpam-7055	184	54	ζi	ζi	NOUN
ejpam-7055	184	55	,	,	PUNCT
ejpam-7055	184	56	ωi)}i∈i	ωi)}i∈i	NOUN
ejpam-7055	184	57	forms	form	VERB
ejpam-7055	184	58	a	a	DET
ejpam-7055	184	59	set	set	NOUN
ejpam-7055	184	60	of	of	ADP
ejpam-7055	184	61	sbcki	sbcki	NOUN
ejpam-7055	184	62	-morphisms	-morphism	NOUN
ejpam-7055	184	63	.	.	PUNCT
ejpam-7055	185	1	it	it	PRON
ejpam-7055	185	2	is	be	AUX
ejpam-7055	185	3	evident	evident	ADJ
ejpam-7055	185	4	that	that	SCONJ
ejpam-7055	185	5	ζ̃(α	ζ̃(α	VERB
ejpam-7055	185	6	)	)	PUNCT
ejpam-7055	185	7	⊆	⊆	NUM
ejpam-7055	185	8	ζi(µi(α	ζi(µi(α	NUM
ejpam-7055	185	9	)	)	PUNCT
ejpam-7055	185	10	)	)	PUNCT
ejpam-7055	186	1	foralli	foralli	PROPN
ejpam-7055	187	1	∈	∈	PROPN
ejpam-7055	188	1	i	i	PRON
ejpam-7055	188	2	and	and	CCONJ
ejpam-7055	188	3	α	α	PROPN
ejpam-7055	188	4	∈	∈	PROPN
ejpam-7055	188	5	ω	ω	PROPN
ejpam-7055	188	6	.	.	PUNCT
ejpam-7055	189	1	thus	thus	ADV
ejpam-7055	189	2	,	,	PUNCT
ejpam-7055	189	3	ζ̃(α	ζ̃(α	ADJ
ejpam-7055	189	4	)	)	PUNCT
ejpam-7055	189	5	⊆	⊆	NUM
ejpam-7055	189	6	ζi(µi(α	ζi(µi(α	NUM
ejpam-7055	189	7	)	)	PUNCT
ejpam-7055	189	8	)	)	PUNCT
ejpam-7055	190	1	=	=	SYM
ejpam-7055	190	2	ζ(α	ζ(α	PROPN
ejpam-7055	190	3	)	)	PUNCT
ejpam-7055	190	4	,	,	PUNCT
ejpam-7055	190	5	implying	imply	VERB
ejpam-7055	190	6	ζ̃	ζ̃	PROPN
ejpam-7055	190	7	⊆	⊆	NUM
ejpam-7055	190	8	ζ	ζ	NOUN
ejpam-7055	190	9	.	.	PUNCT
ejpam-7055	191	1	conversely	conversely	ADV
ejpam-7055	191	2	,	,	PUNCT
ejpam-7055	191	3	for	for	ADP
ejpam-7055	191	4	the	the	DET
ejpam-7055	191	5	sbcki	sbcki	NOUN
ejpam-7055	191	6	-entities	-entitie	NOUN
ejpam-7055	191	7	(	(	PUNCT
ejpam-7055	191	8	ζ	ζ	NOUN
ejpam-7055	191	9	,	,	PUNCT
ejpam-7055	191	10	ω	ω	NOUN
ejpam-7055	191	11	)	)	PUNCT
ejpam-7055	191	12	and	and	CCONJ
ejpam-7055	191	13	identity	identity	NOUN
ejpam-7055	191	14	mapping	mapping	NOUN
ejpam-7055	191	15	iδω	iδω	PROPN
ejpam-7055	191	16	:	:	PUNCT
ejpam-7055	191	17	ω	ω	PROPN
ejpam-7055	191	18	→	→	SYM
ejpam-7055	191	19	ω	ω	PROPN
ejpam-7055	191	20	,	,	PUNCT
ejpam-7055	191	21	given	give	VERB
ejpam-7055	191	22	that	that	SCONJ
ejpam-7055	191	23	{	{	PUNCT
ejpam-7055	191	24	µi	µi	INTJ
ejpam-7055	191	25	:	:	PUNCT
ejpam-7055	191	26	(	(	PUNCT
ejpam-7055	191	27	ζ̃,ω	ζ̃,ω	NOUN
ejpam-7055	191	28	)	)	PUNCT
ejpam-7055	191	29	→	→	SYM
ejpam-7055	191	30	(	(	PUNCT
ejpam-7055	191	31	ζi	ζi	NOUN
ejpam-7055	191	32	,	,	PUNCT
ejpam-7055	191	33	ωi)}i∈i	ωi)}i∈i	NOUN
ejpam-7055	191	34	serves	serve	VERB
ejpam-7055	191	35	as	as	ADP
ejpam-7055	191	36	a	a	DET
ejpam-7055	191	37	sbcki	sbcki	NOUN
ejpam-7055	191	38	initial	initial	ADJ
ejpam-7055	191	39	lift	lift	NOUN
ejpam-7055	191	40	of	of	ADP
ejpam-7055	191	41	{	{	PUNCT
ejpam-7055	191	42	µi	µi	INTJ
ejpam-7055	191	43	:	:	PUNCT
ejpam-7055	191	44	ω	ω	PROPN
ejpam-7055	191	45	→	→	SYM
ejpam-7055	191	46	ωi}i∈i	ωi}i∈i	NOUN
ejpam-7055	191	47	,	,	PUNCT
ejpam-7055	191	48	we	we	PRON
ejpam-7055	191	49	find	find	VERB
ejpam-7055	191	50	that	that	SCONJ
ejpam-7055	191	51	µi	µi	ADP
ejpam-7055	191	52	◦	◦	NOUN
ejpam-7055	191	53	iδω	iδω	NOUN
ejpam-7055	191	54	=	=	SYM
ejpam-7055	191	55	µi	µi	PROPN
ejpam-7055	191	56	,	,	PUNCT
ejpam-7055	191	57	where	where	SCONJ
ejpam-7055	191	58	µi	µi	PROPN
ejpam-7055	191	59	represents	represent	VERB
ejpam-7055	191	60	a	a	DET
ejpam-7055	191	61	sbcki	sbcki	NOUN
ejpam-7055	191	62	-morphism	-morphism	NOUN
ejpam-7055	191	63	for	for	ADP
ejpam-7055	191	64	all	all	PRON
ejpam-7055	191	65	i	i	PRON
ejpam-7055	191	66	∈	∈	PROPN
ejpam-7055	191	67	i	i	PRON
ejpam-7055	191	68	,	,	PUNCT
ejpam-7055	191	69	and	and	CCONJ
ejpam-7055	191	70	iδω	iδω	ADV
ejpam-7055	191	71	:	:	PUNCT
ejpam-7055	191	72	(	(	PUNCT
ejpam-7055	191	73	ζ	ζ	NOUN
ejpam-7055	191	74	,	,	PUNCT
ejpam-7055	191	75	ω	ω	NOUN
ejpam-7055	191	76	)	)	PUNCT
ejpam-7055	191	77	→	→	SYM
ejpam-7055	191	78	(	(	PUNCT
ejpam-7055	191	79	ζ̃,ω	ζ̃,ω	NOUN
ejpam-7055	191	80	)	)	PUNCT
ejpam-7055	191	81	is	be	AUX
ejpam-7055	191	82	also	also	ADV
ejpam-7055	191	83	a	a	DET
ejpam-7055	191	84	sbcki	sbcki	NOUN
ejpam-7055	191	85	-morphism	-morphism	NOUN
ejpam-7055	191	86	.	.	PUNCT
ejpam-7055	192	1	consequently	consequently	ADV
ejpam-7055	192	2	,	,	PUNCT
ejpam-7055	192	3	ζ(α	ζ(α	PROPN
ejpam-7055	192	4	)	)	PUNCT
ejpam-7055	192	5	⊆	⊆	NUM
ejpam-7055	192	6	ζ̃(iδω(α	ζ̃(iδω(α	PROPN
ejpam-7055	192	7	)	)	PUNCT
ejpam-7055	192	8	)	)	PUNCT
ejpam-7055	192	9	=	=	SYM
ejpam-7055	192	10	ζ̃(α	ζ̃(α	NOUN
ejpam-7055	192	11	)	)	PUNCT
ejpam-7055	192	12	for	for	ADP
ejpam-7055	192	13	each	each	DET
ejpam-7055	192	14	α	α	PROPN
ejpam-7055	192	15	∈	∈	PROPN
ejpam-7055	192	16	ω	ω	PROPN
ejpam-7055	192	17	,	,	PUNCT
ejpam-7055	192	18	indicating	indicate	VERB
ejpam-7055	192	19	ζ	ζ	PRON
ejpam-7055	192	20	⊆	⊆	SYM
ejpam-7055	192	21	ζ̃.	ζ̃.	ADJ
ejpam-7055	192	22	in	in	ADP
ejpam-7055	192	23	summary	summary	NOUN
ejpam-7055	192	24	,	,	PUNCT
ejpam-7055	192	25	it	it	PRON
ejpam-7055	192	26	is	be	AUX
ejpam-7055	192	27	established	establish	VERB
ejpam-7055	192	28	that	that	SCONJ
ejpam-7055	192	29	ζ	ζ	NOUN
ejpam-7055	192	30	⊆	⊆	NUM
ejpam-7055	192	31	ζ̃.	ζ̃.	ADJ
ejpam-7055	192	32	combining	combine	VERB
ejpam-7055	192	33	the	the	DET
ejpam-7055	192	34	outcomes	outcome	NOUN
ejpam-7055	192	35	of	of	ADP
ejpam-7055	192	36	steps	step	NOUN
ejpam-7055	192	37	(	(	PUNCT
ejpam-7055	192	38	1	1	NUM
ejpam-7055	192	39	)	)	PUNCT
ejpam-7055	192	40	and	and	CCONJ
ejpam-7055	192	41	(	(	PUNCT
ejpam-7055	192	42	2	2	NUM
ejpam-7055	192	43	)	)	PUNCT
ejpam-7055	192	44	,	,	PUNCT
ejpam-7055	192	45	it	it	PRON
ejpam-7055	192	46	can	can	AUX
ejpam-7055	192	47	be	be	AUX
ejpam-7055	192	48	concluded	conclude	VERB
ejpam-7055	192	49	that	that	SCONJ
ejpam-7055	192	50	sbcki	sbcki	NOUN
ejpam-7055	192	51	forms	form	VERB
ejpam-7055	192	52	a	a	DET
ejpam-7055	192	53	topological	topological	ADJ
ejpam-7055	192	54	construct	construct	NOUN
ejpam-7055	192	55	.	.	PUNCT
ejpam-7055	193	1	6	6	X
ejpam-7055	193	2	.	.	X
ejpam-7055	193	3	special	special	ADJ
ejpam-7055	193	4	objects	object	NOUN
ejpam-7055	193	5	in	in	ADP
ejpam-7055	193	6	sbcki	sbcki	NOUN
ejpam-7055	193	7	it	it	PRON
ejpam-7055	193	8	is	be	AUX
ejpam-7055	193	9	evident	evident	ADJ
ejpam-7055	193	10	that	that	SCONJ
ejpam-7055	193	11	the	the	DET
ejpam-7055	193	12	set	set	NOUN
ejpam-7055	193	13	{	{	PUNCT
ejpam-7055	193	14	0	0	NUM
ejpam-7055	193	15	}	}	PUNCT
ejpam-7055	193	16	constitutes	constitute	VERB
ejpam-7055	193	17	a	a	DET
ejpam-7055	193	18	bci	bci	PROPN
ejpam-7055	193	19	/	/	SYM
ejpam-7055	193	20	bck	bck	NOUN
ejpam-7055	193	21	-	-	PUNCT
ejpam-7055	193	22	algebra	algebra	NOUN
ejpam-7055	193	23	.	.	PUNCT
ejpam-7055	194	1	consequently	consequently	ADV
ejpam-7055	194	2	,	,	PUNCT
ejpam-7055	194	3	it	it	PRON
ejpam-7055	194	4	follows	follow	VERB
ejpam-7055	194	5	trivially	trivially	ADV
ejpam-7055	194	6	that	that	SCONJ
ejpam-7055	194	7	the	the	DET
ejpam-7055	194	8	pair	pair	NOUN
ejpam-7055	194	9	(	(	PUNCT
ejpam-7055	194	10	ζ	ζ	NOUN
ejpam-7055	194	11	,	,	PUNCT
ejpam-7055	194	12	{	{	PUNCT
ejpam-7055	194	13	0	0	NUM
ejpam-7055	194	14	}	}	PUNCT
ejpam-7055	194	15	)	)	PUNCT
ejpam-7055	194	16	represents	represent	VERB
ejpam-7055	194	17	a	a	DET
ejpam-7055	194	18	”	"	PUNCT
ejpam-7055	194	19	soft	soft	ADJ
ejpam-7055	194	20	bci	bci	NOUN
ejpam-7055	194	21	/	/	SYM
ejpam-7055	194	22	bck	bck	NOUN
ejpam-7055	194	23	-	-	PUNCT
ejpam-7055	194	24	algebra	algebra	NOUN
ejpam-7055	194	25	over	over	ADP
ejpam-7055	194	26	x̃	x̃	PROPN
ejpam-7055	194	27	”	"	PUNCT
ejpam-7055	194	28	.	.	PUNCT
ejpam-7055	195	1	now	now	ADV
ejpam-7055	195	2	,	,	PUNCT
ejpam-7055	195	3	for	for	ADP
ejpam-7055	195	4	any	any	DET
ejpam-7055	195	5	other	other	ADJ
ejpam-7055	195	6	object	object	NOUN
ejpam-7055	195	7	(	(	PUNCT
ejpam-7055	195	8	ϕ,ω	ϕ,ω	NOUN
ejpam-7055	195	9	)	)	PUNCT
ejpam-7055	195	10	in	in	ADP
ejpam-7055	195	11	sbcki	sbcki	NOUN
ejpam-7055	195	12	,	,	PUNCT
ejpam-7055	195	13	there	there	PRON
ejpam-7055	195	14	is	be	VERB
ejpam-7055	195	15	only	only	ADV
ejpam-7055	195	16	one	one	NUM
ejpam-7055	195	17	morphism	morphism	NOUN
ejpam-7055	195	18	from	from	ADP
ejpam-7055	195	19	0	0	NUM
ejpam-7055	195	20	→	→	SYM
ejpam-7055	195	21	ω	ω	NUM
ejpam-7055	195	22	i.e	i.e	PROPN
ejpam-7055	195	23	,	,	PUNCT
ejpam-7055	195	24	0	0	NUM
ejpam-7055	195	25	→	→	SYM
ejpam-7055	195	26	0	0	NUM
ejpam-7055	195	27	and	and	CCONJ
ejpam-7055	195	28	also	also	ADV
ejpam-7055	195	29	there	there	PRON
ejpam-7055	195	30	is	be	VERB
ejpam-7055	195	31	only	only	ADV
ejpam-7055	195	32	morphism	morphism	NOUN
ejpam-7055	195	33	ω	ω	PROPN
ejpam-7055	195	34	→	→	SYM
ejpam-7055	195	35	{	{	PUNCT
ejpam-7055	195	36	0	0	NUM
ejpam-7055	195	37	}	}	PUNCT
ejpam-7055	195	38	i.e	i.e	PROPN
ejpam-7055	195	39	,	,	PUNCT
ejpam-7055	195	40	α	α	PROPN
ejpam-7055	195	41	→	→	SYM
ejpam-7055	195	42	0	0	NUM
ejpam-7055	195	43	,	,	PUNCT
ejpam-7055	195	44	∀α	∀α	VERB
ejpam-7055	195	45	∈	∈	PROPN
ejpam-7055	195	46	ω.trivially	ω.trivially	NOUN
ejpam-7055	195	47	,	,	PUNCT
ejpam-7055	195	48	the	the	DET
ejpam-7055	195	49	0	0	NUM
ejpam-7055	195	50	-	-	PUNCT
ejpam-7055	195	51	morphism	morphism	NOUN
ejpam-7055	195	52	is	be	AUX
ejpam-7055	195	53	a	a	DET
ejpam-7055	195	54	soft	soft	ADJ
ejpam-7055	195	55	morphism	morphism	NOUN
ejpam-7055	195	56	.	.	PUNCT
ejpam-7055	196	1	thus	thus	ADV
ejpam-7055	196	2	sbcki	sbcki	NOUN
ejpam-7055	196	3	has	have	VERB
ejpam-7055	196	4	zero	zero	NUM
ejpam-7055	196	5	objects	object	NOUN
ejpam-7055	196	6	.	.	PUNCT
ejpam-7055	197	1	proposition	proposition	NOUN
ejpam-7055	197	2	4	4	NUM
ejpam-7055	197	3	.	.	PUNCT
ejpam-7055	198	1	the	the	DET
ejpam-7055	198	2	empty	empty	ADJ
ejpam-7055	198	3	set	set	NOUN
ejpam-7055	198	4	(	(	PUNCT
ejpam-7055	198	5	accompanied	accompany	VERB
ejpam-7055	198	6	by	by	ADP
ejpam-7055	198	7	an	an	DET
ejpam-7055	198	8	empty	empty	ADJ
ejpam-7055	198	9	function	function	NOUN
ejpam-7055	198	10	mapping	mapping	NOUN
ejpam-7055	198	11	into	into	ADP
ejpam-7055	198	12	p	p	PROPN
ejpam-7055	198	13	(	(	PUNCT
ejpam-7055	198	14	x̃	x̃	PROPN
ejpam-7055	198	15	)	)	PUNCT
ejpam-7055	198	16	)	)	PUNCT
ejpam-7055	198	17	serves	serve	VERB
ejpam-7055	198	18	as	as	ADP
ejpam-7055	198	19	a	a	DET
ejpam-7055	198	20	zero	zero	NUM
ejpam-7055	198	21	object	object	NOUN
ejpam-7055	198	22	within	within	ADP
ejpam-7055	198	23	sbcki	sbcki	NOUN
ejpam-7055	198	24	.	.	PUNCT
ejpam-7055	199	1	proof	proof	NOUN
ejpam-7055	199	2	.	.	PUNCT
ejpam-7055	200	1	for	for	ADP
ejpam-7055	200	2	each	each	DET
ejpam-7055	200	3	object	object	NOUN
ejpam-7055	200	4	(	(	PUNCT
ejpam-7055	200	5	ζ	ζ	NOUN
ejpam-7055	200	6	,	,	PUNCT
ejpam-7055	200	7	ω	ω	NOUN
ejpam-7055	200	8	)	)	PUNCT
ejpam-7055	200	9	∈	∈	PROPN
ejpam-7055	200	10	sbcki	sbcki	NOUN
ejpam-7055	200	11	,	,	PUNCT
ejpam-7055	200	12	there	there	PRON
ejpam-7055	200	13	exist	exist	VERB
ejpam-7055	200	14	unique	unique	ADJ
ejpam-7055	200	15	morphism	morphism	NOUN
ejpam-7055	200	16	the	the	DET
ejpam-7055	200	17	inequalities	inequality	NOUN
ejpam-7055	200	18	are	be	AUX
ejpam-7055	200	19	satisfied	satisfied	ADJ
ejpam-7055	200	20	by	by	ADP
ejpam-7055	200	21	default	default	NOUN
ejpam-7055	200	22	.	.	PUNCT
ejpam-7055	201	1	therefore	therefore	ADV
ejpam-7055	201	2	soft	soft	ADJ
ejpam-7055	201	3	bci	bci	PROPN
ejpam-7055	201	4	/	/	SYM
ejpam-7055	201	5	bck	bck	NOUN
ejpam-7055	201	6	-	-	PUNCT
ejpam-7055	201	7	algebras	algebras	X
ejpam-7055	201	8	(	(	PUNCT
ejpam-7055	201	9	(	(	PUNCT
ejpam-7055	201	10	ζ	ζ	PROPN
ejpam-7055	201	11	,	,	PUNCT
ejpam-7055	201	12	ω	ω	NOUN
ejpam-7055	201	13	)	)	PUNCT
ejpam-7055	201	14	,	,	PUNCT
ejpam-7055	201	15	(	(	PUNCT
ejpam-7055	201	16	φ	φ	PROPN
ejpam-7055	201	17	,	,	PUNCT
ejpam-7055	201	18	φ	φ	NOUN
ejpam-7055	201	19	)	)	PUNCT
ejpam-7055	201	20	)	)	PUNCT
ejpam-7055	201	21	and	and	CCONJ
ejpam-7055	201	22	(	(	PUNCT
ejpam-7055	201	23	(	(	PUNCT
ejpam-7055	201	24	φ	φ	PROPN
ejpam-7055	201	25	,	,	PUNCT
ejpam-7055	201	26	φ	φ	NOUN
ejpam-7055	201	27	)	)	PUNCT
ejpam-7055	201	28	,	,	PUNCT
ejpam-7055	201	29	(	(	PUNCT
ejpam-7055	201	30	ζ	ζ	NOUN
ejpam-7055	201	31	,	,	PUNCT
ejpam-7055	201	32	ω	ω	NOUN
ejpam-7055	201	33	)	)	PUNCT
ejpam-7055	201	34	)	)	PUNCT
ejpam-7055	201	35	each	each	PRON
ejpam-7055	201	36	contain	contain	VERB
ejpam-7055	201	37	only	only	ADV
ejpam-7055	201	38	one	one	NUM
ejpam-7055	201	39	-morphism	-morphism	NOUN
ejpam-7055	201	40	.	.	PUNCT
ejpam-7055	202	1	proposition	proposition	NOUN
ejpam-7055	202	2	5	5	NUM
ejpam-7055	202	3	.	.	PUNCT
ejpam-7055	203	1	the	the	DET
ejpam-7055	203	2	category	category	NOUN
ejpam-7055	203	3	sbcki	sbcki	NOUN
ejpam-7055	203	4	has	have	VERB
ejpam-7055	203	5	a	a	DET
ejpam-7055	203	6	terminal	terminal	ADJ
ejpam-7055	203	7	object	object	NOUN
ejpam-7055	203	8	.	.	PUNCT
ejpam-7055	204	1	proof	proof	NOUN
ejpam-7055	204	2	.	.	PUNCT
ejpam-7055	205	1	define	define	VERB
ejpam-7055	205	2	a	a	DET
ejpam-7055	205	3	mapping	mapping	NOUN
ejpam-7055	205	4	t{φ	t{φ	NOUN
ejpam-7055	205	5	}	}	PUNCT
ejpam-7055	205	6	:	:	PUNCT
ejpam-7055	205	7	φ	φ	PROPN
ejpam-7055	205	8	→	→	SYM
ejpam-7055	205	9	p	p	X
ejpam-7055	205	10	(	(	PUNCT
ejpam-7055	205	11	u	u	NOUN
ejpam-7055	205	12	)	)	PUNCT
ejpam-7055	205	13	φ	φ	PROPN
ejpam-7055	205	14	7→	7→	NUM
ejpam-7055	205	15	u	u	NOUN
ejpam-7055	205	16	g.	g.	PROPN
ejpam-7055	205	17	muhiuddin	muhiuddin	PROPN
ejpam-7055	205	18	et	et	PROPN
ejpam-7055	205	19	al	al	PROPN
ejpam-7055	205	20	.	.	PUNCT
ejpam-7055	205	21	/	/	SYM
ejpam-7055	205	22	eur	eur	PROPN
ejpam-7055	205	23	.	.	PUNCT
ejpam-7055	206	1	j.	j.	PROPN
ejpam-7055	206	2	pure	pure	PROPN
ejpam-7055	206	3	appl	appl	PROPN
ejpam-7055	206	4	.	.	PROPN
ejpam-7055	206	5	math	math	PROPN
ejpam-7055	206	6	,	,	PUNCT
ejpam-7055	206	7	18	18	NUM
ejpam-7055	206	8	(	(	PUNCT
ejpam-7055	206	9	4	4	NUM
ejpam-7055	206	10	)	)	PUNCT
ejpam-7055	206	11	(	(	PUNCT
ejpam-7055	206	12	2025	2025	NUM
ejpam-7055	206	13	)	)	PUNCT
ejpam-7055	206	14	,	,	PUNCT
ejpam-7055	206	15	7055	7055	NUM
ejpam-7055	206	16	10	10	NUM
ejpam-7055	206	17	of	of	ADP
ejpam-7055	206	18	13	13	NUM
ejpam-7055	206	19	figure	figure	NOUN
ejpam-7055	206	20	7	7	NUM
ejpam-7055	206	21	:	:	PUNCT
ejpam-7055	206	22	figure	figure	NOUN
ejpam-7055	206	23	8	8	NUM
ejpam-7055	206	24	:	:	PUNCT
ejpam-7055	206	25	trivially	trivially	ADV
ejpam-7055	206	26	(	(	PUNCT
ejpam-7055	206	27	t{φ	t{φ	NOUN
ejpam-7055	206	28	}	}	PUNCT
ejpam-7055	206	29	,	,	PUNCT
ejpam-7055	206	30	{	{	PUNCT
ejpam-7055	206	31	φ	φ	NOUN
ejpam-7055	206	32	}	}	PUNCT
ejpam-7055	206	33	in	in	ADP
ejpam-7055	206	34	a	a	DET
ejpam-7055	206	35	soft	soft	ADJ
ejpam-7055	206	36	bck	bck	NOUN
ejpam-7055	206	37	-	-	PUNCT
ejpam-7055	206	38	algebra	algebra	NOUN
ejpam-7055	206	39	for	for	ADP
ejpam-7055	206	40	any	any	DET
ejpam-7055	206	41	object	object	NOUN
ejpam-7055	206	42	(	(	PUNCT
ejpam-7055	206	43	tm	tm	NOUN
ejpam-7055	206	44	,	,	PUNCT
ejpam-7055	206	45	m	m	PROPN
ejpam-7055	206	46	)	)	PUNCT
ejpam-7055	206	47	,	,	PUNCT
ejpam-7055	206	48	define	define	VERB
ejpam-7055	206	49	a	a	DET
ejpam-7055	206	50	map	map	NOUN
ejpam-7055	206	51	µ	µ	X
ejpam-7055	206	52	:	:	PUNCT
ejpam-7055	206	53	m	m	VERB
ejpam-7055	206	54	→	→	SYM
ejpam-7055	206	55	{	{	PUNCT
ejpam-7055	206	56	φ	φ	NOUN
ejpam-7055	206	57	}	}	PUNCT
ejpam-7055	206	58	by	by	ADP
ejpam-7055	206	59	m	m	PROPN
ejpam-7055	206	60	→	→	SYM
ejpam-7055	206	61	φ	φ	PROPN
ejpam-7055	206	62	.	.	PUNCT
ejpam-7055	207	1	then	then	ADV
ejpam-7055	207	2	,	,	PUNCT
ejpam-7055	207	3	for	for	ADP
ejpam-7055	207	4	each	each	DET
ejpam-7055	207	5	m	m	NOUN
ejpam-7055	207	6	∈	∈	PROPN
ejpam-7055	207	7	m	m	NOUN
ejpam-7055	207	8	,	,	PUNCT
ejpam-7055	207	9	the	the	DET
ejpam-7055	207	10	relationship	relationship	NOUN
ejpam-7055	207	11	tm	tm	PROPN
ejpam-7055	207	12	(	(	PUNCT
ejpam-7055	207	13	m	m	PROPN
ejpam-7055	207	14	)	)	PUNCT
ejpam-7055	207	15	⊆	⊆	NUM
ejpam-7055	207	16	t{φ}(µ(m	t{φ}(µ(m	NOUN
ejpam-7055	207	17	)	)	PUNCT
ejpam-7055	207	18	)	)	PUNCT
ejpam-7055	208	1	=	=	SYM
ejpam-7055	208	2	t{φ}(φ	t{φ}(φ	X
ejpam-7055	208	3	)	)	PUNCT
ejpam-7055	208	4	=	=	SYM
ejpam-7055	208	5	u	u	NOUN
ejpam-7055	208	6	holds	hold	VERB
ejpam-7055	208	7	,	,	PUNCT
ejpam-7055	208	8	indicating	indicate	VERB
ejpam-7055	208	9	that	that	SCONJ
ejpam-7055	208	10	µ	µ	NOUN
ejpam-7055	208	11	functions	function	NOUN
ejpam-7055	208	12	as	as	ADP
ejpam-7055	208	13	a	a	DET
ejpam-7055	208	14	soft	soft	ADJ
ejpam-7055	208	15	bck	bck	NOUN
ejpam-7055	208	16	-	-	PUNCT
ejpam-7055	208	17	morphism	morphism	NOUN
ejpam-7055	208	18	from	from	ADP
ejpam-7055	208	19	(	(	PUNCT
ejpam-7055	208	20	tm	tm	PROPN
ejpam-7055	208	21	,	,	PUNCT
ejpam-7055	208	22	m	m	PROPN
ejpam-7055	208	23	)	)	PUNCT
ejpam-7055	208	24	to	to	ADP
ejpam-7055	208	25	(	(	PUNCT
ejpam-7055	208	26	t{φ},φ	t{φ},φ	ADJ
ejpam-7055	208	27	)	)	PUNCT
ejpam-7055	208	28	.	.	PUNCT
ejpam-7055	209	1	it	it	PRON
ejpam-7055	209	2	is	be	AUX
ejpam-7055	209	3	evident	evident	ADJ
ejpam-7055	209	4	that	that	SCONJ
ejpam-7055	209	5	µ	µ	NOUN
ejpam-7055	209	6	is	be	AUX
ejpam-7055	209	7	uniquely	uniquely	ADV
ejpam-7055	209	8	defined	define	VERB
ejpam-7055	209	9	.	.	PUNCT
ejpam-7055	210	1	hence	hence	ADV
ejpam-7055	210	2	,	,	PUNCT
ejpam-7055	210	3	(	(	PUNCT
ejpam-7055	210	4	t{φ},φ	t{φ},φ	PROPN
ejpam-7055	210	5	)	)	PUNCT
ejpam-7055	210	6	stands	stand	VERB
ejpam-7055	210	7	as	as	ADP
ejpam-7055	210	8	a	a	DET
ejpam-7055	210	9	terminal	terminal	ADJ
ejpam-7055	210	10	object	object	NOUN
ejpam-7055	210	11	in	in	ADP
ejpam-7055	210	12	sbcki	sbcki	NOUN
ejpam-7055	210	13	.	.	PUNCT
ejpam-7055	211	1	proposition	proposition	NOUN
ejpam-7055	211	2	6	6	NUM
ejpam-7055	211	3	.	.	PUNCT
ejpam-7055	212	1	the	the	DET
ejpam-7055	212	2	category	category	NOUN
ejpam-7055	212	3	sbcki	sbcki	NOUN
ejpam-7055	212	4	has	have	VERB
ejpam-7055	212	5	an	an	DET
ejpam-7055	212	6	initial	initial	ADJ
ejpam-7055	212	7	object	object	NOUN
ejpam-7055	212	8	.	.	PUNCT
ejpam-7055	213	1	proof	proof	NOUN
ejpam-7055	213	2	.	.	PUNCT
ejpam-7055	214	1	similar	similar	ADJ
ejpam-7055	214	2	proof	proof	NOUN
ejpam-7055	214	3	for	for	ADP
ejpam-7055	214	4	a	a	DET
ejpam-7055	214	5	terminal	terminal	ADJ
ejpam-7055	214	6	object	object	NOUN
ejpam-7055	214	7	.	.	PUNCT
ejpam-7055	215	1	proposition	proposition	NOUN
ejpam-7055	215	2	7	7	NUM
ejpam-7055	215	3	.	.	PUNCT
ejpam-7055	216	1	the	the	DET
ejpam-7055	216	2	category	category	NOUN
ejpam-7055	216	3	sbcki	sbcki	NOUN
ejpam-7055	216	4	has	have	VERB
ejpam-7055	216	5	zero	zero	NUM
ejpam-7055	216	6	objects	object	NOUN
ejpam-7055	216	7	.	.	PUNCT
ejpam-7055	217	1	proof	proof	NOUN
ejpam-7055	217	2	.	.	PUNCT
ejpam-7055	218	1	trivially	trivially	ADV
ejpam-7055	218	2	,	,	PUNCT
ejpam-7055	218	3	the	the	DET
ejpam-7055	218	4	empty	empty	ADJ
ejpam-7055	218	5	set	set	NOUN
ejpam-7055	218	6	φ	φ	PROPN
ejpam-7055	218	7	forms	form	VERB
ejpam-7055	218	8	a	a	DET
ejpam-7055	218	9	bck	bck	NOUN
ejpam-7055	218	10	-	-	PUNCT
ejpam-7055	218	11	algebra	algebra	NOUN
ejpam-7055	218	12	.	.	PUNCT
ejpam-7055	219	1	then	then	ADV
ejpam-7055	219	2	(	(	PUNCT
ejpam-7055	219	3	φ	φ	PROPN
ejpam-7055	219	4	,	,	PUNCT
ejpam-7055	219	5	φ	φ	NUM
ejpam-7055	219	6	)	)	PUNCT
ejpam-7055	219	7	is	be	AUX
ejpam-7055	219	8	a	a	DET
ejpam-7055	219	9	soft	soft	ADJ
ejpam-7055	219	10	bckalgebra	bckalgebra	NOUN
ejpam-7055	219	11	(	(	PUNCT
ejpam-7055	219	12	φ	φ	PROPN
ejpam-7055	219	13	:	:	PUNCT
ejpam-7055	219	14	φ	φ	PROPN
ejpam-7055	219	15	→	→	SYM
ejpam-7055	219	16	p	p	X
ejpam-7055	219	17	(	(	PUNCT
ejpam-7055	219	18	u	u	NOUN
ejpam-7055	219	19	)	)	PUNCT
ejpam-7055	219	20	)	)	PUNCT
ejpam-7055	219	21	.	.	PUNCT
ejpam-7055	220	1	again	again	ADV
ejpam-7055	220	2	,	,	PUNCT
ejpam-7055	220	3	for	for	ADP
ejpam-7055	220	4	each	each	DET
ejpam-7055	220	5	object	object	NOUN
ejpam-7055	220	6	(	(	PUNCT
ejpam-7055	220	7	ζ	ζ	NOUN
ejpam-7055	220	8	,	,	PUNCT
ejpam-7055	220	9	ω	ω	NOUN
ejpam-7055	220	10	)	)	PUNCT
ejpam-7055	220	11	in	in	ADP
ejpam-7055	220	12	sbcki	sbcki	NOUN
ejpam-7055	220	13	,	,	PUNCT
ejpam-7055	220	14	there	there	PRON
ejpam-7055	220	15	exists	exist	VERB
ejpam-7055	220	16	a	a	DET
ejpam-7055	220	17	unique	unique	ADJ
ejpam-7055	220	18	morphism	morphism	NOUN
ejpam-7055	220	19	.	.	PUNCT
ejpam-7055	221	1	figure	figure	NOUN
ejpam-7055	221	2	9	9	NUM
ejpam-7055	221	3	:	:	PUNCT
ejpam-7055	221	4	g.	g.	PROPN
ejpam-7055	221	5	muhiuddin	muhiuddin	PROPN
ejpam-7055	221	6	et	et	PROPN
ejpam-7055	221	7	al	al	PROPN
ejpam-7055	221	8	.	.	PUNCT
ejpam-7055	221	9	/	/	SYM
ejpam-7055	221	10	eur	eur	PROPN
ejpam-7055	221	11	.	.	PUNCT
ejpam-7055	222	1	j.	j.	PROPN
ejpam-7055	222	2	pure	pure	PROPN
ejpam-7055	222	3	appl	appl	PROPN
ejpam-7055	222	4	.	.	PROPN
ejpam-7055	222	5	math	math	PROPN
ejpam-7055	222	6	,	,	PUNCT
ejpam-7055	222	7	18	18	NUM
ejpam-7055	222	8	(	(	PUNCT
ejpam-7055	222	9	4	4	NUM
ejpam-7055	222	10	)	)	PUNCT
ejpam-7055	222	11	(	(	PUNCT
ejpam-7055	222	12	2025	2025	NUM
ejpam-7055	222	13	)	)	PUNCT
ejpam-7055	222	14	,	,	PUNCT
ejpam-7055	222	15	7055	7055	NUM
ejpam-7055	222	16	11	11	NUM
ejpam-7055	222	17	of	of	ADP
ejpam-7055	222	18	13	13	NUM
ejpam-7055	222	19	the	the	DET
ejpam-7055	222	20	inequalities	inequality	NOUN
ejpam-7055	222	21	are	be	AUX
ejpam-7055	222	22	satisfied	satisfied	ADJ
ejpam-7055	222	23	by	by	ADP
ejpam-7055	222	24	default	default	NOUN
ejpam-7055	222	25	.	.	PUNCT
ejpam-7055	223	1	thus	thus	ADV
ejpam-7055	223	2	there	there	PRON
ejpam-7055	223	3	is	be	VERB
ejpam-7055	223	4	only	only	ADV
ejpam-7055	223	5	one	one	NUM
ejpam-7055	223	6	morphism	morphism	NOUN
ejpam-7055	223	7	from	from	ADP
ejpam-7055	223	8	(	(	PUNCT
ejpam-7055	223	9	ζ	ζ	PROPN
ejpam-7055	223	10	,	,	PUNCT
ejpam-7055	223	11	ω	ω	NOUN
ejpam-7055	223	12	)	)	PUNCT
ejpam-7055	223	13	to	to	ADP
ejpam-7055	223	14	(	(	PUNCT
ejpam-7055	223	15	φ	φ	PROPN
ejpam-7055	223	16	,	,	PUNCT
ejpam-7055	223	17	φ	φ	NUM
ejpam-7055	223	18	)	)	PUNCT
ejpam-7055	223	19	and	and	CCONJ
ejpam-7055	223	20	also	also	ADV
ejpam-7055	223	21	only	only	ADV
ejpam-7055	223	22	one	one	NUM
ejpam-7055	223	23	morphism	morphism	NOUN
ejpam-7055	223	24	from	from	ADP
ejpam-7055	223	25	(	(	PUNCT
ejpam-7055	223	26	φ	φ	PROPN
ejpam-7055	223	27	,	,	PUNCT
ejpam-7055	223	28	φ	φ	NUM
ejpam-7055	223	29	)	)	PUNCT
ejpam-7055	223	30	to	to	ADP
ejpam-7055	223	31	(	(	PUNCT
ejpam-7055	223	32	ζ	ζ	PROPN
ejpam-7055	223	33	,	,	PUNCT
ejpam-7055	223	34	ω	ω	NOUN
ejpam-7055	223	35	)	)	PUNCT
ejpam-7055	223	36	.	.	PUNCT
ejpam-7055	224	1	thus	thus	ADV
ejpam-7055	224	2	,	,	PUNCT
ejpam-7055	224	3	sbck	sbck	NOUN
ejpam-7055	224	4	has	have	VERB
ejpam-7055	224	5	no	no	DET
ejpam-7055	224	6	objects	object	NOUN
ejpam-7055	224	7	.	.	PUNCT
ejpam-7055	225	1	7	7	X
ejpam-7055	225	2	.	.	X
ejpam-7055	225	3	conclusion	conclusion	NOUN
ejpam-7055	225	4	in	in	ADP
ejpam-7055	225	5	conclusion	conclusion	NOUN
ejpam-7055	225	6	,	,	PUNCT
ejpam-7055	225	7	this	this	DET
ejpam-7055	225	8	study	study	NOUN
ejpam-7055	225	9	delves	delve	VERB
ejpam-7055	225	10	into	into	ADP
ejpam-7055	225	11	the	the	DET
ejpam-7055	225	12	realm	realm	NOUN
ejpam-7055	225	13	of	of	ADP
ejpam-7055	225	14	soft	soft	ADJ
ejpam-7055	225	15	bck	bck	NOUN
ejpam-7055	225	16	/	/	SYM
ejpam-7055	225	17	bci	bci	NOUN
ejpam-7055	225	18	-	-	PUNCT
ejpam-7055	225	19	algebras	algebras	X
ejpam-7055	225	20	,	,	PUNCT
ejpam-7055	225	21	introducing	introduce	VERB
ejpam-7055	225	22	novel	novel	ADJ
ejpam-7055	225	23	concepts	concept	NOUN
ejpam-7055	225	24	and	and	CCONJ
ejpam-7055	225	25	elucidating	elucidate	VERB
ejpam-7055	225	26	categorical	categorical	ADJ
ejpam-7055	225	27	structures	structure	NOUN
ejpam-7055	225	28	such	such	ADJ
ejpam-7055	225	29	as	as	ADP
ejpam-7055	225	30	finite	finite	ADJ
ejpam-7055	225	31	products	product	NOUN
ejpam-7055	225	32	,	,	PUNCT
ejpam-7055	225	33	equalizers	equalizer	NOUN
ejpam-7055	225	34	,	,	PUNCT
ejpam-7055	225	35	and	and	CCONJ
ejpam-7055	225	36	co	co	NOUN
ejpam-7055	225	37	-	-	NOUN
ejpam-7055	225	38	equalizers	equalizer	NOUN
ejpam-7055	225	39	within	within	ADP
ejpam-7055	225	40	this	this	DET
ejpam-7055	225	41	domain	domain	NOUN
ejpam-7055	225	42	.	.	PUNCT
ejpam-7055	226	1	by	by	ADP
ejpam-7055	226	2	demonstrating	demonstrate	VERB
ejpam-7055	226	3	that	that	SCONJ
ejpam-7055	226	4	the	the	DET
ejpam-7055	226	5	category	category	NOUN
ejpam-7055	226	6	of	of	ADP
ejpam-7055	226	7	soft	soft	ADJ
ejpam-7055	226	8	bck	bck	NOUN
ejpam-7055	226	9	/	/	SYM
ejpam-7055	226	10	bci	bci	NOUN
ejpam-7055	226	11	-	-	PUNCT
ejpam-7055	226	12	algebras	algebras	NOUN
ejpam-7055	226	13	adheres	adhere	VERB
ejpam-7055	226	14	to	to	ADP
ejpam-7055	226	15	a	a	DET
ejpam-7055	226	16	topological	topological	ADJ
ejpam-7055	226	17	construct	construct	NOUN
ejpam-7055	226	18	,	,	PUNCT
ejpam-7055	226	19	we	we	PRON
ejpam-7055	226	20	provide	provide	VERB
ejpam-7055	226	21	insights	insight	NOUN
ejpam-7055	226	22	into	into	ADP
ejpam-7055	226	23	the	the	DET
ejpam-7055	226	24	underlying	underlie	VERB
ejpam-7055	226	25	organizational	organizational	ADJ
ejpam-7055	226	26	principles	principle	NOUN
ejpam-7055	226	27	of	of	ADP
ejpam-7055	226	28	these	these	DET
ejpam-7055	226	29	algebraic	algebraic	ADJ
ejpam-7055	226	30	systems	system	NOUN
ejpam-7055	226	31	.	.	PUNCT
ejpam-7055	227	1	moreover	moreover	ADV
ejpam-7055	227	2	,	,	PUNCT
ejpam-7055	227	3	our	our	PRON
ejpam-7055	227	4	exploration	exploration	NOUN
ejpam-7055	227	5	reveals	reveal	VERB
ejpam-7055	227	6	the	the	DET
ejpam-7055	227	7	presence	presence	NOUN
ejpam-7055	227	8	of	of	ADP
ejpam-7055	227	9	special	special	ADJ
ejpam-7055	227	10	objects	object	NOUN
ejpam-7055	227	11	in	in	ADP
ejpam-7055	227	12	the	the	DET
ejpam-7055	227	13	category	category	NOUN
ejpam-7055	227	14	of	of	ADP
ejpam-7055	227	15	soft	soft	ADJ
ejpam-7055	227	16	bck	bck	NOUN
ejpam-7055	227	17	/	/	SYM
ejpam-7055	227	18	bci	bci	NOUN
ejpam-7055	227	19	-	-	PUNCT
ejpam-7055	227	20	algebras	algebra	NOUN
ejpam-7055	227	21	,	,	PUNCT
ejpam-7055	227	22	including	include	VERB
ejpam-7055	227	23	terminal	terminal	NOUN
ejpam-7055	227	24	,	,	PUNCT
ejpam-7055	227	25	initial	initial	ADJ
ejpam-7055	227	26	,	,	PUNCT
ejpam-7055	227	27	and	and	CCONJ
ejpam-7055	227	28	zero	zero	NUM
ejpam-7055	227	29	objects	object	NOUN
ejpam-7055	227	30	.	.	PUNCT
ejpam-7055	228	1	these	these	DET
ejpam-7055	228	2	findings	finding	NOUN
ejpam-7055	228	3	contribute	contribute	VERB
ejpam-7055	228	4	to	to	ADP
ejpam-7055	228	5	a	a	DET
ejpam-7055	228	6	deeper	deep	ADJ
ejpam-7055	228	7	understanding	understanding	NOUN
ejpam-7055	228	8	of	of	ADP
ejpam-7055	228	9	the	the	DET
ejpam-7055	228	10	categorical	categorical	ADJ
ejpam-7055	228	11	properties	property	NOUN
ejpam-7055	228	12	and	and	CCONJ
ejpam-7055	228	13	structural	structural	ADJ
ejpam-7055	228	14	nuances	nuance	NOUN
ejpam-7055	228	15	inherent	inherent	ADJ
ejpam-7055	228	16	in	in	ADP
ejpam-7055	228	17	soft	soft	ADJ
ejpam-7055	228	18	bck	bck	NOUN
ejpam-7055	228	19	/	/	SYM
ejpam-7055	228	20	bci	bci	NOUN
ejpam-7055	228	21	-	-	PUNCT
ejpam-7055	228	22	algebras	algebra	NOUN
ejpam-7055	228	23	.	.	PUNCT
ejpam-7055	229	1	by	by	ADP
ejpam-7055	229	2	uncovering	uncover	VERB
ejpam-7055	229	3	and	and	CCONJ
ejpam-7055	229	4	elucidating	elucidate	VERB
ejpam-7055	229	5	these	these	DET
ejpam-7055	229	6	categorical	categorical	ADJ
ejpam-7055	229	7	structures	structure	NOUN
ejpam-7055	229	8	and	and	CCONJ
ejpam-7055	229	9	properties	property	NOUN
ejpam-7055	229	10	,	,	PUNCT
ejpam-7055	229	11	this	this	DET
ejpam-7055	229	12	work	work	NOUN
ejpam-7055	229	13	not	not	PART
ejpam-7055	229	14	only	only	ADV
ejpam-7055	229	15	expands	expand	VERB
ejpam-7055	229	16	the	the	DET
ejpam-7055	229	17	theoretical	theoretical	ADJ
ejpam-7055	229	18	foundations	foundation	NOUN
ejpam-7055	229	19	of	of	ADP
ejpam-7055	229	20	soft	soft	ADJ
ejpam-7055	229	21	bck	bck	NOUN
ejpam-7055	229	22	/	/	SYM
ejpam-7055	229	23	bci	bci	NOUN
ejpam-7055	229	24	-	-	PUNCT
ejpam-7055	229	25	algebras	algebra	NOUN
ejpam-7055	229	26	but	but	CCONJ
ejpam-7055	229	27	also	also	ADV
ejpam-7055	229	28	sets	set	VERB
ejpam-7055	229	29	the	the	DET
ejpam-7055	229	30	stage	stage	NOUN
ejpam-7055	229	31	for	for	ADP
ejpam-7055	229	32	further	further	ADJ
ejpam-7055	229	33	exploration	exploration	NOUN
ejpam-7055	229	34	and	and	CCONJ
ejpam-7055	229	35	applications	application	NOUN
ejpam-7055	229	36	in	in	ADP
ejpam-7055	229	37	the	the	DET
ejpam-7055	229	38	broader	broad	ADJ
ejpam-7055	229	39	context	context	NOUN
ejpam-7055	229	40	of	of	ADP
ejpam-7055	229	41	algebraic	algebraic	ADJ
ejpam-7055	229	42	structures	structure	NOUN
ejpam-7055	229	43	and	and	CCONJ
ejpam-7055	229	44	categorical	categorical	ADJ
ejpam-7055	229	45	theory	theory	NOUN
ejpam-7055	229	46	.	.	PUNCT
ejpam-7055	230	1	acknowledgements	acknowledgement	NOUN
ejpam-7055	230	2	the	the	DET
ejpam-7055	230	3	authors	author	NOUN
ejpam-7055	230	4	would	would	AUX
ejpam-7055	230	5	like	like	VERB
ejpam-7055	230	6	to	to	PART
ejpam-7055	230	7	express	express	VERB
ejpam-7055	230	8	their	their	PRON
ejpam-7055	230	9	sincere	sincere	ADJ
ejpam-7055	230	10	thanks	thank	NOUN
ejpam-7055	230	11	to	to	ADP
ejpam-7055	230	12	the	the	DET
ejpam-7055	230	13	referees	referee	NOUN
ejpam-7055	230	14	for	for	ADP
ejpam-7055	230	15	their	their	PRON
ejpam-7055	230	16	valuable	valuable	ADJ
ejpam-7055	230	17	comments	comment	NOUN
ejpam-7055	230	18	and	and	CCONJ
ejpam-7055	230	19	suggestions	suggestion	NOUN
ejpam-7055	230	20	,	,	PUNCT
ejpam-7055	230	21	which	which	PRON
ejpam-7055	230	22	helped	help	VERB
ejpam-7055	230	23	improve	improve	VERB
ejpam-7055	230	24	the	the	DET
ejpam-7055	230	25	presentation	presentation	NOUN
ejpam-7055	230	26	of	of	ADP
ejpam-7055	230	27	this	this	DET
ejpam-7055	230	28	paper	paper	NOUN
ejpam-7055	230	29	.	.	PUNCT
ejpam-7055	231	1	references	reference	NOUN
ejpam-7055	231	2	[	[	X
ejpam-7055	231	3	1	1	NUM
ejpam-7055	231	4	]	]	X
ejpam-7055	231	5	y.	y.	PROPN
ejpam-7055	231	6	imai	imai	PROPN
ejpam-7055	231	7	and	and	CCONJ
ejpam-7055	231	8	k.	k.	PROPN
ejpam-7055	231	9	iseki	iseki	PROPN
ejpam-7055	231	10	.	.	PUNCT
ejpam-7055	232	1	on	on	ADP
ejpam-7055	232	2	axiom	axiom	NOUN
ejpam-7055	232	3	systems	system	NOUN
ejpam-7055	232	4	of	of	ADP
ejpam-7055	232	5	propositional	propositional	ADJ
ejpam-7055	232	6	calculi	calculi	PROPN
ejpam-7055	232	7	.	.	PUNCT
ejpam-7055	233	1	proceedings	proceeding	NOUN
ejpam-7055	233	2	of	of	ADP
ejpam-7055	233	3	the	the	DET
ejpam-7055	233	4	japan	japan	PROPN
ejpam-7055	233	5	academy	academy	PROPN
ejpam-7055	233	6	,	,	PUNCT
ejpam-7055	233	7	42:19–22	42:19–22	NUM
ejpam-7055	233	8	,	,	PUNCT
ejpam-7055	233	9	1966	1966	NUM
ejpam-7055	233	10	.	.	PUNCT
ejpam-7055	234	1	[	[	X
ejpam-7055	234	2	2	2	NUM
ejpam-7055	234	3	]	]	PUNCT
ejpam-7055	234	4	k.	k.	PROPN
ejpam-7055	234	5	iseki	iseki	PROPN
ejpam-7055	234	6	.	.	PUNCT
ejpam-7055	235	1	an	an	DET
ejpam-7055	235	2	algebra	algebra	NOUN
ejpam-7055	235	3	related	relate	VERB
ejpam-7055	235	4	with	with	ADP
ejpam-7055	235	5	a	a	DET
ejpam-7055	235	6	propositional	propositional	ADJ
ejpam-7055	235	7	calculus	calculus	NOUN
ejpam-7055	235	8	.	.	PUNCT
ejpam-7055	236	1	proceedings	proceeding	NOUN
ejpam-7055	236	2	of	of	ADP
ejpam-7055	236	3	the	the	DET
ejpam-7055	236	4	japan	japan	PROPN
ejpam-7055	236	5	academy	academy	PROPN
ejpam-7055	236	6	,	,	PUNCT
ejpam-7055	236	7	42:26–29	42:26–29	PROPN
ejpam-7055	236	8	,	,	PUNCT
ejpam-7055	236	9	1966	1966	NUM
ejpam-7055	236	10	.	.	PUNCT
ejpam-7055	237	1	[	[	X
ejpam-7055	237	2	3	3	X
ejpam-7055	237	3	]	]	X
ejpam-7055	237	4	l.	l.	PROPN
ejpam-7055	237	5	a.	a.	PROPN
ejpam-7055	237	6	zadeh	zadeh	PROPN
ejpam-7055	237	7	.	.	PUNCT
ejpam-7055	237	8	fuzzy	fuzzy	ADJ
ejpam-7055	237	9	sets	set	NOUN
ejpam-7055	237	10	.	.	PUNCT
ejpam-7055	238	1	information	information	NOUN
ejpam-7055	238	2	and	and	CCONJ
ejpam-7055	238	3	control	control	NOUN
ejpam-7055	238	4	,	,	PUNCT
ejpam-7055	238	5	8:338–353	8:338–353	NUM
ejpam-7055	238	6	,	,	PUNCT
ejpam-7055	238	7	1965	1965	NUM
ejpam-7055	238	8	.	.	PUNCT
ejpam-7055	239	1	[	[	X
ejpam-7055	239	2	4	4	X
ejpam-7055	239	3	]	]	PUNCT
ejpam-7055	239	4	l.	l.	PROPN
ejpam-7055	239	5	a.	a.	PROPN
ejpam-7055	239	6	zadeh	zadeh	PROPN
ejpam-7055	239	7	.	.	PUNCT
ejpam-7055	240	1	toward	toward	ADP
ejpam-7055	240	2	a	a	DET
ejpam-7055	240	3	generalized	generalized	ADJ
ejpam-7055	240	4	theory	theory	NOUN
ejpam-7055	240	5	of	of	ADP
ejpam-7055	240	6	uncertainty	uncertainty	NOUN
ejpam-7055	240	7	(	(	PUNCT
ejpam-7055	240	8	gtu	gtu	NOUN
ejpam-7055	240	9	)	)	PUNCT
ejpam-7055	240	10	—	—	PUNCT
ejpam-7055	240	11	an	an	DET
ejpam-7055	240	12	outline	outline	NOUN
ejpam-7055	240	13	.	.	PUNCT
ejpam-7055	241	1	information	information	NOUN
ejpam-7055	241	2	sciences	sciences	PROPN
ejpam-7055	241	3	,	,	PUNCT
ejpam-7055	241	4	172:1–40	172:1–40	NUM
ejpam-7055	241	5	,	,	PUNCT
ejpam-7055	241	6	2005	2005	NUM
ejpam-7055	241	7	.	.	PUNCT
ejpam-7055	242	1	[	[	X
ejpam-7055	242	2	5	5	X
ejpam-7055	242	3	]	]	PUNCT
ejpam-7055	242	4	d.	d.	PROPN
ejpam-7055	242	5	molodtsov	molodtsov	PROPN
ejpam-7055	242	6	.	.	PUNCT
ejpam-7055	243	1	soft	soft	ADJ
ejpam-7055	243	2	set	set	ADJ
ejpam-7055	243	3	theory	theory	NOUN
ejpam-7055	243	4	first	first	ADJ
ejpam-7055	243	5	results	result	NOUN
ejpam-7055	243	6	.	.	PUNCT
ejpam-7055	244	1	computers	computer	NOUN
ejpam-7055	244	2	and	and	CCONJ
ejpam-7055	244	3	mathematics	mathematic	NOUN
ejpam-7055	244	4	with	with	ADP
ejpam-7055	244	5	applications	application	NOUN
ejpam-7055	244	6	,	,	PUNCT
ejpam-7055	244	7	37:19–31	37:19–31	NUM
ejpam-7055	244	8	,	,	PUNCT
ejpam-7055	244	9	1999	1999	NUM
ejpam-7055	244	10	.	.	PUNCT
ejpam-7055	245	1	[	[	X
ejpam-7055	245	2	6	6	NUM
ejpam-7055	245	3	]	]	PUNCT
ejpam-7055	245	4	p.	p.	NOUN
ejpam-7055	245	5	k.	k.	PROPN
ejpam-7055	246	1	maji	maji	PROPN
ejpam-7055	246	2	,	,	PUNCT
ejpam-7055	246	3	r.	r.	PROPN
ejpam-7055	246	4	biswas	biswas	PROPN
ejpam-7055	246	5	,	,	PUNCT
ejpam-7055	246	6	and	and	CCONJ
ejpam-7055	247	1	a.	a.	PROPN
ejpam-7055	247	2	r.	r.	PROPN
ejpam-7055	247	3	roy	roy	PROPN
ejpam-7055	247	4	.	.	PROPN
ejpam-7055	247	5	fuzzy	fuzzy	ADJ
ejpam-7055	247	6	soft	soft	ADJ
ejpam-7055	247	7	sets	set	NOUN
ejpam-7055	247	8	.	.	PUNCT
ejpam-7055	248	1	journal	journal	NOUN
ejpam-7055	248	2	of	of	ADP
ejpam-7055	248	3	fuzzy	fuzzy	ADJ
ejpam-7055	248	4	mathematics	mathematic	NOUN
ejpam-7055	248	5	,	,	PUNCT
ejpam-7055	248	6	9(3):589–602	9(3):589–602	NOUN
ejpam-7055	248	7	,	,	PUNCT
ejpam-7055	248	8	2001	2001	NUM
ejpam-7055	248	9	.	.	PUNCT
ejpam-7055	249	1	[	[	X
ejpam-7055	249	2	7	7	X
ejpam-7055	249	3	]	]	PUNCT
ejpam-7055	249	4	p.	p.	NOUN
ejpam-7055	249	5	k.	k.	PROPN
ejpam-7055	250	1	maji	maji	PROPN
ejpam-7055	250	2	,	,	PUNCT
ejpam-7055	250	3	a.	a.	PROPN
ejpam-7055	250	4	r.	r.	PROPN
ejpam-7055	250	5	roy	roy	PROPN
ejpam-7055	250	6	,	,	PUNCT
ejpam-7055	250	7	and	and	CCONJ
ejpam-7055	250	8	r.	r.	PROPN
ejpam-7055	250	9	biswas	biswas	PROPN
ejpam-7055	250	10	.	.	PUNCT
ejpam-7055	251	1	an	an	DET
ejpam-7055	251	2	application	application	NOUN
ejpam-7055	251	3	of	of	ADP
ejpam-7055	251	4	soft	soft	ADJ
ejpam-7055	251	5	sets	set	NOUN
ejpam-7055	251	6	in	in	ADP
ejpam-7055	251	7	a	a	DET
ejpam-7055	251	8	decision	decision	NOUN
ejpam-7055	251	9	making	make	VERB
ejpam-7055	251	10	problem	problem	NOUN
ejpam-7055	251	11	.	.	PUNCT
ejpam-7055	252	1	computers	computer	NOUN
ejpam-7055	252	2	and	and	CCONJ
ejpam-7055	252	3	mathematics	mathematic	NOUN
ejpam-7055	252	4	with	with	ADP
ejpam-7055	252	5	applications	application	NOUN
ejpam-7055	252	6	,	,	PUNCT
ejpam-7055	252	7	44:1077–1083	44:1077–1083	PROPN
ejpam-7055	252	8	,	,	PUNCT
ejpam-7055	252	9	2002	2002	NUM
ejpam-7055	252	10	.	.	PUNCT
ejpam-7055	253	1	[	[	X
ejpam-7055	253	2	8	8	NUM
ejpam-7055	253	3	]	]	PUNCT
ejpam-7055	253	4	m.	m.	NOUN
ejpam-7055	253	5	i.	i.	PROPN
ejpam-7055	253	6	ali	ali	PROPN
ejpam-7055	253	7	,	,	PUNCT
ejpam-7055	253	8	f.	f.	PROPN
ejpam-7055	253	9	feng	feng	PROPN
ejpam-7055	253	10	,	,	PUNCT
ejpam-7055	253	11	x.	x.	PROPN
ejpam-7055	253	12	liu	liu	PROPN
ejpam-7055	253	13	,	,	PUNCT
ejpam-7055	253	14	w.	w.	PROPN
ejpam-7055	253	15	k.	k.	PROPN
ejpam-7055	253	16	min	min	PROPN
ejpam-7055	253	17	,	,	PUNCT
ejpam-7055	253	18	and	and	CCONJ
ejpam-7055	253	19	m.	m.	NOUN
ejpam-7055	253	20	shabir	shabir	PROPN
ejpam-7055	253	21	.	.	PUNCT
ejpam-7055	254	1	on	on	ADP
ejpam-7055	254	2	some	some	DET
ejpam-7055	254	3	new	new	ADJ
ejpam-7055	254	4	operations	operation	NOUN
ejpam-7055	254	5	in	in	ADP
ejpam-7055	254	6	soft	soft	ADJ
ejpam-7055	254	7	set	set	NOUN
ejpam-7055	254	8	theory	theory	NOUN
ejpam-7055	254	9	.	.	PUNCT
ejpam-7055	255	1	computers	computer	NOUN
ejpam-7055	255	2	and	and	CCONJ
ejpam-7055	255	3	mathematics	mathematic	NOUN
ejpam-7055	255	4	with	with	ADP
ejpam-7055	255	5	applications	application	NOUN
ejpam-7055	255	6	,	,	PUNCT
ejpam-7055	255	7	57:1547–1553	57:1547–1553	NUM
ejpam-7055	255	8	,	,	PUNCT
ejpam-7055	255	9	2009	2009	NUM
ejpam-7055	255	10	.	.	PUNCT
ejpam-7055	256	1	[	[	X
ejpam-7055	256	2	9	9	NUM
ejpam-7055	256	3	]	]	X
ejpam-7055	256	4	y.	y.	PROPN
ejpam-7055	256	5	b.	b.	PROPN
ejpam-7055	256	6	jun	jun	PROPN
ejpam-7055	256	7	,	,	PUNCT
ejpam-7055	256	8	s.	s.	PROPN
ejpam-7055	256	9	s.	s.	PROPN
ejpam-7055	256	10	ahn	ahn	PROPN
ejpam-7055	256	11	,	,	PUNCT
ejpam-7055	256	12	and	and	CCONJ
ejpam-7055	256	13	k.	k.	PROPN
ejpam-7055	256	14	j.	j.	PROPN
ejpam-7055	256	15	lee	lee	PROPN
ejpam-7055	256	16	.	.	PROPN
ejpam-7055	256	17	intersection	intersection	NOUN
ejpam-7055	256	18	-	-	PUNCT
ejpam-7055	256	19	soft	soft	ADJ
ejpam-7055	256	20	filters	filter	NOUN
ejpam-7055	256	21	in	in	ADP
ejpam-7055	256	22	r0	r0	NOUN
ejpam-7055	256	23	-	-	PUNCT
ejpam-7055	256	24	algebras	algebras	PROPN
ejpam-7055	256	25	.	.	PUNCT
ejpam-7055	257	1	discrete	discrete	ADJ
ejpam-7055	257	2	dynamics	dynamic	NOUN
ejpam-7055	257	3	in	in	ADP
ejpam-7055	257	4	nature	nature	NOUN
ejpam-7055	257	5	and	and	CCONJ
ejpam-7055	257	6	society	society	NOUN
ejpam-7055	257	7	,	,	PUNCT
ejpam-7055	257	8	2013	2013	NUM
ejpam-7055	257	9	:	:	PUNCT
ejpam-7055	257	10	article	article	NOUN
ejpam-7055	257	11	i	i	PROPN
ejpam-7055	257	12	d	d	PROPN
ejpam-7055	257	13	950897	950897	NUM
ejpam-7055	257	14	,	,	PUNCT
ejpam-7055	257	15	7	7	NUM
ejpam-7055	257	16	pages	page	NOUN
ejpam-7055	257	17	,	,	PUNCT
ejpam-7055	257	18	2013	2013	NUM
ejpam-7055	257	19	.	.	PUNCT
ejpam-7055	258	1	g.	g.	PROPN
ejpam-7055	258	2	muhiuddin	muhiuddin	PROPN
ejpam-7055	258	3	et	et	PROPN
ejpam-7055	258	4	al	al	PROPN
ejpam-7055	258	5	.	.	PUNCT
ejpam-7055	258	6	/	/	SYM
ejpam-7055	258	7	eur	eur	PROPN
ejpam-7055	258	8	.	.	PUNCT
ejpam-7055	259	1	j.	j.	PROPN
ejpam-7055	259	2	pure	pure	PROPN
ejpam-7055	259	3	appl	appl	PROPN
ejpam-7055	259	4	.	.	PROPN
ejpam-7055	259	5	math	math	PROPN
ejpam-7055	259	6	,	,	PUNCT
ejpam-7055	259	7	18	18	NUM
ejpam-7055	259	8	(	(	PUNCT
ejpam-7055	259	9	4	4	NUM
ejpam-7055	259	10	)	)	PUNCT
ejpam-7055	259	11	(	(	PUNCT
ejpam-7055	259	12	2025	2025	NUM
ejpam-7055	259	13	)	)	PUNCT
ejpam-7055	259	14	,	,	PUNCT
ejpam-7055	259	15	7055	7055	NUM
ejpam-7055	259	16	12	12	NUM
ejpam-7055	259	17	of	of	ADP
ejpam-7055	259	18	13	13	NUM
ejpam-7055	260	1	[	[	SYM
ejpam-7055	260	2	10	10	NUM
ejpam-7055	260	3	]	]	X
ejpam-7055	260	4	e.	e.	PROPN
ejpam-7055	260	5	h.	h.	PROPN
ejpam-7055	260	6	roh	roh	PROPN
ejpam-7055	260	7	and	and	CCONJ
ejpam-7055	260	8	y.	y.	PROPN
ejpam-7055	260	9	b.	b.	PROPN
ejpam-7055	260	10	jun	jun	PROPN
ejpam-7055	260	11	.	.	PROPN
ejpam-7055	261	1	positive	positive	ADJ
ejpam-7055	261	2	implicative	implicative	ADJ
ejpam-7055	261	3	ideals	ideal	NOUN
ejpam-7055	261	4	of	of	ADP
ejpam-7055	261	5	bck	bck	NOUN
ejpam-7055	261	6	-	-	PUNCT
ejpam-7055	261	7	algebras	algebras	PROPN
ejpam-7055	261	8	based	base	VERB
ejpam-7055	261	9	on	on	ADP
ejpam-7055	261	10	intersectional	intersectional	ADJ
ejpam-7055	261	11	soft	soft	ADJ
ejpam-7055	261	12	sets	set	NOUN
ejpam-7055	261	13	.	.	PUNCT
ejpam-7055	262	1	journal	journal	NOUN
ejpam-7055	262	2	of	of	ADP
ejpam-7055	262	3	applied	apply	VERB
ejpam-7055	262	4	mathematics	mathematic	NOUN
ejpam-7055	262	5	,	,	PUNCT
ejpam-7055	262	6	2013	2013	NUM
ejpam-7055	262	7	:	:	PUNCT
ejpam-7055	262	8	article	article	NOUN
ejpam-7055	262	9	i	i	PROPN
ejpam-7055	262	10	d	d	PROPN
ejpam-7055	262	11	853907	853907	NUM
ejpam-7055	262	12	,	,	PUNCT
ejpam-7055	262	13	9	9	NUM
ejpam-7055	262	14	pages	page	NOUN
ejpam-7055	262	15	,	,	PUNCT
ejpam-7055	262	16	2013	2013	NUM
ejpam-7055	262	17	.	.	PUNCT
ejpam-7055	263	1	[	[	X
ejpam-7055	263	2	11	11	NUM
ejpam-7055	263	3	]	]	PUNCT
ejpam-7055	263	4	a.	a.	PROPN
ejpam-7055	263	5	r.	r.	PROPN
ejpam-7055	263	6	roy	roy	PROPN
ejpam-7055	263	7	and	and	CCONJ
ejpam-7055	263	8	p.	p.	PROPN
ejpam-7055	263	9	k.	k.	PROPN
ejpam-7055	264	1	maji	maji	PROPN
ejpam-7055	264	2	.	.	PUNCT
ejpam-7055	265	1	a	a	DET
ejpam-7055	265	2	fuzzy	fuzzy	ADJ
ejpam-7055	265	3	soft	soft	ADJ
ejpam-7055	265	4	set	set	ADJ
ejpam-7055	265	5	theoretic	theoretic	ADJ
ejpam-7055	265	6	approach	approach	NOUN
ejpam-7055	265	7	to	to	ADP
ejpam-7055	265	8	decision	decision	NOUN
ejpam-7055	265	9	making	make	VERB
ejpam-7055	265	10	problems	problem	NOUN
ejpam-7055	265	11	.	.	PUNCT
ejpam-7055	266	1	journal	journal	NOUN
ejpam-7055	266	2	of	of	ADP
ejpam-7055	266	3	computational	computational	ADJ
ejpam-7055	266	4	and	and	CCONJ
ejpam-7055	266	5	applied	applied	ADJ
ejpam-7055	266	6	mathematics	mathematic	NOUN
ejpam-7055	266	7	,	,	PUNCT
ejpam-7055	266	8	203:412–418	203:412–418	NUM
ejpam-7055	266	9	,	,	PUNCT
ejpam-7055	266	10	2007	2007	NUM
ejpam-7055	266	11	.	.	PUNCT
ejpam-7055	267	1	[	[	X
ejpam-7055	267	2	12	12	NUM
ejpam-7055	267	3	]	]	PUNCT
ejpam-7055	267	4	a.	a.	NOUN
ejpam-7055	267	5	aygünoǧlu	aygünoǧlu	PROPN
ejpam-7055	267	6	and	and	CCONJ
ejpam-7055	267	7	h.	h.	PROPN
ejpam-7055	267	8	aygün	aygün	PROPN
ejpam-7055	267	9	.	.	PUNCT
ejpam-7055	268	1	introduction	introduction	NOUN
ejpam-7055	268	2	to	to	ADP
ejpam-7055	268	3	fuzzy	fuzzy	ADJ
ejpam-7055	268	4	soft	soft	ADJ
ejpam-7055	268	5	groups	group	NOUN
ejpam-7055	268	6	.	.	PUNCT
ejpam-7055	269	1	computers	computer	NOUN
ejpam-7055	269	2	and	and	CCONJ
ejpam-7055	269	3	mathematics	mathematic	NOUN
ejpam-7055	269	4	with	with	ADP
ejpam-7055	269	5	applications	application	NOUN
ejpam-7055	269	6	,	,	PUNCT
ejpam-7055	269	7	58:1279–1286	58:1279–1286	NUM
ejpam-7055	269	8	,	,	PUNCT
ejpam-7055	269	9	2009	2009	NUM
ejpam-7055	269	10	.	.	PUNCT
ejpam-7055	270	1	[	[	X
ejpam-7055	270	2	13	13	NUM
ejpam-7055	270	3	]	]	X
ejpam-7055	270	4	y.	y.	PROPN
ejpam-7055	270	5	b.	b.	PROPN
ejpam-7055	270	6	jun	jun	PROPN
ejpam-7055	270	7	,	,	PUNCT
ejpam-7055	270	8	k.	k.	PROPN
ejpam-7055	270	9	j.	j.	PROPN
ejpam-7055	270	10	lee	lee	PROPN
ejpam-7055	270	11	,	,	PUNCT
ejpam-7055	270	12	and	and	CCONJ
ejpam-7055	270	13	c.	c.	PROPN
ejpam-7055	270	14	h.	h.	PROPN
ejpam-7055	270	15	park	park	PROPN
ejpam-7055	270	16	.	.	PUNCT
ejpam-7055	271	1	fuzzy	fuzzy	ADJ
ejpam-7055	271	2	soft	soft	ADJ
ejpam-7055	271	3	set	set	NOUN
ejpam-7055	271	4	theory	theory	NOUN
ejpam-7055	271	5	applied	apply	VERB
ejpam-7055	271	6	to	to	PART
ejpam-7055	271	7	bck	bck	VERB
ejpam-7055	271	8	/	/	SYM
ejpam-7055	271	9	bcialgebras	bcialgebra	NOUN
ejpam-7055	271	10	.	.	PUNCT
ejpam-7055	272	1	computers	computer	NOUN
ejpam-7055	272	2	and	and	CCONJ
ejpam-7055	272	3	mathematics	mathematic	NOUN
ejpam-7055	272	4	with	with	ADP
ejpam-7055	272	5	applications	application	NOUN
ejpam-7055	272	6	,	,	PUNCT
ejpam-7055	272	7	59:3180–3192	59:3180–3192	NUM
ejpam-7055	272	8	,	,	PUNCT
ejpam-7055	272	9	2010	2010	NUM
ejpam-7055	272	10	.	.	PUNCT
ejpam-7055	273	1	[	[	X
ejpam-7055	273	2	14	14	NUM
ejpam-7055	273	3	]	]	PUNCT
ejpam-7055	273	4	a.	a.	PROPN
ejpam-7055	273	5	al	al	PROPN
ejpam-7055	273	6	-	-	PUNCT
ejpam-7055	273	7	roqi	roqi	PROPN
ejpam-7055	273	8	,	,	PUNCT
ejpam-7055	273	9	g.	g.	PROPN
ejpam-7055	273	10	muhiuddin	muhiuddin	PROPN
ejpam-7055	273	11	,	,	PUNCT
ejpam-7055	273	12	and	and	CCONJ
ejpam-7055	273	13	s.	s.	PROPN
ejpam-7055	273	14	aldhafeeri	aldhafeeri	PROPN
ejpam-7055	273	15	.	.	PUNCT
ejpam-7055	274	1	normal	normal	ADJ
ejpam-7055	274	2	unisoft	unisoft	ADJ
ejpam-7055	274	3	filters	filter	NOUN
ejpam-7055	274	4	in	in	ADP
ejpam-7055	274	5	r0	r0	NOUN
ejpam-7055	274	6	-	-	PUNCT
ejpam-7055	274	7	algebras	algebras	PROPN
ejpam-7055	274	8	.	.	PUNCT
ejpam-7055	275	1	cogent	cogent	NOUN
ejpam-7055	275	2	mathematics	mathematic	NOUN
ejpam-7055	275	3	,	,	PUNCT
ejpam-7055	275	4	4:1–9	4:1–9	NUM
ejpam-7055	275	5	,	,	PUNCT
ejpam-7055	275	6	2017	2017	NUM
ejpam-7055	275	7	.	.	PUNCT
ejpam-7055	276	1	[	[	X
ejpam-7055	276	2	15	15	NUM
ejpam-7055	276	3	]	]	X
ejpam-7055	276	4	g.	g.	PROPN
ejpam-7055	276	5	muhiuddin	muhiuddin	PROPN
ejpam-7055	276	6	,	,	PUNCT
ejpam-7055	276	7	a.	a.	PROPN
ejpam-7055	276	8	m.	m.	NOUN
ejpam-7055	276	9	al	al	PROPN
ejpam-7055	276	10	-	-	PUNCT
ejpam-7055	276	11	roqi	roqi	ADJ
ejpam-7055	276	12	,	,	PUNCT
ejpam-7055	276	13	and	and	CCONJ
ejpam-7055	276	14	s.	s.	PROPN
ejpam-7055	276	15	aldhafeeri	aldhafeeri	PROPN
ejpam-7055	276	16	.	.	PUNCT
ejpam-7055	277	1	filter	filter	NOUN
ejpam-7055	277	2	theory	theory	NOUN
ejpam-7055	277	3	in	in	ADP
ejpam-7055	277	4	mtl	mtl	PROPN
ejpam-7055	277	5	-	-	PUNCT
ejpam-7055	277	6	algebras	algebras	PROPN
ejpam-7055	277	7	based	base	VERB
ejpam-7055	277	8	on	on	ADP
ejpam-7055	277	9	uni	uni	ADJ
ejpam-7055	277	10	-	-	ADJ
ejpam-7055	277	11	soft	soft	ADJ
ejpam-7055	277	12	property	property	NOUN
ejpam-7055	277	13	.	.	PUNCT
ejpam-7055	278	1	bulletin	bulletin	NOUN
ejpam-7055	278	2	of	of	ADP
ejpam-7055	278	3	the	the	DET
ejpam-7055	278	4	iranian	iranian	PROPN
ejpam-7055	278	5	mathematical	mathematical	PROPN
ejpam-7055	278	6	society	society	NOUN
ejpam-7055	278	7	,	,	PUNCT
ejpam-7055	278	8	43(7):2293–2306	43(7):2293–2306	NUM
ejpam-7055	278	9	,	,	PUNCT
ejpam-7055	278	10	2017	2017	NUM
ejpam-7055	278	11	.	.	PUNCT
ejpam-7055	279	1	[	[	X
ejpam-7055	279	2	16	16	NUM
ejpam-7055	279	3	]	]	X
ejpam-7055	279	4	g.	g.	PROPN
ejpam-7055	279	5	muhiuddin	muhiuddin	PROPN
ejpam-7055	279	6	and	and	CCONJ
ejpam-7055	279	7	a.	a.	PROPN
ejpam-7055	279	8	m.	m.	PROPN
ejpam-7055	279	9	al	al	PROPN
ejpam-7055	279	10	-	-	PUNCT
ejpam-7055	279	11	roqi	roqi	PROPN
ejpam-7055	279	12	.	.	PUNCT
ejpam-7055	280	1	unisoft	unisoft	ADJ
ejpam-7055	280	2	filters	filter	NOUN
ejpam-7055	280	3	in	in	ADP
ejpam-7055	280	4	r0	r0	NOUN
ejpam-7055	280	5	-	-	PUNCT
ejpam-7055	280	6	algebras	algebras	PROPN
ejpam-7055	280	7	.	.	PUNCT
ejpam-7055	281	1	journal	journal	PROPN
ejpam-7055	281	2	of	of	ADP
ejpam-7055	281	3	computational	computational	ADJ
ejpam-7055	281	4	analysis	analysis	NOUN
ejpam-7055	281	5	and	and	CCONJ
ejpam-7055	281	6	applications	application	NOUN
ejpam-7055	281	7	,	,	PUNCT
ejpam-7055	281	8	19(1):133–143	19(1):133–143	NOUN
ejpam-7055	281	9	,	,	PUNCT
ejpam-7055	281	10	2015	2015	NUM
ejpam-7055	281	11	.	.	PUNCT
ejpam-7055	282	1	[	[	X
ejpam-7055	282	2	17	17	NUM
ejpam-7055	282	3	]	]	X
ejpam-7055	282	4	g.	g.	PROPN
ejpam-7055	282	5	muhiuddin	muhiuddin	PROPN
ejpam-7055	282	6	,	,	PUNCT
ejpam-7055	282	7	f.	f.	PROPN
ejpam-7055	282	8	feng	feng	PROPN
ejpam-7055	282	9	,	,	PUNCT
ejpam-7055	282	10	and	and	CCONJ
ejpam-7055	282	11	y.	y.	PROPN
ejpam-7055	282	12	b.	b.	PROPN
ejpam-7055	282	13	jun	jun	PROPN
ejpam-7055	282	14	.	.	PUNCT
ejpam-7055	283	1	subalgebras	subalgebras	PROPN
ejpam-7055	283	2	of	of	ADP
ejpam-7055	283	3	bck	bck	PROPN
ejpam-7055	283	4	/	/	SYM
ejpam-7055	283	5	bci	bci	NOUN
ejpam-7055	283	6	-	-	PUNCT
ejpam-7055	283	7	algebras	algebras	PROPN
ejpam-7055	283	8	based	base	VERB
ejpam-7055	283	9	on	on	ADP
ejpam-7055	283	10	cubic	cubic	ADJ
ejpam-7055	283	11	soft	soft	ADJ
ejpam-7055	283	12	sets	set	NOUN
ejpam-7055	283	13	.	.	PUNCT
ejpam-7055	284	1	the	the	DET
ejpam-7055	284	2	scientific	scientific	ADJ
ejpam-7055	284	3	world	world	NOUN
ejpam-7055	284	4	journal	journal	NOUN
ejpam-7055	284	5	,	,	PUNCT
ejpam-7055	284	6	2014	2014	NUM
ejpam-7055	284	7	:	:	PUNCT
ejpam-7055	284	8	article	article	NOUN
ejpam-7055	284	9	i	i	PROPN
ejpam-7055	284	10	d	d	PROPN
ejpam-7055	284	11	458638	458638	NUM
ejpam-7055	284	12	,	,	PUNCT
ejpam-7055	284	13	9	9	NUM
ejpam-7055	284	14	pages	page	NOUN
ejpam-7055	284	15	,	,	PUNCT
ejpam-7055	284	16	2014	2014	NUM
ejpam-7055	284	17	.	.	PUNCT
ejpam-7055	285	1	[	[	X
ejpam-7055	285	2	18	18	NUM
ejpam-7055	285	3	]	]	X
ejpam-7055	285	4	g.	g.	PROPN
ejpam-7055	285	5	muhiuddin	muhiuddin	PROPN
ejpam-7055	285	6	and	and	CCONJ
ejpam-7055	285	7	a.	a.	PROPN
ejpam-7055	285	8	m.	m.	PROPN
ejpam-7055	285	9	al	al	PROPN
ejpam-7055	285	10	-	-	PUNCT
ejpam-7055	285	11	roqi	roqi	PROPN
ejpam-7055	285	12	.	.	PUNCT
ejpam-7055	286	1	cubic	cubic	ADJ
ejpam-7055	286	2	soft	soft	ADJ
ejpam-7055	286	3	sets	set	NOUN
ejpam-7055	286	4	with	with	ADP
ejpam-7055	286	5	applications	application	NOUN
ejpam-7055	286	6	in	in	ADP
ejpam-7055	286	7	bck	bck	PROPN
ejpam-7055	286	8	/	/	SYM
ejpam-7055	286	9	bcialgebras	bcialgebra	NOUN
ejpam-7055	286	10	.	.	PUNCT
ejpam-7055	287	1	annals	annal	NOUN
ejpam-7055	287	2	of	of	ADP
ejpam-7055	287	3	fuzzy	fuzzy	ADJ
ejpam-7055	287	4	mathematics	mathematic	NOUN
ejpam-7055	287	5	and	and	CCONJ
ejpam-7055	287	6	informatics	informatic	NOUN
ejpam-7055	287	7	,	,	PUNCT
ejpam-7055	287	8	8(2):291–304	8(2):291–304	NUM
ejpam-7055	287	9	,	,	PUNCT
ejpam-7055	287	10	2014	2014	NUM
ejpam-7055	287	11	.	.	PUNCT
ejpam-7055	288	1	[	[	X
ejpam-7055	288	2	19	19	NUM
ejpam-7055	288	3	]	]	X
ejpam-7055	288	4	g.	g.	PROPN
ejpam-7055	288	5	muhiuddin	muhiuddin	PROPN
ejpam-7055	288	6	and	and	CCONJ
ejpam-7055	288	7	a.	a.	NOUN
ejpam-7055	288	8	mahboob	mahboob	PROPN
ejpam-7055	288	9	.	.	PUNCT
ejpam-7055	289	1	int	int	NOUN
ejpam-7055	289	2	-	-	PUNCT
ejpam-7055	289	3	soft	soft	ADJ
ejpam-7055	289	4	ideals	ideal	NOUN
ejpam-7055	289	5	over	over	ADP
ejpam-7055	289	6	the	the	DET
ejpam-7055	289	7	soft	soft	ADJ
ejpam-7055	289	8	sets	set	NOUN
ejpam-7055	289	9	in	in	ADP
ejpam-7055	289	10	ordered	order	VERB
ejpam-7055	289	11	semigroups	semigroup	NOUN
ejpam-7055	289	12	.	.	PUNCT
ejpam-7055	290	1	aims	aim	VERB
ejpam-7055	290	2	mathematics	mathematic	NOUN
ejpam-7055	290	3	,	,	PUNCT
ejpam-7055	290	4	5(3):2412–2423	5(3):2412–2423	NUM
ejpam-7055	290	5	,	,	PUNCT
ejpam-7055	290	6	2020	2020	NUM
ejpam-7055	290	7	.	.	PUNCT
ejpam-7055	291	1	[	[	X
ejpam-7055	291	2	20	20	NUM
ejpam-7055	291	3	]	]	PUNCT
ejpam-7055	291	4	t.	t.	PROPN
ejpam-7055	291	5	s.	s.	PROPN
ejpam-7055	291	6	blyth	blyth	PROPN
ejpam-7055	291	7	.	.	PUNCT
ejpam-7055	292	1	categories	category	NOUN
ejpam-7055	292	2	.	.	PUNCT
ejpam-7055	293	1	longman	longman	PROPN
ejpam-7055	293	2	,	,	PUNCT
ejpam-7055	293	3	new	new	PROPN
ejpam-7055	293	4	york	york	PROPN
ejpam-7055	293	5	,	,	PUNCT
ejpam-7055	293	6	1987	1987	NUM
ejpam-7055	293	7	.	.	PUNCT
ejpam-7055	294	1	[	[	X
ejpam-7055	294	2	21	21	NUM
ejpam-7055	294	3	]	]	X
ejpam-7055	294	4	p.	p.	PROPN
ejpam-7055	294	5	freyd	freyd	PROPN
ejpam-7055	294	6	.	.	PUNCT
ejpam-7055	295	1	abelian	abelian	PROPN
ejpam-7055	295	2	categories	category	NOUN
ejpam-7055	295	3	.	.	PUNCT
ejpam-7055	296	1	harper	harper	NOUN
ejpam-7055	296	2	and	and	CCONJ
ejpam-7055	296	3	row	row	NOUN
ejpam-7055	296	4	,	,	PUNCT
ejpam-7055	296	5	new	new	PROPN
ejpam-7055	296	6	york	york	PROPN
ejpam-7055	296	7	,	,	PUNCT
ejpam-7055	296	8	1964	1964	NUM
ejpam-7055	296	9	.	.	PUNCT
ejpam-7055	297	1	[	[	X
ejpam-7055	297	2	22	22	NUM
ejpam-7055	297	3	]	]	X
ejpam-7055	297	4	n.	n.	PROPN
ejpam-7055	297	5	jacobson	jacobson	PROPN
ejpam-7055	297	6	.	.	PUNCT
ejpam-7055	298	1	lectures	lecture	NOUN
ejpam-7055	298	2	in	in	ADP
ejpam-7055	298	3	abstract	abstract	ADJ
ejpam-7055	298	4	algebra	algebra	NOUN
ejpam-7055	298	5	,	,	PUNCT
ejpam-7055	298	6	vol	vol	NOUN
ejpam-7055	298	7	.	.	PUNCT
ejpam-7055	298	8	i.	i.	PROPN
ejpam-7055	298	9	d.	d.	PROPN
ejpam-7055	298	10	van	van	PROPN
ejpam-7055	298	11	nostrand	nostrand	PROPN
ejpam-7055	298	12	company	company	PROPN
ejpam-7055	298	13	,	,	PUNCT
ejpam-7055	298	14	inc	inc	PROPN
ejpam-7055	298	15	.	.	PROPN
ejpam-7055	298	16	,	,	PUNCT
ejpam-7055	298	17	new	new	PROPN
ejpam-7055	298	18	york	york	PROPN
ejpam-7055	298	19	,	,	PUNCT
ejpam-7055	298	20	1965	1965	NUM
ejpam-7055	298	21	.	.	PUNCT
ejpam-7055	299	1	[	[	X
ejpam-7055	299	2	23	23	NUM
ejpam-7055	299	3	]	]	X
ejpam-7055	299	4	s.	s.	PROPN
ejpam-7055	299	5	maclane	maclane	PROPN
ejpam-7055	299	6	.	.	PUNCT
ejpam-7055	300	1	categories	category	NOUN
ejpam-7055	300	2	for	for	ADP
ejpam-7055	300	3	working	work	VERB
ejpam-7055	300	4	mathematicians	mathematician	NOUN
ejpam-7055	300	5	.	.	PUNCT
ejpam-7055	301	1	graduate	graduate	NOUN
ejpam-7055	301	2	texts	text	NOUN
ejpam-7055	301	3	in	in	ADP
ejpam-7055	301	4	mathematics	mathematic	NOUN
ejpam-7055	301	5	.	.	PUNCT
ejpam-7055	302	1	springer	springer	PROPN
ejpam-7055	302	2	,	,	PUNCT
ejpam-7055	302	3	1972	1972	NUM
ejpam-7055	302	4	.	.	PUNCT
ejpam-7055	303	1	[	[	X
ejpam-7055	303	2	24	24	NUM
ejpam-7055	303	3	]	]	PUNCT
ejpam-7055	303	4	b.	b.	PROPN
ejpam-7055	303	5	mitchell	mitchell	PROPN
ejpam-7055	303	6	.	.	PUNCT
ejpam-7055	304	1	theory	theory	NOUN
ejpam-7055	304	2	of	of	ADP
ejpam-7055	304	3	categories	category	NOUN
ejpam-7055	304	4	.	.	PUNCT
ejpam-7055	305	1	academic	academic	ADJ
ejpam-7055	305	2	press	press	NOUN
ejpam-7055	305	3	,	,	PUNCT
ejpam-7055	305	4	new	new	PROPN
ejpam-7055	305	5	york	york	PROPN
ejpam-7055	305	6	,	,	PUNCT
ejpam-7055	305	7	1965	1965	NUM
ejpam-7055	305	8	.	.	PUNCT
ejpam-7055	306	1	[	[	X
ejpam-7055	306	2	25	25	NUM
ejpam-7055	306	3	]	]	X
ejpam-7055	306	4	o.	o.	PROPN
ejpam-7055	306	5	zahiri	zahiri	PROPN
ejpam-7055	306	6	.	.	PUNCT
ejpam-7055	307	1	category	category	NOUN
ejpam-7055	307	2	of	of	ADP
ejpam-7055	307	3	soft	soft	ADJ
ejpam-7055	307	4	sets	set	NOUN
ejpam-7055	307	5	.	.	PUNCT
ejpam-7055	308	1	annals	annal	NOUN
ejpam-7055	308	2	of	of	ADP
ejpam-7055	308	3	the	the	DET
ejpam-7055	308	4	university	university	PROPN
ejpam-7055	308	5	of	of	ADP
ejpam-7055	308	6	craiova	craiova	PROPN
ejpam-7055	308	7	,	,	PUNCT
ejpam-7055	308	8	mathematics	mathematics	NOUN
ejpam-7055	308	9	and	and	CCONJ
ejpam-7055	308	10	computer	computer	NOUN
ejpam-7055	308	11	science	science	NOUN
ejpam-7055	308	12	series	series	NOUN
ejpam-7055	308	13	,	,	PUNCT
ejpam-7055	308	14	40(2):154–166	40(2):154–166	PROPN
ejpam-7055	308	15	,	,	PUNCT
ejpam-7055	308	16	2013	2013	NUM
ejpam-7055	308	17	.	.	PUNCT
ejpam-7055	309	1	[	[	X
ejpam-7055	309	2	26	26	NUM
ejpam-7055	309	3	]	]	PUNCT
ejpam-7055	309	4	s.	s.	PROPN
ejpam-7055	309	5	k.	k.	PROPN
ejpam-7055	309	6	sardar	sardar	PROPN
ejpam-7055	309	7	and	and	CCONJ
ejpam-7055	309	8	s.	s.	PROPN
ejpam-7055	309	9	gupta	gupta	PROPN
ejpam-7055	309	10	.	.	PUNCT
ejpam-7055	309	11	soft	soft	ADJ
ejpam-7055	309	12	category	category	NOUN
ejpam-7055	309	13	—	—	PUNCT
ejpam-7055	309	14	an	an	DET
ejpam-7055	309	15	introduction	introduction	NOUN
ejpam-7055	309	16	.	.	PUNCT
ejpam-7055	310	1	journal	journal	PROPN
ejpam-7055	310	2	of	of	ADP
ejpam-7055	310	3	hyperstructures	hyperstructure	NOUN
ejpam-7055	310	4	,	,	PUNCT
ejpam-7055	310	5	2(2):118–135	2(2):118–135	NOUN
ejpam-7055	310	6	,	,	PUNCT
ejpam-7055	310	7	2013	2013	NUM
ejpam-7055	310	8	.	.	PUNCT
ejpam-7055	311	1	[	[	X
ejpam-7055	311	2	27	27	NUM
ejpam-7055	311	3	]	]	PUNCT
ejpam-7055	311	4	m.	m.	NOUN
ejpam-7055	311	5	zhou	zhou	PROPN
ejpam-7055	311	6	,	,	PUNCT
ejpam-7055	311	7	s.	s.	PROPN
ejpam-7055	311	8	li	li	PROPN
ejpam-7055	311	9	,	,	PUNCT
ejpam-7055	311	10	and	and	CCONJ
ejpam-7055	311	11	m.	m.	PROPN
ejpam-7055	311	12	akram	akram	PROPN
ejpam-7055	311	13	.	.	PUNCT
ejpam-7055	312	1	categorical	categorical	ADJ
ejpam-7055	312	2	properties	property	NOUN
ejpam-7055	312	3	of	of	ADP
ejpam-7055	312	4	soft	soft	ADJ
ejpam-7055	312	5	sets	set	NOUN
ejpam-7055	312	6	.	.	PUNCT
ejpam-7055	313	1	scientific	scientific	ADJ
ejpam-7055	313	2	world	world	NOUN
ejpam-7055	313	3	journal	journal	NOUN
ejpam-7055	313	4	,	,	PUNCT
ejpam-7055	313	5	2014	2014	NUM
ejpam-7055	313	6	:	:	PUNCT
ejpam-7055	313	7	article	article	NOUN
ejpam-7055	313	8	i	i	PROPN
ejpam-7055	313	9	d	d	PROPN
ejpam-7055	313	10	783056	783056	NUM
ejpam-7055	313	11	,	,	PUNCT
ejpam-7055	313	12	10	10	NUM
ejpam-7055	313	13	pages	page	NOUN
ejpam-7055	313	14	,	,	PUNCT
ejpam-7055	313	15	2014	2014	NUM
ejpam-7055	313	16	.	.	PUNCT
ejpam-7055	314	1	[	[	X
ejpam-7055	314	2	28	28	NUM
ejpam-7055	314	3	]	]	X
ejpam-7055	314	4	r.	r.	PROPN
ejpam-7055	314	5	a.	a.	PROPN
ejpam-7055	314	6	borzooei	borzooei	PROPN
ejpam-7055	314	7	,	,	PUNCT
ejpam-7055	314	8	m.	m.	NOUN
ejpam-7055	314	9	mobini	mobini	NOUN
ejpam-7055	314	10	,	,	PUNCT
ejpam-7055	314	11	and	and	CCONJ
ejpam-7055	314	12	m.	m.	NOUN
ejpam-7055	314	13	m.	m.	PROPN
ejpam-7055	314	14	ebrahimi	ebrahimi	PROPN
ejpam-7055	314	15	.	.	PUNCT
ejpam-7055	315	1	the	the	DET
ejpam-7055	315	2	category	category	NOUN
ejpam-7055	315	3	of	of	ADP
ejpam-7055	315	4	soft	soft	ADJ
ejpam-7055	315	5	sets	set	NOUN
ejpam-7055	315	6	.	.	PUNCT
ejpam-7055	316	1	journal	journal	NOUN
ejpam-7055	316	2	of	of	ADP
ejpam-7055	316	3	intelligent	intelligent	ADJ
ejpam-7055	316	4	&	&	CCONJ
ejpam-7055	316	5	fuzzy	fuzzy	ADJ
ejpam-7055	316	6	systems	system	NOUN
ejpam-7055	316	7	,	,	PUNCT
ejpam-7055	316	8	28:157–167	28:157–167	NUM
ejpam-7055	316	9	,	,	PUNCT
ejpam-7055	316	10	2015	2015	NUM
ejpam-7055	316	11	.	.	PUNCT
ejpam-7055	317	1	[	[	X
ejpam-7055	317	2	29	29	NUM
ejpam-7055	317	3	]	]	X
ejpam-7055	317	4	s.	s.	PROPN
ejpam-7055	317	5	öztunç	öztunç	PROPN
ejpam-7055	317	6	.	.	PUNCT
ejpam-7055	318	1	some	some	DET
ejpam-7055	318	2	properties	property	NOUN
ejpam-7055	318	3	of	of	ADP
ejpam-7055	318	4	soft	soft	ADJ
ejpam-7055	318	5	categories	category	NOUN
ejpam-7055	318	6	.	.	PUNCT
ejpam-7055	319	1	international	international	ADJ
ejpam-7055	319	2	journal	journal	NOUN
ejpam-7055	319	3	of	of	ADP
ejpam-7055	319	4	modeling	modeling	NOUN
ejpam-7055	319	5	and	and	CCONJ
ejpam-7055	319	6	optimization	optimization	NOUN
ejpam-7055	319	7	,	,	PUNCT
ejpam-7055	319	8	6(2):91–95	6(2):91–95	NUM
ejpam-7055	319	9	,	,	PUNCT
ejpam-7055	319	10	2016	2016	NUM
ejpam-7055	319	11	.	.	PUNCT
ejpam-7055	320	1	[	[	X
ejpam-7055	320	2	30	30	NUM
ejpam-7055	320	3	]	]	X
ejpam-7055	320	4	n.	n.	NOUN
ejpam-7055	320	5	shirmohammadi	shirmohammadi	NOUN
ejpam-7055	320	6	and	and	CCONJ
ejpam-7055	320	7	h.	h.	PROPN
ejpam-7055	320	8	rasouli	rasouli	PROPN
ejpam-7055	320	9	.	.	PUNCT
ejpam-7055	321	1	categorical	categorical	ADJ
ejpam-7055	321	2	approach	approach	NOUN
ejpam-7055	321	3	to	to	ADP
ejpam-7055	321	4	soft	soft	ADJ
ejpam-7055	321	5	s	s	NOUN
ejpam-7055	321	6	-	-	PUNCT
ejpam-7055	321	7	acts	act	NOUN
ejpam-7055	321	8	.	.	PUNCT
ejpam-7055	322	1	filomat	filomat	NOUN
ejpam-7055	322	2	,	,	PUNCT
ejpam-7055	322	3	31(13):4185–4198	31(13):4185–4198	PROPN
ejpam-7055	322	4	,	,	PUNCT
ejpam-7055	322	5	2017	2017	NUM
ejpam-7055	322	6	.	.	PUNCT
ejpam-7055	323	1	[	[	X
ejpam-7055	323	2	31	31	NUM
ejpam-7055	323	3	]	]	PUNCT
ejpam-7055	323	4	p.	p.	PROPN
ejpam-7055	323	5	k.	k.	PROPN
ejpam-7055	324	1	sharma	sharma	PROPN
ejpam-7055	324	2	,	,	PUNCT
ejpam-7055	324	3	chandni	chandni	PROPN
ejpam-7055	324	4	,	,	PUNCT
ejpam-7055	324	5	and	and	CCONJ
ejpam-7055	324	6	n.	n.	PROPN
ejpam-7055	324	7	bhardwaj	bhardwaj	PROPN
ejpam-7055	324	8	.	.	PUNCT
ejpam-7055	324	9	category	category	NOUN
ejpam-7055	324	10	of	of	ADP
ejpam-7055	324	11	intuitionistic	intuitionistic	ADJ
ejpam-7055	324	12	fuzzy	fuzzy	ADJ
ejpam-7055	324	13	modules	module	NOUN
ejpam-7055	324	14	.	.	PUNCT
ejpam-7055	325	1	mathematics	mathematic	NOUN
ejpam-7055	325	2	,	,	PUNCT
ejpam-7055	325	3	10:399	10:399	NUM
ejpam-7055	325	4	,	,	PUNCT
ejpam-7055	325	5	2022	2022	NUM
ejpam-7055	325	6	.	.	PUNCT
ejpam-7055	326	1	g.	g.	PROPN
ejpam-7055	326	2	muhiuddin	muhiuddin	PROPN
ejpam-7055	326	3	et	et	PROPN
ejpam-7055	326	4	al	al	PROPN
ejpam-7055	326	5	.	.	PUNCT
ejpam-7055	326	6	/	/	SYM
ejpam-7055	326	7	eur	eur	PROPN
ejpam-7055	326	8	.	.	PUNCT
ejpam-7055	327	1	j.	j.	PROPN
ejpam-7055	327	2	pure	pure	PROPN
ejpam-7055	327	3	appl	appl	PROPN
ejpam-7055	327	4	.	.	PROPN
ejpam-7055	327	5	math	math	PROPN
ejpam-7055	327	6	,	,	PUNCT
ejpam-7055	327	7	18	18	NUM
ejpam-7055	327	8	(	(	PUNCT
ejpam-7055	327	9	4	4	NUM
ejpam-7055	327	10	)	)	PUNCT
ejpam-7055	327	11	(	(	PUNCT
ejpam-7055	327	12	2025	2025	NUM
ejpam-7055	327	13	)	)	PUNCT
ejpam-7055	327	14	,	,	PUNCT
ejpam-7055	327	15	7055	7055	NUM
ejpam-7055	327	16	13	13	NUM
ejpam-7055	327	17	of	of	ADP
ejpam-7055	327	18	13	13	NUM
ejpam-7055	328	1	[	[	X
ejpam-7055	328	2	32	32	NUM
ejpam-7055	328	3	]	]	PUNCT
ejpam-7055	328	4	j.	j.	PROPN
ejpam-7055	328	5	meng	meng	PROPN
ejpam-7055	328	6	and	and	CCONJ
ejpam-7055	328	7	y.	y.	PROPN
ejpam-7055	328	8	b.	b.	PROPN
ejpam-7055	329	1	jun	jun	PROPN
ejpam-7055	329	2	.	.	PUNCT
ejpam-7055	330	1	bck	bck	PROPN
ejpam-7055	330	2	-	-	PUNCT
ejpam-7055	330	3	algebras	algebras	PROPN
ejpam-7055	330	4	.	.	PUNCT
ejpam-7055	331	1	kyung	kyung	PROPN
ejpam-7055	331	2	moon	moon	PROPN
ejpam-7055	331	3	sa	sa	PROPN
ejpam-7055	331	4	co.	co.	PROPN
ejpam-7055	331	5	,	,	PUNCT
ejpam-7055	331	6	seoul	seoul	PROPN
ejpam-7055	331	7	,	,	PUNCT
ejpam-7055	331	8	korea	korea	PROPN
ejpam-7055	331	9	,	,	PUNCT
ejpam-7055	331	10	1994	1994	NUM
ejpam-7055	331	11	.	.	PUNCT
ejpam-7055	332	1	[	[	X
ejpam-7055	332	2	33	33	NUM
ejpam-7055	332	3	]	]	X
ejpam-7055	332	4	y.	y.	PROPN
ejpam-7055	332	5	b.	b.	PROPN
ejpam-7055	332	6	jun	jun	PROPN
ejpam-7055	332	7	.	.	PROPN
ejpam-7055	332	8	soft	soft	ADJ
ejpam-7055	332	9	bck	bck	PROPN
ejpam-7055	332	10	/	/	SYM
ejpam-7055	332	11	bci	bci	NOUN
ejpam-7055	332	12	-	-	PUNCT
ejpam-7055	332	13	algebras	algebra	NOUN
ejpam-7055	332	14	.	.	PUNCT
ejpam-7055	333	1	computers	computer	NOUN
ejpam-7055	333	2	and	and	CCONJ
ejpam-7055	333	3	mathematics	mathematic	NOUN
ejpam-7055	333	4	with	with	ADP
ejpam-7055	333	5	applications	application	NOUN
ejpam-7055	333	6	,	,	PUNCT
ejpam-7055	333	7	56:1408–1413	56:1408–1413	NUM
ejpam-7055	333	8	,	,	PUNCT
ejpam-7055	333	9	2008	2008	NUM
ejpam-7055	333	10	.	.	PUNCT