Borceux F. — Handbook of Categorical Algebra 3 :: Электронная библиотека попечительского совета мехмата МГУ

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Borceux F. — Handbook of Categorical Algebra 3

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Название: Handbook of Categorical Algebra 3

Автор: Borceux F.

Аннотация:

The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. This third volume turns to topos theory and the idea of sheaves. The theory of locales is considered first, and Grothendieck toposes are introduced. Notions of sketchability and accessible categories are discussed, and an axiomatic generalization of the category of sheaves is given.There is ample material here for a graduate course in category theory, and the book should also serves as a reference for users.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 522

Добавлена в каталог: 13.01.2007

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Предметный указатель

$\mathscr{C}^{\infty}$ -algebra      II.136
$\Omega$ -set      144
$\Omega$ -set, complete      156
$\Omega$ -set, epimorphism of      148
$\Omega$ -set, monomorphism of      150
$\Omega$ -set, morphism of      145
$\Omega$ -set, singleton of a      157
$\Omega$ -subset      152
Abelian      II.13
Addition      468
Adjoint arrows      I.284 I.305
Adjoint functor theorem      I.109
Adjoint functor theorem, special      I.110
Adjoint functor theorem, the more general      I.277
Adjoint functors      I.98
Adjoint functors, fibred      II.394
Adjoint lifting theorem      II.230
Adjunction      I.98
Algebra      II.189
Algebra, free      II.191
Algebra, morphism      II.189
Algebraic theory      II.130
Algebraic theory, commutative      II.166
Algebraic theory, morphisrn of      II.143
Algebraic theory, presentation of an      II.125 II.133
Algebraic theory, tensor product of      II.174 II.176
arrow      I.4
Arrow, codomain of an      I.5
Arrow, domain of an      I.5
Arrow, identity      I.4
Arrow, source of an      I.5
Arrow, target of an      I.5
Associated sheaf functor      121 497
Asterisk      II.359
Axiom      II.123 II.125 II.2
Axiom of Choice      447
Axiom of extensionality      410
Axiom of replacement      411
Axiom, power set      416
Banach spaces      II.257
Beck condition      316 341
Bicategory      I.302
Bifunctor      I.23
Bihomomorphism      II.167
Bilimit      I.295
Bimodule      I.307 I.308
Biproduct      II.5
Boolean algebra      II.135 II.9
Calculus of fractions      I.183
Cardinal      I.268
Cardinal, finite      481
Cardinal, regular      I.268
Cartesian closed category      II.294
Cartesian functor      II.382
Cartesian morphism      II.375
Cartesian natural transformation      II.382
Category      I.4 370
Category of arrows over      7 I.7
Category of arrows under I      I.7
Category of elements      I.22
Category of fractions      I.181
Category with absolute colimits      I.272
Category with enough projectives      I.164
Category, $\alpha$ -filtered      I.268
Category, 2-category      I.282
Category, 3-category      I.292
Category, abelian      II.13 II.109
Category, accessible      II.263
Category, additive      II.6
Category, algebraic      II.158 II.257
Category, bicategory      I.302
Category, cartesian closed      I.335 II.349
Category, Cauchy complete      I.274 II.266 II.289
Category, comma      I.20 I.91
Category, complete      I.59 I.107
Category, connected      I.58
Category, cotensored      II.320
Category, discrete      I.7
Category, dual      I.33
Category, enriched $\mathscr{V}$       II.300 see
Category, exact      II.105 II.109
Category, fibred      II.375
Category, fibred comma      II.434
Category, filtered      I.76 371
Category, finitely complete      I.59
Category, finitely generated      I.63
Category, finitely well-complete      I.147
Category, locally cartesian closed      I.339
Category, locally presentable      I.241 II.256
Category, Mal’cev      II.121
Category, monoidal      II.291
Category, n-category      I.293
Category, preadditive      II.4
Category, regular      I.236 II.90 II.92 II.93
Category, small      I.6
Category, symmetric monoidal closed      II.167
Category, tensored      II.320
Category, well-powered      I.132
Cauchy completeness      I.319
Cauchy completion      I.277 II.289
cell      I.283
Cell, 0-cell      I.283
Cell, 1-cell      I.283
Cell, 2-cell      I.283
Cell, 3-cell      I.292
class      I.3
Class, colimit closed      I.205
Class, saturated      I.190
Closed subset      70
Closed subset, irreducible      70
CoCone      I.57
Coend      II.329
Coequalizer      I.49
Coequalizer, split      II.212
Cofibration      II.382
Cogenerator      I.167
Coherent theory      367
Coherent theory, model of a      368
Coherent theory, morphism of models of a      368
Cokernel      II.2
Colimit      I.57
Colimit, $\alpha$ -filtered      I.268
Colimit, absolute      I.66
Colimit, filtered      I.76
Colimit, universal      I.85
Colimit, weighted      II.327
Commutative diagram      I.5
Commutativity condition      I.177
Comonad      II.219
Compact element      II.141 74
Compact space      II.236
Compactly continuous      II.360
Compatible family      88
Complemented element      436
Comprehension scheme      414
Cone      I.56
Cone, lax-cone      I.300
Cone, pseudo-cone      I.300
Congruence      II.139
Constant      II.122 346
Continuous mapping      16
Continuous mapping, open      44
Coproduct      I.44
Coproduct in a fibration      II.412
Coproduct, associativity of      I.45
Coproduct, disjoint      216
Coreflection along a functor      I.98
Cotensor      II.320 II.331
Covering      373
Crossed module      I.339

de Morgan’s laws      9
Decidable object      444
Deduction rule      2
Definable class      II.424
Definable class of arrows      II.424
Definable class of diagrams      II.431
Definable class of objects      II.424
Definable subfibration      II.424
Descent data      II.240
Descent morphism      II.253
Descent morphism, effective      II.242
Descent theory      II.237
Diaconescu theorem      280
distributor      I.308
Division      477
Double Negation      8 510
Duality principle      I.33
Eilenberg — Moore category      II.189
Element      373
Embedding theorem      II.112
END      II.329
Enriched      II.300
Enriched adjunction      II.340
Enriched category      II.300
Enriched distributor      II.306
Enriched functor      II.301
Enriched Kan extension      II.344
Enriched natural transformation      II.301
Enriched Yoneda embedding      II.313
Enriched Yoneda lemma      II.311
Epimorphism      I.27
Epimorphism, extremal      I.136
Epimorphism, regular      I.136
Epimorphism, strong      I.137 I.197
Epimorphism, universal      II.120
Equality      304
Equalizer      I.48
EQUIVALENCE      I.284
Equivalence of categories      I.116
Etale mapping      108
Exact sequence      II.32 II.33 II.95
Exact sequence, short      II.34 II.87
Excluded Middle      432
Factorization      I.148
Factorization system      I.209
Factorization, epi-strong-mono      I.149
Factorization, strong-epi-mono      I.148
Faithful embedding theorem      II.73
FALSE      344
Fibration      II.375
Fibration, cocomplete      II.412
Fibration, complete      II.402
Fibration, dual      II.393
Fibration, finitely complete      II.402
Fibration, internally complete      II.402
Fibration, localized      II.402
Fibration, locally small      II.412
Fibration, power      II.398
Fibration, small      II.379
Fibration, split      II.392
Fibre      II.374
Fibred adjunction      II.394
Fibred internal limit      II.402
Fibred limit      II.401
Field      II.182 370
Filter      62
Filter, completely prime      62
Filter, prime      62
Final object      I.48
Finite object      480 481
Five lemma      II.41
Fixed element      299
Formula      346
Formula, coherent      363 367
Formula, valid      358
Free Abelian group      I.102
Free group      I.102
Free monoid      I.102
Free ring      I.103
Frobenius identity      38
Fubini formula      II.347
Full and faithful embedding theorem      II.80
functor      I.5
Functor $\pi_f$       327
Functor $\Sigma_f$       327
Functor preserving monomorphisms      I.24
Functor reflecting monomorphisms      I.24
Functor with rank      II.272
Functor, $\alpha$ -flat      I.270
Functor, 2-functor      I.287
Functor, absolutely flat      I.271
Functor, additive      II.8
Functor, additive representable      II.12
Functor, algebraic      II.145
Functor, cartesian      II.382
Functor, collectively faithful family      I.154
Functor, contravariant      I.16
Functor, cotopological      II.368
Functor, covariant      I.16
Functor, dominated      II.183
Functor, exact      II.50 II.97
Functor, faithful      I.19
Functor, family of functors collectively reflecting isomorphisms      I.154
Functor, fibre small      II.370
Functor, final      I.69
Functor, flat      I.260 II.274
Functor, forgetful      I.8
Functor, full      I.19
Functor, full and faithful      I.19
Functor, hom-functor      I.34
Functor, identity      I.6
Functor, inverse image      II.393
Functor, lax-functor      I.296
Functor, left adjoint      I.98
Functor, left exact      I.250 II.50
Functor, limit preserving      I.64
Functor, limit reflecting      I.65
Functor, monadic      II.212
Functor, pseudo-functor      I.297
Functor, representable      I.9
Functor, right adjoint      I.98
Functor, right exact      II.50
Functor, topological      II.367
Functor, \alpha$-left-exact      I.269
G-sets      II.136 II.297 II.298
Galois connection      I.105
Generator      I.151
Generator, dense      I.153
Generator, dense family of -s      I.153
Generator, family      I.151 138
Generator, strong family      I.152 I.157
Generator, strong-      I.152 I.157
Geometric morphism      183
Germ      113
Giraud theorem      230
Global element      291
Global support      II.120
Graph      I.176
Graph, conditional      I.178
Graph, morphism      I.176
Grothendieck topology      196
Group      II.122
Group, torsion free      II.232
Groupoid      I.287
Hereditary covering      192
Hereditary subset      192
Heyting algebra      II.300 5
Heyting algebra, complete      14
Hilbert spaces      II.289
Homomorphism      II.126 II.130

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