Borceux F. — Handbook of Categorical Algebra: Categories and Structures, Vol. 2 :: Электронная библиотека попечительского совета мехмата МГУ

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Borceux F. — Handbook of Categorical Algebra: Categories and Structures, Vol. 2

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Название: Handbook of Categorical Algebra: Categories and Structures, Vol. 2

Автор: Borceux F.

Аннотация:

The second volume, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibered categories.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 461

Добавлена в каталог: 02.05.2008

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Предметный указатель

$\alpha$ -filtered category      I.287
$\alpha$ -filtered colimit      I.287
$\alpha$ -flat functor      I.289
$\alpha$ -left exact functor      I.288
$\alpha$ -limit      I.287
$\alpha$ -limit      I.287
$\mathcal{Y}^{\infty}$ -algebra      136
$\vee$ -lattice      233
$\vee$ -lattice      233
2-category      I.302
2-functor      I.308
2-limit      1.344 339
2-natural transformation      I.309
2-natural transformation      I.309
3-category      I.312
Abelian category      13 109
Abelian duality principle      13
Absolute colimit      I.82
Absolutely flat functor      I.290
Accessible category      263
Additive category      6
Additive functor      8
Additive representable functor      12
Additive Yoneda lemma      12
Additive Yoneda lemma      12
Adjoint arrows      I.304 I.326
Adjoint functor theorem      I.124
Adjoint functors      I.113
Adjoint lifting theorem      226
Adjunction      I.113
Algebra      189
Algebra for a monad      189
Algebra for a monad      189
Algebraic category      158 257
Algebraic functor      144
Algebraic lattice      141
Algebraic lattice      141
Algebraic subcategory      185
Algebraic subcategory      185
Algebraic theory      130
arrow      I.19
Associativity of      I.55 I.56
Associativity of      I.55 I.56
Associativity of coproduct      I.60
Associativity of pullback      I.69
Associativity of pullback      I.69
Asterisk      359
Axiom      123 125
Axiom of universes      I.17
Axiom of universes      I.17
Banach spaces      257
Bicategory      I.323
Biclosed monoidal category      293
Biclosed monoidal category      293
Bidense morphism      I.253
Bidense morphism      I.253
Bifunctor      I.38
Bihomomorphism      167
Bilimit      I.315
Bimodule      I.328 I.329
Biproduct      5
Boolean algebra      135
Calculus of fractions      1.198
Cartesian closed category      294
Cartesian functor      382
Cartesian morphism      375
Cartesian natural transformation      382
Cartesian natural transformation      382
Category      I.19
Category of relations      114
Category of relations      114
Category, n-category      I.313
Category, n-category of arrows over J      I.22
Category, n-category of arrows under J      I.22
Category, n-category of elements      I.37
Category, n-category of fractions      I.196
Category, n-category with absolute colimits      I.291
Category, n-category with enough projectives      I.179
Cauchy complete category      I.270 266 289
Cauchy completeness      I339
Cauchy completion      I.353 289
cell      I.303
Cell, 0-cell      I.303
Cell, 1-cell      I.303
Cell, 2-cell      I.303
Cell, 3-cell      I.313
class      I.18
Close subobject      I.246
Close subobject      I.246
Closure of subobject      I.244
Closure of subobject      I.244
Cocomplete fibration      412
CoCone      I.72
Codomain of an arrow      I.19
Coend      329
Coequalizer      I.64
Cofibration      382
Cogenerator      I.181
Cokernel      1
Colimit      I.72
Colimit closed class      I.221
Collectively faithful family of functors      I.169
Comma category      I.35 I.106
Commutative algebraic theory      166
Commutative diagram      I.19
Commutativity condition      I.193
Comonad      219
Compact element      141
Compact open topology      356
Compact space      236
Compactly continuous      360
Compactly generated space      364
Compactly generated space      364
Complete category      I.74 I.122
Complete fibration      402
Complete lattice      135 183 253
Complete lattice      135 183 253
Composite relation      114
Conditional graph      I.193
Cone      I.71
Cone, lax-cone      I.321
Cone, pseudo-cone      I.321
Congruence      139
Connected category      I.73
Constant      122
Constant natural transformation      I.30
Constant natural transformation      I.30
Contravariant functor      I.30
Coproduct      1.59
Coproduct in a fibration      412
Coreflection along a functor      I.113
Cotensor      320 331
Cotensored category      320
Cotopological functor      368
Covariant functor      I.31
Crossed module      I.360
Definable class      424
Definable class of arrows      424
Definable class of diagrams      431
Definable class of objects      424
Definable subfibration      424
Dens subobject      I.245
Dens subobject      I.245
Dense family of generators      I.167
Dense generator      I.167
Descent data      240
Descent morphism      253
Descent theory      237
Discrete category      I.21
Distributive lattice      135

Distributive lattice      135
distributor      I.329
Domain of an arrow      I.19
Dominated functor      183
Dual category      I.48
Dual fibration      393
Duality principle      I.48
Effectiv      242
Effective equivalence relation      102
Effective equivalence relation      102
Effective union      27
Effective union      27
Eilenberg — Moore category      189
Embedding theorem      112
END      329
Enriched      300
Enriched $\nu$ -category      300
Enriched, adjunction      340
Enriched, category      300
Enriched, distributor      306
Enriched, functor      301
Enriched, Kan extension      344
Enriched, natural transformation      301
Enriched, Yoneda embedding      313
Enriched, Yoneda lemma      311
Epi-strong-mono factorization      I.164
Epimorphism      I.42
Epireflective subcategory      I.135
Epireflective subcategory      I.135
Equalizer      I.63
EQUIVALENCE      I.304
Equivalence of categories      I.132
Equivalence relation      102
Equivalence relation      102
Essential limit      I.134
Essential limit      I.134
Exact category      109
Exact functor      50 97
Exact sequence      32 33 95
Exponentiable space      355
Exponentiable space      355
Extremal epimorphism      I.151
Factorization      I.162
Factorization system      1.225
Faithful embedding theorem      73
Faithful functor      I.33
Family of functors collectively reflecting isomorphisms      1.169
Family of generators      I.166
Fibration      375
Fibre      374
Fibre small functor      370
Fibred adjoint functors      394
Fibred adjunction      394
Fibred category      375
Fibred comma category      434
Fibred internal limit      401
Fibred internal limit      401
Fibred Kan extension      434
Fibred Kan extension      434
Fibred limit      400
Fibred limit      400
Fibred Yoneda Lemma      385
Fibred Yoneda Lemma      385
Field      182
Filtered category      I.91
Filtered colimit      I.91
Final functor      I.84
Final object      I.62
Finitely complete category      I.74
Finitely complete fibration      402
Finitely generated -      146
Finitely generated -      146
Finitely generated category      I.78
Finitely presentable -      146
Finitely presentable -      146
Finitely well-complete category      I.161
First Noether isomorphism theorems      44
First Noether isomorphism theorems      44
Five lemma      41
Flat functor      274 I.268
Flat module      249
Flat module      249
Forgetful functor      I.23
Free -      127 146
Free Abelian group      I.117
Free algebra      191
Free algebra for a monad      191
Free algebra for a monad      191
Free group      I.117
Free module      157
Free module      157
Free monoid      I.117
Free ring      I.118
Fubini formula      347
Full and faithful embedding theorem      80
Full and faithful functor      I.34
Full functor      I.33
Full subcategory      I.34
functor      I.20
Functor with rank      272
Functor, preserving monomorphisms      I.39
Functor, reflecting monomorphisms      I.39
G-set      136 297 298
Galois connection      I.120
Generator      I.166
Global support      120
Godement product of natural transformations      1.28
Godement product of natural transformations      1.28
Graph      I.191
Group      122
Groupoid      I.307
Hereditary torsion theory      56
Heyting algebra      300
Hilbert spaces      289
Hom-functor      I.49
Homomorphism      126 130
Homotopy      I.306
Idempotent      I.290
Idempotent monad      196
Idempotent monad      196
Identity arrow      I.19
Identity functor      I.20
Image      19 92
Initial object      I.62
Initial structure      366
Injective object      I.181
Internal      I.345
Internal automorphism      I.307
Internal base-valued functor      I.349
Internal category      I.345
Internal category of elements      I.351
Internal colimit      I.354
Internal constant functor      I.348 I.350
Internal distributor      I.359
Internal dual category      I.348
Internal filtered category      I.352
Internal flat functor      I.353
Internal functor      I.347
Internal limit      I.354
Internal natural transformation      I.347 I.350
Internal power      I.356
Internal product      I.356
Internally complete fibration      402
Intersection      I.133 26
Inverse image functor      393
Isomorphism      I.34 I.46
Kan extension      I.129 I.304
Kan extension      I.129 I.304
Kelley space      364
Kelley space      364

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