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

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Kernel      2
Kernel      2
Kernel pair      1.67
Kernel pair      1.67
Kernels lemma      40
Kernels lemma      40
Kleisli category      192
Kleisli category      192
Lattice      135
Lattice      135
Lax-functor      I.317
Lax-limit      I.344 339
Lax-limit      I.344 339
Lax-natural transformation      1.318
Lax-natural transformation      1.318
Left adjoint functor      I.113
Left exact functor      50 I.268
Left exact monad      252
Left exact monad      252
LIMIT      I.71
LIMIT      I.71
Limit preserving functor      I.79
Limit reflecting functor      I.80
Localization of a category      I.134
Localized fibration      402
Localizing subcategory      64
Localizing subcategory      64
Locally cartesian closed -      I.359
Locally compact space      356
Locally compact space      356
Locally presentable category      I.260 256
Locally small fibration      412
Loewenheim — Skolem theorem      278
Loewenheim — Skolem theorem      278
Loop      I.119
Loop      I.119
Mal’cev category      121
Metric space      347
Metric space      347
Model      124 125 130 174 277
Model      124 125 130 174 277
Model of a sketch      277 290
Model of a sketch      277 290
Modification      1.311 1.320
Modification      1.311 1.320
Module      135
Module      135
Monad      189
Monad      189
Monad generated by an adjunction      193
Monad generated by an adjunction      193
Monad of families      433
Monad with finite rank      231 252
Monad with finite rank      231 252
Monad with rank      231 276
Monad with rank      231 276
Monadic functor      212
Monoid      186
Monoid      186
Monoidal category      291
Monomorphism      I.38
Monomorphism      I.38
More general adjoint functor theorem      I.296
More general adjoint functor theorem      I.296
Morita equivalence      180
Morita equivalence      180
Morita equivalent categories      I.341
Morita equivalent categories      I.341
Morphism      I.19
Morphism      I.19
Morphism of algebraic theory’es      143
Morphism of algebras      189
Morphism of algebras for a monad      189
Morphism of graph      I.191
Morphism of monads      229
Morphism of monads      229
Morphism of monoidal categorys      313
Morphism of monoidal categorys      313
Morphism of sketches      290
Natural transformation      I.24 I.31
Natural transformation      I.24 I.31
Nine lemma      42 87
Noether isomorphism theorems      44
Noether isomorphism theorems      44
Normal subgroup      3
Normal subgroup      3
Object      I.19
Object      I.19
Object of $\mathcal{V}$—natural transformation      311
Object of $\mathcal{V}$—natural transformation      311
Opposite relation      114
Opposite relation      114
Orthogonal subcategory      I.213
Orthogonal subcategory      I.213
Orthogonality      I.209
Orthogonality      I.209
Partial bisections      289
Partial bisections      289
Path      I.192
Path      I.192
Path category      I.192
Pointed set      86 136
Pointed set      86 136
Pointwise Kan extension      1.140
Pointwise Kan extension      1.140
Pointwise topology      299 357
POSET      133 183
POSET      133 183
Power fibration      398
Preadditiv category      4
Precartesian morphism      376
Precartesian morphism      376
Presentable object      I.259 62
Presentable object      I.259 62
Presentation of an algebraic theory      125 133
PRODUCT      I.54 I.56
PRODUCT      I.54 I.56
Product in a fibration      411
Product in a fibration      411
Product of categories      I.37
Product of categories      I.37
Profunctor      I.329
Profunctor      I.329
Projective object      I.177
Projective object      I.177
Pseudo-element      35
Pseudo-element      35
Pseudo-equality      35
Pseudo-equality      35
Pseudo-functor      I.318
Pseudo-image      35
Pseudo-image      35
Pseudo-limit      I.344 339
Pseudo-limit      I.344 339
Pseudo-natural transformation      1.320
Pseudo-natural transformation      1.320
Pullback      I.65
Pullback      I.65
Pure monoidal category      249
Pure monoidal category      249
Pure monomorphism      249
Pushout      I.67
Pushout      I.67
Quotient      I.147
Quotient      I.147
Rank      272
Rank      272
Reflection along a functor      I.112
Reflective subcategory      I.133
Reflexive pair      252
Reflexive pair      252
Regula category      I.91 90 91 252
Regular cardinal      I.287
Regular cardinal      I.287
Regular epimorphism      I.151
Relation      101 114
Relation      101 114
Replete subcategory      I.133
Representable functor      I.24
Restricted snake lemma      45
retract      I.39
retract      I.39
Retraction      I.39
Retraction      I.39
Right adjoint functor      I.113
Right exact functor      50
Saturated class      I.206
Second Noether isomorphism theorems      44
Second Noether isomorphism theorems      44
Section      I.39
Section      I.39
Semi-lattice      134
Semi-lattice      134
Separator      1.166
Separator      1.166
Set      1.18
Set      1.18
Sharply less      267
Sharply less      267
Short exact sequence      34 87
Short Five Lemma      42
Short Five Lemma      42
Sketch      277
Sketch      277
Small category      I.21
Small fibration      379
Small set      I.17
Small set      I.17
Snake lemma      48
Snake lemma      48
Solution set condition      I.124 274
Source of an arrow      I.19
Space      353
Space      353
span      I.326
span      I.326
Special adjoint functor theorem      I.125
Split coequalizer      212
Split fibration      392
Split idempotent      I.290
Stone — Cech compactification      I.128
Stone — Cech compactification      I.128
Strong epimorphism      I.152 I.209
Strong family of generators      I.166 I.171
Strong generator      I.166 I.268 I.171
Strong-epi-mon, factorization      I.162
Struct ure-semantics adjunction      184
Struct ure-semantics adjunction      184
Subcategory      I.34
Subcategory      I.34
Subobject      I.147
Subobject      I.147
Suspension      I.119
Suspension      I.119
Symmetric monoidal category      292
Symmetric monoidal category      292
Symmetric monoidal closed category      167
Target of an arrow      I.19
Tensor      320 331
Tensor      320 331
Tensor product of algebraic theory’es      174 176
Tensor product of Set-valued functors      I.145
Tensored category      320
Term      123 125
Term      123 125
Terminal object      I.62
Terminal object      I.62
The more general adjoint functor theorem      I.296
Topological functor      367
topology      355
topology      355
Torsion free group      232
Torsion theory      52
union      I.147 26
union      I.147 26
Universal algebra      125
Universal algebra      125
Universal closure operation      I.244
Universal closure operation      I.244
Universal colimit      I.99
Universal epimorphism      120
Universe      I.16
Universe      I.16
Weighte colimit      327
Weighted limit      327
Weighted limit      327
Well-powered category      I.147
Yoneda embedding      I.31 I.32
Yoneda embedding      I.31 I.32
Yoneda Lemma      I.25
Yoneda Lemma      I.25
Zero morphism      1
Zero morphism      1
Zero object      1
Zero object      1
1 2
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