Borceux F. — Handbook of Categorical Algebra, Volume 1: Basic Category Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Borceux F. — Handbook of Categorical Algebra, Volume 1: Basic Category Theory

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Название: Handbook of Categorical Algebra, Volume 1: Basic Category Theory

Автор: Borceux F.

Аннотация:

A Handbook of Categorical Algebra, in three volumes, is a detailed account of everything a mathematician needs to know about category theory. Each volume is self-contained and is accessible to graduate students with a good background in mathematics. Volume 1 is devoted to general concepts. After introducing the terminology and proving the fundamental results concerning limits, adjoint functors and Kan extensions, the categories of fractions are studied in detail; special consideration is paid to the case of localizations. The remainder of the first volume studies various "refinements" of the fundamental concepts of category and functor.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 345

Добавлена в каталог: 18.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\alpha$ -filtered category      268
$\alpha$ -filtered colimit      268
$\alpha$ -flat functor      270
$\alpha$ -left-exact functor      269
$\alpha$ -limit      268
2-category      282
3-category      292
Absolute colimit      66
Absolutely flat functor      271
Adjoint arrows      284 305
Adjoint functor theorem      109
Adjoint functors      98
Adjunction      98
arrow      4
Associativity of coproduct      45
Associativity of pullback      54
Axiom of universes      3
Bicategory      302
Bidense morphism      235
Bifunctor      23
Bilimit      295
Bimodule      307 308
Calculus of fractions      183
Cartesian closed category      335
Category      4
Category of arrows over I      7
Category of arrows under I      7
Category of elements      22
Category of fractions      181
Category with absolute colimits      272
Category with enough projectives      164
Category, n-category      293
Cauchy complete category      274
Cauchy completeness      319
Cauchy completion      277
cell      283
Cell, 0-cell      283
Cell, 1-cell      283
Cell, 2-cell      283
Cell, 3-cell      292
class      3
Closed subobject      228
Closure of a subobject      227
CoCone      57
Codomain of an arrow      5
Coequalizer      49
Cogenerator      167
Colimit      57
Colimit closed class      205
Collectively faithful family of functors      154
Comma category      20 91
Commutative diagram      5
Commutativity condition      177
Complete category      59 107
Conditional graph      178
Cone      56
Cone, lax cone      300
Cone, pseudo-cone      300
Connected category      58
Constant natural transformation      15
Contravariant functor      16
Coproduct      44
Coreflection along a functor      98
Covariant functor      16
Crossed module      339
Dense family of generators      153
Dense generator      153
Dense subobject      228
Discrete category      7
distributor      308
Domain of an arrow      5
Dual category      33
Duality principle      33
Epimorphism      27
Epireflective subcategory      120
Equalizer      48
EQUIVALENCE      284
Equivalence of categories      116
Essential localization of a category      119
Extremal epimorphism      136
Factorization      148
Factorization system      209
Faithful functor      19
Family of functors collectively reflecting isomorphisms      154
Family of generators      151
Filtered category      76
Filtered colimit      76
Final functor      69
Final object      48
Finitely complete category      59
Finitely generated category      63
Finitely well-complete category      147
Flat functor      260
Forgetful functor      8
Free Abelian group      102
Free group      102
Free monoid      102
Free ring      103
Full and faithful functor      19
Full functor      19
Full subcategory      19
functor      5
Functor 2-functor      287
Functor horn-functor      34
Functor lax functor      296
Functor preserving monomorphisms      24
Functor pseudo-functor      297
Functor reflecting monomorphisms      24
Galois connection      105

Generator      151
Godement product of natural transformations      13
Graph      176
Groupoid      287
Homotopy      285
Idempotent      271
Identity arrow      4
Identity functor      6
Initial object      48
Injective object      167
Internal      325
Internal automorphism      287
Internal base-valued functor      329
Internal category      325
Internal category of elements      331
Internal colimit      333
Internal constant functor      328 330
Internal distributor      339
Internal dual category      328
Internal filtered category      331
Internal flat functor      333
Internal functor      327
Internal limit      333
Internal natural transformation      327 329
Internal power      335
Internal presheaf      329
Internal product      335
Intersection      133
Isomorphism      19 31
Kan extension      113 284
Kernel pair      52
Left adjoint functor      98
Left exact functor      250
Lepi-strong-mono factorization      149
LIMIT      56
Limit preserving functor      64
Limit reflecting functor      65
Limit, 2-limit      293
Limit, bilimit      395
Limit, lax-limit      300
Limit, pseudo-limit      300
Localization of a category      119
Locally Cartesian closed category      339
Locally presentable category      241
Loop      104
Modification      290 298
Monomorphism      23
More general adjoint functor theorem      277
Morita equivalent categories      321
Morphism      4
Morphism of graphs      176
Natural transformation      10 16
Natural transformation, 2-natural transformation      289
Natural transformation, lax-natural transformation      297
Natural transformation, pseudo-natural transformation      298
Object      4
Orthogonal subcategory      197
Orthogonality      193 194
Path      176
Path category      177
Pointwise Kan extension      124
Presentable object      297
PRODUCT      39 40
Product of categories      22
Product, associativity of      40 41
Profunctor      308
Projective object      163
Pullback      51
Pushout      52
Quotient      132
Reflection along a functor      97
Reflective subcategory      118
Regular cardinal      268
Regular category      236
Regular epimorphism      136
Replete subcategory      118
Representable functor      9
retract      24
Retraction      24
Right adjoint functor      98
Saturated class      190
Section      24
Separator      151
Set      3
Small category      6
Small set      3
Solution set condition      109
Source of an arrow      5
span      305
Special adjoint functor theorem      110
Split idempotent      271
Stone — Cech compactification      113
Strong epimorphism      137 193
Strong family of generators      152 157
Strong generator      152 157
Strong-epi-mono factorization      148
Subcategory      19
Subobject      132
Suspension      104
Target of an arrow      5
Tensor product of Set-valued functors      129
Terminal object      48
The more general adjoint functor theorem      277
union      133
Universal closure operation      227
Universal colimit      85
Universe      2
Well-powered category      132
Yoneda embedding      17
Yoneda Lemma      11

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