Pedicchio M. C., Tholen W. — Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Pedicchio M. C., Tholen W. — Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory

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Название: Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory

Авторы: Pedicchio M. C., Tholen W.

Аннотация:

Researchers, teachers and graduate students in algebra and topology — familiar with the very basic notions of category theory — will welcome this categorical introduction to some of the key areas of modern mathematics, without being forced to study category theory. Rather, each of the eight largely independent chapters analyzes a particular subject, revealing the power and applicability of the categorical foundations in each case.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 417

Добавлена в каталог: 22.10.2010

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Предметный указатель

$(\mathcal{E},\mathcal{M})$ -closed class of morphisms      III.112
$T_{D}$ -space      II.66
$\mathbb{T}$ -algebra      VI.275
$\mathcal{F}$ -biquotient map      III.150
$\mathcal{F}$ -closed embedding      III.112
$\mathcal{F}$ -closed morphism      III.112
$\mathcal{F}$ -closure      III.156
$\mathcal{F}$ -compact object      III.119
$\mathcal{F}$ -compactification      III.133
$\mathcal{F}$ -cowellpowered subcategory      III.159
$\mathcal{F}$ -dense morphism      III.113
$\mathcal{F}$ -discrete object      III.139
$\mathcal{F}$ -exponentiable morphism      III.148
$\mathcal{F}$ -exponentiable object      III.151
$\mathcal{F}$ -final morphism      III.143
$\mathcal{F}$ -Hausdorff object      III.126
$\mathcal{F}$ -open morphism      III.136
$\mathcal{F}$ -open subobject      III.137
$\mathcal{F}$ -perfect morphism      III.129
$\mathcal{F}$ -proper morphism      III.118
$\mathcal{F}$ -quotient morphism      III.145
$\mathcal{F}$ -separated morphism      III.124
$\mathcal{F}$ -separated object      III.126
$\mathcal{F}$ -Tychonoff morphism      III.132
$\mathcal{F}$ -Tychonoff object      III.131
$\mathcal{J}$ -closed arrow      VII.337
$\mathcal{T}$ -Models, category of      VI.270
$\mathcal{T}$ -sheaf      VII.329
2-dimensional exponent      VIII.390
2-functor      I.38
Abelian category      IV.203
Abelian group, internal      IV.191
Abelian group, torsion-free      IV.180
Abelian object      IV.194
Absolute coequalizer      V.224
Absolutely $\mathcal{F}$ -closed morphism      III.132
Absolutely $\mathcal{F}$ -closed object      III.131
Abstractly finite object      VI.289
Additive category      IV.200
Additive category, regular      VI.294
Adjoint, left      I.12 15
Adjoint, right      I.12 15
Adjunction      I.6 12 15
Adjunction, Isbell conjugation      I.38
Alexandroff topology      I.35
Algebra of an endomorphism      V.254
Algebra, boolean      I.23
Algebra, Eilenberg — Moore      V.217
Algebra, Heyting      I.24
Algebra, Lie      V.246
Algebra, separable      VIII.399
Algebra, split      VIII.399
Algebra, trivial      VIII.399
Algebraic $\Omega$ -set      III.131
Algebraic category      VI.270
Algebraic theory      VI.270
Algebraic variety      IV.179
Antisymmetric relation      I.16
Arrow, $\mathcal{J}$ -closed      VII.337
Arrow, cartesian      IV.168
Arrow, fibrant      IV.168
Axiom $T_{D}$       II.66
Barr — Kock Theorem      IV.176
Barr-exact category      IV.179
Beck — Chevalley Property      III.145
Beck’s criterion      V.228
Bi-quotient map      VIII.362
Bicategory      I.12
Bidense morphism      VII.324
Biproduct      IV.201
Birkhoff — Witt Theorem      V.247
Boolean algebra      I.23
Boolean topos      I.7
Booleanization      II.65
Bundle      VIII.395
Bundle, induced      VIII.395
Bundle, locally trivial fibre, with fibre F      VIII.402
Bundle, locally trivial, of topological spaces      VIII.401
Bundle, split      VIII.395
Bundle, trivial      VIII.395
Bundle, trivial, of topological spaces      VIII.401
Calculus of fractions, left      VII.325
Calculus of relations      VII.346
Cancellation property, strong right      VIII.364
Cartesian arrow      IV.168
Cartesian closed category      VII.329
Category      I.5
Category of $\mathbb{T}$ -algebras      VI.275
Category of $\mathcal{T}$ -Models      VI.270
Category of Abelian groups      III.117
Category of categories      I.8
Category of complete atomic Boolean algebras      V.231
Category of fractions      VII.325
Category of frames      II.52 V.230
Category of graphs      V.231
Category of internal abelian groups      IV.192
Category of internal groups      IV.191
Category of locales      II.54 III.138
Category of meet-semilattices      II.70
Category of presheaves      IV.179
Category of sets      IV.179
Category of shapes      V.242
Category of small categories      IV.180
Category of topological groups      IV.180
Category of topological spaces      III.137 IV.180
Category with enough regular projectives      VII.336
Category, abelian      IV.203
Category, additive      IV.200
Category, additive regular      VI.294
Category, algebraic      VI.270
Category, Barr-exact      IV.179
Category, cartesian closed      VII.329
Category, comma      III.117
Category, distributive      VII.343
Category, exact      V.234 VI.281
Category, extensive      III.115 VII.342
Category, fibre-determined      III.146
Category, finitely extensive      III.115
Category, Kleisli      V.220 251
Category, lextensive      VII.342
Category, linear      IV.200
Category, locally finitely presentable      VI.298
Category, Maltsev      IV.189 VI.290
Category, monadic      V.222
Category, monadic, over Set      V.234
Category, monoidal      V.215
Category, multi-sorted      VI.277
Category, naturally Maltsev      VI.294
Category, non-associative      VIII.392
Category, pointed      IV.172
Category, protomodular      IV.184 VI.294
Category, quasi-algebraic      VI.288
Category, regular      IV.177 VI.279 VII.336
Category, S-sorted algebraic      VI.277
Category, skeletal      I.10
Category, strict monoidal      V.258
Chasles relation      IV.191 194
Chu space, extensive Boolean      III.117
Clementino — Tholen Theorem      III.141
Clopen map      III.115
Closed localic map      II.83
Closed map      III.112
Closed sublocale      II.62
Closed under limits      III 109
Closure of a sublocale      II.64
Closure operator      III.156
Closure operator, hereditary      III.156
Closure operator, idempotent      III.156
Closure operator, universal      III.114 VII.323
Closure, down-      II.70

Co-dense localic map      II.82
Co-Frobenius Identity      II.87
Coarse relation      IV.168
Cocycle condition, Grothendieck’s      VIII.383
Coequalizer, absolute      V.224
Coequalizer, reflexive      VI.274
Coherence, classical      V.242
Cokernel      IV.172
Colimit, weak      VI.292
Comma category      III.117
Commutative monad      V.257 261
Commutative monoid      V.262
Compact clement      II.89
Compact locale      II.83
Compactification of a locale      II.94
Compactification, Stone — Cech      II.93 III.134 159
Comparison functor      VI.276
Comparison functor, Grothendieck’s      VIII.385
Compatible family      VII.316
Complement      I.23
Complement, pseudo-      I.24 II.53
Complete filter      II.56
Complete Heyting algebra      II.53
Complete Heyting homomorphism      II.84
Complete Heyting lattice      I.42
Complete lattice, (CCD)      I.44
Complete lattice, (CD)      I.44
Complete lattice, completely distributive      I.44
Complete lattice, constructively completely distributive      I.44
Complete ordered set      I.36
Complete ring of sets      I.46
Completely distributive complete lattice      I.44
Completely distributive complete lattice, constructively      I.44
Completely prime filter      II.56
Completely regular locale      II.78
Completion, exact      VI.295 VII.351
Composite relation      I.11
Congruence      II.61
Conjunctive locale      II.77
Connected object      VII.353
Continuous lattice      II.95
Continuous section      VII.315
Coproduct completion      VII.339
Coproduct in Frm      II.71
Coreflective full suborder      I.32
Coreflector      I.32
Cosmos theory      VIII.390
Cover of a locale      II.83
Cover, regular projective      VII.336
Covering space      VIII.402
Covering, etale      VIII.399
Day — Kelly Theorem      III.152
de Morgan law      II.53
Decidable object      III.128
Dense factorization      II.65
Dense generator      VI.300 VII.347
Dense localic map      II.64
Dense sublocale      II.64
Dense subobject      VII.324
Descent data      VIII.375
Descent map      III.150
Descent morphism      VIII.375
Descent theory, elementary      VIII.375 381
Descent theory, global      VIII.375
Descent theory, Grothedieck’s (original)      VIII.381
Descent theory, monadic      VIII.381
Diamond Principle      V.240
Difunctional relation      VI.291
Direct sum      IV.201
Discrete order      I.29
Discrete ordered set      I.19
Discrete relation      IV.168
Distributive category      VII.343
Distributive lattice      I.23
Distributive, infinite, law      II.52
Down-interior      I.31
Downset      I.30
Downset functor      II.70
Duality, Gelfand      II.51
Duality, Hofmann — Lawson      II.97
Effective descent morphism      V.237 VIII.375
Effective discrete fibration of equivalence relations      VIII.368
Effective equivalence relation      IV.169 VI.281 VIII.367
Effective projective object      VI.303
Eilenberg — Moore algebra      V.217
Eilenberg — Moore comparison functor      V.222
Eilenberg — Moore object      V.253
Element, compact      II.89
Element, finite      II.89
Element, R-related      I.11
Element, R-saturated      II.66
Element, regular      VII.334
Elementary topos      I.5 VII.330
Embedding      III.109
Embedding, $\mathcal{F}$ -closed      III.112
Enough regular projectives      VII.336
Epic pair of arrows, jointly strongly      IV.185
Epimorphism      VIII.360
Epimorphism, extremal      VIII.361
Epimorphism, normal      VIII.360
Epimorphism, regular      IV.171 VIII.360
Epimorphism, split      IV.171 VIII.360
Epimorphism, stably extremal      VIII.365
Epimorphism, stably regular      VIII.361
Epimorphism, stably strong      VIII.361
Epimorphism, strong      IV.170 VIII.361
Equivalence functor      I.10
Equivalence relation      IV.167 VI.280
Equivalence relation, effective      IV.169 VI.281 VIII.367
Equivalence relation, stably effective      VIII.369
Essentially algebraic theory      VI.299
Etale covering      VIII.399
Etale map      VII.315
Exact category      V.234 VI.281
Exact completion      VI.295 VII.351
Exact diagram      VIII.368
Exact fork      IV.178
Exact sequence      IV.198
Extension (in homological algebra)      VIII.396
Extension space      VIII.401
Extension, finite separable      VIII.398
Extension, Galois, of a commutative ring      VIII.399
Extensive category      III.115 VII.342
Extremal epimorphism      VIII.361
Extremal epimorphism, stably      VIII.365
Extremal monomorphism      II.60
Factorization system      III.107
Factorization system, orthogonal      III.107
Factorization system, proper      III.107
Factorization theorem      II.68
Factorization, antiperfect-perfect      III.135
Factorization, canonical      V.262
Factorization, dense      II.65
Fibrant arrow      IV.168
Fibration of pointed objects      IV.184
Fibration, effective discrete, of equivalence relations      VIII.368
Fibre (of a map)      VIII.402
Fibre (over a point)      VIII.401
Fibre-determined category      III.146
Filter, complete      II.56
Filter, completely prime      II.56
Filtering functor      VII.352
Finitary localization      VI.297
Finitary monad      VI.275
Finite element      II.89
Finitely extensive category      III.115
Finitely presentable object      VI.282
Fit locale      II.82
Fork      IV.178
Fork, exact      IV.178

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