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| Pedicchio M. C., Tholen W. — Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory |
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| Предметный указатель |
Fractions, category of VII.325
Fractions, left calculus of VII.325
Frame I.42 II.52
Frame congruence II.61
Frame homomorphism II.52
Frobenius identity II.84
Frobenius Identity, co- II.87
Frolik Theorem III.159
Full suborder I.32
Full suborder, coreflective I.32
Full suborder, reflective I.32
Full suborder, replete I.32
Fully faithful function I.31
Functor, comparison V.225 VI.276
Functor, comparison, Eilenberg — Moore V.222
Functor, comparison, Grothendieck’s VIII.385
Functor, downset II.70
Functor, equivalence I.10
Functor, filtering VII.352
Functor, left covering VII.350
Functor, left exact VII.322
Functor, monadic V.222
Functor, nerve VIII.393
Functor, nerve, truncated VIII.393
Functor, rank V.241
Fundamental group(oid) VIII.403
Galois connection I.15
Galois extension of a commutative ring VIII.399
Galois, Grothendieck’s form of the fundamental theorem of, theory VIII.399
Gelfand duality II.51
Generalized local-to-global constructions VIII.402
Generator, dense VI.300 VII.347
Generator, regular VI.271 278
Generator, small VII.345
Generator, strong VI.271 278
Geometric morphism VII.335
Glueing VII.316
Graph VI.274
Graph of a function I.11
Graph, reflexive VI.274
Grothendieck topology VII.328
Grothendieck topology, sheaf for a VII.329
Grothendieck topos VII.333
Grothendieck’s (original) descent theory VIII.381
Grothendieck’s cocycle condition VIII.383
Grothendieck’s comparison functor VIII.385
Grothendieck’s form of the fundamental theorem of Galois theory VIII.399
Group, internal IV.191
Group, torsion-free abelian IV.180
H-closed space III.131
Hausdorff locale II.80
Hausdorff locale, strongly II.80
Hereditary closure operator III.156
Heyting algebra I.24 II.53
Heyting implication II.53 54 67
Heyting lattice I.24
Heyting lattice, complete I.42
Hofmann — Lawson Duality II.97
Hom-sets I.10
Ideal II.92
Ideal, regular II.92
Idempotent closure operator III.156
Idempotent monad V.257 265
Identity, co-Frobenius II.87
Identity, Frobenius II.84
Image III.110
Image of a sublocale II.69
Image, inverse III.110
Infimum I.21
Infinite distributive law II.52
Initial object, strict VI.285
Internal abelian group IV.191
Internal group IV.191
Internal monoid IV.191
Interpolative relation II.78
Inverse image III.110
Irreducible element, meet- II.54
Isbell conjugation adjunction I.38
Isbell Density Theorem II.65
Isbell — Henriksen characterization III.135
j-closed monomorphism VII.331
j-dense monomorphism VII.331
j-sheaf VII.331
Janelidze’s criterion V.235
Johnstone Theorem III.139
Join-semilattice I.20
Jointly strongly epic pair of arrows IV.185
Joyal — Tierney Theorem V.235
K-algebraic object III.131
Kan extension VII.348
Kernel IV.172
Kernel relation IV.169
Kernel, simplicial IV.189
Kleisli category V.220 251
Kleisli object V.255
Kleisli triple V.249
Kuratowski — Mrowka Theorem II.91 III.120
Lattice I.20
Lattice, complete, completely distributive I.44
Lattice, complete, constructively completely distributive I.44
Lattice, continuous II.95
Lattice, distributive I.23
Lattice, Heyting I.24
Lawvere Characterization Theorem VI.283
Lawvere theory VI.270
Lawvere — Tierney topology VII.330
Least upper bound I.21
Left adjoint I.12 15
Left calculus of fractions VII.325
Left covering VI.296
Left covering functor VII.350
Left exact functor VII.322
Lemma, short five IV.196
Lemma, Short Five, Split IV.186
Lextensive category VII.342
Lie algebra V.246
Limit, weak VI.292 VII.337
Linear category IV.200
Local  -homeomorphism III.139
Local homeomorphism VII.315
Local section VII.315
Locale I.42 II.54 VII.334
Locale compactification II.94
Locale cover II.83
Locale, compact II.83
Locale, compactifiable II.94
Locale, completely regular II.78
Locale, conjunctive II.77
Locale, fit II.82
Locale, Hausdorff II.80
Locale, Hausdorff, strongly II.80
Locale, Lindeloef II.83
Locale, locally compact II.95
Locale, normal II.79
Locale, point of a II.55
Locale, regular II.78
Locale, spatial II.58
Locale, subfit II.77
Locales, closed map of II.83
Locales, co-dense map of II.82
Locales, dense map of II.64
Locales, map of II.54
Locales, open map of II.83 III
Locales, proper map of II.88
Locales, surjection of II.59
Localic map II.54
Localic map, closed II.83
Localic map, co-dense II.82
Localic map, dense II.64
Localic map, open II.83 III.138
| Localic map, proper II.88
Localic topos VII.334
localization VI.297 VII.322
Localization, finitary VI.297
Locally -Hausdorff object III.153
Locally -perfect morphism III.140
Locally -separated morphism III.153
Locally -separated object III.153
Locally compact locale II.95
Locally finitely presentable category VI.298
Maltsev category IV.189 VI.290
Maltsev category, naturally VI.294
Maltsev Theorem VI.292
MAP I.12
Map, -biquotient III.150
Map, clopen III.115
Map, closed III.112
Map, descent III.150
Map, etale VII.315
Map, universal quotient III.150
Meet-irreducible element II.54
Meet-semilattice I.20 II.70
Meet-stable relation II.67
Model VI.270
Monad V.216
Monad of state transformers V.252
Monad, commutative V.257 261
Monad, finitary VI.275
Monad, idempotent V.257 265
Monad, monicity of the, unit V.245
Monad, strict 2- V.258
Monadic category V.222
Monadic category over Set V.234
Monadic descent theory VIII.381
Monic span I.11
Monoid V.215 258
Monoid, commutative V.262
Monoid, internal IV.191
Monoidal categories of ordinals V.259
Monoidal category V.215
Monomorphism, extremal — II.60
Monomorphism, normal IV.181
Monomorphism, pure V.237
Morphism, -antiperfect III.136
Morphism, -closed III.112
Morphism, -dense III.113
Morphism, -exponentiable III.148
Morphism, -final III.143
Morphism, -initial III 134
Morphism, -open III.136
Morphism, -perfect III.129
Morphism, -proper III.118
Morphism, -quotient III.145
Morphism, -separated III.124
Morphism, -Tychonoff III.132
Morphism, absolutely -closed III.132
Morphism, allowable V.242
Morphism, bidense VII.324
Morphism, descent VIII.375
Morphism, effective descent V.237 VIII.375
Morphism, geometric VII.335
Morphism, locally -perfect III.140
Morphism, locally -separated III.153
Morphism, separated III.124
Multi-sorted category VI.277
Naturally Maltsev category VI.294
Negation I.24 II.53
Nerve functor VIII.393
Nerve functor, truncated VIII.393
Normal epimorphism VIII.360
Normal locale II.79
Normal monomorphism IV.181
Nucleus II.67
Nucleus, pre- II.89
Object, -compact III.119
Object, -discrete III.139
Object, -exponentiable III.151
Object, -Hausdorff III.126
Object, -separated III.126
Object, -Tychonoff III.131
Object, abelian IV.194
Object, absolutely -closed III.131
Object, abstractly finite VI.289
Object, connected VII.353
Object, decidable III.128
Object, effective projective VI.303
Object, Eilenberg — Moore V.253
Object, finitely presentable VI.282
Object, G-reducible V.240
Object, Kleisli V.255
Object, locally -compact III.140
Object, locally -compact Hausdorff III.140
Object, locally -Hausdorff III.153
Object, locally -separated III.153
Object, reduced V.240
Object, regular projective VI.282
Object, strict initial VI.285
Open map of locales II.83 III.138
Open map of topological spaces III.137
Open sublocale II.62
Order, discrete I.29
Ordered set I.14
Ordered set, complete I.36
Ordered set, discrete I.19
Ordered set, partially I.16
Ordered set, pre- I.16
Orthogonal III 107
Pair of arrows, jointly strongly epic IV.185
Pair, contractible V.224
Pair, G-contractible coequalizer V.225
Part I.9
Partial product III.155
Partially ordered set I.16
Path-connected space VIII.402
Point of a locale II.55
Pointed category IV.172
Pointed objects, fibration of IV.184
Precategoiy VIII.390
Preimage III.110
Preimage of a sublocale II.74
Prenucleus II.89
Preordered set I.16
Presheaf IV.179 VII.316
Pretopology VII.338
Principle of Connectedness V.241
Principle, Diamond V.240
Principle, Strong Embedding V.241
Projective object, effective VI.303
Projective object, regular VI.282 VII.336
Proper localic map II.88
Protomodular category IV.184 VI.294
Pseudo-complement I.24 II.53
Pseudo-equalizer diagram VIII.389
Pseudo-equalizer, reflexive, diagram VIII.389
Pullback I.8
Pure monomorphism V.237
Quasi-algebraic category VI.288
R-related element I.11
R-saturated element II.66
Rank functor V.241
Reduced object V.240
Reduced subcategory V.240
Reflective full suborder I.32
Reflector I.32
Reflects -density III.137
Reflects -quotient maps III.148
Reflexive coequalizer VI.274
Reflexive graph VI.274
Reflexive lax equalizer diagram VIII.388
Reflexive pseudo-equalizer diagram VIII.389
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