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MacLane S., Moerdijk L. — Sheaves in Geometry and Logic |
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Предметный указатель |
Abelian group, object 95
Abelian group, sheaf of 95
Action of a group 24 238 361
Action of an internal category 243 354
Adjoint functor 17
Adjoint functor on the right 181
Adjoint functor to pullback 58 193
Adjoint functor, counit an iso 375
Adjoint functor, left 17
Adjoint functor, right- 17
Adjoint functor, unit an iso 369
Affine map 450
Affine simplex 450
Affine space 119
Algebra (for monad) 177
Algebra (for monad), finitely presented- 119
Algebra (for monad), free- 177 249
Alphabetic variant 541
Amalgamation 121 123\
Analytic complex-manifold 78
Analytic continuation 83
Ancestor (in a tree) 336
Antisymmetry (internal) 199
arrow 10
Arrow, category 27
Arrow, conditions (for a topology) 110
Arrow, universal- 18
Artin glueing 265 Ex. 9
Associated bundle 82
Associated sheaf 87 128 133 227
Atlas 74
Atom of a Boolean algebra 522 Ex.3
Atomic, Boolean algebra 150
Atomic, formulas 527
Atomic, topology 115 126 152 467
Atomless Boolean algebra 379
Axiom of a theory 529
Axiom of Choice 275 291ff 332 344
Axiom of infinity 268 332
Baire space 345 Ex. 12
Balanced 167
Barr’s theorem 513
Barycentric coordinates 452
Base 26
Base, change of- 59 193 349
Base, space 79
Basis for Grothendieck topology 111
Beck — Chevalley Cond’n 159 Ex. 15 174 205 492
Beck — Chevalley Cond’n, external- 174
Beck — Chevalley Cond’n, internal- 174 206
Beck’s theorem 179 372
Benabou (language) 296ff
Beth, E.W. 298
Boolean algebra 48 50 513 590
Boolean ring 514
Boolean topos 270 311
Boolean valued models 283 591
Bottom element 198
Bound variable 527
Boundary 452
Bounded Zermelo 332
Brouwerian lattice 50
Brouwer’s theorem 324ff
Bundle 79
Bundle, associated- 82
Bundle, etale 88
Bundle, G 34 81 421
Bundle, induced 30
Bundle, vector 80
C-action 243
C-module 354
C-object 243 244
Canonical morphism 170
Canonical topology 126 488
Cantor 277
Cantor space 468 Ex.10 523 571
Cardinal inequalities 283
cardinal number 277
Cartesian closed 20 46 167
Category 10
Category of elements 41 386
Category of fractions 596 600
Category of generalized elements 397
Category, 2-category of topoi 352
Category, cartesian closed 20 46 167 598
Category, comma 12 26 28
Category, discrete 27
Category, dual 12
Category, internal 240
Category, locally small 12
Category, object 240
Category, opposite 12 242
Category, simplicial 450
Category, slice 12 26
Category, small 12
Category, syntactic 553ff
Category, well-powered 32
Chain 451
Chain, condition 288
Change of base 59 193 349
Characteristic function 31
Characteristic map 163
Chart 74
Choice sequences 325
Classifying bundle 34
Classifying map 163
Classifying space 34 420ff
Classifying topos 432ff
Classifying topos for decidable objects 468 Ex. 8 570
Classifying topos for G-torsors 432
Classifying topos for geometric theory 559ff
Classifying topos for objects 434ff
Classifying topos for orders 455ff
Classifying topos for rings 437 445
Classifying topos for T-models 433 559ff
Classifying topos, simplicial sets as a 455ff
Closed ideal 590
Closed sieve 140
Closed sublocale 486
Closed subobjects 221 225
Closure of a sieve 141
Closure of a subobject 221
Closure, downward 335
Closure, operator 220 221
Closure, upward 336
Coalgebra 249
Coalgebra, cofree 251
Coarsest topology 113
Cocomplete 40 575
CoCone 22
Cocontinuous functor 410
Codomain 10
Coequalizer 17
Cohen, P. 277ff
Cohen, poset 278
Cohen, topos 278 318
Coherent topos 519
Cohomology 420 597 601
Colimit 22
Colimit as coequalizer 355
Colimit of Grothendieck topoi 600
Colimit of sheaves 135
Colimit, filtered 96
Colimit, internal 265 Ex. 11
Collatable 65 104
collate 64
Collating 64
Comma category 12 26 28
Comonad 218 247
Comonad and surjections 372
| Comparison, functor 178
Comparison, lemma 155 588
Complement 48 50
Complemented subobject 466 Ex. 1
Complete, Heyting algebra 114 146 473 495
Complete, lattice 51
Complete, poset 56
Complex, affine space 116
Complex, affine variety 116
Component 13
Composable pair (internal) 241
composition 10
Composition of arrows 10
Composition of functors 13
Composition, internal 170 241
Comprehension axiom 332 340
Comprehension axiom, restricted 332
Comultiplication 247
Condition 278
Cone 21 385
Constructible set 279
Constructive proof 302
Continuity of all functions 325ff
Continuous functions 324ff
Continuous functor 384 393
Continuous G-sets 26 150
Continuum Hypothesis 277ff
Contravariant functor 13 26
Contravariant hom-functor 26
Coproduct 17
Coproduct of topoi 417 Ex. 13
Coproduct, disjoint 572
Coproduct, inclusions 17
Coproduct, stable 572
Coreflective subcategory 90
Coring 439
Cotangent vector 76
Cotriple 247
Counit 19 247
Countable chain condition 288
Covariant functor 13
Covariant Hom-functor 13
Cover, an arrow 110
Cover, empty 149
Covering 82 108
Covering, family 109ff
Covering, lifting property 410 507
Covering, map 82
Covering, regular 107
Covering, sieve 70 110
Covering, system 522 Ex. 5
Covering, transformation 107
Covering, universal 82
Covers (in a tree) 336
Creates limits 72
Crible (=sieve) 37
Cross-section 60 78 79
Cumulative hierarchy 279 292
Cut and paste 455
Cycles 452
De Morgan laws 50
Decidable 468 Ex. 8 570
Dedekind cut 321
Dedekind reals 318ff 327
Definable arrow 541
Definable object 539
Definable subobject 541
Degeneracy 450
Deligne’s theorem 521
Dense, below 115 590
Dense, subobject 221
Dependent choice 345 Ex. 12
Derivation rules 558
Diaconescu, cover 511
Diaconescu, IAC = Boolean 346 Ex. 16
Diaconescu, R. 275
Diagonal argument 277
Diagonal functor 19 20
Diagonal map 166
Diagram 20
Diagram of a functor 386
Diagram, internal 243 392
Differential form 78
Dinatural 45 164 174
Direct image 68 99 171 348
Discrete category 27
Disjoint, coproduct 572
Disjoint, sum 17
Disjoint, union 17 195
Distributive lattice 49
Distributive law 49
Distributive law, infinite 114
Domain 10
Domain of definition 298
Down segment 258
Downward closure 335 486
Dual category 12
Duality 480 515
Effective family 551
Effective topos 599
Eilenberg — MacLane space 420 452
Eilenberg — Moore Theorem 248 249
Eilenberg — Zilber theorem 452
Elementary topos 48 161ff 591
Elements (of a presheaf) 41
Elements (of a presheaf), category of 41 386
Elements (of a presheaf), generalized 237 397
Embedding of locales 481
Embedding of topoi 366
Enough points 478 521
Enough projectives 216 Ex. 15
Enriched hom 362
Epi 11
Epi-mono factorization 40 185
Epimorphic family 382 393ff
Epimorphism 11
Epimorphism of sheaves 92 143
Epimorphism, object of 284ff
Equality, predicate 166 310
Equalizer 16
Equalizer as a pullback 30
Equivalence of categories 14
Equivalence of G-bundles 422
Equivalence, relation 573
Equivalent (monomorphism) 11
Equivariant sheaf 594 600
Erasing identities 543
Essential 360
Etale 88 89
Etale, G-space 594
Etale, map of locales 524 Ex. 9
Evaluation 20 45
Evaluation, map 45 168
Exact fork 574
Exact fork, stably 574
Excluded Middle 302
Exponentiable object 20
Exponential 20 45 167
Exponential for coalgebras 251
Exponential for G-objects 239
Exponential for presheaves 46
Exponential for sheaves 97 136 224
Exponential from power object 167
Extension of a field 106
Extension of predicate 165
Extensionality 165 332 337
EXTERNAL 200 235
External axiom of choice 291ff
External composition 170
Face map 450
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