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MacLane S., Moerdijk L. — Sheaves in Geometry and Logic |
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Предметный указатель |
Factorization (epi-mono) 185
Factorization (epi-mono) for locales 484ff
Factorization (epi-mono) for topoi 373 376
Factors through sheaves 370
Faisceau 64
Faithful 13
Fiber 79
Fibered product 14 15 29
Fibration (of categories) 44 596
Field, splitting 108
Filter 257 514
Filter, completely prime 522 Ex. 4
Filter, maximal 514
Filter, principal 257
Filter, proper 344 Ex. 4
Filter, quotient 256ff
Filtered category 385
Filtered colimit 96 390
Filtered limit 385
Filtering category 385
Filtering equals flat 386 399
Filtering functor 386 394 395
Final object 194
Finer topology 113 263
Finite limit 30
Finite states of knowledge 283
Finitely presented algebra 119
Finitely presented ring 438
First order theories 527ff
Flat 381
Flat, equals filtering 386 399
Flat, equals left exact 390
Flat, functor 381 386 392
Flat, module 381
Floppy (tree) 336
Forces 303
Forcing 115 278 304ff 315ff
Forcing condition 278
Forcing notion of 278
Forcing relation 304 316
Forgetful functor 31 177
Fork 574
Formula (of language) 299
Formula (of language), geometric 536
Foundation (axiom of) 332 340
Foundations 331ff 599
Fourman, M. 279
fp algebra 119
fp ring 438
Frame 471
Free category 435
Free G-action 81 422
Free G-object 239
Free T-algebra 177 249
Free variable 527
Freely generated (for rings) 438
Freyd, P. 291
Frobenius identity 204 500
Full (functor) 13
functor 12
Functor, adjoint 17
Functor, category 13
Functor, comparison 178
Functor, contravariant 13 26
Functor, covariant 13
Functor, faithful 13
Functor, flat 381 386 392
Functor, forgetful 31 177
Functor, full 13
Functor, identity 13
Functor, internal 241
Functor, opposite 180
Functor, representable 26 33
G-action 238
G-bundle 34 81 421
G-bundle, principal 81 421
G-map 238
G-object 238 361ff
G-set 24 26 150ff
G-space 81
G-torsor 424 427
G-torsor, universal 428
Galois group 106ff
Generalized element 162 237
Generalized element over U 397
Generate a category 139 275 574
Generate a sieve 112
Generate a topology 112
Generators, category 139 574
Generators, sieve 112
Generic element 305
Generic set 283
Generic T-model 433
Gentzen, G. 558 599
Geometric formula 536
Geometric morphism 348
Geometric morphism, direct image of 348
Geometric morphism, essential 360
Geometric morphism, inverse image of 348
Geometric morphism, open 495ff 534 535 600
Geometric morphism, surjective 366
Geometric realization 454 460
Geometric theory 537
Geometric theory, classifying topos for 559ff
Germ 83
Giraud theorem 575
Global element 164 236
Global section 47
Global sections functor 47 135 350
Global truth values 274
Godel, completeness 297 521
Godel, K. 279
Godement resolution 513
Graph (of arrow) 214 227 540
Grassmann manifold 34 421
Gros topos 325 414
Grothendieck, construction 44 386
Grothendieck, topology 110 222 233
Grothendieck, topology (arrow form) 110
Grothendieck, topos 127 143
Group, action 24 238 361
Group, internal 237
Group, object 237
Group, proper action by 158 Ex. 10
Groupoid 343 Ex. 2 600
Heyting algebra 48 50ff 114
Heyting algebra of subobjects 146 201
Heyting algebra, complete 114 146 473 495
Heyting algebra, internal 199ff
Hilbert nullstellensatz 116
Holds (in ) 301
Holomorphic function 78 82
Hom-functor 13 32
Hom-set 12
Hom-tensor adjunction 357ff 578
Homology groups 452
Homomorphism of Heyting algebras (internal) 200
Homomorphism of interpretations 530 532
Homomorphism of lattices (internal) 200
Homomorphism of models 530 532
Hypersurface 117
Ideal 116
Ideal in a poset 590
Ideal, closed 590
Ideal, maximal 117 344 Ex.
Ideal, prime 117
Ideal, principal 590
Ideal, radical 117
Identity morphism 10
Image 184 570
| Image of sublocale 503
Image, direct 68 99 171 348
Image, inverse 33 99 147 348
Implication 48 50 114 146 199
Inclusion in coproduct 17
Incompatible conditions 290
Indeterminates 439
Indexed family 28
Indexed set 28
Indirect proof 302
Induction 269
Inference (rules of-) 296
Infima 145
Infinite object 468 Ex. 9
Infinity (axiom of) 268 332 341
Initial object 17
Initial object, strict 194
Injective object 210
Integers, object of 321
Internal 201 235ff
Internal, adjoint 206
Internal, axiom of choice 275 291ff 312
Internal, category 240
Internal, colimit 265 Ex. 11
Internal, composition 170
Internal, diagram 243 392
Internal, functor 241
Internal, group 237
Internal, hom 98 170
Internal, lattice 198
Internal, meet 189
Internal, partial order 199
Internal, presheaf 244
Interpretation of a term 298
Interpretation of language 527 530
Intersection 48 186
Intuitionism 48 55 318
Inverse (of an arrow) 11
Inverse image 33 101 147 348
Irreducible subset 475
Irreducible variety 117
Isomorphism 11
Isotropy subgroup 62 Ex. 6 151 365
Join 56 198
Jointly surjective 521
Joyal, A. (semantics) 302 318
Kan extension 380 415
Kernel 474
Kernel pair 30 197 229 574
Killing points 523 Ex. 8
Kripke — Joyal semantics 302ff
Kripke, S. 298 318
Kronecker delta 166
Lambda calculus 299 598
Language, first-order 527
Language, Mitchell — Benabou 296ff
Lattice 49
Lattice, internal 198
Lattice, object 198
Lawvere — Tierney topology 219ff
Left adjoint 17
Left adjoint, internal 206
LIMIT 21
Limit of Grothendieck topoi 600
Limit of sheaves 128
Limit, create 72 178
Limit, pointwise 22
Limiting cone 21
Linear order 455ff
Local character (of forcing) 304 316
Local coordinates 74
Local geometric morphism 600
Local homeomorphism 88 524
Local ring 118 445 526 538
Local trivialization 421
Locale 472 600
Locale presentation of 523 Ex. 5
Localic reflection 489
Localic topos 470ff 488
Locally closed 504
Locally constant functions 319
Locally constant sheaf 104 Ex. 5
Locally small 12
Locally surjective 143
Logic 267ff
Logic, first-order 296 527ff
Logic, intuitionistic 268
Logical morphism 170 193
Logical morphism, manifold 73ff
Logical morphism, smooth 75
Maps of locales 489
Maps of sheaves 127
Matching family 121 122
Maximal filter 514
Maximal ideal 117 344 Ex.
Maximal sieve 38
Meet 56 198
Meet of subsheaves 145
Meet, internal 189
Membership, predicate 165
Membership, relation 171 310\
Minimal model 568
Mitchell — Benabou language 296ff 598
Mitchell, W. 343
Model of a theory 529 532
Model, universal 433 566ff
Module 354
Monad 176
Monad from adjunction 177
Monadic functor 178
Monic 30
Monic, universal 32
Mono 11
Monoid 25 27 248
Monomorphism 11
Monomorphism in terms of p.b. 16
Monotonic 450
Monotonicity (of forcing) 304 316
Morphism 10
Morphism of C-objects 243
Morphism of frames 471
Morphism of orders 458
Morphism of sheaves 67 92 127
Morphism of sites 409
Morphism, canonical 170
Morphism, geometric 348
Morphism, logical 170 193 600
NAME 165
Natural isomorphism 13
Natural numbers object 268
Natural transformation 13
Negation 52
Negation, double 272
Nerve of a category 451
Node (of a tree) 336
Non-degenerate topos 275
Notion of forcing 278
Nucleus 483
Null set 332 337
Nullstellensatz 116
Object 10
Object, classifier 434ff
Open cover 65 113
Open cover topology 113
Open geometric morphism 495ff 535 600
Open map of locales 500ff
Open map of spaces 492
Open object 189
Open sublocale 486
Opposite category 12 242
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