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MacLane S., Moerdijk L. — Sheaves in Geometry and Logic
MacLane S., Moerdijk L. — Sheaves in Geometry and Logic



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Название: Sheaves in Geometry and Logic

Авторы: MacLane S., Moerdijk L.

Аннотация:

This book is an introduction to the theory of toposes, as first developed by Grothendieck and later developed by Lawvere and Tierney. Beginning with several illustrative examples, the book explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic. This is the first text to address all of these various aspects of topos theory at the graduate student level.


Язык: en

Рубрика: Математика/Алгебра/Теория категорий/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 627

Добавлена в каталог: 19.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\large\varepsilon$)      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
1 2 3 4
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