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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
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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