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Goldblatt R. — Topoi
Goldblatt R. — Topoi

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Название: Topoi

Автор: Goldblatt R.

Язык: en

Рубрика: Математика/Алгебра/Теория категорий/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-е издание

Год издания: 1984

Количество страниц: 568

Добавлена в каталог: 23.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathscr{E}$-topos      467
Abstraction      25
Abstraction, functional      288
Action, empty      117
Action, empty, of a monoid      100
Action, empty, preserving function      101
Actual existence      274
Addition on $\omega$      335
Addition on N      337
Adjoint, left      439
Adjoint, right      439
Adjoint, right, situation      438.
Adjunction      439
Adjunction, co-unit of      440
Adjunction, co-unit of, in posets      446
Adjunction, unit of      440
Algebra of classes      125
Algebra of classes, Boolean      134
Algebra of classes, Brouwerian      178
Algebra of classes, closure      178
Algebra of classes, Heyting      183
Alphabet for elementary languages      234
Alphabet for PL      129
and-Or map      420
Antecedent      132
antisymmetric      29
Apartness      425
Appropriate to $\phi$      239 484
Appropriate to t      484
arrow      23 24
Arrow in $\Omega$-Set      277
Arrow, category      34
Arrow, name of      78
Arrow, partial      268
Arrow, strong      395
Arrow, weak      395
Associative law      21 24
atom      481
Atomic formula      234
Atomic sentence      483
Axiom of Choice      290—301 312
Axiom of extensionality      307
Axiom of infinity      311
Axiom of null set      308
Axiom of order-completeness      421
Axiom of pairs      308
Axiom of partial transitivity      330
Axiom of patching for sheaves (COM)      362 376 391
Axiom of powersets      308
Axiom of regularity      312
Axiom of replacement      312
Axiom of separation      308
Axiom of transitive representation      328
Axiom of transitivity      314
Axiom of unions      308
Axioms for CL      131 237 238
Axioms for continuous functions      427
Axioms for Dedekind cuts      415 423 427 430
Axioms for geometric modality      382
Axioms for GL      497
Axioms for identity      238
Axioms for IL      177 249
Axioms for propositional logic      131
Axioms for quantifiers      238
Axioms for set theory      307ff.
bar      193
Barr's Theorem      482 495
Beth model      193 388
Bi-complete      69 466 469
Biconditional      274
Bijective      39
Bivalent      118
Boolean algebra      134
Boolean topos      156
Bound variable      235
Bounded frame      191
Bounded functor      470
Bounded IL-model      191
Bounded ite      386
Bounded lattice      133
Bounded protopology      471
Bounded separation      309
Brouwerian algebra      178
Bundle      89
Canonical $\mathscr{C}$-model      487
Cartesian closed category      72
Cartesian product      19
Cartesian square      64
Categories, equivalent      200
Categories, functor      202
Categories, ismorphic      200
Category      24
Category as first-order concept      232
Category, arrow      34
Category, comma      35
Category, degenerate      72
Category, discrete      30
Category, one-object, (monoid)      32
Category, opposite      45
Category, preorder      28
Category, product      34
Category, skeletal      42
Category, sub-      32
Cauchy-reals      414 418
Chain      72
Change of variables      505
CHARACTER      81
Characteristic arrow      81
Characteristic function      79
Choice function      290
class      10
Class, abstracts      309ff
Class, proper      10
Classical Completeness Theorem      498 512
Classical logic      131
Classical topos      118
Classifier      81
Classifying topos      514
Closure algebra      178
Closure operator      372
Co-complete      69
Co-equaliser      60
Co-free      441
Co-unit      440
Codomain for arrow      24
Codomain for function      17
Cofinality      386
Coherent topos      481
Cokernel      114
Collapsing Lemma      317
Comma category      35
Commutative diagram      21
Commutativity of addition      338
Compact space      481
Compactness Theorem      500 502
Compatible      361 376 390 391
Compatible family      472
Complement of lattice element      134
Complement of set      7
Complement of subobject      147
Complement, pseudo      179
Complement, relative pseudo      181
Complemented lattice      134
Complete $\Omega$-set      388ff
Complete category      69
Complete Heyting algebra      276
Complete model      404
Complete, bi-      69
Complete, finitely      69
Complete, order-      421
Complete, со-      69
Completeness Theorem for $\mathscr{E}$-validity      227 265
Completeness Theorem for BA and B-validity      136
Completeness Theorem for CL      132
Completeness Theorem for HA-validity      185
Completeness Theorem for poset (frame)-validity      191
Completeness Theorem Goedel's      238
Completeness Theorem Infinitary      502
Completeness Theorem, Classical      498 512
Completion of an $\Omega$-set      393—397
complex numbers      423
Component (of a natural transformation)      199
Composition of arrows      24
Composition of functions      20
Composition of functors      198
Comprehension and descriptions      288
Comprehension for $\Omega$-sheaves      405
Comprehension, $\Omega$ and      107
Comprehension, principle of      6
Cone      58
Conjunction      126
Conjunction, truth-arrow      139
Conjunction, truth-function      127
Connectives      126
Consequent      132
Conservative functor      461
Consistent      12
Constant      231
Constructivism      173ff.
Continuous, function as generalised real number      427
Continuous, morphism      473
Continuous, section      98
Continuously variable real number      417
Continuum Hypothesis      381
Contravariant functor      196
Contravariant hom-functor      197
Contravariant powerset functor      197
Copower      413 469
Coproduct      54
Coproduct as adjoint      443
Coproduct, arrow      54 55
Coproduct, preserves pullback      115
Covariant functor      196
Cover      374
Cover, open      361
Crible      208 368 376
De Morgan's law      423 434
Decidable ordering      425
Dedekind-reals      414ff.
Dedekind-reals as continuous functions      416
Dedekind-reals in $C\Omega$-Set      419 421
Dedekind-reals in $\Omega$-Set      416 421
Dedekind-reals, *R equals -      434
Degenerate category      72
Deligne's Theorem      481 495 512
Deligne's Theorem, proof of      500
Denned over $\mathscr{E}$      467
Dense monic      372
Dense monic, j      379
Density of $\mathbb{Q}$      434
Descriptions      287
Descriptions, interpreted in sheaves      404
Detachment      131
Diaconescu's Theorem      297
Diagram      58
Diagram, commutative      21
Diagram, empty -      59
Diagram, finite      69
Direct image part      464
Directed poset      192
Discrete category      30
Discrete topology      406
Disjoint arrows      119
Disjoint selection      408
Disjoint sets      54
Disjoint union      54
Disjunction      126
Disjunction, truth-arrow      139
Disjunction, truth-function      128
Disjunctive topos      171 229
Distributive lattice      134
Domain of arrow      24
Domain of function      17
Double Negation      184 379
Duality      45
Duality principle      46
Effectively epimorphic      472
Element of a set      6
Element of an object      78
Element, existing      274
Element, global      398
Element, partial      268
Elementary, language      231 234
Elementary, logic in a-Set      284
Elementary, site      378
Elementary, topos      84
Empty action      117
Empty diagram      59
empty function      43
Empty section      283
Empty set      7
Empty, non-      115
Endo arrow      445
Enough points      436
Epi-monic factorisation      114
Epic arrow      39
Epic arrow, splitting      290
Epimorphic family      471
Epimorphic family, effectively      472
Epimorphic family, provably      507
Equaliser      56
Equaliser, monic as      109
Equality      274
Equality as local equality      385
Equality of set-objects      326
Equality, rigid      406
equation      487
EQUIVALENCE      274
Equivalence class      61
Equivalence of categories      200
Equivalence of set-models and topoi      328ff
Equivalence relation      61—63
Equivalence, logical      144
Equivariant function      101
Evaluation arrow      70 71
Exact functor      461
Exact functor, Left      461
Exact functor, Right      461
Examples of adjoint situations      442ff
Examples of categories      26—36
Examples of elementary sites      379
Examples of functors      195ff
Examples of Heyting algebras      179—183
Examples of limits      59—60
Examples of monoid actions      101
Examples of natural transformations      199—200
Examples of pseudo-complements      179
Examples of pullbacks      64—68
Examples of relative pseudo-complements      181
Examples of sites      375
Examples of topoi      85—103
Examples of truth-arrows      139—140
Examples of variable sets      219
Excluded Middle      161
Excluded Middle and Intuitionism      175
Existence, actual      274
Existence, degree of      275
Existence, equals local existence      387
Existence, potential (partial)      274
Existence, predicate      267
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