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Jacobs B. — Categorical Logic and Type Theory
Jacobs B. — Categorical Logic and Type Theory



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Название: Categorical Logic and Type Theory

Автор: Jacobs B.

Аннотация:

This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1999

Количество страниц: 760

Добавлена в каталог: 02.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Track      33
Track, uniform      52 54 394
Transition system      513 526
Transitivity combinator      197
Transitivity combinator in polymorphic type theory      450
Transitivity rule in equational logic      179
Tripos      332 374 377
Tripos, realisability      334
Truth      223
Tuple morphism      xiii
Tuple term      139
Type, 1 context      171 224 445
Type, 1 scheme      455
Type, 1, (co-)inductively defined      145
Type, 1, (co-)inductively defined in second order polymorphic type theory      456
Type, 1, abstract      461
Type, 1, atomic      134
Type, 1, basic      134
Type, 1, Cartesian product      138
Type, 1, Cartesian product, definable      453 483
Type, 1, coproduct      140
Type, 1, coproduct, definable      453 483
Type, 1, coproduct, disjoint      526
Type, 1, coproduct, distributive      142
Type, 1, coproduct, in polymorphic type theory      457
Type, 1, coproduct, strong      591
Type, 1, coproduct, universal      526
Type, 1, coproduct, weak      591
Type, 1, data      7 162 456
Type, 1, data, proof principles for -s      526 532 533
Type, 1, disjoint union      591
Type, 1, empty      141
Type, 1, equality, dependent      586
Type, 1, equality, strong      589 590 680
Type, 1, equality, very strong      681
Type, 1, equality, weak      588 680
Type, 1, exponent      xv
Type, 1, Hagino      145 457
Type, 1, identity      584
Type, 1, power      316
Type, 1, product, dependent      586
Type, 1, product, higher order      448
Type, 1, product, second order      446
Type, 1, quotient      283
Type, 1, quotient in dependent predicate logic      650
Type, 1, quotient in simple predicate logic      283
Type, 1, singleton      138 586
Type, 1, subset in dependent predicate logic      650
Type, 1, subset in simple predicate logic      272
Type, 1, sum, definable      453 459
Type, 1, sum, dependent      586
Type, 1, sum, higher order      448
Type, 1, sum, second order      446
Type, 1, sum, strong      589 675
Type, 1, sum, very strong      675
Type, 1, sum, weak      588 674
Type, 1, unit      138 586
Uniformity Principle      402
Unique choice      304 371 391
Universal colimits in a topos      349
Universal coproduct      58 90 266 637
Universal coproduct in a fibration      533
Universal coproduct type      526
Universal quantification      223
Validity of a conditional equation in a category      184
Validity of a conditional equation in a fibration      202
Validity of a predicate      247
Validity of a sequent      247
Validity of an algebraic equation      183
Valuation      67
Veritas      582
Vertical mono      351
Vertical morphism      26
Vertical subobject      351
Very strong coproduct wrt. a comprehension category      678
Very strong equality      209 306 362 371 410
Very strong equality type      681
Very strong equality wrt. a comprehension category      682
Very strong sum type      675
Weak completeness, for a fibration      708
Weak coproduct type, in dependent type theory      591
Weak coproduct, in a comprehension category      624
Weak equality type      680
Weak equality type in dependent type theory      588
Weak equality, in a comprehension category      624
Weak FhoDTT-structure      694
Weak full higher order dependent type theory      688
Weak generic object      325
Weak initial algebra      457 458
Weak natural numbers object      456
Weak sum type      674
Weak sum type in dependent type theory      588
Weak terminal co-algebra      457 458
Weakening      24 175 230 604
Weakening functor      176
Weakening functor wrt, a comprehension category      614
Weakening functor wrt. a weakening and contraction comonad      537
Weakening rule for propositions      172
Weakening rule for types      172
Weakening rule in dependent type theory      585
Weakening rule in simple type theory      122
Weakening, notation for      176
Well-powered category      351
Well-powered fibration      351
Yoneda functor      428
Yoneda functor, fibred      440
Yoneda lemma, fibred      323
1 2 3 4 5
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