Pierce B.C. — Basic category theory for computer scientists :: Электронная библиотека попечительского совета мехмата МГУ

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Pierce B.C. — Basic category theory for computer scientists

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Название: Basic category theory for computer scientists

Автор: Pierce B.C.

Аннотация:

Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories.

Язык:

Рубрика: Математика/Алгебра/Теория категорий/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 100

Добавлена в каталог: 12.03.2005

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Предметный указатель

$(\Omega,E)$ -Alg      4
$D_{\infty}$       32 61—72
$\lambda$ -calculus      32 53—57 61 73 75 78 79
$\lambda$ -calculus, algebraic treatment of      55
$\lambda$ -theory      55
$\Omega$ -Alg      4
$\Omega$ -algebra      4
$\omega$ -category      70
$\omega$ -chain      63
$\omega$ -colimit      63
$\omega$ -complete      66
$\omega$ -complete pointed category      70
$\omega$ -complete pointed partial order      66
$\Omega$ -homomorphism      4
$\omega$ -sequence      66
$\omega^{op}$ -chain      63
$\omega^{op}$ -limit      63
0      5
1      5
2      5
2-category      79
3      6
Abstract machine, categorical      57 77
AcyclicGraph      52
Adjoint      47
Adjoint pair      47
Adjoint, left      47
Adjoint, right      47
Adjunction      47
Adjunction, co-unit of      48
Adjunction, colimit as      49 51 52
Adjunction, coproduct as      52
Adjunction, exponentiation as      50—51
Adjunction, floor and ceiling functions as      51
Adjunction, initial object as      49
Adjunction, limit as      49 51 52
Adjunction, List functor as      46—48
Adjunction, product as      49
Adjunction, strongly connected components as      51
Adjunction, terminal object as      52
Adjunction, unit of      47
Algebra, $\Omega$ -      4
Algebra, anarchic      41
Algebra, carrier of      4
Algebra, category-sorted      58
Algebra, F-      40 63
Algebra, free      60
Algebra, initial      16 60
Algebra, many-sorted      58
Algebra, term      16
Algebra, universal      5 78
Algebraic semantics      59 60
Algebraic theory      60 75
Algebraic treatment of $\lambda$ -calculus      55
Algol 60      59
Anarchic algebra      41
Arity      4
arrow      1
Arrow category      9
Arrow over C      9
Arrow, injection      19
Arrow, inverse      15
Arrow, mediating      18 21
Arrow, projection      18
Associative law      1
Automata theory      78
Behavior-of functor      52
Bifunctor      38
Block structured programming languages      78
CAM      57 77
Cardinality (foundational issues)      38
Carrier (of an algebra)      4
Cartesian closed category      34 53—57 75
Cartesian closed functor      55
cat      38
Categorical abstract machine      57 77
Categorical combinators      77
Categorical logic      7 77 80
Categorical type constructors      79
Category      1
Category from functional language      7
Category from monoid      6
Category from set      44
Category of embeddings      67
Category, $\omega$ -      70
Category, $\omega$ -complete pointed      70
Category, 2-      79
Category, arrow      9
Category, cartesian closed      34 53—57 75
Category, concrete      5
Category, discrete      29 44
Category, dual      8
Category, enriched      66
Category, finite      5
Category, functor      43
Category, indexed      76 79
Category, large      38
Category, locally small      39
Category, naked      3
Category, partial order as      6
Category, pre-      3
Category, product      9
Category, small      38
Category, sub-      9
Category-sorted algebra      58
CCC      see cartesian closed category
Ceiling function as adjunction      51
Chain, $\omega$ -( $\omega^{op}$ -)      63
Chosen      see distinguished
Co-unit      48
Co-universal construction      21
CoCone      28
Codomain      1
Coequalizer      22
Colimit      28
Colimit as adjunction      49 51 52
Colimit, locally determined      71
Combinators, categorical      77
Commutative diagram      11
Componentwise ordering      69
Composition of arrows      1
Composition of functors      38
Composition of natural transformations      43
Composition, order of      13
Computational category theory      74
Concrete category      5
Concurrency      79
Cone      26
Constant      17
Constant functor      67
Constrained product      24
context      53
Continuation      79
continuous      66
Continuous functor      70
Continuous, locally      71
Contra variant functor      38
Contra variant horn-functor      39
Conversion, implicit      57—59
Coproduct      19
Coproduct as adjunction      52
Covariant functor      38
CPO      34 66
Currying      33
Diagonal functor      39 49
Diagram      11
Diagram, commutative      11
Diagram, small      29
Diagrammatic order      13
Discrete category      29 44

Disjoint union, analog of      19
Distinguished (product, etc.)      18
Domain      1
Domain equations      see recursive domain equations
Domain theory      60
Domain, profinite      80
Dual category      8
Duality      9
Dynamic, F-      see F-algebra
Element, global      17
Embedding      62 67
Embeddings, category of      67
Endofunctor      40
Enriched category      66
EPIC      14
Epimorphism      14
Equalizer      22
Equation (in an algebra)      4
Equations, domain      see recursive domain equations
Equivalence relation, analog of      22
Equivalence rules (for a typed $\lambda$ -calculus)      54
Evaluation as natural transformation      43
Exponential object      34
Exponentiation as adjunction      50—51
Exponentiation, has      34 51
Extension, homomorphic      46
Extensionality      54 62
F-Alg      41 63
F-algebra      40 63
F-dynamic      see F-algebra
Finite category      5
Fixed point      41 63
Floor function as adjunction      51
Forgetful functor      37
Forsythe programming language      59 79
Foundational issues      38
FPL      7
Free algebra      60
Free algebra functor      48
Free monoid      37
Free variable      53
Function, semantic interpretation      16
Functional order      13
Functional programming language as category      7
functor      36
Functor category      43 78
Functor composition      38
Functor, behavior-of      52
Functor, bi-      38
Functor, cartesian closed      55
Functor, constant      67
Functor, continuous      70
Functor, contra variant      38
Functor, contravariant horn-      39
Functor, covariant      38
Functor, diagonal      39 49
Functor, endo-      40
Functor, horn-      39
Functor, identity      37
Functor, List      36
Functor, minimal realization      52
Functor, product      49
Functor, representable      44
Functor, right product      37 50
Functor,Forgetful      37
Functor,Free algebra      48
Functorial semantics      55
Galois connection      51
Generic operator      57—59
Global element      17
Graph      51
Grothendieck construction      73
Has exponentiation      34 51
Has products      18
History of terminology      10
Hom-functor      39
Hom-functor, contravariant      39
Hom-set      39
Homomorphic extension      46
Homomorphism, $\Omega$ -      4
Homomorphism, F-      40
Homomorphism, monoid      4
Identity arrow      1
Identity functor      37
Identity Law      1
Identity natural transformation      42
Imperative languages      59
implicit conversion      57—59
Indexed category      76 79
Indexed product      19
Initial algebra      16 60
Initial object      16
Initial object as adjunction      49
Injection arrow      19
Interdefinability of categorical constructions      24
Internal language      55
Interpretation function      16
Interpretation function for an algebra      4
Inverse arrow      15
Inverse image      23
Inverse limit      28 32 62
Inverse limit construction      61—72
Isomorphism      15
Isomorphism, natural      42
Isomorphism, up to      15
Isomorphism, within      15
Language, internal      55
Large category      38
Least upper bound      66
Left adjoint      47
Length      46
LIMIT      26
Limit as adjunction      49 51 52
Limit theorem      29
Limit, inverse      28 62
Limit/colimit coincidence      70
LIST      42 45
List functor      36
List functor as adjunction      46—48
Lists, length function on      46
Lists, maplist function on      36
Lists, rev function on      42
Locally continuous      71
Locally determined colimits of embeddings      71
Locally monotonic      69
Locally small category      39
Logic, categorical      7 77 80
Lub      66
Many-sorted algebra      58
maplist      36
Mathematical semantics      59
Meaning function      60
Mediating arrow      18 21
Minimal realization functor      52
ML      74 79
Model (of a typed $\lambda$ -calculus)      60
Modules      79
mon      4
Monad      77 79
Monk      13
Monoid      4
Monoid as category      6
Monoid homomorphism      4
Monoid, free      37
Monomorphism      13
Monotone      3
Monotonic      66
Monotonic, locally      69
Morphism      see arrow
Naked category      3

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