Arbib M.A., Manes E.G. — Arrows structures and functors. The categorical imperative :: Электронная библиотека попечительского совета мехмата МГУ

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Arbib M.A., Manes E.G. — Arrows structures and functors. The categorical imperative

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Название: Arrows structures and functors. The categorical imperative

Авторы: Arbib M.A., Manes E.G.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1975

Количество страниц: 185

Добавлена в каталог: 13.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

      58
, -category      78
, -structure      77
      147
, in a -category      155
      53
$L_{X}$       99
-ary      157
      108
      31
-      84
-module      84
( $f^{\blacktriangle}$ )      103
      5
$Set^{op}$       5
$Set_{*}$       109
      71
-category      149
      30
$X_{0}$ -dynamics      95
$X_{0}$ -dynamorphism      95
$\Omega$ — Alg      158
${}^{op}$       32
3 $\times$ 3 lemma      41
Abelian monoid      58 77
Action of a monoid      166
Addition of vectors      25
Additive category      82
Adjoint functor theorem      135
Adjoint of a functor      see also adjunction
Adjoint, left      116 122
Adjoint, left, and preservation of equalizers      133
Adjoint, left, and preservation of products      131
Adjoint, right      117
Adjoint, right, and preservation of coproducts and coequalizers      134
Adjunction      125
Admissible maps      85
Algebra,       167
Algebra, -, free      171
Algebra, -, homomorphism      171
Algebra, $\Omega$       157
Algebra, $\Omega$ -, Homomorphism      158
Algebra, ( $\Omega, E$ )      160 172
Algebra, universal      157
Antisymmetry      28
Arbib, M. A.      177
Arity      see $n$

-ary
arrows      1
Associativity of group multiplication      52
Associativity of monad      164
Associativity of monoid multiplication      52
Associativity of monoid multiplication, in a monoidal category      145
Associativity of morphism composition      30
Automata theory      93
Behavior of a machine      99
Benson, D. B.      148
Bijection      6
Bijection, equals isomorphism in       7
Bilinear map      141
Birkhoff, G.      176
Bobrow, L. S.      177
Boolean group      138
Bushaw, D.      177
C-structure      85
Canonical map of an equivalence relation      18
Canonical realization      104
cartesian      142
Cartesian closed category      142
Cartesian product      9 15 42
Category      29
Category,       77
Category,       149
Category, additive      82
Category, admits an -structure      77
Category, as domain of discourse      29
Category, as generalized monoids      107
Category, cartesian closed      142
Category, closed      152
Category, functor      153
Category, has (finite) limits      46
Category, has small hom sets      138
Category, locally small      138
Category, monoidal      144
Category, of sets with structure      85
Category, pointed      78
Category, semiadditive      82
Category, small      156
Category, strictly monoidal      143
Category, sub      30
Category, sub-, full      30 33
Category, sub-, reflexive      174
Characteristic function      142
Choice, axiom of      9
circle      63
City metric      61
Closed category      152
Closed, with respect to operations      27
Co- $\mathcal{W}$ = dual of $\mathcal{W}$       13 33
Co-optimal family of morphisms      88
Co-optimal family of morphisms, in       72
Co-optimal lift      88
Co-optimal lift, in       72
Codecomposition of an object      75
Codomain      1 29
Coequalizer      20 34
Coequalizer, in and       57
Coequalizer, in       22
Coequalizer, in       36
Coequalizer, in a category of structured sets      91
Coequalizer, in a poset      38
Coequalizer, in metric spaces      68
Cofree      see also adjoint free
Cofree dynamics      100 118
Cofree object      115
Coherence axioms      144
Cohn, P.      176
Colimit      45
Collective equalizer      138
Commutative diagram      2 4 45
Composition theorem      130
Composition, internal      149
Composition, of maps      2
Composition, of morphisms      29
Composition, of natural transformations, horizontal      153
Composition, of natural transformations, vertical      153
Concatenation      111
Congruence monoid      56
Congruence of geometric figures      63
Congruence of sets with structure      91
Continuous map      70 71
Contraction      62
Contravariant functor      108
Coproduct      41
Coproduct, as a limit      45
Coproduct, in and       55
Coproduct, in       13 15
Coproduct, in s with structure      91
Coproduct, in       42
Coproduct, in a poset      43
Coproduct, in metric spaces      67
Coretraction      36
Couniversal property      45
Covariant functor      109
Decomposition of an object      76
Descartes, R $\acute{e}$ n $\acute{e}$       9
Diagonal fill-in lemma      39
Diagram      45
Diagram, of maps      2
Direct sum of vector spaces      42
Disjoint union of sets      13

Disjoint union of sets, equals coproduct      7 42
Distance function      see metric
Distributive laws for -category      77
Distributive laws for (semi)ring      83
Domain      1 29
Domain, of definition of a partial function      109
Dual category      32
Dual concepts      6 33
Dual of $\mathcal{W}$ =co- $\mathcal{W}$       13 33
Duality principle for category theory      33
Dyn( $X_{0}$ )      95
Dynamics      93
Dynamics, $X_{0}$       95
Dynamics, cofree      100
Dynamics, free      98
Dynamorphic image lemma      104
Dynamorphism, $X_{0}$       95
EDGE      45
Eilenberg, S.      176
Epi-mono factorization      8 (see also image factorization)
Epi-quotient object      36
Epimorphism      3 34
Epimorphism, dual of monomorphism      6
Epimorphism, in and       57
Epimorphism, in       3
Epimorphism, in       36
Epimorphism, in a poset      37
Epimorphism, split      36
Equalizer      20 34
Equalizer, as a limit      46
Equalizer, collective      138
Equalizer, in and       55
Equalizer, in       22
Equalizer, in       36
Equalizer, in a category of structured sets      90
Equalizer, in a poset      38
Equalizer, in metric spaces      66
Equation, $\Omega$       160
Equivalence class      17
Equivalence relation      17
Equivalence relation, generated by a relation      19
Equivalence relation, of a map      18
Equivalence, natural      122
Euclidian metric      61
External representation functor      110
Factor set      see quotient set
Fill-in lemma      39
Finite machine      93
Forgetful functor      109
Frechet      176
Free object      112 (see also adjoint)
Free object, dynamics      100 118
Free object, group      113
Free object, monoid      53 111
Free object, vector space      113
Full subcategory      30 33
functor      108
Functor, as generalized homomorphism      107
Functor, category      153
Functor, contravariant      109
Functor, covariant      109
Functor, forgetful      109
Functor, identity      108
Functor, preserves equalizers      131
Functor, preserves products      131
Functor, reflection      174
Functor, representation of a set      163
Functor, satisfies solution set condition      134
Functor, sub      156
Galois, E.      176
Generators of a free monoid      53 111
Geometric figure      63
Geometry      63
Glb      see greatest lower bound
Godement’s rules      154
Graph, directed      45
Graph, state      100
Greater lower bound      43
Greever, J.      177
Grothendieck topology      143
Group      52
Group, boolean      138
Group, in universal algebra setting      158 160
Group, torsion      119
Herrlich, H.      176
Heyting algebra      143
Hom      110
Homomorphic, separately      141
Homomorphism $\Omega$ -algebra      158
Homomorphism group      53
Homomorphism monoid      53
Homomorphism monoid, in a monoidal category      145
Homomorphism, generalized to yield functors      107
Horizontal composition of natural transformations      153
Hu, S.      176
Identity functor      108
Identity internal      149
identity map      1
Identity morphism      30
Identity of a group      52
Identity of a monoid      52
Image factorization      38
Inclusion of sets      28
Indiscrete structure      91
Indiscrete topology      72
Infimum      43
Initial object      43
Initial state      93
Injection      13 41
Input      93
Internal composition      249
Internal identity      149
Intersection of mono-subobjects      49
Intersection of sets      43
Intuitionistic logic      143
Inverse of a group element      52
Inverse of a morphism      35
Isbell, J. R.      162
Isometry      61
Isomorphic objects      35
Isomorphism      6 35
Isomorphism, as self-dual concept      8 14
Isomorphism, in       7
Isomorphism, in Met      61 62
Isomorphism, of categories of sets with structure      86
Isomorphism, uniqueness up to isomorphism      14
Kernel      44
Kernel, in a pointed category      83
Label set      157
Lawvere, F. W.      143 151
Least upper bound      43
Left adjoint      116 122
Left translation      99
LIMIT      45
Linear map      27
Linearly ordered set      29 139
Lipschitz map      61
Locally small category      138
Loset      138
Mac Lane, S.      50 145 176
Mach( $X_{0}, Y$ )      97
Machine, sequential      93 161
Manes, E. G.      172 176 177
Matrices in a category      74
McCarty, G.      177
Mendelson, B.      177
Met      61
Met*$      63
Metone      63
Metric      60

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