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| Arbib M.A., Manes E.G. — Arrows structures and functors. The categorical imperative |
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| Предметный указатель |
Metric, -stretcher 63
Metric, extended 69
Middle four interchange 80
Minimal realization 103
Minimal realization, theorem 105
Mirror category see opposite category
Module over a ring 84
mon 53
Monad 164
Monad, finitary 174
Monad, tree 165
Mono-subobject 35
Mono-subobject, intersections of 49
Monoid 52 112
Monoid, Abelian 58 77 141
Monoid, arrow characterization 139
Monoid, as monoid in  163
Monoid, congruence 56
Monoid, free 53 111
Monoid, in a category 139
Monoid, in a monoidal category 145
Monoidal category 141 144
Monomorphism 4 34
Monomorphism, dual of epimorphism 6
Monomorphism, in  and  57
Monomorphism, in  5
Monomorphism, in  36
Monomorphism, in a poset 37
Monomorphism, preserved by pullbacks 49
Monomorphism, split 9 36
Morphism 29
Multiplication by a scalar 25
Multiplication in monoids 52
Multiplication ingroups 52
Natural equivalence 122
Natural transformation 116 120
Natural transformation, composition of, horizontal 153
Natural transformation, composition of, vertical 153
Object 29
Observability 97
Observability, map 99
Observable machine 100
One-to-one map 4 5
Onto map 1 3
Open set 70
Opposite category 5 32
Optimal family of morphisms 88
Optimal family of morphisms, in  40
Optimal family of morphisms, in  72
Optimal lift 88
Optimal lift, in 72
Order-preserving map 28
Output 93
Output, map 93
Parity map 54
Partial function 108
Partially ordered set see poset
Partition 23
Permutation 51
Pointed category 78
Pointed sets and maps 109
POSET 28
Poset, as a category 32
Poset, as a topological space 87
Power set 9 27
Pre-ordered set 28 40 87
Preservation of limits by functor 132
PRODUCT 41
Product, as a limit 45
Product, in and 54
Product, in 9 11 15
Product, in 42
Product, in a poset 43
Product, in category of structured sets 90
Product, in metric spaces 64
Product, of categories 110
Projection 10 11 41
Pullback 44
Pullback, as a limit 46
Pullback, preserves epimorphisms 49
Pushout 44
Quotient object 36
Quotient set 17
Quotient structure 91
Quotient topology 92
Reachability 97
Reachability, map 98
Reachable machine 99
Realization 103
Realization, canonical 104
| Realization, minimal 103
Reflection 174
Reflexive subcategory 174
Reflexivity 17
Relation as a morphism 83
Relation as a pair of maps 19
Relation equivalence 17
Relation equivalence, generated by a relation 19
Response of a machine 99
Response of a machine, total 102
retract 36
Retraction 36
Rewrite System 148
Right adjoint 117
Ring 83
Run map 97 167
Scalars 26
Section 36
Semilattice 58
Semiring 83 147
Semivector space 82
Separately homomorphic 141
Separation property 87
Sequential machine 93 161
Set inclusion 27
Set represented as functor 163
Sets with structure see structured sets
Sheaves 143
Sierpinski space 72
Simulation lemma 104
Small 137
Small collection 50
Small diagram 50
Small hom sets 138
Small, locally 138
Solution set 134
Solution set, condition 134
Sphere 70
Split epimorphism 36
Split monomorphism 9 36
State 93
State, graph 100
State, initial 93
Strecker, G. E. 176
Structure 85
Subcategory 30
Subcategory, full 30 33
Subcategory, reflexive 174
Subfunctor 156
Subgroup 52
Submonoid 52
Subobject 36
Subobject, classifier 143
Substructure 89
Support of a function 26
Surjection see onto map
Symmetry 17
Tensor product 141
Term 158
Terminal object 43
TO space 87
Topological space 71
topology 71
Topology, discrete 72
Topology, indiscrete 72
Topos 143
Tor$ 119
Torsion group 119
Total response of a machine 102
Transformation see Natural transformation
Transitivity 17
TREE 159
Tree, monad 165
Triangle inequality 61
Tychonoff product 72
Union of sets 43
Unit of a ring 83 185
Unitary laws for monad 164
Unitary laws for monoid in monoidal category 145
Universal algebra 157
Universal property 45
Vector 26
Vector, in a category 74
Vector, space 25
Vector, space, subspace of 27
Vertical composition of natural transformations 153
Yoneda Lemma 128
Yoneda proposition 124
Zero law 78
Zero object 44
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