|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Lawvere F.W., Rosebrugh R. — Sets for Mathematics |
|
|
|
| Предметный указатель |
action 76 171ff
Action, left  -action 171
Action, right -action 173
Addition 161
Adjoint functors 190 231 246
Algebraic topology 232
Aristotle 193
Arithmetic 160ff
arrow 10
Associative law 7 10 233
Automorphism group 170
Averaging 148ff
Axiom for sets,  is a category 11 111
Axiom for sets, 1 separates mappings 12
Axiom for sets, binary products 61
Axiom for sets, binary sums 29
Axiom for sets, Booleanness 112
Axiom for sets, choice 84 112 220ff
Axiom for sets, Dedekind — Peano 156
Axiom for sets, exponentiation 102 111
Axiom for sets, finite colimits 80 111
Axiom for sets, finite inverse limits 73 111
Axiom for sets, initial set 12
Axiom for sets, nondegeneracy of S 18
Axiom for sets, terminal set 6
Axiom for sets, truth values represent parts 111
Axiom for sets, two-valuedness 112
Axiomatic method ix
Banach — Tarski paradox 87
Belongs to 37
Bernays 130
Bijective mapping 8
Binary product 61
Boole 239
Boolean property 92
Bornological set 144
Bounded part 144f
Bourbaki, Fixed-Point Theorem 224
Brouwer 131 240
Cancellation property 120
Cantor v 129 242 245 247
Cardinality 57
Category 10f
Category of abstract sets and arbitrary mappings 113
Category of categories 235 250
Category theory 233
Cayley 175 249
Cell of partition 85
Chain 223
Characteristic function 19 38 233
Choice, axiom of 84 220ff
Closed part 143ff
Co-surjective 125
Codomain 2
Coequalizer 79
Cograph 2 8 29
Colimit 78
Colimit axiom 80
Commutative ring 213 230
Complement 51 92
Component of a natural transformation 241
Composite relation 92 212
composition 2 10 233
Cone, universal 72
Congruence 95
Constant arrow 22
Constant map 168
Continuous category 52
Continuous space 143
Continuum Hypothesis 245 246
Contrapositive statement 234
Contravariant 103
Converse statement 234
Coproduct 78
Coseparator 18
Cospan 78
Coterminal object 78
Covariant functoriality 103
Data type 71
de Morgan’s law 200
Dedekind v 175 243 249
Dedekind-finite 58
Dedekind-infinite 58
Dedekind–Peano axiom 156
Determined by 37
Diagonal argument, Cantor’s 129ff
Diagonal functor 109
Diagonal map 65
Dirac delta 126
Directed poset 221
Distance-decreasing 145
Distributive law 126ff
Distributive law in computer science 134
Domain 2
Dual, category 25
Dual, proof 67
Dual, property 21
Duality, concrete 120ff
Dynamical system 155
Eilenberg v 233
Element 6 235
Element, generalized 16 235
Elementary topos 111
Empty set 12
Endomapping 13
Entails 196
Entails, versus implies 198
Epimorphism 80 235
Equality, rule of inference for 209
Equalizer 66
Equinumerous 57
Equivalence relation 89
Equivalent categories 46
Equivalent parts 40 138
Equivariant 77
Evaluation 6 99
Excluded Middle 200
Existential quantifier 201ff
Existential quantifier, unique 209
Expectation 149
exponentiation 98
External diagram 3
F-chain 224
Family 5
Feedback 186ff
Feedback, control 187
Fiber 84
Fibered product 69
Fiberwise 45
Field 213 230
Finite state machines, category of 24
Finite, Dedekind 58
Fixed point 131 224
Fixed-point property 131
Fixed-point-free 131
For all 36 203
Foundation v 235
Foundation, category of categories as 235
Fourier transform 126
Fraenkel 130
Free monoid 77
Frege 130
Function 236
Functionals 101
functor 109 236
Functor, representable 248
Functoriality of function spaces 102ff
Functoriality of products 98
Gaifman 229
Galileo 57
| Generalized Continuum Hypothesis 246
Generalized element 16 235
Generalized point 150
Giraud 247
Godel 130
Graph 63 212
Graph of a mapping 63 211ff
Graph, chaotic 180ff
Graph, reversible 176
Grassmann 239
Grothendieck 242
Grothendieck, topos 247
Groupoid 170
Groups, category of 24
Hausdorff 175 220 243
Hausdorff, maximal principle 226
Heyting 240
Homomorphism 172
Ideal 230
Idempotent 189 217
Identity, arrow 10
Identity, law 11
Identity, mapping 4
Image 90 136
Image, existential quantification and 137 139 194 203ff
Implication 35 198
inclusion 34 237
Indexed families 45
Indicator 38
Inference rules 35 195ff
Infinite, Dedekind 58
Inflationary 224 228ff
Initial object 12
Injective mapping 8 238
Injective object 124 238
Integral domain 216
Internal diagram 2
Intersection 43 44 237
Intersection of a family 223
Inverse image 41 237
Inverse limit 71ff
Involution 168
Isbell 151
Isomorphic 18
Isomorphism 54
Isomorphism of categories 185
Iteration 160ff
Kan 233
Left action (set) 171
Left -set 171
Left adjoint 118
Left adjoint functor 231
Left cancellation 238
Leibniz rule 201
Lift 82
LIMIT 58 72
Lincoln 13
Linear transformation 24
listing 5
Localic 93
Logic 193ff 239
Logic, intuitionistic 240
Logic, objective 239
Logic, positive 195
Loop in reflexive graph 180
Loop in reversible graph 176f
Loop, degenerate 180
Loop, one-lane 177
Lower bound 221
Lower bound, greatest 77 221
M-sets, category of 77
Mac Lane v 233
Mapping 2 240
Mapping set 98
Matrix 127
Maximal object 221
Maximal Principle of Hausdorff 226
Maximal Principle of Zorn 85 220ff
Maximal Principle of Zorn, chain version 226
Maximal Principle of Zorn, directed version 222
Maximum object 221
Measurable cardinals 151
membership 34 241
Metric space 144
Monoid 77 167
Monomapping 238
Monomorphism 32 238
Morphism 10
Motion 100
Multiplication 162
Natural 126
Natural isomorphism 232 241
Natural map 172
Natural number object 156
Natural transformation 135 173 241
Negation 200
Nilpotent 217
Number theory 154ff
Object 10
One element set 241
One-to-one correspondence 54
Operators 101
Opposite category 25 174
Order of nilpotency 217
Pairs of sets, category of 46
Parameterization 5
Part 33 242
Part, bounded 144
Part, closed 143ff
Partially ordered sets, category of 24
Partition 85
Peano’s postulate 163
Pointed sets, category of 25 46
Pointwise 118
Posets 169
Posets, arise concretely 169
Posets, strict 224
Power set functor, contravariant 122ff
Power set functor, covariant 141ff
Predicate 194
PRODUCT 61
Property 5 17
Pullback 69
Pushout 79
Reciprocal 213
Recursion 157ff
Reflexive 88
Relation 87
Representable functor 248
Representation of membership 39
Restriction 40
Retraction 48
Right action (set) 173
Right adjoint functor 231
Right cancellation 80 235
Ring 213
Russell 130
Schroder 239 249
Section 48
Self-mapping 13
Separator 11 242
Set theory 242
Set theory, axiomatic 243
Set theory, naive 243
Set theory, parameterization 243
Singleton map 124 142
Skolem 239
Slice category 25
Small hom-sets 250
Space, topological 143
|
|
|
| Реклама |
|
|
|
|
|
О проекте