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| Lawvere F.W., Schanuel S.H. — Conceptual Mathematics: A First Introduction to Categories |
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| Предметный указатель |
Point (= map from terminal object), distinguished 295
Point in general 214
Point in graphs, dynamical systems 214
Point in part 339
Point in sets 19
Point of map object 314 323
Point of product 217 258
Point of sum 222
Pointed sets (cat. of) 216 223 295ff
Polygonal figure (Euclid’s cat.) 67
Positive properties 170ff
Presentation, of dyn. syst. 182ff
Presentation, of dyn. syst., of graph 253
Preserve distinctness 106 see
Probe, figure as, in dyn. system 180
Product of objects 216 236ff see
Product of objects, points of 217 258
Product of objects, projections 217
Product of objects, uniqueness of 217 255ff 263ff
Projection maps see Product
Quadratic polynomial 292
Quiz 108 116
Rational numbers 83 102
reality 84
Reciprocal versus inverse 61
Reduced fraction 102
Relations (in presentation) 183
retract 99
Retract and idempotent 1OOff
Retract as comparison 1OOf
Retraction (for map) 49 59 108 117 see Retract Idempotent
Retraction (for map) and injectivity 52 59
Retraction (for map) as case of determination 49 59 73
Retraction (for map) is epimorphism 59 248
Retraction (for map), number in sets (Danilo) 106 117
Russell, Bertrand 306ff
Sampling 82
Section (for a map) 49 72ff see Idempotent
Section (for a map) and epimorphism 53 59
Section (for a map) and stacking, sorting 74
Section (for a map) as case of choice 50 72
Section (for a map) is monomorphism 52 59
Section (for a map) of a composite 54
Section (for a map), number in sets (Chad) 75 94 117
Separating 215 see
Shadow as map 4 236
Shadow vs sharper image 136f
Shape, (graph) domain of diagram 149 200ff
Shape, (object) domain of figure 83
Shoes and socks rule for inverse of composite 55
singleton set see Terminal object Point
Singleton set and constant map 71
Singleton set as domain of point 19
Singleton set as terminal object 29 225
Singular figure 245
Smooth categories 120 135 323ff
Sorting 81 103 104
Sorting in graphs 270f
Sorting, gender as 162
Sorts (as codomain of map) 81ff
Source, target 141 150 156 189 251
| Space as product 4ff
Space, motion in 4ff 323f
Space, travel 199
Spheres and balls 120ff
Splitting of idempotent 102 106 117
State (in dynamical system) 137
State (in dynamical system) and configuration 318
State (in dynamical system), naming of 177ff
Structure in abstract sets 136
Structure, types of 149ff
Structure-preserving map 136 152ff 175f
Subcategories 138 143
Subgraph 337ff {see subobject)
Subjective contained in objective 84 86
Subjective contained in objective in dynamical systems 180ff
Subobject 335ff
Subobject classifier see Truth value object
Successor map on natural numbers as dynamical system 177ff 247
Successor map on natural numbers vs truth value object 342
Sum of objects 222f 265ff
Sum of objects as dual of product 260
Sum of objects, distributive law 222 275ff 315
Sum of objects, injections 222
Sum of objects, uniqueness 266
Supermarket 71
Surjective for maps from T 51 59
TARGET see Source
Tarski, Alfred 306ff
Terminal object 213 225ff
Terminal object in dynamical systems 214 226f
Terminal object in dynamical systems, in sets 213 214
Terminal object in graphs 214 227f
Terminal object, point as map from 214
Terminal object, uniqueness of 213
Time (as object) 4 217 323
Topological spaces 120 135
topology 67
Topos 348
Transformation of map objects 323
Transformation of map objects, lambda-calculus 319
Truth 306ff 338ff
Truth value object 306ff 340ff
Truth value object in dynamical systems 342
Truth value object in dynamical systems, chaotic 343
Truth value object in graphs 340f
Truth value object in sets 339f
Truth, level of 338ff
Turing, Alan 309
Type of structure 149ff
Unary operation 302
Underlying configuration 318
Uniqueness of initial object 215
Uniqueness of inverse 42 54 62
Uniqueness of product 239 263
Uniqueness of sum 266
Uniqueness of terminal object 213
Velocity 324
Vertices (in Pick’s formula) 47
violin string 106
Wishful thinking 328
Zero maps 279
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