Lawvere F.W., Schanuel S.H. — Conceptual Mathematics: A First Introduction to Categories :: Электронная библиотека попечительского совета мехмата МГУ

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Lawvere F.W., Schanuel S.H. — Conceptual Mathematics: A First Introduction to Categories

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Название: Conceptual Mathematics: A First Introduction to Categories

Авторы: Lawvere F.W., Schanuel S.H.

Аннотация:

The idea of a category — a sort of mathematical universe — has brought about a remarkable unification and simplification of mathematics. Written by two of the best known names in categorical logic, this is the first book to apply categories to the most elementary mathematics.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 376

Добавлена в каталог: 10.07.2008

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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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