Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Lawvere F.W., Rosebrugh R. — Sets for Mathematics
Lawvere F.W., Rosebrugh R. — Sets for Mathematics

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Sets for Mathematics

Авторы: Lawvere F.W., Rosebrugh R.

Аннотация:

Advanced undergraduate or beginning graduate students need a unified foundation for their study of mathematics. For the first time in a text, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of categories of sets.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 276

Добавлена в каталог: 14.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
action      76 171ff
Action, left $\mathcal{A}$-action      171
Action, right $\mathcal{A}$-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, $\mathcal{S}$ 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 $\mathcal{A}$ action (set)      171
Left $\mathcal{A}$-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 $\mathcal{A}$ 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
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте