Category theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
2006
|
| Schriftenreihe: | Oxford logic guides
49 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (S. [249]) and index |
| Beschreibung: | XI, 256 S. Ill., graph. Darst. |
| ISBN: | 0198568614 9780198568612 |
Internformat
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| 490 | 1 | |a Oxford logic guides |v 49 | |
| 500 | |a Includes bibliographical references (S. [249]) and index | ||
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Datensatz im Suchindex
| _version_ | 1804135755976540160 |
|---|---|
| adam_text | CONTENTS
Preface vi
1
1
З
4
5
11
13
16
21
23
25
25
28
29
33
34
36
41
42
45
47
47
49
54
57
63
65
65
68
70
73
74
77
77
80
Categories
1.1
Introduction
1.2
Functions of sets
1.3
Definition of a category
1.4
Examples of categories
1.5
Isomorphisms
1.6
Constructions on categories
1.7
Free categories
1.8
Foundations: large, small, and locally small
1.9
Exercises
Abstract structures
2.1
Epis
and
monos
2.2
Initial and terminal objects
2.3
Generalized elements
2.4
Sections and retractions
2.5
Products
2.6
Examples of products
2.7
Categories with products
2.8
Hom-sets
2.9
Exercises
Duality
3.1
The duality principle
3.2
Coproducts
3.3
Equalizers
3.4
Coequalizers
3.5
Exercises
Groups and categories
4.1
Groups in a category
4.2
The category of groups
4.3
Groups as categories
4.4
Finitely presented categories
4.5
Exercises
Limits and colimits
5.1
Subobjects
5.2
Pullbacks
5.3
Properties of pullbacks
84
5.4
Limits
89
5.5
Preservation of limits
94
5.6
Colimits
95
5.7
Exercises
102
Exponentials
105
6.1
Exponential in a category
105
6.2
Cartesian closed categories
108
113
118
119
123
125
125
127
131
133
135
139
142
146
150
155
159
159
160
162
166
167
168
172
174
176
Adjoints
179
9.1
Preliminary definition
179
9.2
Hom-set definition
183
9.3
Examples of
adjoints
187
9.4
Order
adjoints
191
9.5
Quantifiers as
adjoints
193
9.6
RAPL
197
9.7
Locally cartesian closed categories
202
6.3
Heyting algebras
6.4
Equational definition
6.5
λ
-calculus
6.6
Exercises
Functors and naturality
7.1
Category of categories
7.2
Representable structure
7.3
Stone duality
7.4
Naturality
7.5
Examples of natural transformations
7.6
Exponentials of categories
7.7
Functor categories
7.8
Equivalence of categories
7.9
Examples of equivalence
7.10
Exercises
Categories of diagrams
8.1
Set-valued functor categories
8.2
The Yoneda embedding
8.3
The Yoneda Lemma
8.4
Applications of the Yoneda Lemma
8.5
Limits in categories of diagrams
8.6
Colimits in categories of diagrams
8.7
Exponentials in categories of diagrams
8.8
Topoi
8.9
Exercises
CONTENTS
9.8
Adjoint functor theorem
9.9
Exercises
10
Monads and algebras
10.1
The triangle identities
10.2
Monads and
adjoints
10.3
Algebras for a monad
10.4
Comonads and coalgebras
210
219
223
223
225
229
234
10.5
Algebras for endofunctors
236
10.6
Exercises
244
References
249
Index
251
|
| adam_txt |
CONTENTS
Preface vi
1
1
З
4
5
11
13
16
21
23
25
25
28
29
33
34
36
41
42
45
47
47
49
54
57
63
65
65
68
70
73
74
77
77
80
Categories
1.1
Introduction
1.2
Functions of sets
1.3
Definition of a category
1.4
Examples of categories
1.5
Isomorphisms
1.6
Constructions on categories
1.7
Free categories
1.8
Foundations: large, small, and locally small
1.9
Exercises
Abstract structures
2.1
Epis
and
monos
2.2
Initial and terminal objects
2.3
Generalized elements
2.4
Sections and retractions
2.5
Products
2.6
Examples of products
2.7
Categories with products
2.8
Hom-sets
2.9
Exercises
Duality
3.1
The duality principle
3.2
Coproducts
3.3
Equalizers
3.4
Coequalizers
3.5
Exercises
Groups and categories
4.1
Groups in a category
4.2
The category of groups
4.3
Groups as categories
4.4
Finitely presented categories
4.5
Exercises
Limits and colimits
5.1
Subobjects
5.2
Pullbacks
5.3
Properties of pullbacks
84
5.4
Limits
89
5.5
Preservation of limits
94
5.6
Colimits
95
5.7
Exercises
102
Exponentials
105
6.1
Exponential in a category
105
6.2
Cartesian closed categories
108
113
118
119
123
125
125
127
131
133
135
139
142
146
150
155
159
159
160
162
166
167
168
172
174
176
Adjoints
179
9.1
Preliminary definition
179
9.2
Hom-set definition
183
9.3
Examples of
adjoints
187
9.4
Order
adjoints
191
9.5
Quantifiers as
adjoints
193
9.6
RAPL
197
9.7
Locally cartesian closed categories
202
6.3
Heyting algebras
6.4
Equational definition
6.5
λ
-calculus
6.6
Exercises
Functors and naturality
7.1
Category of categories
7.2
Representable structure
7.3
Stone duality
7.4
Naturality
7.5
Examples of natural transformations
7.6
Exponentials of categories
7.7
Functor categories
7.8
Equivalence of categories
7.9
Examples of equivalence
7.10
Exercises
Categories of diagrams
8.1
Set-valued functor categories
8.2
The Yoneda embedding
8.3
The Yoneda Lemma
8.4
Applications of the Yoneda Lemma
8.5
Limits in categories of diagrams
8.6
Colimits in categories of diagrams
8.7
Exponentials in categories of diagrams
8.8
Topoi
8.9
Exercises
CONTENTS
9.8
Adjoint functor theorem
9.9
Exercises
10
Monads and algebras
10.1
The triangle identities
10.2
Monads and
adjoints
10.3
Algebras for a monad
10.4
Comonads and coalgebras
210
219
223
223
225
229
234
10.5
Algebras for endofunctors
236
10.6
Exercises
244
References
249
Index
251 |
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| isbn | 0198568614 9780198568612 |
| language | English |
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| physical | XI, 256 S. Ill., graph. Darst. |
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| series | Oxford logic guides |
| series2 | Oxford logic guides |
| spelling | Awodey, Steve 1959- Verfasser (DE-588)141982721 aut Category theory Steve Awodey Oxford Clarendon Press 2006 XI, 256 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 49 Includes bibliographical references (S. [249]) and index Categorieën (wiskunde) gtt Categories (Mathematics) Kategorientheorie (DE-588)4120552-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Kategorientheorie (DE-588)4120552-2 s DE-604 Oxford logic guides 49 (DE-604)BV000013997 49 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015039560&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Awodey, Steve 1959- Category theory Oxford logic guides Categorieën (wiskunde) gtt Categories (Mathematics) Kategorientheorie (DE-588)4120552-2 gnd |
| subject_GND | (DE-588)4120552-2 (DE-588)4123623-3 |
| title | Category theory |
| title_auth | Category theory |
| title_exact_search | Category theory |
| title_exact_search_txtP | Category theory |
| title_full | Category theory Steve Awodey |
| title_fullStr | Category theory Steve Awodey |
| title_full_unstemmed | Category theory Steve Awodey |
| title_short | Category theory |
| title_sort | category theory |
| topic | Categorieën (wiskunde) gtt Categories (Mathematics) Kategorientheorie (DE-588)4120552-2 gnd |
| topic_facet | Categorieën (wiskunde) Categories (Mathematics) Kategorientheorie Lehrbuch |
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