Category theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u. a.]
Oxford Univ. Press
2010
|
| Edition: | 2. ed. |
| Series: | Oxford logic guides
52 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XV, 311 S. |
| ISBN: | 9780199237180 9780199587360 |
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Record in the Search Index
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| adam_text | Titel: Category theory
Autor: Awodey, Steve
Jahr: 2010
CONTENTS
Preface to the second edition vii
Preface
IX
1 Categories 1
1.1 Introduction 1
1.2 Functions of sets 3
1.3 Definition of a category 4
1.4 Examples of categories 5
1.5 Isomorphisms 12
1.6 Constructions on categories 14
1.7 Free categories 18
1.8 Foundations: large, small, and locally small 23
1.9 Exercises 25
2 Abstract structures 29
2.1 Epis and monos 29
2.2 Initial and terminal objects 33
2.3 Generalized elements 35
2.4 Products 38
2.5 Examples of products 41
2.6 Categories with products 46
2.7 Hom-sets 48
2.8 Exercises 50
3 Duality 53
3.1 The duality principle 53
3.2 Coproducts 55
3.3 Equalizers 62
3.4 Coequalizers 65
3.5 Exercises 71
4 Groups and categories 75
4.1 Groups in a category 75
4.2 The category of groups 80
4.3 Groups as categories 83
4.4 Finitely presented categories 85
4.5 Exercises 87
CONTENTS
5 Limits and colimits 89
5.1 Subobjects 89
5.2 Pullbacks 91
5.3 Properties of pullbacks 95
5.4 Limits 100
5.5 Preservation of limits 105
5.6 Colimits 108
5.7 Exercises 114
6 Exponentials 119
6.1 Exponential in a category 119
6.2 Cartesian closed categories 122
6.3 Heyting algebras 129
6.4 Propositional calculus 131
6.5 Equational definition of CCC 134
6.6 A-calculus 135
6.7 Variable sets 140
6.8 Exercises 144
7 Naturality 147
7.1 Category of categories 147
7.2 Representable structure 149
7.3 Stone duality 153
7.4 Naturality 155
7.5 Examples of natural transformations 157
7.6 Exponentials of categories 161
7.7 Functor categories 164
7.8 Monoidal categories 168
7.9 Equivalence of categories 171
7.10 Examples of equivalence 175
7.11 Exercises 181
8 Categories of diagrams 185
8.1 Set-valued functor categories 185
8.2 The Yoneda embedding 187
8.3 The Yoneda lemma 188
8.4 Applications of the Yoneda lemma 193
8.5 Limits in categories of diagrams 194
8.6 Colimits in categories of diagrams 195
8.7 Exponentials in categories of diagrams 199
8.8 Topoi 201
8.9 Exercises 203
9 Adjoints 207
9.1 Preliminary definition 207
9.2 Hom-set definition 211
CONTENTS
9.3 Examples of adjoints 215
9.4 Order adjoints 219
9.5 Quantifiers as adjoints 221
9.6 RAPL 225
9.7 Locally cartesian closed categories 231
9.8 Adjoint functor theorem 239
9.9 Exercises 248
10 Monads and algebras 253
10.1 The triangle identities 253
10.2 Monads and adjoints 255
10.3 Algebras for a monad 259
10.4 Comonads and coalgebras 264
10.5 Algebras for endofunctors 266
10.6 Exercises 274
Solutions to selected exercises 279
References 303
Index 305
|
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| discipline | Mathematik Philosophie |
| edition | 2. ed. |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:35:20Z |
| institution | BVB |
| isbn | 9780199237180 9780199587360 |
| language | English |
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| physical | XV, 311 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | Oxford logic guides |
| series2 | Oxford logic guides |
| spelling | Awodey, Steve 1959- Verfasser (DE-588)141982721 aut Category theory Steve Awodey 2. ed. Oxford [u. a.] Oxford Univ. Press 2010 XV, 311 S. txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 52 Literaturangaben 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 52 (DE-604)BV000013997 52 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020107973&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Awodey, Steve 1959- Category theory Oxford logic guides 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_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 | Kategorientheorie (DE-588)4120552-2 gnd |
| topic_facet | Kategorientheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020107973&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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