Category theory:
Saved in:
| 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: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XV, 311 S. graph. Darst. 24 cm |
| ISBN: | 0199587361 9780199587360 9780199237180 |
Staff View
MARC
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| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2010 | |
| 300 | |a XV, 311 S. |b graph. Darst. |c 24 cm | ||
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Record in the Search Index
| _version_ | 1804143119805972480 |
|---|---|
| adam_text | 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
Limits and colimits
5.1
Subobjects
5.2
Pullbacks
5.3
Properties of
pullbacks
5.4
Limits
5.5
Preservation of limits
5.6
Colimits
5.7
Exercises
Exponentials
6.1
Exponential in a category
6.2
Cartesian closed categories
6.3
Heyting algebras
6.4
Propositional calculus
6.5
Equational definition of
CCC
6.6
λ
-calculus
6.7
Variable sets
6.8
Exercises
89
89
91
95
100
105
108
114
119
119
122
129
131
134
135
140
144
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
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
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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| bvnumber | BV036548563 |
| classification_rvk | SK 320 |
| ctrlnum | (OCoLC)654401582 (DE-599)GBV619773405 |
| discipline | Mathematik |
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| id | DE-604.BV036548563 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:42:36Z |
| institution | BVB |
| isbn | 0199587361 9780199587360 9780199237180 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020470178 |
| oclc_num | 654401582 |
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| owner | DE-703 DE-29T DE-384 |
| owner_facet | DE-703 DE-29T DE-384 |
| physical | XV, 311 S. graph. Darst. 24 cm |
| 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. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Oxford logic guides 52 Hier auch später erschienene, unveränderte Nachdrucke Kategorientheorie (DE-588)4120552-2 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Kategorientheorie (DE-588)4120552-2 s DE-604 Oxford logic guides 52 (DE-604)BV000013997 52 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020470178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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=020470178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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