An introduction to category theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
North Holland
1981
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 173 S. graph.Darst. |
| ISBN: | 0444003835 |
Staff View
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| 245 | 1 | 0 | |a An introduction to category theory |c V. Sankrithi Krishnan |
| 264 | 1 | |a New York u.a. |b North Holland |c 1981 | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface ix
CHAPTER ONE. BASICS FROM ALGEBRA AND TOPOLOGY 1
1.1 Set Theory 1
1.2 Some Typical Algebraic Structures 3
1.3 Algebras in General 5
1.4 Topological Spaces 10
1.5 Semimetric and Semiuniform Spaces 18
1.6 Completeness and the Canonical Completion 20
CHAPTER TWO. CATEGORIES, DEFINITIONS, AND EXAMPLES 33
2.1 Concrete and General Categories 33
2.2 Subcategories and Quotient Categories 37
2.3 Products and Coproducts of Categories 38
2.4 The Dual Category and Duality of Properties 39
2.5 Arrow Category and Comma Categories over a Category 40
CHAPTER THREE. DISTINGUISHED MORPHISMS AND OBJECTS 43
3.1 Distinguished Morphisms 43
3.2 Distinguished Objects 44
3.3 Equalizers and Coequalizers 46
3.4 Constant Morphisms and Pointed Categories 47
3.5 Separators and Coseparators 50
CHAPTER FOUR. TYPES OF FUNCTORS 52
4.1 Full, Faithful, Dense, Embedding Functors 52
4.2 Reflection and Preservation of Categorical Properties 54
4.3 The Feeble Functor and Reverse Quotient Functor 56
viii CONTENTS
CHAPTER FIVE. NATURAL TRANSFORMATIONS AND
EQUIVALENCES 62
5.1 Natural Transformations and Their Compositions 62
5.2 Equivalence of Categories and Skeletons 64
5.3 Functor Categories 73
5.4 Natural Transformations for Feeble Functors 74
CHAPTER SIX. LIMITS, COLIMITS, COMPLETENESS,
COCOMPLETENESS 78
6.1 Predecessors and Limits of a Functor 78
6.2 Successors and Colimits of a Functor 85
6.3 Factorizations of Morphisms 86
6.4 Completeness 91
CHAPTER SEVEN. ADJOINT FUNCTORS 99
7.1 The Path Category 99
7.2 Adjointness 100
7.3 Near equivalence and Adjointness 105
7.4 Composing and Resolving Shortest Paths or Adjoints 107
7.5 Adjoint Functor Theorems 111
7.6 Examples of Adjoints 115
7.7 Monads 121
7.8 Weak Adjoints 127
APPENDIX ONE. SEMIUNIFORM, BITOPOLOGICAL, AND
PREORDERED ALGEBRAS 143
APPENDIX TWO. ALGEBRAIC FUNCTORS 155
APPENDIX THREE. TOPOLOGICAL FUNCTORS 162
Bibliography 167
Index 169
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| any_adam_object | 1 |
| author | Krishnan, Viakalathur S. |
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| discipline | Mathematik |
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| id | DE-604.BV001998003 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:37Z |
| institution | BVB |
| isbn | 0444003835 |
| language | English |
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| physical | X, 173 S. graph.Darst. |
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| publishDate | 1981 |
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| publisher | North Holland |
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| spelling | Krishnan, Viakalathur S. Verfasser aut An introduction to category theory V. Sankrithi Krishnan New York u.a. North Holland 1981 X, 173 S. graph.Darst. txt rdacontent n rdamedia nc rdacarrier Categories (Mathematics) Functor theory HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001303295&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krishnan, Viakalathur S. An introduction to category theory Categories (Mathematics) Functor theory |
| title | An introduction to category theory |
| title_auth | An introduction to category theory |
| title_exact_search | An introduction to category theory |
| title_full | An introduction to category theory V. Sankrithi Krishnan |
| title_fullStr | An introduction to category theory V. Sankrithi Krishnan |
| title_full_unstemmed | An introduction to category theory V. Sankrithi Krishnan |
| title_short | An introduction to category theory |
| title_sort | an introduction to category theory |
| topic | Categories (Mathematics) Functor theory |
| topic_facet | Categories (Mathematics) Functor theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001303295&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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