Handbook of categorical algebra: 1 Basic category theory
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Univ. Press
1994
|
| Edition: | 1. publ. |
| Series: | Encyclopedia of mathematics and its applications
50 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XV, 345 S. graph. Darst. |
| ISBN: | 0521441781 9780521441780 9780521061193 0521061199 |
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Record in the Search Index
| _version_ | 1804124148727808000 |
|---|---|
| adam_text | IMAGE 1
ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS
HANDBOOK OF CATEGORICAL ALGEBRA 1
BASIC CATEGORY THEORY
FRANCIS BORCEUX DEPARTEMENT DE MATHEMATIQUE UNIVERSITE CATHOLIQUE DE
LOUVAIN
CAMBRIDGE UNIVERSITY PRESS
IMAGE 2
CONTENTS
PREFACE TO VOLUME 1 INTRODUCTION TO THIS HANDBOOK
1
1.1 1.2 1.3 1.4
1.5 1.6 1.7 1.8
1.9 1.10 1.11
2
2.1 2.2 2.3 2.4
2.5 2.6 2.7
2.8 2.9 2.10 2.11
T HE LANGUAGE OF CATEGORIES LOGICAL FOUNDATIONS OF THE THEORY CATEGORIES
AND FUNCTORS NATURAL TRANSFORMATIONS
CONTRAVARIANT FUNCTORS FUELL AND FAITHFUL FUNCTORS COMMA CATEGORIES
MONOMORPHISMS
EPIMORPHISMS ISOMORPHISMS THE DUALITY PRINCIPLE EXERCISES
LIMITS PRODUCTS COPRODUCTS INITIAL AND TERMINAL OBJECTS
EQUALIZERS, COEQUALIZERS PULLBACKS, PUSHOUTS LIMITS AND COLIMITS
COMPLETE CATEGORIES
EXISTENCE THEOREM FOR LIMITS LIMIT PRESERVING FUNCTORS ABSOLUTE COLIMITS
FINAL FUNCTORS
PAGE X
XIII
1
1
4
10 15 18 20 23 27 31 33 36
38 38 44 47
48 51 56 59
60 63 66 69
VLL
IMAGE 3
V L LL
CONTENTS
2.12 INTERCHANGE OF LIMITS 72
2.13 FILTERED COLIMITS 75
2.14 UNIVERSALITY OF COLIMITS 84
2.15 LIMITS IN CATEGORIES OF FUNCTORS 87
2.16 LIMITS IN COMMA CATEGORIES 91
2.17 EXERCISES 93
3 ADJOINT FUNCTORS 96
3.1 REFLECTION ALONG A FUNCTOR 96
3.2 PROPERTIES OF ADJOINT FUNCTORS 106
3.3 THE ADJOINT FUNCTOR THEOREM 108
3.4 FULLY FAITHFUL ADJOINT FUNCTORS 114
3.5 REFLECTIVE SUBCATEGORIES 118
3.6 EPIREFLECTIVE SUBCATEGORIES 120
3.7 KAN EXTENSIONS 122
3.8 TENSOR PRODUCT OF SET-VALUED FUNCTORS 128
3.9 EXERCISES 130
4 GENERATORS AND PROJECTIVES 132
4.1 WELL-POWERED CATEGORIES 132
4.2 INTERSECTION AND UNION 133
4.3 STRONG EPIMORPHISMS 136
4.4 EPI-MONO FACTORIZATIONS 147
4.5 GENERATORS 150
4.6 PROJECTIVES 163
4.7 INJECTIVE COGENERATORS 167
4.8 EXERCISES 174
5 CATEGORIES OF FRACTIONS 176
5.1 GRAPHS AND PATH CATEGORIES 176
5.2 CALCULUS OF FRACTIONS 181
5.3 REFLECTIVE SUBCATEGORIES AS CATEGORIES OF FRACTIONS 190
5.4 THE ORTHOGONAL SUBCATEGORY PROBLEM 193
5.5 FACTORIZATION SYSTEMS 209
5.6 THE CASE OF LOCALIZATIONS 218
5.7 UNIVERSAL CLOSURE OPERATIONS 227
5.8 THE CALCULUS OF BIDENSE MORPHISMS 235
5.9 EXERCISES 248
IMAGE 4
CONTENTS IX
6
6.1 6.2 6.3 6.4
6.5 6.6 6.7
7
7.1 7.2 7.3 7.4
7.5 7.6 7.7 7.8
7.9 7.10
8
8.1 8.2 8.3 8.4
FIAT FUNCTORS AND CAUCHY COMPLETENESS EXACT FUNCTORS LEFT EXACT
REFLECTION OF A FUNCTOR FIAT FUNCTORS
THE RELEVANCE OF REGULAER CARDINALS THE SPLITTING OF IDEMPOTENTS THE MORE
GENERAL ADJOINT FUNCTOR THEOREM EXERCISES
BICATEGORIES AND DISTRIBUTORS 2-CATEGORIES 2-FUNCTORS AND 2-NATURAL
TRANSFORMATIONS MODIFICATIONS AND N-CATEGORIES
2-LIMITS AND BILIMITS LAX FUNCTORS AND PSEUDO-FUNCTORS LAX LIMITS AND
PSEUDO-LIMITS BICATEGORIES
DISTRIBUTORS CAUCHY COMPLETENESS VERSUS DISTRIBUTORS EXERCISES
INTERNAL CATEGORY THEORY INTERNAL CATEGORIES AND FUNCTORS INTERNAL
BASE-VALUED FUNCTORS INTERNAL LIMITS AND COLIMITS EXERCISES
BIBLIOGRAPH]) INDEX
250 250 253 260
267 271 277 279
281 281 287 290
293 296 300 302
308 314 323
325 325 328
333 339 341 343
|
| any_adam_object | 1 |
| author | Borceux, Francis 1948- |
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| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:41:04Z |
| institution | BVB |
| isbn | 0521441781 9780521441780 9780521061193 0521061199 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006483709 |
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| physical | XV, 345 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Borceux, Francis 1948- Verfasser (DE-588)11084825X aut Handbook of categorical algebra 1 Basic category theory Francis Borceux 1. publ. Cambridge Univ. Press 1994 XV, 345 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 50 Encyclopedia of mathematics and its applications ... Hier auch später erschienene, unveränderte Nachdrucke Categories (Mathematics) (DE-604)BV009799500 1 Encyclopedia of mathematics and its applications 50 (DE-604)BV000903719 50 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006483709&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borceux, Francis 1948- Handbook of categorical algebra Encyclopedia of mathematics and its applications Categories (Mathematics) |
| title | Handbook of categorical algebra |
| title_auth | Handbook of categorical algebra |
| title_exact_search | Handbook of categorical algebra |
| title_full | Handbook of categorical algebra 1 Basic category theory Francis Borceux |
| title_fullStr | Handbook of categorical algebra 1 Basic category theory Francis Borceux |
| title_full_unstemmed | Handbook of categorical algebra 1 Basic category theory Francis Borceux |
| title_short | Handbook of categorical algebra |
| title_sort | handbook of categorical algebra basic category theory |
| topic | Categories (Mathematics) |
| topic_facet | Categories (Mathematics) |
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