Category theory: an introduction
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Lemgo
Heldermann
2007
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Sigma series in pure mathematics
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 332 - 380 |
| Beschreibung: | XI, 380 S. Ill., graph. Darst. 25 cm |
| ISBN: | 9783885380016 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804137785635897344 |
|---|---|
| adam_text | CONTENTS PREFACE IX I. INTRODUCTION 1 II. FOUNDATIONS 9 1 SETS, CLASSES,
AND CONGLOMERATES 9 III. CATEGORIES 13 2 CONCRETE CATEGORIES 13 3
ABSTRACT CATEGORIES 15 4 NEW CATEGORIES FROM OLD 23 IV. SPECIAL
MORPHISMS AND SPECIAL OBJECTS 32 5 SECTIONS, RETRACTIONS, AND
ISOMORPHISMS 32 6 MONOMORPHISMS, EPIMORPHISMS, AND BIMORPHISMS 38 7
INITIAL, TERMINAL, AND ZERO OBJECTS 46 8 CONSTANT MORPHISMS, ZERO
MORPHISMS, AND POINTED CATEGORIES 48 V. FUNCTORS AND NATURAL
TRANSFORMATIONS 53 9 FUNCTORS 53 10 HOM-FUNCTORS 61 11 CATEGORIES OF
CATEGORIES 64 12 PROPERTIES OF FUNCTORS 67 13 NATURAL TRANSFORMATIONS
AND NATURAL ISOMORPHISMS 77 14 ISOMORPHISMS AND EQUIVALENCES OF
CATEGORIES 86 15 FUNCTOR CATEGORIES 93 VI. LIMITS IN CATEGORIES 100 16
EQUALIZERS AND COEQUALIZERS 100 17 INTERSECTIONS AND FACTORIZATIONS 107
18 PRODUCTS AND COPRODUCTS 115 WI GESCANNT DURCH BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/987634224 DIGITALISIERT DURCH INDEX 383
VIII CONTENTS 19 SOURCES AND SINKS 126 20 LIMITS AND COLIMITS 133 21
PULLBACKS AND PUSHOUTS 138 22 INVERSE AND DIRECT LIMITS 151 23 COMPLETE
CATEGORIES 155 24 FUNCTORS THAT PRESERVE AND REFLECT LIMITS 166 25
LIMITS IN FUNCTOR CATEGORIES 171 VII. ADJOINT SITUATIONS 177 26
UNIVERSAL MAPS 177 27 ADJOINT FUNCTORS 194 28 EXISTENCE OF ADJOINTS 207
VIII. SET-VALUED FUNCTORS 217 29 HOM-FUNCTORS 217 30 REPRESENTABLE
FUNCTORS 221 31 FREE OBJECTS 231 32 ALGEBRAIC CATEGORIES AND ALGEBRAIC
FUNCTORS 236 IX. SUBOBJECTS, QUOTIENT OBJECTS, AND FACTORIZATIONS 249 33
(SS, JL) CATEGORIES 249 34 (EPI, EXTREMAL MONO) AND (EXTREMAL EPI, MONO)
CATEGORIES 255 35 (GENERATING, EXTREMAL MONO) AND (EXTREMAL GENERATING,
MONO)- FACTORIZATIONS 267 X. REFLECTIVE SUBCATEGORIES 275 36 GENERAL
REFLECTIVE SUBCATEGORIES 275 37 CHARACTERIZATION AND GENERATION OF
^-REFLECTIVE SUBCATEGORIES 281 38 ALGEBRAIC SUBCATEGORIES 288 XI.
POINTED CATEGORIES 293 39 NORMAL AND EXACT CATEGORIES 294 40 ADDITIVE
CATEGORIES 305 41 ABELIAN CATEGORIES 318 APPENDIX: FOUNDATIONS 328
BIBLIOGRAPHY 332 INDEX OF SYMBOLS 381
|
| adam_txt |
CONTENTS PREFACE IX I. INTRODUCTION 1 II. FOUNDATIONS 9 1 SETS, CLASSES,
AND CONGLOMERATES 9 III. CATEGORIES 13 2 CONCRETE CATEGORIES 13 3
ABSTRACT CATEGORIES 15 4 NEW CATEGORIES FROM OLD 23 IV. SPECIAL
MORPHISMS AND SPECIAL OBJECTS 32 5 SECTIONS, RETRACTIONS, AND
ISOMORPHISMS 32 6 MONOMORPHISMS, EPIMORPHISMS, AND BIMORPHISMS 38 7
INITIAL, TERMINAL, AND ZERO OBJECTS 46 8 CONSTANT MORPHISMS, ZERO
MORPHISMS, AND POINTED CATEGORIES 48 V. FUNCTORS AND NATURAL
TRANSFORMATIONS 53 9 FUNCTORS 53 10 HOM-FUNCTORS 61 11 CATEGORIES OF
CATEGORIES 64 12 PROPERTIES OF FUNCTORS 67 13 NATURAL TRANSFORMATIONS
AND NATURAL ISOMORPHISMS 77 14 ISOMORPHISMS AND EQUIVALENCES OF
CATEGORIES 86 15 FUNCTOR CATEGORIES 93 VI. LIMITS IN CATEGORIES 100 16
EQUALIZERS AND COEQUALIZERS 100 17 INTERSECTIONS AND FACTORIZATIONS 107
18 PRODUCTS AND COPRODUCTS 115 WI GESCANNT DURCH BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/987634224 DIGITALISIERT DURCH INDEX 383
VIII CONTENTS 19 SOURCES AND SINKS 126 20 LIMITS AND COLIMITS 133 21
PULLBACKS AND PUSHOUTS 138 22 INVERSE AND DIRECT LIMITS 151 23 COMPLETE
CATEGORIES 155 24 FUNCTORS THAT PRESERVE AND REFLECT LIMITS 166 25
LIMITS IN FUNCTOR CATEGORIES 171 VII. ADJOINT SITUATIONS 177 26
UNIVERSAL MAPS 177 27 ADJOINT FUNCTORS 194 28 EXISTENCE OF ADJOINTS 207
VIII. SET-VALUED FUNCTORS 217 29 HOM-FUNCTORS 217 30 REPRESENTABLE
FUNCTORS 221 31 FREE OBJECTS 231 32 ALGEBRAIC CATEGORIES AND ALGEBRAIC
FUNCTORS 236 IX. SUBOBJECTS, QUOTIENT OBJECTS, AND FACTORIZATIONS 249 33
(SS, JL) CATEGORIES 249 34 (EPI, EXTREMAL MONO) AND (EXTREMAL EPI, MONO)
CATEGORIES 255 35 (GENERATING, EXTREMAL MONO) AND (EXTREMAL GENERATING,
MONO)- FACTORIZATIONS 267 X. REFLECTIVE SUBCATEGORIES 275 36 GENERAL
REFLECTIVE SUBCATEGORIES 275 37 CHARACTERIZATION AND GENERATION OF
^-REFLECTIVE SUBCATEGORIES 281 38 ALGEBRAIC SUBCATEGORIES 288 XI.
POINTED CATEGORIES 293 39 NORMAL AND EXACT CATEGORIES 294 40 ADDITIVE
CATEGORIES 305 41 ABELIAN CATEGORIES 318 APPENDIX: FOUNDATIONS 328
BIBLIOGRAPHY 332 INDEX OF SYMBOLS 381 |
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| author | Herrlich, Horst 1937-2015 Strecker, George E. |
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| callnumber-subject | QA - Mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 3. ed. |
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| isbn | 9783885380016 |
| language | English |
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| spelling | Herrlich, Horst 1937-2015 Verfasser (DE-588)105921580 aut Category theory an introduction Horst Herrlich ; George E. Strecker 3. ed. Lemgo Heldermann 2007 XI, 380 S. Ill., graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Sigma series in pure mathematics 1 Literaturverz. S. 332 - 380 Categories (Mathematics) Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Kategorientheorie (DE-588)4120552-2 s DE-604 Kategorie Mathematik (DE-588)4129930-9 s 2\p DE-604 Mathematik (DE-588)4037944-9 s 3\p DE-604 Strecker, George E. Verfasser aut Sigma series in pure mathematics 1 (DE-604)BV000012120 1 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016584983&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Herrlich, Horst 1937-2015 Strecker, George E. Category theory an introduction Sigma series in pure mathematics Categories (Mathematics) Kategorie Mathematik (DE-588)4129930-9 gnd Mathematik (DE-588)4037944-9 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| subject_GND | (DE-588)4129930-9 (DE-588)4037944-9 (DE-588)4120552-2 (DE-588)4151278-9 |
| title | Category theory an introduction |
| title_auth | Category theory an introduction |
| title_exact_search | Category theory an introduction |
| title_exact_search_txtP | Category theory an introduction |
| title_full | Category theory an introduction Horst Herrlich ; George E. Strecker |
| title_fullStr | Category theory an introduction Horst Herrlich ; George E. Strecker |
| title_full_unstemmed | Category theory an introduction Horst Herrlich ; George E. Strecker |
| title_short | Category theory |
| title_sort | category theory an introduction |
| title_sub | an introduction |
| topic | Categories (Mathematics) Kategorie Mathematik (DE-588)4129930-9 gnd Mathematik (DE-588)4037944-9 gnd Kategorientheorie (DE-588)4120552-2 gnd |
| topic_facet | Categories (Mathematics) Kategorie Mathematik Mathematik Kategorientheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016584983&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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