Locally presentable and accessible categories:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge ; New York, NY
Cambridge University Press
1994
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society: London Mathematical Society lecture note series
189 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006338899&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIV, 316 Seiten Illustrationen, Diagramme 23 cm |
| ISBN: | 0521422612 |
Staff View
MARC
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| 100 | 1 | |a Adámek, Jiří |d 1947- |e Verfasser |0 (DE-588)113295219 |4 aut | |
| 245 | 1 | 0 | |a Locally presentable and accessible categories |c Jiří Adámek ; Jiří Rosicky |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge ; New York, NY |b Cambridge University Press |c 1994 | |
| 300 | |a XIV, 316 Seiten |b Illustrationen, Diagramme |c 23 cm | ||
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| 490 | 1 | |a London Mathematical Society: London Mathematical Society lecture note series |v 189 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 505 | 8 | |a Partial contents: Preface -- Introduction -- Preliminaries -- Locally presentable categories -- Accessible categories -- Algebraic categories -- Injectivity classes -- Categories of models -- Vopĕnka's principle -- Appendix: large cardinals | |
| 505 | 8 | |a Review: "The concepts of a locally presentable category and an accessible category have turned out to be extremely useful in formulating connections between universal algebra, model theory, logic and computer science. The aim of this book is to provide an exposition of both the theory and the applications of these categories at a level accessible to graduate students." "First the concepts of [lambda]-presentable objects, locally [lambda]-presentable categories, and [lambda]-accessible categories are discussed in detail. The authors go on to prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapter they treat some advanced topics in model theory." "For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase."--BOOK JACKET | |
| 650 | 4 | |a Infinitäre Logik | |
| 650 | 4 | |a Kategorie <Mathematik> | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
Introduction xi
0 Preliminaries 1
1 Locally Presentable Categories 7
l.A Locally Finitely Presentable Categories 8
l.B Locally Presentable Categories 18
l.C Representation Theorem 27
l.D Properties of Locally Presentable Categories 45
l.E Locally Generated Categories 53
Exercises 59
Historical Remarks 65
2 Accessible Categories 67
2.A Accessible Categories 68
2.B Accessible Functors 78
2.C Accessible Categories as Free Cocompletions 81
2.D Pure Subobjects 84
2.E Properties of Accessible Categories 95
2.F Accessible Categories and Sketches 105
2.G Accessible Embeddings Into the Category of Graphs .... Ill
2.H Limits of Accessible Categories 115
Exercises 125
Historical Remarks 128
3 Algebraic Categories 131
3.A Finitary Varieties 132
3.B Finitary Quasivarieties 151
vii
viii CONTENTS
3.C Infinitary Varieties and Quasivarieties 158
3.D Essentially Algebraic Categories 161
Exercises 169
Historical Remarks 171
4 Injectivity Classes 173
4.A Weakly Locally Presentable Categories 174
4.B A Characterization of Accessible Categories 184
4.C Locally Multipresentable Categories 187
Exercises 196
Historical Remarks 198
5 Categories of Models 199
5.A Finitary Logic 199
5.B Infinitary Logic 221
Exercises 237
Historical Remarks 238
6 Vbpenka s Principle 241
6.A Vopenka s Principle 242
6.B A Characterization of Locally Presentable Categories .... 248
6.C A Characterization of Accessible
and Axiomatizable Categories 254
6.D A Characterization of Reflective Sub categories 256
6.E A Characterization of Accessible Functors 264
6.F Colimit dense Subcategories 268
Exercises 277
Historical Remarks 278
Appendix: Large Cardinals 281
Historical Remarks 294
Open Problems 295
Bibliography 299
List of Symbols 309
Index 313
|
| any_adam_object | 1 |
| author | Adámek, Jiří 1947- Rosický, Jiří 1946- |
| author_GND | (DE-588)113295219 (DE-588)136237118 |
| author_facet | Adámek, Jiří 1947- Rosický, Jiří 1946- |
| author_role | aut aut |
| author_sort | Adámek, Jiří 1947- |
| author_variant | j a ja j r jr |
| building | Verbundindex |
| bvnumber | BV009590430 |
| classification_rvk | SI 320 SK 320 |
| contents | Partial contents: Preface -- Introduction -- Preliminaries -- Locally presentable categories -- Accessible categories -- Algebraic categories -- Injectivity classes -- Categories of models -- Vopĕnka's principle -- Appendix: large cardinals Review: "The concepts of a locally presentable category and an accessible category have turned out to be extremely useful in formulating connections between universal algebra, model theory, logic and computer science. The aim of this book is to provide an exposition of both the theory and the applications of these categories at a level accessible to graduate students." "First the concepts of [lambda]-presentable objects, locally [lambda]-presentable categories, and [lambda]-accessible categories are discussed in detail. The authors go on to prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapter they treat some advanced topics in model theory." "For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase."--BOOK JACKET |
| ctrlnum | (OCoLC)246644390 (DE-599)BVBBV009590430 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV009590430 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:38:51Z |
| institution | BVB |
| isbn | 0521422612 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006338899 |
| oclc_num | 246644390 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-739 DE-355 DE-BY-UBR DE-703 DE-634 DE-11 DE-188 DE-29T |
| owner_facet | DE-12 DE-384 DE-739 DE-355 DE-BY-UBR DE-703 DE-634 DE-11 DE-188 DE-29T |
| physical | XIV, 316 Seiten Illustrationen, Diagramme 23 cm |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | London Mathematical Society: London Mathematical Society lecture note series |
| series2 | London Mathematical Society: London Mathematical Society lecture note series |
| spellingShingle | Adámek, Jiří 1947- Rosický, Jiří 1946- Locally presentable and accessible categories London Mathematical Society: London Mathematical Society lecture note series Partial contents: Preface -- Introduction -- Preliminaries -- Locally presentable categories -- Accessible categories -- Algebraic categories -- Injectivity classes -- Categories of models -- Vopĕnka's principle -- Appendix: large cardinals Review: "The concepts of a locally presentable category and an accessible category have turned out to be extremely useful in formulating connections between universal algebra, model theory, logic and computer science. The aim of this book is to provide an exposition of both the theory and the applications of these categories at a level accessible to graduate students." "First the concepts of [lambda]-presentable objects, locally [lambda]-presentable categories, and [lambda]-accessible categories are discussed in detail. The authors go on to prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapter they treat some advanced topics in model theory." "For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase."--BOOK JACKET Infinitäre Logik Kategorie <Mathematik> Kategorielle Logik Kategorie Mathematik (DE-588)4129930-9 gnd |
| subject_GND | (DE-588)4129930-9 |
| title | Locally presentable and accessible categories |
| title_auth | Locally presentable and accessible categories |
| title_exact_search | Locally presentable and accessible categories |
| title_full | Locally presentable and accessible categories Jiří Adámek ; Jiří Rosicky |
| title_fullStr | Locally presentable and accessible categories Jiří Adámek ; Jiří Rosicky |
| title_full_unstemmed | Locally presentable and accessible categories Jiří Adámek ; Jiří Rosicky |
| title_short | Locally presentable and accessible categories |
| title_sort | locally presentable and accessible categories |
| topic | Infinitäre Logik Kategorie <Mathematik> Kategorielle Logik Kategorie Mathematik (DE-588)4129930-9 gnd |
| topic_facet | Infinitäre Logik Kategorie <Mathematik> Kategorielle Logik Kategorie Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006338899&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
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