Model categories:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
1999
|
| Schriftenreihe: | Mathematical surveys and monographs
63 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 209 S. |
| ISBN: | 0821813595 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804127010620964864 |
|---|---|
| adam_text | Contents
Preface ix
Chapter 1. Model categories 1
1.1. The definition of a model category 2
1.2. The homotopy category 7
1.3. Quillen functors and derived functors 13
1.3.1. Quillen functors 14
1.3.2. Derived functors and naturality 16
1.3.3. Quillen equivalences 19
1.4. 2 categories and pseudo 2 functors 22
Chapter 2. Examples 27
2.1. Cofibrantly generated model categories 28
2.1.1. Ordinals, cardinals, and transfinite compositions 28
2.1.2. Relative / cell complexes and the small object argument 30
2.1.3. Cofibrantly generated model categories 34
2.2. The stable category of modules 36
2.3. Chain complexes of modules over a ring 40
2.4. Topological spaces 49
2.5. Chain complexes of comodules over a Hopf algebra 60
2.5.1. The category of B comodules 60
2.5.2. Weak equivalences 65
2.5.3. The model structure 67
Chapter 3. Simplicial sets 73
3.1. Simplicial sets 73
3.2. The model structure on simplicial sets 79
3.3. Anodyne extensions 81
3.4. Homotopy groups 83
3.5. Minimal fibrations 88
3.6. Fibrations and geometric realization 95
Chapter 4. Monoidal model categories 101
4.1. Closed monoidal categories and closed modules 101
4.2. Monoidal model categories and modules over them 107
4.3. The homotopy category of a monoidal model category 115
Chapter 5. Framings 119
5.1. Diagram categories 120
5.2. Diagrams over Reedy categories and framings 123
5.3. A lemma about bisimplicial sets 128
vii
viii CONTENTS
5.4. Function complexes 129
5.5. Associativity 133
5.6. Naturality 136
5.7. Framings on pointed model categories 144
Chapter 6. Pointed model categories 147
6.1. The suspension and loop functors 147
6.2. Cofiber and fiber sequences 152
6.3. Properties of cofiber and fiber sequences 156
6.4. Naturality of cofiber sequences 163
6.5. Pre triangulated categories 170
6.6. Pointed monoidal model categories 173
Chapter 7. Stable model categories and triangulated categories 177
7.1. Triangulated categories 177
7.2. Stable homotopy categories 186
7.3. Weak generators 187
7.4. Finitely generated model categories 190
Chapter 8. Vistas 195
Bibliography 201
Index 205
|
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| dewey-ones | 514 - Topology |
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| discipline | Mathematik |
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| id | DE-604.BV012378971 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:26:33Z |
| institution | BVB |
| isbn | 0821813595 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008396345 |
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| physical | XII, 209 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Hovey, Mark Verfasser aut Model categories Mark Hovey Providence, RI American Mathematical Society 1999 XII, 209 S. txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 63 Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Komplex Algebra (DE-588)4164880-8 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 s Komplex Algebra (DE-588)4164880-8 s DE-604 Mathematical surveys and monographs 63 (DE-604)BV000018014 63 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008396345&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hovey, Mark Model categories Mathematical surveys and monographs Homotopietheorie (DE-588)4128142-1 gnd Komplex Algebra (DE-588)4164880-8 gnd |
| subject_GND | (DE-588)4128142-1 (DE-588)4164880-8 |
| title | Model categories |
| title_auth | Model categories |
| title_exact_search | Model categories |
| title_full | Model categories Mark Hovey |
| title_fullStr | Model categories Mark Hovey |
| title_full_unstemmed | Model categories Mark Hovey |
| title_short | Model categories |
| title_sort | model categories |
| topic | Homotopietheorie (DE-588)4128142-1 gnd Komplex Algebra (DE-588)4164880-8 gnd |
| topic_facet | Homotopietheorie Komplex Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008396345&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
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