Axiomatic stable homotopy theory:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
1997
|
| Series: | American Mathematical Society: Memoirs of the American Mathematical Society
610 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 128, Number 610 (second of 4 numbers) |
| Physical Description: | IX, 114 S. graph. Darst. |
| ISBN: | 0821806246 |
Staff View
MARC
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| 245 | 1 | 0 | |a Axiomatic stable homotopy theory |c Mark Hovey ; John H. Palmieri ; Neil P. Strickland |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 1997 | |
| 300 | |a IX, 114 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | Contents
1. Introduction and definitions 1
1.1. The axioms 4
1.2. Examples 6
1.3. Multigrading 8
1.4. Some basic definitions and results 8
2. Smallness, limits and constructibility 12
2.1. Notions of finiteness 12
2.2. Weak colimits and limits 14
2.3. Cellular towers and constructibility 19
3. Bousfield localization 27
3.1. Localization and colocalization functors 27
3.2. Existence of localization functors 34
3.3. Smashing and finite localizations 35
3.4. Geometric morphisms 39
3.5. Properties of localized subcategories 40
3.6. The Bousfield lattice 44
3.7. Rings, fields and minimal Bousfield classes 48
3.8. Bousfield classes of smashing localizations 50
4. Brown representability 53
4.1. Brown categories 53
4.2. Minimal weak colimits 56
4.3. Smashing localizations of Brown categories 59
4.4. A topology on [X, Y] 61
5. Nilpotence and thick subcategories 62
5.1. A naive nilpotence theorem 62
5.2. A thick subcategory theorem 65
6. Noetherian stable homotopy categories 66
6.1. Monochromatic subcategories 68
6.2. Thick subcategories 72
6.3. Localizing subcategories 73
7. Connective stable homotopy theory 75
8. Semisimple stable homotopy theory 77
9. Examples of stable homotopy categories 79
9.1. A general method 79
9.2. Chain complexes 80
9.3. The derived category of a ring 82
9.4. Homotopy categories of equivariant spectra 85
9.5. Cochain complexes of B comodules 87
9.6. The stable category of 2? modules 94
10. Future directions 99
10.1. Grading systems on stable homotopy categories 99
10.2. Other examples 101
vii
viii CONTENTS
Appendix A. Background from category theory 102
A.I. Triangulated categories 102
A.2. Closed symmetric monoidal categories 104
References 109
Index 112
|
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| indexdate | 2024-07-09T18:11:31Z |
| institution | BVB |
| isbn | 0821806246 |
| language | English |
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| physical | IX, 114 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
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| publisher | American Mathematical Society |
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| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Hovey, Mark 1965- Verfasser (DE-588)141476079 aut Axiomatic stable homotopy theory Mark Hovey ; John H. Palmieri ; Neil P. Strickland Providence, RI American Mathematical Society 1997 IX, 114 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 610 Volume 128, Number 610 (second of 4 numbers) Homotopia larpcal Homotopie gtt Homotopy theory Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 s DE-604 Palmieri, John H. 1964- Verfasser (DE-588)173132073 aut Strickland, Neil P. 1966- Verfasser (DE-588)173132081 aut American Mathematical Society: Memoirs of the American Mathematical Society 610 (DE-604)BV008000141 610 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007769655&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hovey, Mark 1965- Palmieri, John H. 1964- Strickland, Neil P. 1966- Axiomatic stable homotopy theory American Mathematical Society: Memoirs of the American Mathematical Society Homotopia larpcal Homotopie gtt Homotopy theory Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4128142-1 |
| title | Axiomatic stable homotopy theory |
| title_auth | Axiomatic stable homotopy theory |
| title_exact_search | Axiomatic stable homotopy theory |
| title_full | Axiomatic stable homotopy theory Mark Hovey ; John H. Palmieri ; Neil P. Strickland |
| title_fullStr | Axiomatic stable homotopy theory Mark Hovey ; John H. Palmieri ; Neil P. Strickland |
| title_full_unstemmed | Axiomatic stable homotopy theory Mark Hovey ; John H. Palmieri ; Neil P. Strickland |
| title_short | Axiomatic stable homotopy theory |
| title_sort | axiomatic stable homotopy theory |
| topic | Homotopia larpcal Homotopie gtt Homotopy theory Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homotopia Homotopie Homotopy theory Homotopietheorie |
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