Homotopy theory of diagrams:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2002
|
| Series: | Memoirs of the American Mathematical Society
736 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 155, number 736 (second of 5 numbers)." |
| Physical Description: | IX, 90 S. graph. Darst. |
| ISBN: | 0821827596 |
Staff View
MARC
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| 245 | 1 | 0 | |a Homotopy theory of diagrams |c Wojciech Chachólski ; Jérôme Scherer |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2002 | |
| 300 | |a IX, 90 S. |b graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction 1
Chapter I. Model approximations and bounded diagrams 5
1. Notation 5
2. Model categories 6
3. Left derived functors 12
4. Left derived functors of colimits and left Kan extensions 14
5. Model approximations 16
6. Spaces and small categories 19
7. The pull-back process and local properties 22
8. Colimits of diagrams indexed by spaces 22
9. Left Kan extensions 24
10. Bounded diagrams 26
Chapter II. Homotopy theory of diagrams 29
11. Statements of the main results 29
12. Cofibrations 30
13. Funb(K, M) as a model category 32
14. Ocolimit of bounded diagrams 35
15. Bousfield-Kan approximation of Fun(I.C) 36
16. Homotopy colimits and homotopy left Kan extensions 37
17. Relative boundedness 38
18. Reduction process 40
19. Relative cofibrations 44
20. Cofibrations and colimits 46
21. Funbf(L,M) as a model category 48
22. Cones 49
23. Diagrams indexed by cones I 51
Chapter III. Properties of homotopy colimits 54
24. Fubini theorem 54
25. Bounded diagrams indexed by Grothendieck constructions 57
26. Thomason s theorem 59
27. Etale spaces 63
28. Diagrams indexed by cones II 67
29. Homotopy colimits as etale spaces 69
30. Cofinality 70
31. Homotopy limits 71
Appendix A. Left Kan extensions preserve boundedness 75
vii
viii CONTENTS
32. Degeneracy Map 75
33. Bounded diagrams and left Kan extensions 78
Appendix B. Categorical Preliminaries 82
34. Categories over and under an object 82
35. Relative version of categories over and under an object 82
36. Pull-back process and Kan extensions 83
37. Cofinality for colimits 83
38. Grothendieck construction 84
39. Grothendieck construction the pull-back process 84
40. Functors indexed by Grothendieck constructions 85
Bibliography 87
Index 89
|
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| author | Chachólski, Wojciech 1968- Scherer, Jérôme 1969- |
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| dewey-full | 514/.24 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology 510 - Mathematics |
| dewey-raw | 514/.24 510 |
| dewey-search | 514/.24 510 |
| dewey-sort | 3514 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV024495918 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:00:49Z |
| institution | BVB |
| isbn | 0821827596 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018470866 |
| oclc_num | 47805100 |
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| physical | IX, 90 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Chachólski, Wojciech 1968- Verfasser (DE-588)1146354258 aut Homotopy theory of diagrams Wojciech Chachólski ; Jérôme Scherer Providence, RI American Math. Soc. 2002 IX, 90 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 736 "Volume 155, number 736 (second of 5 numbers)." Categorieën (wiskunde) gtt Homotopie gtt Categories (Mathematics) Homotopy theory Homotopie (DE-588)4025803-8 gnd rswk-swf Diagramm (DE-588)4012044-2 gnd rswk-swf Homotopie (DE-588)4025803-8 s Diagramm (DE-588)4012044-2 s DE-604 Scherer, Jérôme 1969- Verfasser (DE-588)173520987 aut Memoirs of the American Mathematical Society 736 (DE-604)BV008000141 736 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018470866&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chachólski, Wojciech 1968- Scherer, Jérôme 1969- Homotopy theory of diagrams Memoirs of the American Mathematical Society Categorieën (wiskunde) gtt Homotopie gtt Categories (Mathematics) Homotopy theory Homotopie (DE-588)4025803-8 gnd Diagramm (DE-588)4012044-2 gnd |
| subject_GND | (DE-588)4025803-8 (DE-588)4012044-2 |
| title | Homotopy theory of diagrams |
| title_auth | Homotopy theory of diagrams |
| title_exact_search | Homotopy theory of diagrams |
| title_full | Homotopy theory of diagrams Wojciech Chachólski ; Jérôme Scherer |
| title_fullStr | Homotopy theory of diagrams Wojciech Chachólski ; Jérôme Scherer |
| title_full_unstemmed | Homotopy theory of diagrams Wojciech Chachólski ; Jérôme Scherer |
| title_short | Homotopy theory of diagrams |
| title_sort | homotopy theory of diagrams |
| topic | Categorieën (wiskunde) gtt Homotopie gtt Categories (Mathematics) Homotopy theory Homotopie (DE-588)4025803-8 gnd Diagramm (DE-588)4012044-2 gnd |
| topic_facet | Categorieën (wiskunde) Homotopie Categories (Mathematics) Homotopy theory Diagramm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018470866&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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