Triangulated categories:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton [u.a.]
Princeton Univ. Press
2001
|
| Schriftenreihe: | Annals of mathematics studies
148 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 449 S. |
| ISBN: | 0691086850 pbk 0691086869 9780691086866 |
Internformat
MARC
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| 100 | 1 | |a Neeman, Amnon |d 1957- |e Verfasser |0 (DE-588)112427227 |4 aut | |
| 245 | 1 | 0 | |a Triangulated categories |c by Amnon Neeman |
| 264 | 1 | |a Princeton [u.a.] |b Princeton Univ. Press |c 2001 | |
| 300 | |a VII, 449 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Annals of mathematics studies |v 148 | |
| 650 | 7 | |a Categorieën (wiskunde) |2 gtt | |
| 650 | 4 | |a Catégories (Mathématiques) | |
| 650 | 4 | |a Triangulated categories | |
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| 650 | 0 | 7 | |a Kategorie |g Mathematik |0 (DE-588)4129930-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1811795973378146304 |
|---|---|
| adam_text |
Contents
0. Acknowledgements 3
1. Introduction 3
Chapter 1. Definition and elementary properties of triangulated
categories 29
1.1. Pre triangulated categories 29
1.2. Corollaries of Proposition 1.1.20 37
1.3. Mapping cones, and the definition of triangulated categories 45
1.4. Elementary properties of triangulated categories 52
1.5. Triangulated subcategories 60
1.6. Direct sums and products, and homotopy limits and colimits 63
1.7. Some weak "functoriality" for homotopy limits and colimits 68
1.8. History of the results in Chapter 1 70
Chapter 2. Triangulated functors and localizations of triangulated
categories 73
2.1. Verdier localization and thick subcategories 73
2.2. Sets and classes 99
2.3. History of the results in Chapter 2 100
Chapter 3. Perfection of classes 103
3.1. Cardinals 103
3.2. Generated subcategories 103
3.3. Perfect classes 110
3.4. History of the results in Chapter 3 122
Chapter 4. Small objects, and Thomason's localisation theorem 123
4.1. Small objects 123
4.2. Compact objects 128
4.3. Maps factor through (S}/3 130
4.4. Maps in the quotient 135
4.5. A refinement in the countable case 144
4.6. History of the results in Chapter 4 150
Chapter 5. The category A(§) 153
5.1. The abelian category A(§) 153
5.2. Subobjects and quotient objects in A(§) 172
5.3. The functoriality of A(§) 177
5.4. History of the results in Chapter 5 182
Chapter 6. The category £x(Sop,Ab) 183
6.1. £.x(S°P,Ab) is an abelian category satisfying [AB3] and [AB3*] 183
6.2. The case of 8 = 7a 201
6.3. £x($op,Ab) satisfies [AB4] and [AB4*], but not [AB5] or
[AB5*] 206
6.4. Projectives and injectives in the category 8.x(Sop,Ab) 211
6.5. The relation between A(T) and £.x({7a}op,Ab) 214
6.6. History of the results of Chapter 6 220
Chapter 7. Homological properties of Ex(Sop,Ab) 221
7.1. £.x(Sop,Ab) as a locally presentable category 221
7.2. Homological objects in £,x(S°P,Ab) 224
7.3. A technical lemma and some consequences 230
7.4. The derived functors of colimits in £x(S°p,Ab) 253
7.5. The adjoint to the inclusion of Ex(§op,Ab) 266
7.6. History of the results in Chapter 7 271
Chapter 8. Brown representability 273
8.1. Preliminaries 273
8.2. Brown representability 275
8.3. The first representability theorem 280
8.4. Corollaries of Brown representability 285
8.5. Applications in the presence of injectives 288
8.6. The second representability theorem: Brown representability
for the dual 303
8.7. History of the results in Chapter 8 306
Chapter 9. Bousfield localisation 309
9.1. Basic properties 309
9.2. The six gluing functors 318
9.3. History of the results in Chapter 9 319
Appendix A. Abelian categories 321
A.I. Locally presentable categories 321
A.2. Formal properties of quotients 327
A.3. Derived functors of limits 345
A.4. Derived functors of limits via injectives 354
A.5. A Mittag Leffier sequence with non vanishing lim" 361
A.6. History of the results of Appendix A 366
vi
Appendix B. Homological functors into [AB5Q] categories 369
B.I. A nitration 369
B.2. Abelian categories satisfying [AB5a] 378
B.3. History of the results in Appendix B 385
Appendix C. Counterexamples concerning the abelian category ^4(0") 387
C.I. The submodules plM 387
C.2. A large fl module 392
C.3. The category ,4(8) is not well powered 393
C.4. A category £.x(Sop,Ab) without a cogenerator 395
C.5. History of the results of Appendix C 405
Appendix D. Where 7 is the homotopy category of spectra 407
D.I. Localisation with respect to homology 407
D.2. The lack of injectives 420
D.3. History of the results in Appendix D 426
Appendix E. Examples of non perfectly generated categories 427
E.I. If T is Ko compactly generated, 7op is not even well generated427
E.2. An example of a non Kj perfectly generated 7 432
E.3. For T = K(Z), neither 7 nor 7op is well generated. 437
E.4. History of the results in Appendix E 442
Bibliography 443
Index 445
vii |
| any_adam_object | 1 |
| author | Neeman, Amnon 1957- |
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| ctrlnum | (OCoLC)45202119 (DE-599)BVBBV013692096 |
| dewey-full | 512/.55 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 510 - Mathematics |
| dewey-raw | 512/.55 510 |
| dewey-search | 512/.55 510 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-10-02T10:01:26Z |
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| isbn | 0691086850 pbk 0691086869 9780691086866 |
| language | English |
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| physical | VII, 449 S. |
| publishDate | 2001 |
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| publisher | Princeton Univ. Press |
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| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Neeman, Amnon 1957- Verfasser (DE-588)112427227 aut Triangulated categories by Amnon Neeman Princeton [u.a.] Princeton Univ. Press 2001 VII, 449 S. txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies 148 Categorieën (wiskunde) gtt Catégories (Mathématiques) Triangulated categories Triangulation (DE-588)4186017-2 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Kategorie Mathematik (DE-588)4129930-9 s Triangulation (DE-588)4186017-2 s DE-604 Annals of mathematics studies 148 (DE-604)BV000000991 148 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009356712&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Neeman, Amnon 1957- Triangulated categories Annals of mathematics studies Categorieën (wiskunde) gtt Catégories (Mathématiques) Triangulated categories Triangulation (DE-588)4186017-2 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| subject_GND | (DE-588)4186017-2 (DE-588)4129930-9 |
| title | Triangulated categories |
| title_auth | Triangulated categories |
| title_exact_search | Triangulated categories |
| title_full | Triangulated categories by Amnon Neeman |
| title_fullStr | Triangulated categories by Amnon Neeman |
| title_full_unstemmed | Triangulated categories by Amnon Neeman |
| title_short | Triangulated categories |
| title_sort | triangulated categories |
| topic | Categorieën (wiskunde) gtt Catégories (Mathématiques) Triangulated categories Triangulation (DE-588)4186017-2 gnd Kategorie Mathematik (DE-588)4129930-9 gnd |
| topic_facet | Categorieën (wiskunde) Catégories (Mathématiques) Triangulated categories Triangulation Kategorie Mathematik |
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