Homological and homotopical aspects of Torsion theories:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2007
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
883 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | "Volume 188, number 883 (end of volume)." Includes bibliographical references and index |
| Beschreibung: | VII, 207 S. |
| ISBN: | 9780821839966 |
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| 300 | |a VII, 207 S. | ||
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Datensatz im Suchindex
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| adam_text | Contents
Introduction 1
Chapter I. Torsion Pairs in Abelian and Triangulated Categories 8
1. Torsion Pairs in Abelian Categories 8
2. Torsion Pairs in Triangulated Categories 10
3. Tilting Torsion Pairs 19
Chapter II. Torsion Pairs in Pretriangulated Categories 22
1. Pretriangulated Categories 22
2. Adjoints and Orthogonal Subcategories 28
3. Torsion Pairs 32
4. Torsion Pairs and Localization Sequences 35
5. Lifting Torsion Pairs 37
Chapter III. Compactly Generated Torsion Pairs in Triangulated
Categories 43
1. Torsion Pairs of Finite Type 43
2. Compactly Generated Torsion Pairs 44
3. The Heart of a Compactly Generated Torsion Pair 50
4. Torsion Pairs Induced by Tilting Objects 55
Chapter IV. Hereditary Torsion Pairs in Triangulated Categories 60
1. Hereditary Torsion Pairs 60
2. Hereditary Torsion Pairs and Tilting 66
3. Connections with the Homological Conjectures 70
4. Concluding Remarks and Comments 77
Chapter V. Torsion Pairs in Stable Categories 79
1. A Description of Torsion Pairs 79
2. Comparison of Subcategories 84
3. Torsion and Cotorsion pairs 88
4. Torsion Classes and Cohen Macaulay Objects 93
5. Tilting Modules 99
Chapter VI. Triangulated Torsion ( Free) Classes in Stable Categories 102
1. Triangulated Subcategories 102
2. Triangulated Torsion( Free) Classes 104
3. Cotorsion Triples 108
4. Applications to Gorenstein Artin Algebras 112
v
vi CONTENTS
Chapter VII. Gorenstein Categories and (Co)Torsion Pairs 117
1. Dimensions and Cotorsion Pairs 117
2. Gorenstein Categories, Cotorsion Pairs and Minimal Approximations 121
3. The Gorenstein Extension of a Cohen Macaulay Category 125
4. Cohen Macaulay Categories and (Co)Torsion Pairs 128
Chapter VIII. Torsion Pairs and Closed Model Structures 132
1. Preliminaries on Closed Model Categories 132
2. Closed Model Structures and Approximation Sequences 134
3. Cotorsion Pairs Arising from Closed Model Structures 138
4. Closed Model Structures Arising from Cotorsion Pairs 143
5. A Classification of (Co)Torsion Pairs 154
Chapter IX. (Co)Torsion Pairs and Generalized Tate Vogel
Cohomology 163
1. Hereditary Torsion Pairs and Homological Functors 163
2. Torsion Pairs and Generalized Tate Vogel (Co )Homology 167
3. Relative Homology and Generalized Tate Vogel (Co)Homology 174
4. Cotorsion Triples and Complete Cohomology Theories 181
Chapter X. Nakayama Categories and Cohen Macaulay Cohomology 186
1. Nakayama Categories and Cohen Macaulay Objects 186
2. (Co)Torsion Pairs Induced by (Co)Cohen Macaulay Objects 190
3. Cohen Macaulay Cohomology 194
Bibliography 200
Index 204
|
| adam_txt |
Contents
Introduction 1
Chapter I. Torsion Pairs in Abelian and Triangulated Categories 8
1. Torsion Pairs in Abelian Categories 8
2. Torsion Pairs in Triangulated Categories 10
3. Tilting Torsion Pairs 19
Chapter II. Torsion Pairs in Pretriangulated Categories 22
1. Pretriangulated Categories 22
2. Adjoints and Orthogonal Subcategories 28
3. Torsion Pairs 32
4. Torsion Pairs and Localization Sequences 35
5. Lifting Torsion Pairs 37
Chapter III. Compactly Generated Torsion Pairs in Triangulated
Categories 43
1. Torsion Pairs of Finite Type 43
2. Compactly Generated Torsion Pairs 44
3. The Heart of a Compactly Generated Torsion Pair 50
4. Torsion Pairs Induced by Tilting Objects 55
Chapter IV. Hereditary Torsion Pairs in Triangulated Categories 60
1. Hereditary Torsion Pairs 60
2. Hereditary Torsion Pairs and Tilting 66
3. Connections with the Homological Conjectures 70
4. Concluding Remarks and Comments 77
Chapter V. Torsion Pairs in Stable Categories 79
1. A Description of Torsion Pairs 79
2. Comparison of Subcategories 84
3. Torsion and Cotorsion pairs 88
4. Torsion Classes and Cohen Macaulay Objects 93
5. Tilting Modules 99
Chapter VI. Triangulated Torsion ( Free) Classes in Stable Categories 102
1. Triangulated Subcategories 102
2. Triangulated Torsion( Free) Classes 104
3. Cotorsion Triples 108
4. Applications to Gorenstein Artin Algebras 112
v
vi CONTENTS
Chapter VII. Gorenstein Categories and (Co)Torsion Pairs 117
1. Dimensions and Cotorsion Pairs 117
2. Gorenstein Categories, Cotorsion Pairs and Minimal Approximations 121
3. The Gorenstein Extension of a Cohen Macaulay Category 125
4. Cohen Macaulay Categories and (Co)Torsion Pairs 128
Chapter VIII. Torsion Pairs and Closed Model Structures 132
1. Preliminaries on Closed Model Categories 132
2. Closed Model Structures and Approximation Sequences 134
3. Cotorsion Pairs Arising from Closed Model Structures 138
4. Closed Model Structures Arising from Cotorsion Pairs 143
5. A Classification of (Co)Torsion Pairs 154
Chapter IX. (Co)Torsion Pairs and Generalized Tate Vogel
Cohomology 163
1. Hereditary Torsion Pairs and Homological Functors 163
2. Torsion Pairs and Generalized Tate Vogel (Co )Homology 167
3. Relative Homology and Generalized Tate Vogel (Co)Homology 174
4. Cotorsion Triples and Complete Cohomology Theories 181
Chapter X. Nakayama Categories and Cohen Macaulay Cohomology 186
1. Nakayama Categories and Cohen Macaulay Objects 186
2. (Co)Torsion Pairs Induced by (Co)Cohen Macaulay Objects 190
3. Cohen Macaulay Cohomology 194
Bibliography 200
Index 204 |
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| index_date | 2024-07-02T17:57:05Z |
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| isbn | 9780821839966 |
| language | English |
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| spelling | Beligiannis, Apostolos Verfasser aut Homological and homotopical aspects of Torsion theories Apostolos Beligiannis ; Idun Reiten Providence, RI American Mathematical Society 2007 VII, 207 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 883 "Volume 188, number 883 (end of volume)." Includes bibliographical references and index Homologische algebra gtt Homotopie gtt Torsie gtt Torsion theory (Algebra) Algebra, Homological Homotopy theory Torsionstheorie (DE-588)4451084-6 gnd rswk-swf Homologische Algebra (DE-588)4160598-6 gnd rswk-swf Homotopie (DE-588)4025803-8 gnd rswk-swf Torsionstheorie (DE-588)4451084-6 s Homologische Algebra (DE-588)4160598-6 s Homotopie (DE-588)4025803-8 s DE-604 Reiten, Idun 1942- Verfasser (DE-588)108418413 aut Memoirs of the American Mathematical Society 883 (DE-604)BV008000141 883 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015711919&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beligiannis, Apostolos Reiten, Idun 1942- Homological and homotopical aspects of Torsion theories Memoirs of the American Mathematical Society Homologische algebra gtt Homotopie gtt Torsie gtt Torsion theory (Algebra) Algebra, Homological Homotopy theory Torsionstheorie (DE-588)4451084-6 gnd Homologische Algebra (DE-588)4160598-6 gnd Homotopie (DE-588)4025803-8 gnd |
| subject_GND | (DE-588)4451084-6 (DE-588)4160598-6 (DE-588)4025803-8 |
| title | Homological and homotopical aspects of Torsion theories |
| title_auth | Homological and homotopical aspects of Torsion theories |
| title_exact_search | Homological and homotopical aspects of Torsion theories |
| title_exact_search_txtP | Homological and homotopical aspects of Torsion theories |
| title_full | Homological and homotopical aspects of Torsion theories Apostolos Beligiannis ; Idun Reiten |
| title_fullStr | Homological and homotopical aspects of Torsion theories Apostolos Beligiannis ; Idun Reiten |
| title_full_unstemmed | Homological and homotopical aspects of Torsion theories Apostolos Beligiannis ; Idun Reiten |
| title_short | Homological and homotopical aspects of Torsion theories |
| title_sort | homological and homotopical aspects of torsion theories |
| topic | Homologische algebra gtt Homotopie gtt Torsie gtt Torsion theory (Algebra) Algebra, Homological Homotopy theory Torsionstheorie (DE-588)4451084-6 gnd Homologische Algebra (DE-588)4160598-6 gnd Homotopie (DE-588)4025803-8 gnd |
| topic_facet | Homologische algebra Homotopie Torsie Torsion theory (Algebra) Algebra, Homological Homotopy theory Torsionstheorie Homologische Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015711919&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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