Homological and Homotopical Aspects of Torsion Theories.
Beligiannis, Apostolos.
Homological and Homotopical Aspects of Torsion Theories. - 1st ed. - 1 online resource (224 pages) - Memoirs of the American Mathematical Society ; v.188 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Introduction -- Chapter I. Torsion Pairs in Abelian and Triangulated Categories -- 1. Torsion Pairs in Abelian Categories -- 2. Torsion Pairs in Triangulated Categories -- 3. Tilting Torsion Pairs -- Chapter II. Torsion Pairs in Pretriangulated Categories -- 1. Pretriangulated Categories -- 2. Adjoints and Orthogonal Subcategories -- 3. Torsion Pairs -- 4. Torsion Pairs and Localization Sequences -- 5. Lifting Torsion Pairs -- Chapter III. Compactly Generated Torsion Pairs in Triangulated Categories -- 1. Torsion Pairs of Finite Type -- 2. Compactly Generated Torsion Pairs -- 3. The Heart of a Compactly Generated Torsion Pair -- 4. Torsion Pairs Induced by Tilting Objects -- Chapter IV. Hereditary Torsion Pairs in Triangulated Categories -- 1. Hereditary Torsion Pairs -- 2. Hereditary Torsion Pairs and Tilting -- 3. Connections with the Homological Conjectures -- 4. Concluding Remarks and Comments -- Chapter V. Torsion Pairs in Stable Categories -- 1. A Description of Torsion Pairs -- 2. Comparison of Subcategories -- 3. Torsion and Cotorsion pairs -- 4. Torsion Classes and Cohen-Macaulay Objects -- 5. Tilting Modules -- Chapter VI. Triangulated Torsion (-Free) Classes in Stable Categories -- 1. Triangulated Subcategories -- 2. Triangulated Torsion (-Free) Classes -- 3. Cotorsion Triples -- 4. Applications to Gorenstein Artin Algebras -- Chapter VII. Gorenstein Categories and ( Co) Torsion Pairs -- 1. Dimensions and Cotorsion Pairs -- 2. Gorenstein Categories, Cotorsion Pairs and Minimal Approximations -- 3. The Gorenstein Extension of a Cohen-Macaulay Category -- 4. Cohen-Macaulay Categories and ( Co) Torsion Pairs -- Chapter VIII. Torsion Pairs and Closed Model Structures -- 1. Preliminaries on Closed Model Categories -- 2. Closed Model Structures and Approximation Sequences. 3. Cotorsion Pairs Arising from Closed Model Structures -- 4. Closed Model Structures Arising from Cotorsion Pairs -- 5. A Classification of ( Co) Torsion Pairs -- Chapter IX. ( Co) Torsion Pairs and Generalized Tate-Vogel Cohomology -- 1. Hereditary Torsion Pairs and Homological Functors -- 2. Torsion Pairs and Generalized Tate-Vogel ( Co-) Homology -- 3. Relative Homology and Generalized Tate-Vogel ( Co) Homology -- 4. Cotorsion Triples and Complete Cohomology Theories -- Chapter X. Nakayama Categories and Cohen-Macaulay Cohomology -- 1. Nakayama Categories and Cohen-Macaulay Objects -- 2. ( Co) Torsion Pairs Induced by ( Co) Cohen-Macaulay Objects -- 3. Cohen-Macaulay Cohomology -- Bibliography -- Index.
9781470404871
Torsion theory (Algebra).
Algebra, Homological.
Homotopy theory.
Electronic books.
QA251.3 -- .B46 2007eb
516.36
Homological and Homotopical Aspects of Torsion Theories. - 1st ed. - 1 online resource (224 pages) - Memoirs of the American Mathematical Society ; v.188 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Introduction -- Chapter I. Torsion Pairs in Abelian and Triangulated Categories -- 1. Torsion Pairs in Abelian Categories -- 2. Torsion Pairs in Triangulated Categories -- 3. Tilting Torsion Pairs -- Chapter II. Torsion Pairs in Pretriangulated Categories -- 1. Pretriangulated Categories -- 2. Adjoints and Orthogonal Subcategories -- 3. Torsion Pairs -- 4. Torsion Pairs and Localization Sequences -- 5. Lifting Torsion Pairs -- Chapter III. Compactly Generated Torsion Pairs in Triangulated Categories -- 1. Torsion Pairs of Finite Type -- 2. Compactly Generated Torsion Pairs -- 3. The Heart of a Compactly Generated Torsion Pair -- 4. Torsion Pairs Induced by Tilting Objects -- Chapter IV. Hereditary Torsion Pairs in Triangulated Categories -- 1. Hereditary Torsion Pairs -- 2. Hereditary Torsion Pairs and Tilting -- 3. Connections with the Homological Conjectures -- 4. Concluding Remarks and Comments -- Chapter V. Torsion Pairs in Stable Categories -- 1. A Description of Torsion Pairs -- 2. Comparison of Subcategories -- 3. Torsion and Cotorsion pairs -- 4. Torsion Classes and Cohen-Macaulay Objects -- 5. Tilting Modules -- Chapter VI. Triangulated Torsion (-Free) Classes in Stable Categories -- 1. Triangulated Subcategories -- 2. Triangulated Torsion (-Free) Classes -- 3. Cotorsion Triples -- 4. Applications to Gorenstein Artin Algebras -- Chapter VII. Gorenstein Categories and ( Co) Torsion Pairs -- 1. Dimensions and Cotorsion Pairs -- 2. Gorenstein Categories, Cotorsion Pairs and Minimal Approximations -- 3. The Gorenstein Extension of a Cohen-Macaulay Category -- 4. Cohen-Macaulay Categories and ( Co) Torsion Pairs -- Chapter VIII. Torsion Pairs and Closed Model Structures -- 1. Preliminaries on Closed Model Categories -- 2. Closed Model Structures and Approximation Sequences. 3. Cotorsion Pairs Arising from Closed Model Structures -- 4. Closed Model Structures Arising from Cotorsion Pairs -- 5. A Classification of ( Co) Torsion Pairs -- Chapter IX. ( Co) Torsion Pairs and Generalized Tate-Vogel Cohomology -- 1. Hereditary Torsion Pairs and Homological Functors -- 2. Torsion Pairs and Generalized Tate-Vogel ( Co-) Homology -- 3. Relative Homology and Generalized Tate-Vogel ( Co) Homology -- 4. Cotorsion Triples and Complete Cohomology Theories -- Chapter X. Nakayama Categories and Cohen-Macaulay Cohomology -- 1. Nakayama Categories and Cohen-Macaulay Objects -- 2. ( Co) Torsion Pairs Induced by ( Co) Cohen-Macaulay Objects -- 3. Cohen-Macaulay Cohomology -- Bibliography -- Index.
9781470404871
Torsion theory (Algebra).
Algebra, Homological.
Homotopy theory.
Electronic books.
QA251.3 -- .B46 2007eb
516.36