04553nam 2200625 450 991081726260332120170816143335.01-4704-0487-7(CKB)3360000000465067(EBL)3114107(SSID)ssj0000888988(PQKBManifestationID)11932390(PQKBTitleCode)TC0000888988(PQKBWorkID)10867000(PQKB)11584176(MiAaPQ)EBC3114107(RPAM)14774068(PPN)195417720(EXLCZ)99336000000046506720150417h20072007 uy 0engur|n|---|||||txtccrHomological and homotopical aspects of Torsion theories /Apostolos Beligiannis, Idun ReitenProvidence, Rhode Island :American Mathematical Society,2007.©20071 online resource (224 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 188, Number 883"Volume 188, Number 883 (end of volume)."0-8218-3996-9 Includes bibliographical references and index.""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""Memoirs of the American Mathematical Society ;Volume 188, Number 883.Torsion theory (Algebra)Algebra, HomologicalHomotopy theoryTorsion theory (Algebra)Algebra, Homological.Homotopy theory.516.36Beligiannis Apostolos1969-1671630Reiten Idun1942-MiAaPQMiAaPQMiAaPQBOOK9910817262603321Homological and homotopical aspects of Torsion theories4034336UNINA