LEADER 04553nam 2200625 450 001 9910817262603321 005 20170816143335.0 010 $a1-4704-0487-7 035 $a(CKB)3360000000465067 035 $a(EBL)3114107 035 $a(SSID)ssj0000888988 035 $a(PQKBManifestationID)11932390 035 $a(PQKBTitleCode)TC0000888988 035 $a(PQKBWorkID)10867000 035 $a(PQKB)11584176 035 $a(MiAaPQ)EBC3114107 035 $a(RPAM)14774068 035 $a(PPN)195417720 035 $a(EXLCZ)993360000000465067 100 $a20150417h20072007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHomological and homotopical aspects of Torsion theories /$fApostolos Beligiannis, Idun Reiten 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2007. 210 4$dİ2007 215 $a1 online resource (224 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 188, Number 883 300 $a"Volume 188, Number 883 (end of volume)." 311 $a0-8218-3996-9 320 $aIncludes bibliographical references and index. 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""3. Relative Homology and Generalized Tate-Vogel ( Co) Homology""""4. Cotorsion Triples and Complete Cohomology Theories""; ""Chapter X. Nakayama Categories and Cohen-Macaulay Cohomology""; ""1. Nakayama Categories and Cohen-Macaulay Objects""; ""2. ( Co) Torsion Pairs Induced by ( Co) Cohen-Macaulay Objects""; ""3. Cohen-Macaulay Cohomology""; ""Bibliography""; ""Index"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 188, Number 883. 606 $aTorsion theory (Algebra) 606 $aAlgebra, Homological 606 $aHomotopy theory 615 0$aTorsion theory (Algebra) 615 0$aAlgebra, Homological. 615 0$aHomotopy theory. 676 $a516.36 700 $aBeligiannis$b Apostolos$f1969-$01671630 702 $aReiten$b Idun$f1942- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910817262603321 996 $aHomological and homotopical aspects of Torsion theories$94034336 997 $aUNINA