Description
Book SynopsisThis second volume deals with the relative homological algebra of complexes of modules and their applications. It is a concrete and easy introduction to the kind of homological algebra which has been developed in the last 50 years. The book serves as a bridge between the traditional texts on homological algebra and more advanced topics such as triangulated and derived categories or model category structures. It addresses to readers who have had a course in classical homological algebra, as well as to researchers.
Table of ContentsDedication Preface Chapter I: Complexes of Modules 1. Definitions and basic constructions 2. Complexes formed from Modules 3. Free Complexes 4. Projective and Injective Complexes Chapter II: Short Exact Sequences of Complexe 1. The groups Extn(C, D) 2. The Group Ext1(C, D) 3. The Snake Lemma for Complexes 4. Mapping Cones Chapter III: The Category K(R-Mod) 1. Homotopies 2. The category K(R-Mod) 3. Split short exact sequences 4. The complexes Hom(C, D) 5. The Koszul Complex Chapter IV: Cotorsion Pairs and Triplets in C(R-Mod) 1. Cotorsion Pairs 2. Cotorsion triplets 3. The Dold triplet 4. More on cotorsion pairs and triplets Chapter V: Adjoint Functors 1. Adjoint functors Chapter VI: Model Structures 1. Model Structures on C(R-Mod) Chapter VII: Creating Cotorsion Pairs 1. Creating Cotorsion pairs in C(R-Mod) in a Termwise Manner 2. The Hill lemma 3. More cotorsion pairs 4. More Hovey pairs Chapter VIII: Minimal Complexes 1. Minimal resolutions 2. Decomposing a complex Chapter IX: Cartan and Eilenberg Resolutions 1. Cartan-Eilenberg Projective Complexes 2. Cartan and Eilenberg Projective resolutions 3. C - E injective complexes and resolutions 4. Cartan and Eilenberg Balance Bibliographical Notes References Index
