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This 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.
Edgar E. Enochs, University of Kentucky, Lexington, USA; Overtoun M. G. Jenda, Auburn University, Alabama, USA.
Dedication
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