Relative Homological Algebra

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.

Autorentext

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

Inhalt

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 Ext*n(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