This second volume deals with categories of complexes of modules and their applications. The material provides a good basis for those who want to go on to study derived categories. It starts with the basic definitions and properties of complexes and then moves to more advanced topics such as cotorsion pairs and triplets in categories of complexes. As in the first volume, exercises will be provided both for practice and as suggestions for further research.

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 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