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)

5. The Group Ext1(C, D)
6. The Snake Lemma for Complexes

7. Mapping Cones

   Chapter III: The Category K(R-Mod)
   1. Homotopies

8. The category K(R-Mod)
9. Split short exact sequences
10. The complexes Hom(C, D)

11. The Koszul Complex

    Chapter IV: Cotorsion Pairs and Triplets in C(R-Mod)
    1. Cotorsion Pairs

12. Cotorsion triplets
13. The Dold triplet

14. 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

15. The Hill lemma
16. More cotorsion pairs

17. More Hovey pairs

    Chapter VIII: Minimal Complexes
    1. Minimal resolutions

18. Decomposing a complex

    Chapter IX: Cartan and Eilenberg Resolutions
    1. Cartan-Eilenberg Projective Complexes

19. Cartan and Eilenberg Projective resolutions
20. C - E injective complexes and resolutions

21. Cartan and Eilenberg Balance

    Bibliographical Notes
    References
    Index