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.
"The authors' presentation is original, condensed and carefully written. Even in case the authors' would be right with their claim that the results "are probably well known" it will be an important help for a person who will become familiar with these details to find them in such a compact and clearly presented way." Zentralblatt f r Mathematik
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; No.
Series: De Gruyter Expositions in Mathematics : Book 2
For Ages: 22+ years old
Number Of Pages: 108
Published: 18th August 2011
Publisher: De Gruyter
Country of Publication: DE
Dimensions (cm): 24.0 x 17.0
Weight (kg): 0.38