Relative Homological Algebra.Vol.2
(Sprache: Englisch)
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...
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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.
Klappentext zu „Relative Homological Algebra.Vol.2 “
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.
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.
Inhaltsverzeichnis zu „Relative Homological Algebra.Vol.2 “
DedicationPreface
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
Autoren-Porträt von Edgar E. Enochs, Overtoun M. G. Jenda
Edgar E. Enochs, University of Kentucky, Lexington, USA; Overtoun M. G. Jenda, Auburn University, Alabama, USA.
Bibliographische Angaben
- Autoren: Edgar E. Enochs , Overtoun M. G. Jenda
- 2011, XII, 96 Seiten, mit Abbildungen, Maße: 17,5 x 24,6 cm, Gebunden, Englisch
- Verlag: De Gruyter
- ISBN-10: 3110215225
- ISBN-13: 9783110215229
- Erscheinungsdatum: 23.08.2011
Sprache:
Englisch
Pressezitat
"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 für Mathematik
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