Relative Homological Algebra: Volume 2 Relative Homological Algebra

Publisher: De Gruyter
Year: 2011
Tongue: English
Leaves: 108
Series: De Gruyter Expositions in Mathematics; 54
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Preface
Nomenclature
1 Complexes of Modules
1.1 Definitions and Basic Constructions
1.2 Complexes Formed from Modules
1.3 Free Complexes
1.4 Projective and Injective Complexes
1.5 Exercises
2 Short Exact Sequences of Complexes
2.1 The Groups Extn(C,D)
2.2 The Group ExtI(C,D)
2.3 The Snake Lemma for Complexes
2.4 Mapping Cones
2.5 Exercises
3 The Category K (R-Mod)
3.1 Homotopies
3.2 The Category K(R-Mod)
3.3 Split Short Exact Sequences
3.4 The Complexes Hom (C,D)
3.5 The Koszul Complex
3.6 Exercises
4 Cotorsion Pairs and Triplets in C(R-Mod)
4.1 Cotorsion Pairs
4.2 Cotorsion Triplets
4.3 The Dold Triplet
4.4 More on Cotorsion Pairs and Triplets
4.5 Exercises
5 Adjoint Functors
5.1 Adjoint Functors
5.2 Exercises
6 Model Structures
6.1 Model Structures on C(R-Mod)
6.2 Exercises
7 Creating Cotorsion Pairs
7.1 Creating Cotorsion Pairs in C(R-Mod) in a Termwise Manner
7.2 The Hill Lemma
7.3 More Cotorsion Pairs
7.4 More Hovey Pairs
7.5 Exercises
8 Minimal Complexes
8.1 Minimal Resolutions
8.2 Decomposing a Complex
8.3 Exercises
9 Cartan and Eilenberg Resolutions
9.1 Cartan–Eilenberg Projective Complexes
9.2 Cartan and Eilenberg Projective Resolutions
9.3 C–E Injective Complexes and Resolutions
9.4 Cartan and Eilenberg Balance
9.5 Exercises
Bibliographical Notes
Bibliography
Index

📜 SIMILAR VOLUMES

Algebraic topology: homology and cohomol

📁 Algebraic topology: homology and cohomology

✍ Andrew H Wallace 📂 Library 📅 1970 🏛 W. A. Benjamin 🌐 English

<DIV>This self-contained text is suitable for advanced undergraduate and graduate students and may be used either after or concurrently with courses in general topology and algebra. It surveys several algebraic invariants: the fundamental group, singular and Cech homology groups, and a variety of co

Algebraic Topology: Homology and Cohomol

📁 Algebraic Topology: Homology and Cohomology

✍ Andrew H. Wallace 📂 Library 📅 2007 🏛 Dover Publications 🌐 English

This self-contained text is suitable for advanced undergraduate and graduate students and may be used either after or concurrently with courses in general topology and algebra. It surveys several algebraic invariants: the fundamental group, singular and Cech homology groups, and a variety of cohomol

Relative homological algebra Volume 2

📁 Relative homological algebra Volume 2

✍ Edgar E Enochs; Overtoun M G Jenda 📂 Library 📅 2010 🏛 De Gruyter 🌐 English

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 Le

Relative homological algebra

📁 Relative homological algebra

✍ Edgar E. Enochs, Overtoun M. G. Jenda 📂 Library 📅 2001 🏛 Walter de Gruyter 🌐 English

This book provides a self-contained systematic treatment of the subject of relative homological algebra. It is designed for graduate students as well as researchers and specialists. It contains twelve chapters with abundant supply of important results with complete proofs covering material that is e

Relative Homological Algebra

📁 Relative Homological Algebra

✍ Edgar E. Enochs, Overtoun M. G. Jenda 📂 Library 📅 2011 🏛 De Gruyter 🌐 English

<p>This is the second revised edition of an introduction to contemporary relative homological algebra. It supplies important material essential to understand topics in algebra, algebraic geometry and algebraic topology. Each section comes with exercises providing practice problems for students as we

Relative Homological Algebra

📁 Relative Homological Algebra

✍ Edgar E. Enochs; Overtoun M. G. Jenda 📂 Library 📅 2011 🏛 De Gruyter 🌐 English