Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Introduction and Main Examples
- 1 Additive and Exact Categories
- 2 Cotorsion Pairs
- 3 Stable Categories from Cotorsion Pairs
- 4 Hovey Triples and Abelian Model Structures
- 5 The Homotopy Category of an Abelian Model Structure
- 6 The Triangulated Homotopy Category
- 7 Derived Functors and Abelian Monoidal Model Structures
- 8 Hereditary Model Structures
- 9 Constructing Complete Cotorsion Pairs
- 10 Abelian Model Structures on Chain Complexes
- 11 Mixed Model Structures and Examples
- 12 Cofibrant Generation and Well-Generated Homotopy Categories
- Appendix A Hovey’s Correspondence for General Exact Categories
- Appendix B Right and Left Homotopy Relations
- Appendix C Bibliographical Notes
- References
- Index
Introduction and Main Examples
Published online by Cambridge University Press: 19 December 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Introduction and Main Examples
- 1 Additive and Exact Categories
- 2 Cotorsion Pairs
- 3 Stable Categories from Cotorsion Pairs
- 4 Hovey Triples and Abelian Model Structures
- 5 The Homotopy Category of an Abelian Model Structure
- 6 The Triangulated Homotopy Category
- 7 Derived Functors and Abelian Monoidal Model Structures
- 8 Hereditary Model Structures
- 9 Constructing Complete Cotorsion Pairs
- 10 Abelian Model Structures on Chain Complexes
- 11 Mixed Model Structures and Examples
- 12 Cofibrant Generation and Well-Generated Homotopy Categories
- Appendix A Hovey’s Correspondence for General Exact Categories
- Appendix B Right and Left Homotopy Relations
- Appendix C Bibliographical Notes
- References
- Index
Summary
This section gives a general overview of abelian model structures and their homotopy categories. It is also meant to be a survey of the most fundamental examples of such homotopy categories. These include the chain homotopy category of a ring, the derived category of a ring, and the stable module category of a quasi-Frobenius (or Iwanaga–Gorenstein) ring.
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- Abelian Model Category Theory , pp. xv - xxviPublisher: Cambridge University PressPrint publication year: 2025