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
11 - Mixed Model Structures and 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 chapter shows how two suitably related abelian model structures induce a third “mixed” abelian model structure. The resulting mixed model structure shares the weak equivalences of one but the fibrations of the other. We characterize the cofibrations in the mixed model structure and give several examples of mixed abelian model structures on chain complexes.
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- Abelian Model Category Theory , pp. 351 - 360Publisher: Cambridge University PressPrint publication year: 2025