Contents
Preface vii
Part I. Model Categories 1
Chapter I. An Overview 3
1. Introduction 3
2. Slightly unconventional terminology 3
3. Problems involving the homotopy category 5
4. Problem involving the homotopy colimit functors 8
5. The emergence of the current monograph 11
6. A preview of part II 12
Chapter II. Model Categories and Their Homotopy Categories 19
7. Introduction 19
8. Categorical and homotopical preliminaries 22
9. Model categories 25
10. The homotopy category 29
11. Homotopical comments 32
Chapter III. Quillen Functors 35
12. Introduction 35
13. Homotopical uniqueness 38
14. Quillen functors 40
15. Approximations 42
16. Derived adjunctions 44
17. Quillen equivalences 48
18. Homotopical comments 51
Chapter IV. Homotopical Cocompleteness and Completeness of Model
Categories 55
19. Introduction 55
20. Homotopy colimit and limit functors 59
21. Homotopical cocompleteness and completeness 62
22. Reedy model categories 65
23. Virtually coflbrant and fibrant diagrams 69
24. Homotopical comments 72
Part II. Homotopical Categories 75
Chapter V. Summary of Part II 77
25. Introduction 77
Previous Page Next Page