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
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