Homotopy Limit Functors on Model Categories and Homotopical Categories

Preface......Page 5
Part I.  Model Categories......Page 7
2. Slightly unconventional terminology......Page 9
3. Problems involving the homotopy category......Page 11
4. Problem involving the homotopy colimit functors......Page 14
5. The emergence of the current monograph......Page 17
6. A preview of part II......Page 18
7. Introduction......Page 23
8. Categorical and homotopical preliminaries......Page 26
9. Model categories......Page 29
10. The homotopy category......Page 33
11. Homotopical comments......Page 36
12. Introduction......Page 39
13. Homotopical uniqueness......Page 42
14. Quillen functors......Page 44
15. Approximations......Page 46
16. Derived adjunctions......Page 48
17. Quillen equivalences......Page 52
18. Homotopical comments......Page 55
19. Introduction......Page 59
20. Homotopy colimit and limit functors......Page 63
21. Homotopical cocompleteness and completeness......Page 66
22. Reedy model categories......Page 69
23. Virtually cofibrant and fibrant diagrams......Page 72
24. Homotopical comments......Page 76
Part II.  Homotopical Categories......Page 79
25. Introduction......Page 81
26. Homotopical categories......Page 82
27. The hom-sets of the homotopy categories......Page 84
28. Homotopical uniqueness......Page 86
29. Deformable functors......Page 87
30. Homotopy colimit and limit functors and homotopical ones......Page 89
31. Introduction......Page 93
32. Universes and categories......Page 97
33. Homotopical categories......Page 99
34. A colimit description of the hom-sets of the homotopy category......Page 105
35. A Grothendieck construction......Page 107
36. 3-arrow calculi......Page 111
37. Homotopical uniqueness......Page 116
38. Homotopically initial and terminal objects......Page 119
39. Introduction......Page 123
40. Deformable functors......Page 127
41. Approximations......Page 130
42. Compositions......Page 134
43. Induced partial adjunctions......Page 137
44. Derived adjunctions......Page 142
45. The Quillen condition......Page 147
46. Introduction......Page 151
47. Homotopy colimit and limit functors......Page 152
48. Left and right systems......Page 156
49. Homotopical cocompleteness and completeness (special case)......Page 163
50. Homotopical colimit and limit functors......Page 165
51. Homotopical cocompleteness and completeness (general case)......Page 170
Index......Page 173
Bibliography......Page 175