vi CONTENTS
26. Homotopical categories 78
27. The hom-sets of the homotopy categories 80
28. Homotopical uniqueness 82
29. Deformable functors 83
30. Homotopy colimit and limit functors and homotopical ones 85
Chapter VI. Homotopical Categories and Homotopical Functors 89
31. Introduction 89
32. Universes and categories 93
33. Homotopical categories 96
34. A colimit description of the hom-sets of the homotopy category 101
35. A Grothendieck construction 103
36. 3-arrow calculi 107
37. Homotopical uniqueness 112
38. Homotopically initial and terminal objects 115
Chapter VII. Deformable Functors and Their Approximations 119
39. Introduction 119
40. Deformable functors 123
41. Approximations 126
42. Compositions 130
43. Induced partial adjunctions 133
44. Derived adjunctions 138
45. The Quillen condition 143
Chapter VIII. Homotopy Colimit and Limit Functors
and Homotopical Ones 147
46. Introduction 147
47. Homotopy colimit and limit functors 148
48. Left and right systems 152
49. Homotopical cocompleteness and completeness (special case) 159
50. Homotopical colimit and limit functors 161
51. Homotopical cocompleteness and completeness (general case) 166
Index 171
Bibliography 181
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