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9780821827598

Homotopy Theory of Diagrams

by ;
  • ISBN13:

    9780821827598

  • ISBN10:

    0821827596

  • Format: Paperback
  • Copyright: 2002-02-01
  • Publisher: Amer Mathematical Society

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Table of Contents

Introduction 1(4)
Model approximations and bounded diagrams
5(24)
Notation
5(1)
Model categories
6(6)
Left derived functors
12(2)
Left derived functors of colimits and left Kan extensions
14(2)
Model approximations
16(3)
Spaces and small categories
19(3)
The pull-back process and local properties
22(1)
Colimits of diagrams indexed by spaces
22(2)
Left Kan extensions
24(2)
Bounded diagrams
26(3)
Homotopy theory of diagrams
29(25)
Statements of the main results
29(1)
Cofibrations
30(2)
Funb(K, M) as a model category
32(3)
Ocolimit of bounded diagrams
35(1)
Bousfield-Kan approximation of Fun(I, C)
36(1)
Homotopy colimits and homotopy left Kan extensions
37(1)
Relative boundedness
38(2)
Reduction process
40(4)
Relative cofibrations
44(2)
Cofibrations and colimits
46(2)
Funbf (L, M) as a model category
48(1)
Cones
49(2)
Diagrams indexed by cones I
51(3)
Properties of homotopy colimits
54(21)
Fubini theorem
54(3)
Bounded diagrams indexed by Grothendieck constructions
57(2)
Thomason's theorem
59(4)
Etale spaces
63(4)
Diagrams indexed by cones II
67(2)
Homotopy colimits as etale spaces
69(1)
Cofinality
70(1)
Homotopy linnts
71(4)
Appendix A. Left Kan extensions preserve boundedness 75(7)
Degeneracy Map
75(3)
Bounded diagrams and left Kan extensions
78(4)
Appendix B. Categorical Preliminaries 82(5)
Categories over and under an object
82(1)
Relative version of categories over and under an object
82(1)
Pull-back process and Kan extensions
83(1)
Cofinality for colimits
83(1)
Grothendieck construction
84(1)
Grothendieck construction & the pull-back process
84(1)
Functors indexed by Grothendieck constructions
85(2)
Bibliography 87(2)
Index 89

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