Contents
Introduction ix
Model categories and their homotopy categories ix
Localizing model category structures xi
Acknowledgments xv
Part 1 . Localization of Model Category Structures
Summary of Part 1
Chapter 1. Local Spaces and Localization
1.1.
1.2.
1.3.
1.4.
1.5.
1.6.
1.7.
1.8.
Definitions of spaces and mapping spaces
Local spaces and localization
Constructing an /-localization functor
Concise description of the /-localization
Postnikov approximations
Topological spaces and simplicial sets
A continuous localization functor
Pointed and unpointed localization
Chapter 2. The Localization Model Category for Spaces
2.1.
2.2.
2.3.
The Bousfield localization model category structure
Subcomplexes of relative A{/}-cell complexes
The Bousfield-Smith cardinality argument
Chapter 3. Localization of Model Categories
3.1.
3.2.
3.3.
3.4.
3.5.
Left localization and right localization
C-local objects and C-local equivalences
Bousfield localization
Bousfield localization and properness
Detecting equivalences
Chapter 4. Existence of Left Bousfield Localizations
4.1.
4.2.
4.3.
4.4.
4.5.
4.6.
Existence of left Bousfield localizations
Horns on S and 5-local equivalences
A functorial localization
Localization of subcomplexes
The Bousfield-Smith cardinality argument
Proof of the main theorem
Chapter 5. Existence of Right Bousfield Localizations
5.1. Right Bousfield localization: Cellularization
1
3
5
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20
22
24
29
31
35
35
37
42
47
47
51
57
65
68
71
71
73
74
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78
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V
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