Hirschhorn Philip S.
Model categories and their localizations - Rhode Island: American Mathematical Society, [c2003] - 457 p
Part 1 . Localization of model category structures
1. Local spaces and localization
2. The localization model category for spaces
3. Localization of model categories
4. Existence of left Bousfield localizations
5. Existence of right Bousfield localizations
6. Fiberwise localization
Part 2. Homotopy theory in model categories
7. Model categories
8. Fibrant and cofibrant approximations
9. Simplicial model categories
10. Ordinals, cardinals, and transfinite composition
11. Cofibrantly generated model categories
12. Cellular model categories
13. Proper model categories
14. The classifying space of a small category
15. The reedy model category structure
16. Cosimplicial and simplicial resolutions
17. Homotopy function complexes
18. Homotopy limits in simplicial model categories
19. Homotopy limits in general model categories
The aim of this book is to explain modern homotopy theory in a manner accessible to graduate students yet structured so that experts can skip over numerous linear developments to quickly reach the topics of their interest. Homotopy theory arises from choosing a class of maps, called weak equivalences, and then passing to the homotopy category by localizing with respect to the weak equivalences, i.e., by creating a new category in which the weak equivalences are isomorphisms. Quillen defined a model category to be a category together with a class of weak equivalences and additional structure useful for describing the homotopy category in terms of the original category. This allows you to make constructions analogous to those used to study the homotopy theory of topological spaces.--- summary provided by publisher
9780821849170
QA169
Model categories and their localizations - Rhode Island: American Mathematical Society, [c2003] - 457 p
Part 1 . Localization of model category structures
1. Local spaces and localization
2. The localization model category for spaces
3. Localization of model categories
4. Existence of left Bousfield localizations
5. Existence of right Bousfield localizations
6. Fiberwise localization
Part 2. Homotopy theory in model categories
7. Model categories
8. Fibrant and cofibrant approximations
9. Simplicial model categories
10. Ordinals, cardinals, and transfinite composition
11. Cofibrantly generated model categories
12. Cellular model categories
13. Proper model categories
14. The classifying space of a small category
15. The reedy model category structure
16. Cosimplicial and simplicial resolutions
17. Homotopy function complexes
18. Homotopy limits in simplicial model categories
19. Homotopy limits in general model categories
The aim of this book is to explain modern homotopy theory in a manner accessible to graduate students yet structured so that experts can skip over numerous linear developments to quickly reach the topics of their interest. Homotopy theory arises from choosing a class of maps, called weak equivalences, and then passing to the homotopy category by localizing with respect to the weak equivalences, i.e., by creating a new category in which the weak equivalences are isomorphisms. Quillen defined a model category to be a category together with a class of weak equivalences and additional structure useful for describing the homotopy category in terms of the original category. This allows you to make constructions analogous to those used to study the homotopy theory of topological spaces.--- summary provided by publisher
9780821849170
QA169