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Model Categories and Their Localizations (Mathematical Surveys and Monographs, No. 99) (Mathematical Surveys and Monographs) by Maureen S O'Dougherty; Philip Steven Hirschhorn is a nonfiction available to read on EtoBox.
What is Model Categories and Their Localizations (Mathematical Surveys and Monographs, No. 99) (Mathematical Surveys and Monographs) about?
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. A model category has a class of maps called weak equivalences plus two other classes of maps, called cofibrations and fibrations. Quillen's axioms ensure that the homotopy category exists and that the cofibrations and fibrations have extension and lifting properties similar to those of cofibration and fibration maps of topological spaces. During the past several decades the language of model categories has
Who reads Model Categories and Their Localizations (Mathematical Surveys and Monographs, No. 99) (Mathematical Surveys and Monographs)?
It is typically read by self-directed learners exploring a subject in depth.
Common subject areas: history, science, philosophy, social sciences.
- Author
- Maureen S O'Dougherty; Philip Steven Hirschhorn
- Publisher
- the American Mathematical Society
- Published
- 2003
- Language
- EN
- ISBN
- 9781470413262
- Category
- nonfiction
- Subjects
- Mathematics, Stem
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