Model categories are used as a tool for inverting certain maps in a category in a controllable manner. As such, they are useful in diverse areas of mathematics. The list of such areas is continually growing. This book is a comprehensive study of the relationship between a model category and its homotopy category. The author develops the theory of model categories, giving a careful development of the main examples. One highlight of the theory is a proof that the homotopy category of any model category is naturally a closed ...
Read More
Model categories are used as a tool for inverting certain maps in a category in a controllable manner. As such, they are useful in diverse areas of mathematics. The list of such areas is continually growing. This book is a comprehensive study of the relationship between a model category and its homotopy category. The author develops the theory of model categories, giving a careful development of the main examples. One highlight of the theory is a proof that the homotopy category of any model category is naturally a closed module over the homotopy category of simplicial sets. Little is required of the reader beyond some category theory and set theory, which makes the book accessible to advanced graduate students. The book begins with the basic theory of model categories and proceeds to a careful exposition of the main examples, using the theory of cofibrantly generated model categories. It then develops the general theory more fully, showing in particular that the homotopy category of any model category is a module over the homotopy category of simplicial sets, in an appropriate sense. This leads to a simplification and generalisation of the loop and suspension functors in the homotopy category of a pointed model category. The book concludes with a discussion of the stable case, where the homotopy category is triangulated in a strong sense and has a set of small weak generators.
Read Less
Add this copy of Model Categories (Mathematical Surveys & Monographs) to cart. $88.83, Sold by Zubal Books rated 4.0 out of 5 stars, ships from Cleveland, OH, UNITED STATES, published 1998 by Amer Mathematical Society.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
First edition, first printing, 209 pp, hardcover, new. -If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.
Add this copy of Model Categories (Mathematical Surveys and Monographs, to cart. $103.00, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Hialeah, FL, UNITED STATES, published 2007 by American Mathematical Society.
Add this copy of Model Categories (Mathematical Surveys and Monographs, to cart. $144.27, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Hialeah, FL, UNITED STATES, published 2007 by American Mathematical Society.
