HOMOTOPY LIMIT FUNCTORS ON MODEL CATEGORIES AND HOMOTOPICAL CATEGORIES by William G. Dwyer (Editor), Philip S. Hirschhorn (Editor), Daniel M. Kan (Editor) ( 9780821839751 )

Item Details

Title:

HOMOTOPY LIMIT FUNCTORS ON MODEL CATEGORIES AND HOMOTOPICAL CATEGORIES

By:

William G. Dwyer (Editor), Philip S. Hirschhorn (Editor), Daniel M. Kan (Editor)

Format:

Paperback

List price:	£113.00
We believe that this item is permanently unavailable, and so we cannot source it.

ISBN 10:

0821839756

ISBN 13:

9780821839751

Publisher:

AMERICAN MATHEMATICAL SOCIETY

Pub. date:

15 August, 2005

Series:

Mathematical Surveys and Monographs No. 113

Pages:

181

Description:

Model categories have become a standard tool in algebraic topology and homological algebra and, increasingly, in other fields where homotopy theoretic ideas are becoming important, such as algebraic $K$-theory and algebraic geometry. Suitable for graduate level, this title intends to obtain a deeper understanding of Quillen's model categories.

Synopsis:

The purpose of this monograph, which is aimed at the graduate level and beyond, is to obtain a deeper understanding of Quillen's model categories. A model category is a category together with three distinguished classes of maps, called weak equivalences, cofibrations, and fibrations. Model categories have become a standard tool in algebraic topology and homological algebra and, increasingly, in other fields where homotopy theoretic ideas are becoming important, such as algebraic $K$-theory and algebraic geometry.The authors' approach is to define the notion of a homotopical category, which is more general than that of a model category, and to consider model categories as special cases of this. A homotopical category is a category with only a single distinguished class of maps, called weak equivalences, subject to an appropriate axiom. This enables one to define ""homotopical"" versions of such basic categorical notions as initial and terminal objects, colimit and limit functors, cocompleteness and completeness, adjunctions, Kan extensions, and universal properties.There are two essentially self-contained parts, and part II logically precedes part I.Part II defines and develops the notion of a homotopical category and can be considered as the beginnings of a kind of ""relative"" category theory. The results of part II are used in part I to obtain a deeper understanding of model categories. The authors show in particular that model categories are homotopically cocomplete and complete in a sense stronger than just the requirement of the existence of small homotopy colimit and limit functors. A reader of part II is assumed to have only some familiarity with the above-mentioned categorical notions. Those who read part I, and especially its introductory chapter, should also know something about model categories.

Publication:

Imprint:

American Mathematical Society

Returns:

Returnable

Some other items by this author:

HOMOTOPY LIMITS, COMPLETIONS AND LOCALIZATIONS (PB)

HOMOTOPY THEORETIC METHODS IN GROUP COHOMOLOGY (PB)

INTERACTIONS BETWEEN HOMOTOPY THEORY AND ALGEBRA (PB)

STABLE AND UNSTABLE HOMOTOPY (HB)