Model categories

by Mark Hovey

This book began with the question: when is the homotopy category of a model category a stable homotopy category in the sense of Hovey-Palmieri-Strickland? It grew into a monograph developing the theory of model categories from the ground up to an answer to this question.

Chapters:

Intro:
Introduction + table of contents.
I. Model categories:
standard stuff, except I consider the 2-category of model categories and show the homotopy category is part of a pseudo-2-functor.
II. Examples:
cofibrantly generated model categories, chain complexes of R-modules, topological spaces, chain complexes of B-comodules, where B is a commutative Hopf algebra.
III. Simplicial sets:
Based on excellent book of Goerss-Jardine.
IV. Monoidal model categories:
model categories with an internal tensor product and Hom functor, compatible with model structure.
V. Framings:
the homotopy category of any model category looks like the homotopy category of a simplicial model category.
VI. Pointed model categories:
cofiber and fiber sequences as in Quillen, taking into account the simplicial structure of Chapter V.
VII. Stable model categories and triangulated categories:
New and stronger definition of triangulated category that applies in all known cases. The homotopy category of a pointed model category is triangulated if and only if the suspension is an equivalence. Generators in the homotopy category.
VIII. Vistas:
miscellaneous wild-eyed speculations. +Bibliography and Index.