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
- 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
- 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.