Model Categories, by Mark Hovey

[This book has been published by the AMS as volume 63 of Mathematical Surveys and Monographs, and the dvi file has been removed at the request of the author.]

This is a 1-Meg dvi file of a book on model categories. The original goal was to determine when the homotopy category of a model category is a stable homotopy category in the sense of Hovey-Palmieri-Strickland. In the process, a great deal of new theory had to be developed, and the end result is an exposition of model categories from the ground up. Here is a brief table of contents:

  • I. Model categories. The definition, the homotopy category, Quillen functors and derived functors, 2-categories and pseudo-2-functors.
  • II. Examples. Cofibrantly generated model categories, the stable category of modules, chain complexes of modules, topological spaces, chain complexes of comodules over a Hopf algebra
  • III. Simplicial sets. Simplicial sets, the model structure, anodyne extensions, homotopy groups, minimal fibrations, fibrations and geometric realization
  • IV. Monoidal model categories. Closed monoidal categories and modules, monoidal model categories and modules, the homotopy category of a monoidal model category
  • V. Framings. Diagram categories, diagrams over Reedy categories and framings, a lemma about bisimplicial sets, function complexes, associativity, naturality, framings on pointed model categories
  • VI. Pointed model categories. The suspension and loop functors, cofiber and fiber sequences, properites if cofiber and fiber sequences, naturality of cofiber sequences, pre-triangulated categories, pointed monoidal model categories
  • VII. Stable model categories and triangulated categories. Triangulated categories, stable homotopy categories, weak generators, finitely generated model categories. VIII. Vistas

  • Mark Hovey <hovey@member.ams.org>