Homotopy and homotopical algebra, by J. F. Jardine

This paper is a cook's tour of homotopical algebra, from its origins in Combinatorial Topology in the early part of the century, through the work of Eilenberg-Mac Lane, Kan and Quillen, to modern applications related to sheaves and presheaves of simplicial sets in areas related to algebraic K-theory. This paper is intended as an introduction for algebraists to combinatorial homotopy theoretic concepts.

The current version (July 28, 1995) has been revised and updated in preparation for publication of volume N of the Handbook of Algebra (M. Hazewinkel, ed.). This volume is scheduled to appear late in 1995. The differences between this version and the previous (item no. 5 of this archive) are essentially cosmetic, but the paper should now be substantially easier to read and use.

This paper has appeared in print, in "Handbook of Algebra", Vol. 1, M. Hazewinkel, ed., North-Holland, Amsterdam, 1996, 639-669. We have removed the dvi files.

J. F. Jardine <jardine@uwo.ca>