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.