January 18th lecture

I will start with a discussion of some of the problems that model category theory are intended to solve.  This involves the homotopy categories of topological spaces, localization and group completion, simplicial methods and simplicial localizations.  References include Gabriel-Zisman (1967), Dwyer-Kan (JPAA 1980) and Fiedorowicz (1984), and are available in the documents folder for MAT9580.  Here are my rough notes.