Interchanging homotopy limits and colimits in CAT

Abstract

Let $I$,$J$ be small categories and $C:I\times J@>>>\CAT$ a functor to the category of small categories. We show that if $I$ has a final object then the canonical map ${\mathrm{hocolim}}_J{\mathrm{holim}}_{I}C@>>>{\mathrm{holim}}_I{\mathrm{hocolim}}_{J}C$ is a strong homotopy equivalence.

4 pages, AmsTex; typos corrected