  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
$\operatorname{hocolim}_J\operatorname{holim}_IC@>>>\operatorname{holim}_I
\operatorname{hocolim}_JC$ is a strong homotopy equivalence.
