  An isovariant map between spaces with a group action is an equivariant map
which preserves isotropy groups. In this paper, we show that for a finite group
$G$, the category of $G$-spaces with isovariant maps has a Quillen model
structure. We prove a Piacenza-style model theoretic proof of an isovariant
Elmendorf's theorem, showing that this model structure is Quillen equivalent to
a model category of diagrams.
