  The notion of a continuous $G$-action on a topological space readily
generalizes to that of a continuous $D$-action, where $D$ is any small
category. Dror Farjoun and Zabrodsky introduced a generalized notion of orbit,
which is key to understanding spaces with continuous $D$-action. We give an
overview of the theory of orbits and then prove a generalization of
"Elmendorf's Theorem,'' which roughly states that the homotopical data of of a
$D$-space is precisely captured by the homotopical data of its orbits.
