  In this article, we continue our study of category dynamical systems, that is
functors $s$ from a category $G$ to $\Top^{\op}$, and their corresponding skew
category algebras. Suppose that the spaces $s(e)$, for $e \in \ob(G)$, are
compact Hausdorff. We show that if (i) the skew category algebra is simple,
then (ii) $G$ is inverse connected, (iii) $s$ is minimal and (iv) $s$ is
faithful. We also show that if $G$ is a locally abelian groupoid, then (i) is
equivalent to (ii), (iii) and (iv). Thereby, we generalize results by
\"{O}inert for skew group algebras to a large class of skew category algebras.
