  Given a particular collection of categorical axioms, aimed at capturing
properties of the category of locales, we show that if $\mathcal{C}$ is a
category that satisfies the axioms then so too is the category $[ G,
\mathcal{C}]$ of $G$-objects, for any internal group $G$. To achieve this we
prove a general categorical result: if an object $S$ is double exponentiable in
a category with finite products then so is its associated trivial $G$-object
$(S, \pi_2: G \times S \rightarrow S)$. The result holds even if $S$ is not
exponentiable.
  An example is given of a category $\mathcal{C}$ that satisfies the axioms,
but for which there is no elementary topos $\mathcal{E}$ such that
$\mathcal{C}$ is the category of locales over $\mathcal{E}$.
  It is shown, in outline, how the results can be extended from groups to
groupoids.
