  We prove that for any small category $\mathcal{C}$, the category
$\mathbf{KHausLoc}_{\hat{\mathcal{C}}}$ of compact Hausdorff locales in the
presheaf topos $\hat{\mathcal{C}}$, is equivalent to the category of functors
$\mathcal{C} \to \mathbf{KHausLoc}$.

Category Theory