  We construct a localic groupoid $\mathbb{G}_{KH}$ such that for any locale
$X$ the category of compact Hausdorff locales in the topos of sheaves over $X$
is equivalent to a category whose objects are principal
$\mathbb{G}_{KH}$-bundles over $X$ and whose morphisms are
$\mathbb{S}$-homotopies (where $\mathbb{S}$ is the Sierpi\'{n}ski locale).
  This result can be intuitively viewed as the compact Hausdorff dual of the
well known result from topos theory that there is an object classifier.
