  We characterise proper morphisms of $\infty$-topoi in terms of a relativised
notion of compactness: we show that a geometric morphism of $\infty$-topoi is
proper if and only if it commutes with colimits indexed by filtered internal
$\infty$-categories in the target. In particular, our result implies that for
any $\infty$-topos, the global sections functor is proper if and only if it
preserves filtered colimits. As an application, we show that every proper and
separated map of topological spaces gives rise to a proper morphism between the
associated sheaf $\infty$-topoi, generalising a result of Lurie. Along the way,
we develop some aspects of the theory of localic higher topoi internal to an
$\infty$-topos, which might be of independent interest.
