  We prove a categorical duality between a class of abstract algebras of
partial functions and a class of (small) topological categories. The algebras
are the isomorphs of collections of partial functions closed under the
operations of composition, antidomain, range, and preferential union (or
'override'). The topological categories are those whose space of objects is a
Stone space, source map is a local homeomorphism, target map is open, and all
of whose arrows are epimorphisms.
