A categorical duality for algebras of partial functions

Abstract

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.

25 pages. Very minor changes

Cited by in corpus (2)

• Difference-restriction algebras of partial functions: axiomatisations and representations
• Difference-restriction algebras of partial functions with operators: discrete duality and completion