A categorical duality for algebras of partial functions

TL;DR

This paper establishes a categorical duality linking certain algebraic structures of partial functions with specific topological categories, enhancing understanding of their mathematical relationship.

Contribution

It introduces a new duality between algebras of partial functions and topological categories with particular properties, expanding the theoretical framework.

Findings

Proves a duality between algebraic and topological structures.

Characterizes topological categories with Stone space objects and specific morphism properties.

Identifies algebraic operations corresponding to categorical structures.

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.