Stone Duality for Relations

TL;DR

This paper extends Stone duality from functions to relations by working in an order-enriched setting, establishing dual adjunctions and equivalences for categories of relations.

Contribution

It introduces a novel approach to extend Stone duality to relations using order-enriched categories and subobjects, broadening the duality framework.

Findings

Extended Stone duality to relations via order-enriched categories

Established dual adjunctions and equivalences for categories of relations

Provided a new categorical framework for relations in duality theory

Abstract

We show how Stone duality can be extended from maps to relations. This is achieved by working order enriched and defining a relation from A to B as both an order-preserving function from the opposite of A times B to the 2-element chain and as a subobject of A times B. We show that dual adjunctions and equivalences between regular categories, taken in a suitably order enriched sense, extend to (framed bi)categories of relations.