Stone Duality for Relations
Logic in Computer Science
2021-07-07 v2 Category 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.
Cite
@article{arxiv.1912.08418,
title = {Stone Duality for Relations},
author = {Alexander Kurz and Andrew Moshier and Achim Jung},
journal= {arXiv preprint arXiv:1912.08418},
year = {2021}
}