Topological Dualities for Modal Algebras
Category Theory
2026-04-23 v1 Logic in Computer Science
Logic
Abstract
We display a family of Stone-type dualities linking categories of frames carrying pairs of modal operators to categories of spaces carrying a binary relation. Different notions of morphism used on the relational side lead to significant variations in the point construction. We show how the situation simplifies in the case of semicontinuous relations, allowing for straightforward correspondences between modal axioms and relational properties.
Cite
@article{arxiv.2604.20603,
title = {Topological Dualities for Modal Algebras},
author = {Matthew Collinson},
journal= {arXiv preprint arXiv:2604.20603},
year = {2026}
}