Ordered Locales
Category Theory
2024-06-17 v2 General Topology
Abstract
We extend the Stone duality between topological spaces and locales to include order: there is an adjunction between the category of preordered topological spaces satisfying the so-called open cone condition, and the newly defined category of ordered locales. The adjunction restricts to an equivalence of categories between spatial ordered locales and sober -ordered spaces with open cones.
Cite
@article{arxiv.2303.03813,
title = {Ordered Locales},
author = {Chris Heunen and Nesta van der Schaaf},
journal= {arXiv preprint arXiv:2303.03813},
year = {2024}
}
Comments
23 pages, 5 figures; v2: added sections 7 and 8