Duality for coalgebras for Vietoris and monadicity
Logic
2025-09-17 v2 Category Theory
Abstract
We prove that the opposite of the category of coalgebras for the Vietoris endofunctor on the category of compact Hausdorff spaces is monadic over Set. We deliver an analogous result for the upper, lower and convex Vietoris endofunctors acting on the category of stably compact spaces. We provide axiomatizations of the associated (infinitary) varieties. This can be seen as a version of Jonsson-Tarski duality for modal algebras beyond the 0-dimensional setting.
Cite
@article{arxiv.2302.09529,
title = {Duality for coalgebras for Vietoris and monadicity},
author = {Marco Abbadini and Ivan Di Liberti},
journal= {arXiv preprint arXiv:2302.09529},
year = {2025}
}
Comments
29 pages. Comments are welcome!