Saturated Kripke Structures as Vietoris Coalgebras
Category Theory
2022-02-17 v1 Logic in Computer Science
Abstract
We show that the category of coalgebras for the compact Vietoris endofunctor on the category Top of topological spaces and continuous mappings is isomorphic to the category of all modally saturated Kripke structures. Extending a result of Bezhanishvili, Fontaine and Venema, we also show that Vietoris subcoalgebras as well as bisimulations admit topological closure and that the category of Vietoris coalgebras has a terminal object.
Cite
@article{arxiv.2202.07786,
title = {Saturated Kripke Structures as Vietoris Coalgebras},
author = {Heinz-Peter Gumm and Mona Taheri},
journal= {arXiv preprint arXiv:2202.07786},
year = {2022}
}