Saturated Kripke Structures as Vietoris Coalgebras

Abstract

We show that the category of coalgebras for the compact Vietoris endofunctor $\mathbb{V}$ 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.