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Saturated Kripke Structures as Vietoris Coalgebras (2202.07786v1)
Published 15 Feb 2022 in math.CT and cs.LO
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.