Saturated Kripke Structures as Vietoris Coalgebras

02/15/2022

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by   Heinz-Peter Gumm, et al.

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We show that the category of coalgebras for the compact Vietoris endofunctor 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.