Saturated Kripke structures as Vietoris coalgebras. (English) Zbl 07628068
Hansen, Helle Hvid (ed.) et al., Coalgebraic methods in computer science. 16th IFIP WG 1.3 international workshop, CMCS 2022, colocated with ETAPS 2022, Munich, Germany, April 2–3, 2022. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13225, 88-109 (2022).
Summary: 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 [4], we also show that Vietoris subcoalgebras as well as bisimulations admit topological closure and that the category of Vietoris coalgebras has a terminal object.
For the entire collection see [Zbl 1499.68017].
For the entire collection see [Zbl 1499.68017].
MSC:
| 68Q65 | Abstract data types; algebraic specification |
Keywords:
saturated Kripke structures; Vietoris functor; Vietoris coalgebras; Vietoris convergence; bisimulationsReferences:
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