On Kripke, Vietoris and Hausdorff Polynomial Functors

Adámek J, Milius S, Moss LS (2023)

Publication Type: Conference contribution

Publication year: 2023

Journal

LIPIcs : Leibniz International Proceedings in Informatics Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik

Publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

Book Volume: 270

Conference Proceedings Title: Leibniz International Proceedings in Informatics, LIPIcs

Event location: Bloomington, IN US

ISBN: 9783959772877

DOI: 10.4230/LIPIcs.CALCO.2023.21

Abstract

The Vietoris space of compact subsets of a given Hausdorff space yields an endofunctor V on the category of Hausdorff spaces. Vietoris polynomial endofunctors on that category are built from V, the identity and constant functors by forming products, coproducts and compositions. These functors are known to have terminal coalgebras and we deduce that they also have initial algebras. We present an analogous class of endofunctors on the category of extended metric spaces, using in lieu of V the Hausdorff functor H. We prove that the ensuing Hausdorff polynomial functors have terminal coalgebras and initial algebras. Whereas the canonical constructions of terminal coalgebras for Vietoris polynomial functors take ω steps, one needs ω + ω steps in general for Hausdorff ones. We also give a new proof that the closed set functor on metric spaces has no fixed points.

Authors with CRIS profile

Stefan Milius Lehrstuhl für Informatik 8 (Theoretische Informatik)

Involved external institutions

Czech Technical University in Prague / České vysoké učení technické v Praze CZ Czech Republic (CZ) Indiana University US United States (USA) (US)

How to cite

APA:

Adámek, J., Milius, S., & Moss, L.S. (2023). On Kripke, Vietoris and Hausdorff Polynomial Functors. In Paolo Baldan, Valeria de Paiva (Eds.), Leibniz International Proceedings in Informatics, LIPIcs. Bloomington, IN, US: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing.

MLA:

Adámek, Jiří, Stefan Milius, and Lawrence S. Moss. "On Kripke, Vietoris and Hausdorff Polynomial Functors." Proceedings of the 10th Conference on Algebra and Coalgebra in Computer Science, CALCO 2023, Bloomington, IN Ed. Paolo Baldan, Valeria de Paiva, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2023.

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