Stone Coalgebras

Authors

Clemens Kupke, University of Amsterdam
Alexander Kurz, Chapman UniversityFollow
Yde Venema, University of Amsterdam

Document Type

Article

Publication Date

2003

Abstract

In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue to the power set functor. We prove that the so-called descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. This yields a duality between the category of modal algebras and that of coalgebras over the Vietoris functor. Building on this idea, we introduce the notion of a Vietoris polynomial functor over the category of Stone spaces. For each such functor T we establish a link between the category of T-sorted Boolean algebras with operators and the category of Stone coalgebras over T. Applications include a general theorem providing final coalgebras in the category of T-coalgebras.

Comments

This article was originally published in Electronic Notes in Theoretical Computer Science, volume 82, number 1, in 2003. DOI: 10.1016/S1571-0661(04)80638-8

Recommended Citation

C. Kupke, A. Kurz, and Y. Venema, “Stone Coalgebras,” Electronic Notes in Theoretical Computer Science, vol. 82, no. 1, pp. 170–190, Jul. 2003. DOI: 10.1016/S1571-0661(04)80638-8

Copyright

Elsevier

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.