Stone Coalgebras

Clemens Kupke, Alexander Kurz, Yde Venema
2003 Electronical Notes in Theoretical Computer Science  
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
more » ... 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. The paper presupposes some familiarity with category theory, general topology and the theory of boolean algebras. The main purpose of this section is to fix our notation and terminology.
doi:10.1016/s1571-0661(04)80638-8 fatcat:m2fs3hoggrcl7giex2amwykxim