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arXiv · 2008.01849

Duality for powerset coalgebras

Guram Bezhanishvili·Luca Carai·Patrick Morandi
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Abstract

Let CABA be the category of complete and atomic boolean algebras and complete boolean homomorphisms, and let CSL be the category of complete meet-semilattices and complete meet-homomorphisms. We show that the forgetful functor from CABA to CSL has a left adjoint. This allows us to describe an endofunctor H on CABA such that the category Alg(H) of algebras for H is dually equivalent to the category Coalg(P) of coalgebras for the powerset endofunctor P on Set. As a consequence, we derive Thomason duality from Tarski duality, thus paralleling how J\'onsson-Tarski duality is derived from Stone duality.

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BibTeXRIS

Guram Bezhanishvili, Luca Carai, Patrick Morandi. 2020-08-04. Duality for powerset coalgebras. https://doi.org/10.46298/lmcs-18(1:27)2022

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