Duality for powerset coalgebras
Logic
2023-06-22 v6 Logic in Computer Science
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.
Keywords
Cite
@article{arxiv.2008.01849,
title = {Duality for powerset coalgebras},
author = {Guram Bezhanishvili and Luca Carai and Patrick Morandi},
journal= {arXiv preprint arXiv:2008.01849},
year = {2023}
}