Duality for powerset coalgebras release_gkwwdnkiffbipo3uts3wy4gbre

by Guram Bezhanishvili, Luca Carai, Patrick Morandi

Released as a article .

2021  

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(š¯’«) of coalgebras for the powerset endofunctor š¯’« on Set. As a consequence, we derive Thomason duality from Tarski duality, thus paralleling how JĆ³nsson-Tarski duality is derived from Stone duality.
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Type  article
Stage   submitted
Date   2021-12-23
Version   v5
Language   en ?
arXiv  2008.01849v5
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