Guram Bezhanishvili ; Luca Carai ; Patrick Morandi - Duality for powerset coalgebras

lmcs:7014 - Logical Methods in Computer Science, February 3, 2022, Volume 18, Issue 1 -
Duality for powerset coalgebrasArticle

Authors: Guram Bezhanishvili ; Luca Carai ; Patrick Morandi

    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 Jónsson-Tarski duality is derived from Stone duality.

    Volume: Volume 18, Issue 1
    Published on: February 3, 2022
    Accepted on: December 22, 2021
    Submitted on: December 22, 2020
    Keywords: Mathematics - Logic,Computer Science - Logic in Computer Science,03B45, 06E25, 06E15, 06A12

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