Duality for powerset coalgebras

@article{Bezhanishvili2022DualityFP,
  title={Duality for powerset coalgebras},
  author={Guram Bezhanishvili and Luca Carai and Patrick J. Morandi},
  journal={Log. Methods Comput. Sci.},
  year={2022},
  volume={18}
}
Let CABA be the category of complete 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… 
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