# 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…

## 2 Citations

A Coalgebraic Approach to Dualities for Neighborhood Frames

- MathematicsLogical Methods in Computer Science
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An endofunctor is constructed on the category of complete and atomic Boolean algebras that is dual to the double powerset functor on Set to show that Thomason duality for neighborhood frames can be viewed as an algebra-coalgebra duality.

Remarks on Hyperspaces for Priestley Spaces

- MathematicsSSRN Electronic Journal
- 2022

. The Priestley space X = ( X, π, ≤ ) of a bounded distributive lattice L carries three natural topologies, the Stone topology π , the topology of open upsets, and the topology of open downsets. For…

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