  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.
