Duality for powerset coalgebras
release_gkwwdnkiffbipo3uts3wy4gbre
by
Guram Bezhanishvili, Luca Carai, Patrick Morandi
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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