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Duality Theory for Bounded Lattices: A Comparative Study
Guram Bezhanishvili, Luca Carai, Patrick Morandi
There are numerous generalizations of the celebrated Priestley duality for bounded distributive lattices to the non-distributive setting. The resulting dualities rely on an earlier…
Heyting frames and Esakia duality
Guram Bezhanishvili, Luca Carai, Patrick Morandi
We introduce the category of Heyting frames and show that it is equivalent to the category of Heyting algebras and dually equivalent to the category of Esakia spaces. This provides…
Connecting generalized Priestley duality to Hofmann-Mislove-Stralka duality
Guram Bezhanishvili, Luca Carai, Patrick Morandi
We connect Priestley duality for distributive lattices and its generalization to distributive meet-semilattices to Hofmann-Mislove-Stralka duality for semilattices. Among other thi…
Duality for powerset coalgebras
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-hom…