A coalgebraic view of Heyting duality (Q1419380)

The present paper gives us a coalgebraic view of the restricted Priestley duality between Heyting algebras and Heyting spaces. Its main result states that the category of Heyting spaces is isomorphic to a full subcategory of the category of all \(\Gamma \)-coalgebras, based on Boolean spaces, where \(\Gamma \) is the functor which sends a Boolean space \(X \) to the hyperspace of nonempty closed subset of \(X\) . Another important contribution of the paper is the proof of a well-known result which characterizes the Heyting spaces and the morphisms between them.