A coalgebraic view of Heyting duality

Studia Logica 75 (3):259 - 270 (2003)
We give a coalgebraic view of the restricted Priestley duality between Heyting algebras and Heyting spaces. More precisely, we show that the category of Heyting spaces is isomorphic to a full subcategory of the category of all -coalgebras, based on Boolean spaces, where is the functor which maps a Boolean space to its hyperspace of nonempty closed subsets. As an appendix, we include a proof of the characterization of Heyting spaces and the morphisms between them.
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    M. Menni & C. Smith (2013). Modes of Adjointness. Journal of Philosophical Logic:1-27.
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