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.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1023/B:STUD.0000009559.44998.a3
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M. Menni & C. Smith (2013). Modes of Adjointness. Journal of Philosophical Logic (2-3):1-27.

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