A Coalgebraic View of Heyting Duality |
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Authors: | Brian A. Davey John C. Galati |
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Affiliation: | (1) Mathematics, La Trobe University, Victoria, 3086, Australia;(2) Mathematics, RMIT University, Melbourne, Victoria, 3001, Australia |
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Abstract: | 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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Keywords: | Coalgebra Heyting algebra Priestley duality |
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