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A Coalgebraic View of Heyting Duality

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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 Γ-coalgebras, based on Boolean spaces, where Γ 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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Authors and Affiliations

  1. Mathematics, La Trobe University, Victoria, 3086, Australia

    Brian A. Davey

  2. Mathematics, RMIT University, Melbourne, Victoria, 3001, Australia

    John C. Galati

Authors
  1. Brian A. Davey
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  2. John C. Galati
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Davey, B.A., Galati, J.C. A Coalgebraic View of Heyting Duality. Studia Logica 75, 259–270 (2003). https://doi.org/10.1023/B:STUD.0000009559.44998.a3

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