Abstract
We develop a new duality for implicative semilattices, generalizing Esakia duality for Heyting algebras. Our duality is a restricted version of generalized Priestley duality for distributive semilattices, and provides an improvement of Vrancken-Mawet and Celani dualities. We also show that Heyting algebra homomorphisms can be characterized by means of special partial functions between Esakia spaces. On the one hand, this yields a new duality for Heyting algebras, which is an alternative to Esakia duality. On the other hand, it provides a natural generalization of Köhler’s partial functions between finite posets to the infinite case.
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Bezhanishvili, G., Jansana, R. Esakia Style Duality for Implicative Semilattices. Appl Categor Struct 21, 181–208 (2013). https://doi.org/10.1007/s10485-011-9265-0
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DOI: https://doi.org/10.1007/s10485-011-9265-0