We connect Priestley duality for distributive lattices and its generalization to distributive meet-semilattices to Hofmann-Mislove-Stralka duality for semilattices. Among other things, this involves consideration of various morphisms between algebraic frames. We also show how Stone duality for boolean algebras and generalized boolean algebras fits as a particular case of the general picture we develop.
Connecting generalized Priestley duality to Hofmann-Mislove-Stralka duality / G. Bezhanishvili, L. Carai, P.J. Morandi. - In: THEORY AND APPLICATIONS OF CATEGORIES. - ISSN 1201-561X. - 41:(2024 Nov 21), pp. 54.1937-54.1982.
Connecting generalized Priestley duality to Hofmann-Mislove-Stralka duality
L. Carai
;
2024
Abstract
We connect Priestley duality for distributive lattices and its generalization to distributive meet-semilattices to Hofmann-Mislove-Stralka duality for semilattices. Among other things, this involves consideration of various morphisms between algebraic frames. We also show how Stone duality for boolean algebras and generalized boolean algebras fits as a particular case of the general picture we develop.
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