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.
Keywords: Stone duality; Priestley duality; semilattice; algebraic lattice; algebraic frame; coherent frame
2020 MSC: 06A12; 06D22; 06E15; 18F70; 22A26
Theory and Applications of Categories, Vol. 41, 2024, No. 54, pp 1937-1982.
Published 2024-11-21.
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