Semilattice-based dualities
The authors consider a duality between a variety of universal algebras and a category of what they call ``representation spaces'', such as the Stone duality for the Boolean algebras, etc. They extend their duality to various ``regularizations'' of a given variety using the Płonka sum construction which is also expressed in the language of sheaves and étale spaces. Various examples of regularizations of the Priestley, Stone and Pontryagin dualities are described. In particular the duality for the distributive bisemilattices without constants, deduced [\textit{G. Gierz} and \textit{A. B. Romanowska}, J. Aust. Math. Soc., Ser. A 51, 247-275 (1991; Zbl 0751.06008)] from the Priestley duality for distributive lattices, is obtained as a special case.
scientific article; zbMATH DE number 883891
scientific article