Categorical extension of dualities: From Stone to de Vries and beyond, II

Abstract

Under a general categorical procedure for the extension of dual equivalences as presented in this paper's predecessor, a new algebraically defined category is established that is dually equivalent to the category LKHaus of locally compact Hausdorff spaces and continuous maps, with the dual equivalence extending a Stone-type duality for the category of extremally disconnected locally compact Hausdorff spaces and continuous maps. The new category is then shown to be isomorphic to the category CLCA of complete local contact algebras and suitable morphisms. Thereby, a new proof is presented for the equivalence LKHaus≃CLCAop that was obtained by the first author more than a decade ago. Unlike the morphisms of CLCA, the morphisms of the new category and their composition law are very natural and easy to handle.