A dual equivalence for cofinal quantum B-algebras

Abstract

This paper introduces weak logical algebraic domains and a special class of quantum B-algebras, namely, cofinal quantum B-algebras. It proves that there is a dual equivalence between the category of cofinal quantum B-algebras and that of weak logical algebraic domains. In particular, the category of residuated posets is shown to be dual equivalent to that of logical algebraic domains. This correspondence generalizes the classical duality of posets and algebraic domains.