A duality of quantale-enriched categories (Q456860)

Lawson duality for continuous dcpos is shown to be a special case of a much broader duality theorem. Categories enriched in a quantale provide a uniform treatment for many familiar structures, including generalized metric spaces and ultra-metric spaces, by varying the quantale in which the categories are enriched. The authors show that for a suitable class of modules \(J\), the category of \(J\)-cocomplete quantale-enriched categories and \(J\)-continuous functors is self-dual. The classical Lawson duality is then obtained for a particular specialization of the quantale and the authors also include an interesting discussion resulting from other choices of quantale.