  The familiar adjunction between ordered sets and completely distributive
lattices can be extended to generalised metric spaces, that is, categories
enriched over a quantale (a lattice of "truth values"), via an appropriate
distributive law between the "down-set" monad and the "up-set" monad on the
category of quantale-enriched categories. If the underlying lattice of the
quantale is completely distributive, and if powers distribute over non-empty
joins in the quantale, then this distributive law can be concretely formulated
in terms of operations, equations and choice functions, similar to the familiar
distributive law of lattices.
