The Bicategory of m-regular Involutive Quantales

Abstract

It is well known that rings are the objects of a bicategory, whose arrows are bimodules, composed through the bimodule tensor product. We give an analogous bicategorical description of m-regular involutive quantales. The upshot is that known definition of Morita equivalence for this case amounts to isomorphism of objects in the pertinent bicategory.