Title: Bicategories of bimodules
The notion of a bicategory is a generalisation of the notion
of a category which is obtained by allowing the composition of
morphisms to be associative and unital up to isomorphism,
rather than strictly. This generalisation is useful to capture
many naturally-occurring mathematical structures. For example,
there is a bicategory with rings as objects and bimodules as
morphisms, in which composition of morphisms is given by
tensor product of bimodules.
In this talk, after introducing bicategories, I will review the so-called "bimodule construction” for bicategories, present some examples of it and some new results, based on joint work with Andre’ Joyal.