Since algebras may be identified with one-object categoriesinternal to vector spaces, it is sometimes useful to regard as a strict 2-category, namely as a full sub-2-category of the 2-category . In this case the 2-morphisms between morphisms of algebras come from “intertwiners”: inner endomorphisms of the target algebra.
Precisely analogous statements hold for the category Grp of groups.
With regarded as a strict 2-category this way there is a canonical 2-functor
Alg \hookrightarrow Bimod
to the category Bimod, which sends algebra homomorphisms to the - bimodule . This exhibits as a framed bicategory in the sense of Shulman.