categories: Picard group of a ringoid

[Bill Rowan <rowan@transbay.net>]

Tensor product gives a monoid structure on the class of isomorphism types
of R,R-bimodules, for a ring or ringoid R.  Restricting to those elements
for which there is a two-sided inverse yields a group.  I am inclined to call
this the nonabelian Picard group and denote it by NPic(R).  If we start with
a commutative ring R, then the usual Picard group of R, Pic(R), can be viewed
as an abelian subgroup of NPic(R).

Has anyone seen this before?  Does anyone have some other idea about what this
should be called?

Bill Rowan