  We establish an algebra-isomorphism between the complexified Grothendieck
ring F of certain bimodule categories over a modular tensor category and the
endomorphism algebra of appropriate morphism spaces of those bimodule
categories. This provides a purely categorical proof of a conjecture by Ostrik
concerning the structure of F.
  As a by-product we obtain a concrete expression for the structure constants
of the Grothendieck ring of the bimodule category in terms of endomorphisms of
the tensor unit of the underlying modular tensor category.
