The balanced tensor product of module categories

The balanced tensor product M circle times(A) N of two modules over an algebra A is the vector space corepresenting A-balanced bilinear maps out of the product M x N.The balanced tensor product M boxed times(C) N of two module categories over a monoidal linear category C is the linear category corepresenting C-balanced right-exact bilinear functors out of the product category M x N. We show that the balanced tensor product can be realized as a category of bimodule objects in C, provided the monoidal linear category is finite and rigid.