The balanced tensor product of two modules over an algebra is the vector space corepresenting -balanced bilinear maps out of the product . The balanced tensor product of two module categories over a monoidal linear category is the linear category corepresenting -balanced right-exact bilinear functors out of the product category . We show that the balanced tensor product can be realized as a category of bimodule objects in , provided the monoidal linear category is finite and rigid.
"The balanced tensor product of module categories." Kyoto J. Math. 59 (1) 167 - 179, April 2019. https://doi.org/10.1215/21562261-2018-0006