The balanced tensor product of module categories

By Christopher L. Douglas, Christopher J. Schommer-Pries, Noah Snyder. Kyoto Journal of Mathematics, 2014

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The balanced tensor product M (x)_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 [x]_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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

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