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arXiv · 1406.4204

The balanced tensor product of module categories

Christopher L. Douglas·Christopher Schommer-Pries·Noah Snyder
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Abstract

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.

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Christopher L. Douglas, Christopher Schommer-Pries, Noah Snyder. 2014-06-17. The balanced tensor product of module categories. https://doi.org/10.1215/21562261-2018-0006

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