## Kyoto Journal of Mathematics

### The balanced tensor product of module categories

#### Abstract

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

#### Article information

Source
Kyoto J. Math., Volume 59, Number 1 (2019), 167-179.

Dates
Revised: 5 September 2016
Accepted: 12 January 2017
First available in Project Euclid: 3 October 2018

https://projecteuclid.org/euclid.kjm/1538532153

Digital Object Identifier
doi:10.1215/21562261-2018-0006

Mathematical Reviews number (MathSciNet)
MR3934626

Zentralblatt MATH identifier
07081625

#### Citation

Douglas, Christopher L.; Schommer-Pries, Christopher; Snyder, Noah. The balanced tensor product of module categories. Kyoto J. Math. 59 (2019), no. 1, 167--179. doi:10.1215/21562261-2018-0006. https://projecteuclid.org/euclid.kjm/1538532153

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