Kyoto Journal of Mathematics

The balanced tensor product of module categories

Christopher L. Douglas, Christopher Schommer-Pries, and Noah Snyder

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The balanced tensor product MAN of two modules over an algebra A is the vector space corepresenting A-balanced bilinear maps out of the product M×N. The balanced tensor product MCN 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×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.

Article information

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

Received: 1 February 2016
Revised: 5 September 2016
Accepted: 12 January 2017
First available in Project Euclid: 3 October 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]
Secondary: 13C60: Module categories

tensor category module category Deligne tensor product Kelly tensor product


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.

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