The balanced tensor product of module categories
type: Item
instance of: scholarly article
title: The balanced tensor product of module categories
zbMATH Open document ID: 1478.18006
DOI: 10.1215/21562261-2018-0006
author: Christopher L. Douglas
author: Noah Snyder
author: Christopher J. Schommer-Pries
published in: Kyoto Journal of Mathematics
publication date: 2019-07-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1406.4204
full work available at URL: https://projecteuclid.org/euclid.kjm/1538532153
review text: Let \(\mathcal{C}\) be a finite, rigid, monoidal linear category, \(\mathcal{M}\) a finite, right \(\mathcal{C}\)-module category and \(\mathcal{N}\)-a finite, left \(\mathcal{C}\)-module category. It is a well-known result by Etingof, Gelaki, Nikshych and Ostrik that any such \(\mathcal{M}\) is equivalent to the category of right modules over some algebra object \(A\) in \(\mathcal{C}\) (and analogously for \(\mathcal{N}\)). This elegantly written, clear article provides an alternative construction of the balanced tensor product of these module categories \(\mathcal{M} \boxtimes_\mathcal{C} \mathcal{N}\) in terms of bimodules over the algebra objects associated to each module category by EGNO's theorem. This result allows for an easier, explicit construction of the balanced product -- important for working in higher categorical constructions involving tensor categories.
reviewed by: Ana Ros Camacho
Mathematics Subject Classification ID: 18C40
Mathematics Subject Classification ID: 16B50
zbMATH DE Number: 7081625
zbMATH Keywords: module categories
zbMATH Keywords: balanced tensor product
zbMATH Keywords: algebra objects
zbMATH Keywords: Deligne tensor product
zbMATH Keywords: tensor categories
MaRDI profile type: Publication
OpenAlex ID: W3101913403
arXiv ID: 1406.4204
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description: scientific article