For any 0-cell B in a 2-category , we introduce the notion of adjoint algebra . This is an algebra in the center of . We prove that if is a finite tensor category, this notion applied to the 2-category of -module categories coincides with the one introduced by Shimizu. As a consequence of this general approach, we obtain new results on the adjoint algebra for tensor categories.
Kyoto J. Math.
63(1):
117-154
(February 2023).
DOI: 10.1215/21562261-2022-0035
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