The adjoint algebra for 2-categories

Noelia Bortolussi; Martín Mombelli

doi:10.1215/21562261-2022-0035

February 2023 The adjoint algebra for 2-categories

Noelia Bortolussi, Martín Mombelli

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Abstract

For any 0-cell B in a 2-category $\mathcal{B}$ , we introduce the notion of adjoint algebra ${\mathcal{A}d_{B}}$ . This is an algebra in the center of $\mathcal{B}$ . We prove that if $\mathcal{C}$ is a finite tensor category, this notion applied to the 2-category ${_{\mathcal{C}}}\mathrm{Mod}$ of $\mathcal{C}$ -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.

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Noelia Bortolussi and Martín Mombelli "The adjoint algebra for 2-categories," Kyoto Journal of Mathematics 63(1), 117-154, (February 2023). https://doi.org/10.1215/21562261-2022-0035

Received: 12 May 2020; Accepted: 22 March 2021; Published: February 2023

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