arXiv subjects

Alea Hofstetter

Publications and source records attributed to Alea Hofstetter.

2 recordsLinked to original sources

arXiv2026

The 2-categorical S-matrix of a braided fusion 1-category is a character table

The semisimple module categories over a braided fusion category $\mathcal{C}$ form a connected fusion 2-category $\text{Mod}(\mathcal{C})$. Its Drinfeld center $\mathcal{Z}(\text{Mod}(\mathcal{C}))$ is a braided fusion 2-category. To any braided fusion 2-category, Johnson-Freyd and Reutter arXiv:2105.15167v3 [math.QA] have associated a matrix-valued invariant, the 2-categorical $S$-matrix. In this short note we investigate this matrix of $\mathcal{Z}(\text{Mod}(\mathcal{C}))$ as an invariant for the braided fusion 1-category $\mathcal{C}$ and show that it reduces to the character table of the Müger center of $\mathcal{C}$.

math.QA↗

arXiv2025

Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology

These lecture notes are the product of a week-long learning workshop on the work of Johnson-Freyd and Reutter on the problem of the existence of minimal nondegenerate extensions of braided fusion categories (arXiv:2105.15167). They recount the mathematical arguments of the original paper from an expository angle, with background material covering the algebra and homotopy theory required to understand the statement and follow the proof. The notes are aimed at newcomers to the field of (braided) fusion 1- and 2-categories.

math.QA↗