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

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arxiv 2509.10636 v1 pith:C7DFKEWL submitted 2025-09-12 math.QA math.CTmath.RT

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

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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.

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