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arXiv · 2509.10636

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

Diogo Andrade·Julia Bierent·Jennifer Brown·Tudor Caba·Matthew Cellot·Jonathan Davies·Adrien DeLazzer Meunier·Jannik Gröne·Benjamin Haïoun·Alea Hofstetter·Theo Johnson-Freyd·David Jordan·Tessa Kammermeier·Patrick Kinnear·Cameron Krulewski·Theodoros Lagiotis·Leon Liu·Adrià Marín Salvador·Nivedita·David Reutter·Lorenzo Riva·Iordanis Romaidis·Jack Romo·Sean Sanford·Michail Tagaris·Daniel Teixeira·Jackson van Dyke·Matthias Vancraeynest·Chetan Vuppulury·Matthew Yu·Markus Zetto
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Abstract

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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BibTeXRIS

Diogo Andrade, Julia Bierent, Jennifer Brown, Tudor Caba, Matthew Cellot, Jonathan Davies, Adrien DeLazzer Meunier, Jannik Gröne, Benjamin Haïoun, Alea Hofstetter, Theo Johnson-Freyd, David Jordan, Tessa Kammermeier, Patrick Kinnear, Cameron Krulewski, Theodoros Lagiotis, Leon Liu, Adrià Marín Salvador, Nivedita, David Reutter, Lorenzo Riva, Iordanis Romaidis, Jack Romo, Sean Sanford, Michail Tagaris, Daniel Teixeira, Jackson van Dyke, Matthias Vancraeynest, Chetan Vuppulury, Matthew Yu, Markus Zetto. 2025-09-12. Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology. https://arxiv.org/abs/2509.10636

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