The Classification of Fusion 2-Categories
Category Theory
2024-11-12 v1 Strongly Correlated Electrons
High Energy Physics - Theory
Quantum Algebra
Abstract
We classify (multi)fusion 2-categories in terms of braided fusion categories and group cohomological data. This classification is homotopy coherent -- we provide an equivalence between the 3-groupoid of (multi)fusion 2-categories up to monoidal equivalences and a certain 3-groupoid of commuting squares of -equivariant spaces. Rank finiteness and Ocneanu rigidity for fusion 2-categories are immediate corollaries of our classification.
Keywords
Cite
@article{arxiv.2411.05907,
title = {The Classification of Fusion 2-Categories},
author = {Thibault D. Décoppet and Peter Huston and Theo Johnson-Freyd and Dmitri Nikshych and David Penneys and Julia Plavnik and David Reutter and Matthew Yu},
journal= {arXiv preprint arXiv:2411.05907},
year = {2024}
}
Comments
50 pages