2000 character limit reached
The Classification of Fusion 2-Categories (2411.05907v1)
Published 8 Nov 2024 in math.CT, cond-mat.str-el, hep-th, and math.QA
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 $\mathrm{B}\mathbb{Z}/2$-equivariant spaces. Rank finiteness and Ocneanu rigidity for fusion 2-categories are immediate corollaries of our classification.