Abstract
AbstractIn pointed braided fusion categories knowing the self-symmetry braiding of simples is theoretically enough to reconstruct the associator and braiding on the entire category (up to twisting by a braided monoidal auto-equivalence). We address the problem to provide explicit associator formulas given only such input. This problem was solved by Quinn in the case of finitely many simples. We reprove and generalize this in various ways. In particular, we show that extra symmetries of Quinn’s associator can still be arranged to hold in situations where one has infinitely many isoclasses of simples.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Reference19 articles.
1. Baues, H.: Combinatorial homotopy and 4-dimensional complexes, De Gruyter Expositions in Mathematics, vol. 2. Walter de Gruyter & Co., Berlin (1991). With a preface by Ronald Brown. MR 1096295
2. Bulacu, D., Caenepeel, S., Torrecillas, B.: The braided monoidal structures on the category of vector spaces graded by the Klein group, Proc. Edinb. Math. Soc. (2) 54(3), 613–641. MR 2837470 (2011)
3. Braunling, O.: Braided categorical groups and strictifying associators. Homol. Homotopy Appl. 22(2), 295–321 MR 4098945 (2020)
4. Drinfeld, V., Gelaki, S., Nikshych, D., Ostrik, V.: On braided fusion categories. I, Selecta Math. (N.S.) 16(1), 1–119. MR 2609644 (2010)
5. Etingof, P., Gelaki, S., Nikshych, D., Ostrik, V.: Tensor categories, Mathematical Surveys and Monographs, vol. 205. American Mathematical Society, Providence (2015). MR 3242743
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