Quinn’s Formula and Abelian 3-Cocycles for Quadratic Forms


In 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.


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Correspondence to Oliver Braunling.

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The author was supported by DFG GK1821 “Cohomological Methods in Geometry”. Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

Presented by: Alistair Savage

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Braunling, O. Quinn’s Formula and Abelian 3-Cocycles for Quadratic Forms. Algebr Represent Theor (2020). https://doi.org/10.1007/s10468-020-10001-1

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  • Braided categorical group
  • Picard groupoid
  • Strictification
  • Skeletalization
  • Associator

Mathematics Subject Classification (2010)

  • 18D10
  • 19D23