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.

中文翻译：

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二次形式的奎因公式和Abelian 3-Cocycles

在尖头编织融合类别中，了解简单的自对称编织在理论上足以重构关联器并在整个类别上编织（直到通过编织单等分自对等进行扭曲）。我们仅在给出此类输入的情况下解决该问题，以提供显式的关联器公式。奎因在有限的许多简单情况下解决了这个问题。我们以各种方式对此进行谴责和概括。特别是，我们证明了奎因联结器的额外对称性仍然可以安排，以容纳一个具有无限多个简单同等类的情况。