Braided categorical groups and strictifying associators

Oliver Braunling

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arXiv · 1911.00130

Braided categorical groups and strictifying associators

Oliver Braunling

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Abstract

A key invariant of a braided categorical group is its quadratic form, introduced by Joyal and Street. We show that the categorical group is braided equivalent to a simultaneously skeletal and strictly associative one if and only if the polarization of this quadratic form is the symmetrization of a bilinear form. This generalizes the result of Johnson-Osorno that all Picard groupoids can simultaneously be strictified and skeletalized, except that in the braided case there is a genuine obstruction.

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Oliver Braunling. 2019-10-31. Braided categorical groups and strictifying associators. https://arxiv.org/abs/1911.00130

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