English

Braided categorical groups and strictifying associators

Category Theory 2019-11-04 v1 Quantum Algebra

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.

Keywords

Cite

@article{arxiv.1911.00130,
  title  = {Braided categorical groups and strictifying associators},
  author = {Oliver Braunling},
  journal= {arXiv preprint arXiv:1911.00130},
  year   = {2019}
}
R2 v1 2026-06-23T12:01:41.782Z