  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.
