  We argue that the static non-linear Hall conductivity can always be
represented as a vector in two-dimensions and as a pseudo-tensor in
three-dimensions independent of its microscopic origin. In a single band model
with a constant relaxation rate this vector or tensor is proportional to the
Berry curvature dipole \cite{Sodemann_2015}. Here, we develop a quantum
Boltzmann formalism to second order in electric fields. We find that in
addition to the Berry Curvature Dipole term, there exist additional disorder
mediated corrections to the non-linear Hall tensor that have the same scaling
in impurity scattering rate. These can be thought of as the non-linear
counterparts to the side-jump and skew-scattering corrections to the Hall
conductivity in the linear regime. We illustrate our formalism by computing the
different contributions to the non-linear Hall conductivity of two-dimensional
tilted Dirac fermions.
