  We investigate the first-order correction to the anomalous Hall conductivity
of 2D massive Dirac fermions arising from electron-electron interactions. In a
fully gapped system in the limit of zero temperature, we find that this
correction vanishes, confirming the absence of perturbative corrections to the
topological Hall conductivity. At finite temperature or chemical potential, we
find that the total Hall response decays faster than in the non-interacting
case, depending on the strength of electron-electron interactions. These
features, which could potentially be observed experimentally, show the
importance of two-body interactions for anomalous Hall transport.
