  We present the MMHT2015qed PDF set, resulting from the inclusion of QED
corrections to the existing set of MMHT Parton Distribution Functions (PDFs),
and which contain the photon PDF of the proton. Adopting an input distribution
from the LUXqed formulation, we discuss our methods of including QED effects
for the full, coupled DGLAP evolution of all partons with QED at
$\mathcal{O}(\alpha)$, $\mathcal{O}(\alpha\alpha_{S})$,
$\mathcal{O}(\alpha^2)$. While we find consistency for the photon PDF of the
proton with other recent sets, building on this we also present a set of QED
corrected neutron PDFs and provide the photon PDF separated into its elastic
and inelastic contributions. The effect of QED corrections on the other partons
and the fit quality is investigated, and the sources of uncertainty for the
photon are outlined. Finally we explore the phenomenological implications of
this set, giving the partonic luminosities for both the elastic and inelastic
contributions to the photon and the effect of our photon PDF on fits to high
mass Drell-Yan production, including the photon--initiated channel.
