  We consider topological phases in periodically driven (Floquet) systems
exhibiting many-body localization, protected by a symmetry $G$. We argue for a
general correspondence between such phases and topological phases of undriven
systems protected by symmetry $\mathbb{Z} \rtimes G$, where the additional
$\mathbb{Z}$ accounts for the discrete time translation symmetry. Thus, for
example, the bosonic phases in $d$ spatial dimensions without intrinsic
topological order (SPT phases) are classified by the cohomology group
$H^{d+1}(\mathbb{Z} \rtimes G, \mathrm{U}(1))$. For unitary symmetries, we
interpret the additional resulting Floquet phases in terms of the
lower-dimensional SPT phases that are pumped to the boundary during one time
step. These results also imply the existence of novel symmetry-enriched
topological (SET) orders protected solely by the periodicity of the drive.
