  Symmetry Topological Field Theory (SymTFT) is a framework to capture
universal features of quantum many-body systems by viewing them as a boundary
of topological order in one higher dimension. This has yielded numerous
insights in static low-energy settings. Here we study what SymTFT can reveal
about nonequilibrium, focusing on one-dimensional (1D) periodically driven
systems and their 2D SymTFTs. In driven settings, boundary conditions (BCs) can
be dynamical and can apply both spatially and temporally. We show how this
enters SymTFT via topological operators, which we then use to uncover several
new results. These include revealing time crystals (TCs) as systems with
symmetry-twisted temporal BCs, robust bulk ``dual TCs" in phases thought to be
only boundary TCs, generating drive dualities, or identifying 2D Floquet codes
as space-time duals to 1D systems with duality-twisted spatial BCs. We also
show how, by making duality-twisted BCs dynamical, non-Abelian braiding of
duality defects can enter SymTFT, leading to effects such as the exact pumping
of symmetry charges between a system and its BCs. We illustrate our ideas for
$\mathbb{Z}_2$-symmetric 1D systems, but our construction applies for any
finite Abelian symmetry.
