  Given any symmetry acting on a $d$-dimensional quantum field theory, there is
an associated $(d+1)$-dimensional topological field theory known as the
Symmetry TFT (SymTFT). The SymTFT is useful for decoupling the universal
quantities of quantum field theories, such as their generalized global
symmetries and 't Hooft anomalies, from their dynamics. In this work, we
explore the SymTFT for theories with Kramers-Wannier-like duality symmetry in
both $(1+1)$d and $(3+1)$d quantum field theories. After constructing the
SymTFT, we use it to reproduce the non-invertible fusion rules of duality
defects, and along the way we generalize the concept of duality defects to
\textit{higher} duality defects. We also apply the SymTFT to the problem of
distinguishing intrinsically versus non-intrinsically non-invertible duality
defects in $(1+1)$d.
