  We explore non-invertible symmetries in two-dimensional lattice models with
subsystem $\mathbb Z_2$ symmetry. We introduce a subsystem $\mathbb
Z_2$-gauging procedure, called the subsystem Kramers-Wannier transformation,
which generalizes the ordinary Kramers-Wannier transformation. The
corresponding duality operators and defects are constructed by gaugings on the
whole or half of the Hilbert space. By gauging twice, we derive fusion rules of
duality operators and defects, which enriches ordinary Ising fusion rules with
subsystem features. Subsystem Kramers-Wannier duality defects are mobile in
both spatial directions, unlike the defects of invertible subsystem symmetries.
We finally comment on the anomaly of the subsystem Kramers-Wannier duality
symmetry, and discuss its subtleties.
