  We present a framework to systematically investigate higher categorical
symmetries in two-dimensional spin systems. Though exotic, such generalised
symmetries have been shown to naturally arise as dual symmetries upon gauging
invertible symmetries. Our framework relies on an approach to dualities whereby
dual quantum lattice models only differ in a choice of module 2-category over
some input fusion 2-category. Given an arbitrary two-dimensional spin system
with an ordinary symmetry, we explain how to perform the (twisted) gauging of
any of its sub-symmetries. We then demonstrate that the resulting model has a
symmetry structure encoded into the Morita dual of the input fusion 2-category
with respect to the corresponding module 2-category. We exemplify this approach
by specialising to certain finite group generalisations of the transverse-field
Ising model, for which we explicitly define lattice symmetry operators
organised into fusion 2-categories of higher representations of higher groups.
