Defining internal symmetry in a quantum theory through the lens of topological defects opens the door to generalised notions of symmetry, including some arising from non-invertible transformations, and enables a calculus that leverages well-established methods from topological quantum field theory. In d spatial dimensions, the framework of fusion d-category theory is believed to offer an axiomatisation for finite non-invertible symmetries. Though seemingly exotic, such non-invertible symmetries can be shown to naturally arise as dual symmetries upon gauging invertible symmetries. In this talk, I will present a framework to systematically investigate these aspects in quantum lattice models.