Symmetries are an essential aspect of almost all fields in modern day physics. Conventional symmetries are described by groups, and allow us to understand the classification of phases of matter in terms of symmetry breaking. The discovery of topological order in the late 80s challenged this paradigm, and more general mathematical structures were required to classify these exotic phases. Nowadays it is understood that these topologocal phases of matter are in fact also characterized in terms of symmetry breaking, with the catch that one has to use an appropriately generalized notion of symmetry. These symmetries which do not necessarily act on the full space and are not necessarily invertible are described using category theory. Using insights from quantum information theory and the language of tensor networks it is possible to explicitly represent these generalized symmetries in lattice models. With this language we were able to construct a general theory for duality in 1+1D quantum lattice models, establishing equivalences between seemingly unrelated theories. In this proposal, I aim to further generalize this point of view to higher dimensions, where many open questions regarding dualities remain. The language of generalized symmetry provides a new way to tackle old problems such as conformal invariance and integrability in lattice models, and has the potential to provide a rigorous basis for duality transformations in quantum field theory.