Abstract
The symmetries of a system are of significant interest to characterize its various properties. Traditionally, we resort to the mathematical construction known as a ‘group’ and its representations to study the symmetries of a system. We find the notion of traditional group-like symmetries put to use in Landau’s theory of phase transitions. However, certain cases are not adequately explained by Landau’s theory, such as topologically-ordered states. Such phases can be described using the mathematical objects called ‘categories’. In this talk, we aim to expand on this idea, giving details of categories, in particular, fusion categories. Details of the data required to specify a fusion category shall be studied. We further explore generalized symmetries and discuss regimes where one may expect to find such symmetries. We shall also take a concrete example of a model depicting categorical symmetry, where we attempt to explore the phase diagram.