Description
In this talk, I will discuss a notion of topological order enriched by a non-invertible symmetry. For invertible symmetry enriched topological order, a well-established formalisation is available in terms of a G-crossed braided fusion category. By considering the condensation of an arbitrary algebra of charges in a quantum double model, a generalisation of this framework naturally emerges. In particular, I will show the topological order after condensation can be described as a hypergroup-graded extension of the category of deconfined excitations. This has a hypergroup symmetry which acts in a typically non-invertible manner on the confined and deconfined excitations in a way that is compatible with the grading. I will illustrate the general theory through a simple example.