Constructing modular categories from orbifold data

The notion of an orbifold datum {A} in a modular fusion category C was introduced as part of a generalised orbifold construction for Reshetikhin–Turaev TQFTs by Carqueville, Runkel, and Schaumann in 2018. In this paper, given a simple orbifold datum {A} in C , we introduce a ribbon category C_{{A}} and show that it is again a modular fusion category. The definition of C_{{A}} is motivated by properties of Wilson lines in the generalised orbifold. We analyse two examples in detail: (i) when {A} is given by a simple commutative Δ -separable Frobenius algebra A in C ; (ii) when {A} is an orbifold datum in C = Vect , built from a spherical fusion category S . We show that, in case (i), C_{{A}} is ribbon-equivalent to the category of local modules of A , and, in case (ii), to the Drinfeld centre of S . The category CC_{{A}} thus unifies these two constructions into a single algebraic setting.