Constructing modular categories from orbifold data

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