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In Carqueville et al., arXiv:1809.01483, the notion of an orbifold datum$\mathbb{A}$ in a modular fusion category $\mathcal{C}$ was introduced as partof a generalised orbifold construction for Reshetikhin-Turaev TQFTs. In thispaper, given a simple orbifold datum $\mathbb{A}$ in $\mathcal{C}$, weintroduce a ribbon category $\mathcal{C}_{\mathbb{A}}$ and show that it isagain a modular fusion category. The definition of $\mathcal{C}_{\mathbb{A}}$is motivated by properties of Wilson lines in the generalised orbifold. Weanalyse two examples in detail: (i) when $\mathbb{A}$ is given by a simplecommutative $\Delta$-separable Frobenius algebra $A$ in $\mathcal{C}$; (ii)when $\mathbb{A}$ is an orbifold datum in $\mathcal{C} = \operatorname{Vect}$,built from a spherical fusion category $\mathcal{S}$. We show that in case (i),$\mathcal{C}_{\mathbb{A}}$ is ribbon-equivalent to the category of localmodules of $A$, and in case (ii), to the Drinfeld centre of $\mathcal{S}$. Thecategory $\mathcal{C}_{\mathbb{A}}$ thus unifies these two constructions into asingle algebraic setting.

Constructing modular categories from orbifold data