Abstract: Pivotal bicategories are a natural setting within which to study two-dimensional TQFTs with defects. Inspired by the seminal work of Fröhlich, Fuchs, Runkel and Schweigert on rational CFT, we describe a completion procedure for certain bicategories that captures and generalises orbifolding by finite symmetry groups. In the context of Landau-Ginzburg models, examples include "discrete torsion" orbifolds, as well as the construction of new equivalences for categories of matrix factorisations of ADE singularities.

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