Abstract:
Given a suitable ribbon category C and a so-called orbifold datum A in C, one can obtain a new ribbon category C_A. This construction subsumes several well-known examples, such as the Drinfeld centre of a spherical fusion category, passing to the category of local modules of a commutative algebra in C, and equivariantisation of a G-crossed ribbon category. In a 3d TFT Z which has C as category of line defects, A can be interpreted as a "gaugeable (possibly non-invertible) symmetry", and C_A as the line defects in the gauged theory Z/A. The state spaces of Z/A can be described in terms of commuting projector Hamiltonians acting on state spaces of Z, giving a variant of the Levin-Wen construction.
This is joint work with N. Carqueville, V. Mulevicius, G. Schaumann, D. Scherl, and T. Voß.
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