A new SymSET-based construction shows that changing symmetry fractionalization classes can change fusion rules of self-duality defects under non-invertible gauging, yielding new fusion categories such as Rep D16 and Rep SD16.
Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier D\'ecoppet and Theo Johnson-Freyd)
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abstract
We study group graded extensions of fusion 2-categories. As an application, we obtain a homotopy theoretic classification of fermionic strongly fusion 2-categories. We examine various examples in detail.
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SymSETs and self-dualities under gauging non-invertible symmetries
A new SymSET-based construction shows that changing symmetry fractionalization classes can change fusion rules of self-duality defects under non-invertible gauging, yielding new fusion categories such as Rep D16 and Rep SD16.