An invertible wannabe functor to a symmetric monoidal 2-category automatically extends to a projective 2-representation, recovering the Clifford/Fock construction over Lagrangian correspondences as a special case.
Lecture notes on two-dimensional defect TQFT
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Invertible projective 2-representations from invertible 2d TQFTs with defects
An invertible wannabe functor to a symmetric monoidal 2-category automatically extends to a projective 2-representation, recovering the Clifford/Fock construction over Lagrangian correspondences as a special case.