Invertible projective 2-representations from invertible 2d TQFTs with defects

Abstract

We investigate invertible projective representations and their 2-categorical analogues using the language of TQFTs with defects. The main result is a freeness property for invertible projective representatios. While trivial in the 1-categorical setting, this result becomes interesting for 2-representations: as an application, only relying only on invertibility of Clifford algebras and Fock bimodules in the Morita 2-category of super vector spaces we recover Ludewig--Roos' result that the Clifford/Fock construction is a projective 2-representation of the category of Lagrangian correspondences.

31 pages. A critical inaccuracy in the proof of Theorem 4.32 from v1 has been fixed. We thank Matthias Ludewig for having pointed our attention to this inaccuracy