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

Domenico Fiorenza; Chetan Vuppulury

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arXiv · 2509.16626

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

Domenico Fiorenza·Chetan Vuppulury

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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.

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BibTeX RIS

Domenico Fiorenza, Chetan Vuppulury. 2025-09-20. Invertible projective 2-representations from invertible 2d TQFTs with defects. https://arxiv.org/abs/2509.16626

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