Monoidal categories graded by crossed modules and 3-dimensional HQFTs

Kursat Sozer; Alexis Virelizier

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arXiv · 2207.06534

Monoidal categories graded by crossed modules and 3-dimensional HQFTs

Kursat Sozer·Alexis Virelizier

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Abstract

Given a crossed module $\chi$, we introduce $\chi$-graded monoidal categories and $\chi$-fusion categories. We use spherical $\chi$-fusion categories to construct (via the state sum method) 3-dimensional Homotopy Quantum Field Theories with target the classifying space $B\chi$ of the crossed module $\chi$ (which is a homotopy 2-type).

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Kursat Sozer, Alexis Virelizier. 2022-07-13. Monoidal categories graded by crossed modules and 3-dimensional HQFTs. https://arxiv.org/abs/2207.06534

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