Monoidal categories graded by crossed modules and 3-dimensional HQFTs

Kursat Sozer (1) , Alexis Virelizier (2)

1 Département de Mathématiques - EPFL
2 LPP - Laboratoire Paul Painlevé - UMR 8524

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).

Mots clés: category; homotopy; field theory; graded

Domaines: Topologie géométrique [math.GT]

Kursat Sozer, Alexis Virelizier. Monoidal categories graded by crossed modules and 3-dimensional HQFTs. Adv.Math., 2023, 428, pp.109155. ⟨10.1016/j.aim.2023.109155⟩. ⟨hal-03736640⟩