By Kursat Sozer and Alexis Virelizier

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).

September 28, 2022

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Monoidal categories graded by crossed modules and 3-dimensional HQFTs

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