Anomalous representations of a category with anomaly J are equivalent to Vect-linear functors on the extension C^J and to scalar representations of the Stolz-Teichner subcategory C^J_ST.
The chiral anomaly of the free fermion in functorial field theory
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Projective and anomalous representations of categories and their linearizations
Anomalous representations of a category with anomaly J are equivalent to Vect-linear functors on the extension C^J and to scalar representations of the Stolz-Teichner subcategory C^J_ST.