We investigate the relation between projective and anomalous representations of categories, and show how to any anomaly J: C → 2Vect one can associate an extension C^J of C and a subcategory C^J_ST of C^J with the property that: (i) anomalous representations of C with anomaly J are equivalent to Vect-linear functors E: C^J → Vect, and (ii) these are in turn equivalent to linear representations of C^J_ST where "J acts as scalars". This construction, inspired by and generalizing the technique used to linearize anomalous functorial field theories in the physics literature, can be seen as a multi-object version of the classical relation between projective representations of a group G, with given 2-cocycle α, and linear representations of the central extension G^α of G associated with α.
Keywords: Projective representations; anomalies
2020 MSC: 18D25
Theory and Applications of Categories, Vol. 45, 2026, No. 37, pp 1515-1554.
Published 2026-06-05.
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