Anomalous Actions of Groups on Tensor Categories
For a group $G$ and a 4-cocycle $π\in Z^{4}(G,\mathbb{k}^{\times})$, a $π$-anomalous action of $G$ on a linear monoidal category $C$ is a linear monoidal 2-functor between 3-groups $3\text{-Gr}(G,π)\rightarrow \text{2-Aut}_\otimes(C)$ where the latter denotes the 3-group of autoequivalences of $C$. Given $G$ and $π$, we provide a method of constructing anomalous actions of $3\text{-Gr}(G,π)$ on a tensor categories.
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