Anomalous Actions of Groups on Tensor Categories

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