Remark 2.2.7.9. Let $G$ be a group and let $\Gamma $ be an abelian group with an action of $G$. When applied to the $2$-categories described in Example 2.2.7.4, Proposition 2.2.7.7 reduces to the assertion that every $3$-cocycle $\alpha : G \times G \times G \rightarrow \Gamma $ is cohomologous to a normalized $3$-cocycle $\alpha ': G \times G \times G \rightarrow \Gamma $.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$