of the tensor category ${{\mathcal C}}$.

Given a 2-category ${{\mathcal B}}$ and a 2-monad $T:{{\mathcal B}}\to {{\mathcal B}}$ on ${{\mathcal B}}$, in [@MN], the notion of the *equivariantization* 2-category ${{\mathcal B}}^T$ was presented. The equivariantization of a 2-category by a group was studied later in [@HSV].

One of the purposes of the paper is to explicitly describe an action of a group $G$ on a 2-category ${{\mathcal B}}$, and describe all ingredients of the resulting equivariantization 2-category ${{\mathcal B}}^G$. An action of a group $G$ on a 2-category ${{\mathcal B}}$ consists of

-   a family of pseudofunctors $F_g:{{\mathcal B}}\to {{\mathcal B}}$, $g\in G$,

-   pseudonatural equivalences $\chi_{g,h}: F_g\circ F_h\to F_{gh}$,

-   invertible modifications $$\omega_{g,h,f}: \chi_{gh,f} \circ (\chi_{g,h} {{\otimes}}{\mbox{\rm id\,}}_{F_f }) \Rightarrow \chi_{g,hf}\circ ({\mbox{\rm id\,}}_{F_g} {{\otimes}}\chi_{h,f}),$$

for any $g, h, f\in G$, satisfying certain axioms. We also prove a coherence theorem for group action, stating that there exists another equivalent action of $G$ on ${{\mathcal B}}$, such that all pseudofunctors $F_g$ involved in the group action are 2-functors, $ F_g\circ F_h= F_{gh}$, and $\chi_{g,h}$, $\omega_{g,h,f}$ are all the identity. As an application of the coherent theorem we prove that associated to every action of group $G$ on a 2-category ${{\mathcal B}}$ 