$\chi_{f,g}$ are psedonatural equivalences, we can simultaneously provide the datum $\Pi_{f,g}$ and the pseudonatural equivalences $\chi'_{f,g}:L_f\circ L_g\to L_{fg}$, $f, g\in G$. Now, axiom \[Pi-axiom\] uniquely determines the modifications $\omega_{f,g,h}'$. Axiom \[omega-axiom\] follows from the corresponding axioms of $G$-action via $({{\mathcal F}},\chi,\omega)$. The pseudofunctor $({{\mathcal H}},\gamma, \Pi ):{{\mathcal B}}\to {{\mathcal B}}'$ is a $G$-biequivalence by construction.

\[action with 2-functors\] Every 2-category with a $G$-action is $G$-biequivalent to a 2-category where $G$ acts by 2-functors, that is, all $F_g$ are 2-functors.

By the coherence of theorem for pseudofunctor, see [@tricat-nick Section 2.3], every bicategory ${{\mathcal B}}$ is biequivalent to a 2-category $\operatorname{st}({{\mathcal B}})$ such that every pseudo-functor $F:\operatorname{st}({{\mathcal B}})\to \operatorname{st}({{\mathcal B}})$ is pseudo-natural equivalent to a 2-functor. Then applying Lemma \[transport\] we can transport the action of ${{\mathcal B}}$ to a $G$-biequivalent action on $\operatorname{st}({{\mathcal B}})$ where $G$ acts by 2-functors.

Coherence for group actions on 2-categories {#Section:coherence}
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The main result of this section is to prove the following coherence theorem for a group action on a 2-category.

\[coherence-groupact\] Let $G$ be a group. Every 2-category with an action of $G$ is $G$-biequivalent to a 2-category with a strict action of $G$.

Assume ${{\mathcal B}}$ is a 2-category equipped with a 