Remark 2.2.8.8. Let $\operatorname{\mathcal{C}}$ be a $2$-category. Then every lax functor of bicategories $F: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{C}}$ is automatically a functor. Consequently, there is no need to distinguish between functors and lax functors when working in the setting of $2$-categories.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$