Warning 2.2.4.6. The terminology of Definition 2.2.4.5 is not standard. In [MR0220789], BĂ©nabou uses the term *morphism* for what we call a lax functor of $2$-categories, *homomorphism* for what we call a functor of $2$-categories, and *strict homomorphism* for what we call a strict functor of $2$-categories. Other authors refer to functors of $2$-categories (in the sense of Definition 2.2.4.5) as *weak functors* or *pseudofunctors* (to avoid confusion with the notion of strict functor).

$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$