Kerodon

Warning 2.2.4.6. The terminology of Definition 2.2.4.5 is not standard. In [MR0220789], Bénabou 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).