Kerodon

Remark 2.2.7.8. Let $\operatorname{2Cat}'_{\operatorname{ULax}}$ denote the subcategory of $\operatorname{2Cat}_{\operatorname{Lax}}$ (and full subcategory of $\operatorname{2Cat}_{\operatorname{ULax}}$) whose objects are strictly unitary $2$-categories and whose morphisms are strictly unitary lax functors. It follows from Proposition 2.2.7.7 that the inclusion $\operatorname{2Cat}'_{\operatorname{ULax}} \hookrightarrow \operatorname{2Cat}_{\operatorname{ULax}}$ is an equivalence of categories.