Kerodon

Remark 2.2.5.6. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $2$-categories. Then the collection $\operatorname{Hom}_{ \operatorname{2Cat}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ of functors from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$ can be identified with the set of objects of a certain $2$-category $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$, called the $2$-category of functors from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$. We will return to this point in more detail in §.