Kerodon

Remark 1.5.3.11. Let us abuse notation by identifying each ordinary category $\operatorname{\mathcal{E}}$ with the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{E}})$. In this case, Corollary 1.5.3.5 implies that when $\operatorname{\mathcal{C}}$ is an $\infty $-category and $\operatorname{\mathcal{D}}$ is an ordinary category, then we have a canonical isomorphism $\operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}}) \simeq \operatorname{Fun}( \mathrm{h} \mathit{\operatorname{\mathcal{C}}}, \operatorname{\mathcal{D}})$. In particular, the functor $\infty $-category $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ is also an ordinary category.