Corollary 1.5.3.4. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be categories. Then there is a canonical isomorphism of categories
\[ \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}}) \xrightarrow {\sim } \mathrm{h} \mathit{\operatorname{Fun}}( \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}), \operatorname{N}_{\bullet }(\operatorname{\mathcal{D}}) ). \]