Example 7.7.3.11. Let $\operatorname{QCat}$ denote the (cartesian closed) category of (small) $\infty $-categories (Example 7.7.3.3). Let us regard $\operatorname{QCat}$ as equipped with the simplicial enrichment given in Construction 5.5.4.1, with morphism spaces given by the formula
\[ \operatorname{Hom}_{\operatorname{QCat}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})_{\bullet } = \operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})^{\simeq }. \]
This simplicial enrichment satisfies the hypotheses of Remark 7.7.3.9, so the $\infty $-category $\operatorname{\mathcal{QC}}= \operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{QCat})$ is cartesian closed.