Definition 1.5.3.8. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories. It follows from Theorem 1.5.3.7 that the simplicial set $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ is also an $\infty $-category. We will refer to $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ as the $\infty $-category of functors from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$.
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