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Example 5.5.7.2. Let $\operatorname{\mathcal{C}}$ be an $(\infty ,2)$-category and let $\operatorname{\mathcal{D}}$ be an $\infty$-category. Then every $2$-simplex of $\operatorname{\mathcal{D}}$ is thin, so every morphism of simplicial sets $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is a functor. In particular, when $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ are $\infty$-categories, Definition 5.5.7.1 reduces to Definition 1.4.0.1.