Kerodon

Example 5.4.7.2. 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 5.4.7.1 reduces to Definition 1.5.0.1.