Example 11.10.1.13. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories, so that the projection maps $\operatorname{\mathcal{C}}\rightarrow \Delta ^0$ and $\operatorname{\mathcal{D}}\rightarrow \Delta ^0$ are both cartesian fibrations and cocartesian fibrations. For every functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$, the following conditions are equivalent:
The functor $F$ is an equivalence of cartesian fibrations over $\Delta ^0$.
The functor $F$ is an equivalence of cocartesian fibrations over $\Delta ^0$.
The functor $F$ is an equivalence of $\infty $-categories.