Corollary 9.2.7.23. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be an inner fibration of $\infty $-categories and let $f$ and $g$ be morphisms of $\operatorname{\mathcal{E}}$. Assume either that $f$ is $U$-cocartesian or that $g$ is $U$-cartesian. Then:
If $U(f)$ is left orthogonal to $U(g)$ in the $\infty $-category $\operatorname{\mathcal{C}}$, then $f$ is left orthogonal to $g$ in the $\infty $-category $\operatorname{\mathcal{E}}$.
If $U(f)$ is weakly left orthogonal to $U(g)$ in the $\infty $-category $\operatorname{\mathcal{C}}$, then $f$ is weakly left orthogonal to $g$ in the $\infty $-category $\operatorname{\mathcal{E}}$.