Remark 9.6.9.5. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $f: A \rightarrow B$ be a morphism of $\operatorname{\mathcal{C}}$ which admits a relative codiagonal $\gamma _{A/B}: B \coprod _{A} B \rightarrow B$ (Variant 7.6.2.23). If $S$ is a saturated collection of morphisms which contains $f$, then it also contains $\gamma _{A/B}$. This follows from the observation that there is a (levelwise) pushout diagram
\[ \xymatrix@R =50pt@C=50pt{ f \ar [r] \ar [d] & \operatorname{id}_ B \ar [d] \\ \operatorname{id}_{B} \ar [r] & \gamma _{A/B} } \]
in the $\infty $-category $\operatorname{Fun}( \Delta ^1, \operatorname{\mathcal{C}})$.