Variant 7.6.3.19 (Relative Codiagonals). Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $f: Y \rightarrow X$ be a morphism of $\operatorname{\mathcal{C}}$, and suppose that there exists a pushout square
\[ \xymatrix { Y \ar [r]^{f} \ar [d]^{f} & X \ar [d] \\ X \ar [r] & X \coprod _{Y} X. } \]
Applying the construction of Notation 7.6.3.18 in the opposite $\infty $-category $\operatorname{\mathcal{C}}^{\operatorname{op}}$, we obtain a morphism $\gamma _{Y/X}: X \coprod _{Y} X \rightarrow X$ which we will refer to as the relative codiagonal of the morphism $f$.