Definition 8.1.6.5. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $L$ and $R$ be collections of morphisms of $\operatorname{\mathcal{C}}$. We will say that $L$ and $R$ are pushout-compatible if, for every morphism $f_0: X \rightarrow X_0$ of $\operatorname{\mathcal{C}}$ which belongs to $L$ and every morphism $f_1: X \rightarrow X_1$ of $\operatorname{\mathcal{C}}$ which belongs to $R$, there exists a pushout diagram
\[ \xymatrix@R =50pt@C=50pt{ X \ar [r]^-{f_0} \ar [d]^{ f_1 } & X_0 \ar [d]^{ f'_1 } \\ X_{1} \ar [r]^-{ f'_0 } & X_{01} } \]
where $f'_0$ belongs to $L$ and $f'_1$ belongs to $R$.