Corollary 10.3.3.22. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing a pushout diagram
\[ \xymatrix@R =50pt@C=50pt{ X \ar [d]^{f} \ar [r] & X' \ar [d]^{f'} \\ Y \ar [r] & Y'. } \]
If $\operatorname{\mathcal{C}}$ is has images and $f$ is a quotient morphism, then $f'$ is also a quotient morphism.