Remark 10.3.4.5. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing a $2$-simplex
\[ \xymatrix@R =50pt@C=50pt{ & Y \ar [dr]^{g} & \\ X \ar [ur]^{f} \ar [rr]^{h} & & Z. } \]
If $h$ is a universal quotient morphism, then $g$ is also a universal quotient morphism. This is a special case of Remark 10.3.4.4.