Remark 9.3.4.15. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, and suppose that we are given a commutative diagram
\[ \xymatrix@R =50pt@C=50pt{ & Y \ar [dr]^{g} & \\ X \ar [ur]^{f} \ar [rr]^{h} & & Z } \]
in $\operatorname{\mathcal{C}}$, where $g$ is a monomorphism. Then $f$ is a monomorphism if and only if $h$ is a monomorphism. In particular, the collection of monomorphisms is closed under composition. See Corollary 9.3.3.17.