Example 9.3.4.6. Let $\operatorname{\mathcal{C}}$ be a category and let $f: X_0 \rightarrow X$ be a morphism in $\operatorname{\mathcal{C}}$. Then $f$ is a monomorphism in the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ (in the sense of Definition 9.3.4.1) if and only if it is a monomorphism in the usual category-theoretic sense.
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