Example 9.3.4.10. Let $f: X_0 \rightarrow X$ be a map of Kan complexes. Then $f$ is a monomorphism in the $\infty $-category of spaces $\operatorname{\mathcal{S}}$ if and only if it induces a homotopy equivalence of $X_0$ with a summand of $X$. See Example 9.3.1.4.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$