Corollary 3.4.2.13. Let $f_0: A \rightarrow A_0$ and $f_1: A \rightarrow A_1$ be morphisms of simplicial sets. If either $f_0$ or $f_1$ is a monomorphism, then the comparison map $A_0 {\coprod }_{A}^{\mathrm{h}} A_1 \twoheadrightarrow A_0 {\coprod }_{A} A_{1}$ is a weak homotopy equivalence.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$