Example 3.1.6.3. Let $f: X \rightarrow Y$ be a homotopy equivalence of topological spaces. Then the induced map of singular simplicial sets $\operatorname{Sing}_{\bullet }(f): \operatorname{Sing}_{\bullet }(X) \rightarrow \operatorname{Sing}_{\bullet }(Y)$ is a homotopy equivalence (see Example 3.1.5.6).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$