Example 1.4.6.14. Let $X$ be a topological space. Then the singular simplicial set $\operatorname{Sing}_{\bullet }(X)$ is a Kan complex (Proposition 1.2.5.8), and its fundamental groupoid $\pi _{\leq 1}( \operatorname{Sing}_{\bullet }(X) )$ can be identified with the usual fundamental groupoid $\pi _{\leq 1}(X)$ of the topological space $X$ (where objects are the points of $X$ and morphisms are given by homotopy classes of paths in $X$).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$