Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 1.1.8.14. The proof of Proposition 1.1.8.4 shows that the geometric realization $| S_{\bullet } |$ of a simplicial set $S_{\bullet }$ has a canonical realization as a CW complex, having one cell of dimension $n$ for each nondegenerate $n$-simplex $\sigma $ of $S_{\bullet }$; this cell can be described explicitly as the image of the map

\[ | \Delta ^{n} | \setminus | \operatorname{\partial \Delta }^{n} | \hookrightarrow | \Delta ^{n} | \xrightarrow { \sigma } | S_{\bullet } |. \]