Kerodon

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

Example 1.1.1.5. Let $n$ be a positive integer and let $S_{\bullet }$ be a simplicial set. For $0 \leq i \leq n$, the face operator $d^{n}_{i}$ of Construction 1.1.1.4 carries each $n$-simplex $\sigma $ of $S_{\bullet }$ to an $(n-1)$-simplex $d^{n}_{i}(\sigma )$, which we will refer to as the $i$th face of $\sigma $.