Kerodon

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

Construction 1.1.4.2. Let $\operatorname{\mathcal{C}}$ be a category. For each object $C \in \operatorname{\mathcal{C}}$, we let $\underline{C}_{\bullet }$ denote the constant functor $\operatorname{{\bf \Delta }}^{\operatorname{op}} \rightarrow \{ C \} \hookrightarrow \operatorname{\mathcal{C}}$ taking the value $C$. We regard $\underline{C}_{\bullet }$ as a simplicial object of $\operatorname{\mathcal{C}}$, which we will refer to as the constant simplicial object with value $C$.