Kerodon

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

Construction 1.3.2.2. Let $S_{\bullet }$ be a simplicial set, which we regard as a functor $\operatorname{{\bf \Delta }}^{\operatorname{op}} \rightarrow \operatorname{Set}$. We let $S_{\bullet }^{\operatorname{op}}$ denote the simplicial set given by the composition

\[ \operatorname{{\bf \Delta }}^{\operatorname{op}} \xrightarrow { \mathrm{Op} } \operatorname{{\bf \Delta }}^{\operatorname{op}} \xrightarrow { S_{\bullet } } \operatorname{Set}, \]

where $\mathrm{Op}$ is the functor described in Notation 1.3.2.1. We will refer to $S_{\bullet }^{\operatorname{op}}$ as the opposite of the simplicial set $S_{\bullet }$.