Construction 1.4.2.2. Let $S$ be a simplicial set, which we regard as a functor $\operatorname{{\bf \Delta }}^{\operatorname{op}} \rightarrow \operatorname{Set}$. We let $S^{\operatorname{op}}$ denote the simplicial set given by the composition
\[ \operatorname{{\bf \Delta }}^{\operatorname{op}} \xrightarrow { \mathrm{Op} } \operatorname{{\bf \Delta }}^{\operatorname{op}} \xrightarrow { S } \operatorname{Set}, \]
where $\mathrm{Op}$ is the functor described in Notation 1.4.2.1. We will refer to $S^{\operatorname{op}}$ as the opposite of the simplicial set $S$.