Kerodon

Notation 1.2.3.3. Let $S$ be a simplicial set. It follows immediately from the definitions that if there exists a map $u: S \rightarrow \operatorname{Sing}_{\bullet }(Y)$ which exhibits $Y$ as a geometric realization of $S$, then the topological space $Y$ is determined up to homeomorphism and depends functorially on $S$. We will emphasize this dependence by writing $| S |$ to denote a geometric realization of $S$. By virtue of Example 1.2.3.2, this is compatible with the convention of Notation 1.2.2.1 in the special case where $S = \Delta ^{n}$ is a standard simplex.