# Kerodon

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

Example 1.4.1.9. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category and let $X$ be a topological space. Then we have a canonical bijection

$\xymatrix { \{ \text{Functors of \infty -categories from \operatorname{\mathcal{C}} to \operatorname{Sing}_{\bullet }(X)} \} \ar [d]^{\sim } \\ \{ \text{Continuous functions from | \operatorname{\mathcal{C}}| to X} \} . }$

Here $| \operatorname{\mathcal{C}}|$ denotes the geometric realization of the simplicial set $\operatorname{\mathcal{C}}$ (see Definition 1.1.8.1). Beware that neither side has an obvious interpretation in terms of functors between ordinary categories (even in the special case where $\operatorname{\mathcal{C}}$ is the nerve of a category).