# Kerodon

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

Remark 5.7.6.3. Let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{S}}$ be a functor of $\infty$-categories and let $X \in \operatorname{\mathcal{C}}$ be an object, and let $x \in \mathscr {F}(X)$ be a vertex. The condition that $x$ exhibits $\mathscr {F}$ as corepresented by $X$ depends only on the connected component $[x] \in \pi _0( \mathscr {F}(X) )$.