# Kerodon

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

Example 8.5.8.2. The simplicial set $\operatorname{N}_{\leq 1}(\operatorname{Idem})$ can be identified with the simplicial circle $\Delta ^1 / \operatorname{\partial \Delta }^1$, obtained from the standard simplex $\Delta ^1$ by identifying its endpoints. Consequently, if $\operatorname{\mathcal{C}}$ is an $\infty$-category, then a morphism $\operatorname{N}_{\leq 1}( \operatorname{Idem}) \rightarrow \operatorname{\mathcal{C}}$ can be identified with a pair $(X,e)$, where $X$ is an object of $\operatorname{\mathcal{C}}$ and $e$ is an endomorphism of $X$.