Kerodon

Notation 8.5.6.1. Let $\Delta ^1 / \operatorname{\partial \Delta }^1$ denote the simplicial circle (Example 1.5.7.11). For every $\infty $-category $\operatorname{\mathcal{C}}$, we let $\operatorname{End}_{\operatorname{\mathcal{C}}}$ denote the $\infty $-category of diagrams $\operatorname{Fun}( \Delta ^1 / \operatorname{\partial \Delta }^1, \operatorname{\mathcal{C}})$. Note that objects of $\operatorname{End}_{\operatorname{\mathcal{C}}}$ can be identified with pairs $(X,e)$, where $X$ is an object of $\operatorname{\mathcal{C}}$ and $e: X \rightarrow X$ is an endomorphism of $X$. We will refer to $\operatorname{End}_{\operatorname{\mathcal{C}}}$ as the $\infty $-category of endomorphisms in $\operatorname{\mathcal{C}}$.