Definition 8.5.1.1. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing an object $X$. We say that an object $Y \in \operatorname{\mathcal{C}}$ is a retract of $X$ if there exist morphisms $i: Y \rightarrow X$ and $r: X \rightarrow Y$ for which the identity morphism $\operatorname{id}_{Y}$ is a composition of $i$ and $r$, in the sense of Definition 1.4.4.1.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$