Remark 8.5.1.4. Let $\operatorname{\mathcal{C}}$ be a category containing an object $X$. Then an object $Y \in \operatorname{\mathcal{C}}$ is retract of $X$ if and only if it is a retract of $X$ when viewed as an object of the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ (in the sense of Definition 8.5.1.1). Consequently, Definition 8.5.1.1 can be viewed as a generalization of the classical notion of retract.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$