Remark 8.5.0.1. Let $X$ and $Y$ be objects of a category $\operatorname{\mathcal{C}}$. Then a retraction diagram (8.64) can be viewed as a morphism from $\operatorname{id}_{X}$ to $\operatorname{id}_{Y}$ in the twisted arrow category $\operatorname{Tw}(\operatorname{\mathcal{C}})$ of Construction 8.1.0.1. In particular, $Y$ is a retract of $X$ if and only if there exists a morphism $\operatorname{id}_{X} \rightarrow \operatorname{id}_{Y}$ in $\operatorname{Tw}(\operatorname{\mathcal{C}})$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$