Kerodon

Remark 8.5.1.22. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. A $2$-simplex $\sigma $ of $\operatorname{\mathcal{C}}$ is a retraction diagram if and only if it is a retraction diagram when viewed as an object of the opposite $\infty $-category $\operatorname{\mathcal{C}}^{\operatorname{op}}$. Consequently, if $X$ and $Y$ are objects of $\operatorname{\mathcal{C}}$, then $Y$ is a retract of $X$ in $\operatorname{\mathcal{C}}$ if and only if it is a retract of $X$ in the $\infty $-category $\operatorname{\mathcal{C}}^{\operatorname{op}}$.