Remark 8.5.1.25. In the situation of Notation 8.5.1.24, the map $\sigma : \Delta ^2 \twoheadrightarrow \mathcal{R}$ is an epimorphism of simplicial sets, which fits into a pushout square
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{N}_{\bullet }( \{ 0 < 2 \} ) \ar [r] \ar [d] & \Delta ^0 \ar [d] \\ \Delta ^2 \ar [r]^-{\sigma } & \mathcal{R}. } \]
It follows that, for every $\infty $-category $\operatorname{\mathcal{C}}$, composition with $\sigma $ induces a bijection from $\operatorname{Hom}_{\operatorname{Set_{\Delta }}}( \mathcal{R}, \operatorname{\mathcal{C}})$ to the set of retraction diagrams in $\operatorname{\mathcal{C}}$ (in the sense of Definition 8.5.1.19).