Kerodon

\begin{equation} \begin{gathered}\label{equation:diagram-for-checking-cocartesian} \xymatrix@R =50pt@C=50pt{ \{ c\} \times _{ \operatorname{Hom}_{\overline{\operatorname{\mathcal{E}}}^{+}}(X,Y) } \operatorname{Hom}_{\overline{\operatorname{\mathcal{E}}}^{+}}(X,Y,Z) \ar [r] \ar [d] & \operatorname{Hom}_{\overline{\operatorname{\mathcal{E}}}^{+}}(X,Z) \ar [d] \\ \{ \overline{e} \} \times _{ \operatorname{Hom}_{ \operatorname{\mathcal{C}}\star \Delta ^{n} }( \overline{X}, \overline{Y} ) } \operatorname{Hom}_{\operatorname{\mathcal{C}}\star \Delta ^{n}}( \overline{X}, \overline{Y}, \overline{Z} ) \ar [r] & \operatorname{Hom}_{\operatorname{\mathcal{C}}\star \Delta ^{n}}( \overline{X}, \overline{Z} ) } \end{gathered} \end{equation}