$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
5.4
\begin{equation} \begin{gathered}\label{diagram:trivial-cartesian-poset} \xymatrix@R =50pt@C=50pt{ \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y,Z) \times _{ \operatorname{Hom}_{\operatorname{\mathcal{C}}}(Y,Z) } \{ g\} \ar [r]^-{\theta _ X} \ar [d] & \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Z) \ar [d] \\ \operatorname{Hom}_{\operatorname{N}_{\bullet }(Q)}( q(X), q(Y), q(Z) ) \times _{ \operatorname{Hom}_{\operatorname{N}_{\bullet }(Q)}( q(Y), q(Z)) } \{ q(g) \} \ar [r] & \operatorname{Hom}_{\operatorname{N}_{\bullet }(Q)}( q(X), q(Z) ) } \end{gathered} \end{equation}