Kerodon

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5.56
\begin{equation} \begin{gathered}\label{equation:compare-with-weighted-nerve} \xymatrix@R =50pt@C=50pt{ \Delta ^{n} \ar [r] \ar [d]^{ \overrightarrow {C}} & \operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{Set_{\Delta }})_{ \Delta ^{0} / } \ar [d] \\ \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) \ar [r]^-{ \operatorname{N}_{\bullet }^{\operatorname{hc}}( \mathscr {F}) } & \operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{Set_{\Delta }}), } \end{gathered} \end{equation}