Kerodon

\begin{equation} \begin{gathered}\label{equation:mapping-property-of-Kan} \xymatrix@R =50pt@C=45pt{ & \operatorname{Hom}_{ \operatorname{Fun}( \overline{\operatorname{\mathcal{C}}}, \operatorname{\mathcal{D}}) }( \overline{F}, \overline{G} ) \ar [dl]_{\varphi _{+}} \ar [d]^{\varphi _{\pm }} \ar [dr]^{\varphi _{-}} & \\ \operatorname{Hom}_{ \operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}}) }( F, G ) \ar [r] & \operatorname{Hom}_{ \operatorname{Fun}(\operatorname{\mathcal{K}}, \operatorname{\mathcal{C}})}( F \circ \delta , G \circ \delta ) \ar [r]^-{ \circ [\beta ] } & \operatorname{Hom}_{ \operatorname{Fun}(\operatorname{\mathcal{K}}, \operatorname{\mathcal{D}}) }( F_0, G \circ \delta ). } \end{gathered} \end{equation}