Remark 4.6.7.6. In the formulation of Definition 4.6.7.1, we can replace the Kan complexes $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)$ and $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(Y,Z)$ by their left-pinched variants $\operatorname{Hom}_{\operatorname{\mathcal{C}}}^{\mathrm{L}}(X,Y)$ and $\operatorname{Hom}_{\operatorname{\mathcal{C}}}^{\mathrm{L}}(Y,Z)$, or by their right-pinched variants $\operatorname{Hom}_{\operatorname{\mathcal{C}}}^{\mathrm{R}}(X,Y)$ and $\operatorname{Hom}_{\operatorname{\mathcal{C}}}^{\mathrm{R}}(Y,Z)$ (see Proposition 4.6.5.10).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$