Warning 9.1.2.2. In the formulation of condition $(\ast _ n)$ of Definition 9.1.2.1, postcomposition with $v$ defines a map of Kan complexes $V: \underline{\operatorname{Hom}}_{\operatorname{\mathcal{C}}}( X, Y) \rightarrow \underline{\operatorname{Hom}}_{\operatorname{\mathcal{C}}}(X,Z)$ which is only well-defined up to homotopy. However, the condition that $V \circ \sigma $ is nullhomotopic depends only on the homotopy class of $V$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$