Warning 4.6.6.3. In the situation of Notation 4.6.6.1, the simplicial set $\operatorname{\mathcal{C}}_{ f_{-} / \, / f_{+} }$ depends on the morphism $f_{\pm }: K_{-} \star K_{+} \rightarrow \operatorname{\mathcal{C}}$, and not only on the morphisms $f_{-} = f_{\pm }|_{ K_{-} }$ and $f_{+} = f_{\pm } |_{ K_{+} }$ indicated in the notation.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$