Proposition 9.1.7.9. Let $\operatorname{\mathcal{C}}$ be a small category and let $\mathscr {G}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$ be a diagram of simplicial sets. Then there exists a projectively cofibrant diagram $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$ and a levelwise trivial Kan fibration $\alpha : \mathscr {F} \rightarrow \mathscr {G}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$