Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Proposition 7.5.9.7. 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 $\alpha : \mathscr {F} \rightarrow \mathscr {G}$.

Proof of Proposition 7.5.9.7. Apply Proposition 7.5.9.12 in the special case $\mathscr {F}_{0} = \underline{\emptyset }$ (see Example 7.5.9.9). $\square$