Kerodon

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

Corollary 7.5.4.7. Let $\operatorname{\mathcal{C}}$ be a small category and let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Kan}$ be an isofibrant diagram of Kan complexes. Then $\mathscr {F}$ has a limit in the category $\operatorname{Kan}$, which is preserved by the inclusion functor $\operatorname{N}_{\bullet }( \operatorname{Kan}) \hookrightarrow \operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{Kan}) = \operatorname{\mathcal{S}}$.