Proposition 7.5.1.5. Let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Kan}$ be a diagram of Kan complexes. Then the Kan complex $ \underset {\longleftarrow }{\mathrm{holim}}(\mathscr {F})$ is a limit of the diagram
\[ \operatorname{N}_{\bullet }^{\operatorname{hc}}( \mathscr {F}): \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) \rightarrow \operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{Kan}) = \operatorname{\mathcal{S}} \]
in the $\infty $-category $\operatorname{\mathcal{S}}$.