Corollary 11.6.0.12. Let $n$ be an integer, let $\operatorname{\mathcal{C}}$ be a simplicial set and let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{S}}$ be a diagram. Suppose that, for every vertex $C \in \operatorname{\mathcal{C}}$, the Kan complex $\mathscr {F}(C)$ is $n$-truncated. Then the limit $\varprojlim ( \mathscr {F} )$ is an $n$-truncated Kan complex.$\infty $-category.
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