Corollary 3.5.9.25. Let $X$ be an $n$-truncated Kan complex, let $k$ be an integer, and let $j: A \rightarrow B$ be a $(k-1)$-connective morphism of simplicial sets. Then the induced map $\operatorname{Fun}(B,X) \rightarrow \operatorname{Fun}(A,X)$ is $(n-k)$-truncated.
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