Remark 4.8.9.5. Let $f: A \rightarrow B$ be a morphism of simplicial sets. If $f$ is categorically $n$-connective, then it is $n$-connective. This follows from Remark 4.8.9.4 and Corollary 4.8.7.17. Beware that the converse is false in general (Warning 4.8.7.4).
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