Remark 3.5.1.14. Suppose we are given a diagram of Kan complexes
\[ \xymatrix@R =50pt@C=50pt{ X' \ar [d]^{f'} \ar [r] & X \ar [d]^{f} \\ Y' \ar [r] & Y } \]
which commutes up to homotopy. If the horizontal maps are homotopy equivalences, then $f$ is $n$-connective if and only if $f'$ is $n$-connective.