Corollary 7.6.4.11. Let $n$ be an integer and suppose we are given a pullback diagram
\[ \xymatrix@R =50pt@C=50pt{ X' \ar [r] \ar [d]^{f'} & X \ar [d]^{f} \\ Y' \ar [r] & Y } \]
in the $\infty $-category $\operatorname{\mathcal{S}}$. If $f$ is $n$-truncated, then $f'$ is $n$-truncated. If $f$ is $n$-connective, then $f'$ is $n$-connective.