Remark 4.8.3.31. Let $n$ be an integer and suppose we are given a categorical pullback diagram of $\infty $-categories
\[ \xymatrix@R =50pt@C=50pt{ \operatorname{\mathcal{C}}' \ar [d]^{F'} \ar [r] & \operatorname{\mathcal{C}}\ar [d]^{F} \\ \operatorname{\mathcal{D}}' \ar [r]^-{G} & \operatorname{\mathcal{D}}. } \]
If $F$ is $n$-faithful, then $F'$ is $n$-faithful. In particular, if $F$ is faithful or fully faithful, then $F'$ has the same property. See Corollary 4.8.2.27.