Remark 3.5.9.9. In the situation of Proposition 3.5.9.8, it is not necessary to verify that the fiber $X_{y}$ is $n$-truncated for every vertex $y \in Y$; it is enough to check this condition at one vertex from each connected component of $Y$ (see Remark 3.3.7.3). In particular, if $Y$ is connected, then it is enough to check that the fiber $X_{y}$ is $n$-truncated for any choice of vertex $y \in Y$.
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