Lemma 90.10.6. Let $\mathcal{F}$ be a category cofibered in groupoids over $\mathcal{C}_\Lambda $. Let $x_0 \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{F}(k))$. Let $\mathcal{F}_{x_0}$ be the category cofibred in groupoids over $\mathcal{C}_\Lambda $ constructed in Remark 90.6.4.

If $\mathcal{F}$ satisfies (S1), then so does $\mathcal{F}_{x_0}$.

If $\mathcal{F}$ satisfies (S2), then so does $\mathcal{F}_{x_0}$.

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