Lemma 59.73.12. Let X be an irreducible scheme with generic point \eta .
Let S' \subset S be an inclusion of sets. If we have \underline{S'} \subset \mathcal{G} \subset \underline{S} in \mathop{\mathit{Sh}}\nolimits (X_{\acute{e}tale}) and S' = \mathcal{G}_{\overline{\eta }}, then \mathcal{G} = \underline{S'}.
Let A' \subset A be an inclusion of abelian groups. If we have \underline{A'} \subset \mathcal{G} \subset \underline{A} in \textit{Ab}(X_{\acute{e}tale}) and A' = \mathcal{G}_{\overline{\eta }}, then \mathcal{G} = \underline{A'}.
Let M' \subset M be an inclusion of modules over a ring \Lambda . If we have \underline{M'} \subset \mathcal{G} \subset \underline{M} in \textit{Mod}(X_{\acute{e}tale}, \underline{\Lambda }) and M' = \mathcal{G}_{\overline{\eta }}, then \mathcal{G} = \underline{M'}.
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