Lemma 38.36.2. Let $\mathcal{F}$ be a sheaf on a site $(\mathit{Sch}/S)_{ph}$ as in Topologies, Definition 34.8.11. Let $X \to X'$ be a morphism of $(\mathit{Sch}/S)_{ph}$ which is a thickening. Then $\mathcal{F}(X') \to \mathcal{F}(X)$ is bijective.
Proof. Observe that $X \to X'$ is a proper surjective morphism of and $X \times _{X'} X = X$. By the sheaf property for the ph covering $\{ X \to X'\} $ (Topologies, Lemma 34.8.6) we conclude. $\square$
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