Remark 66.19.10. This remark is the analogue of Étale Cohomology, Remark 59.56.6. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $\overline{x} : \mathop{\mathrm{Spec}}(k) \to X$ be a geometric point of $X$. By Étale Cohomology, Theorem 59.56.3 the category of sheaves on $\mathop{\mathrm{Spec}}(k)_{\acute{e}tale}$ is equivalent to the category of sets (by taking a sheaf to its global sections). Hence it follows from Lemma 66.19.9 part (4) applied to the morphism $\overline{x}$ that the functor

is isomorphic to the functor

Hence we may view the stalk functors as pullback functors along geometric morphisms (and not just some abstract morphisms of topoi as in the result of Lemma 66.19.7).

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