The Stacks project

Example 38.35.1. The “structure sheaf” $\mathcal{O}$ is not a sheaf in the h topology. For example, consider a surjective closed immersion of finite presentation $X \to Y$. Then $\{ X \to Y\} $ is an h covering for example by Lemma 38.34.7. Moreover, note that $X \times _ Y X = X$. Thus if $\mathcal{O}$ where a sheaf in the h topology, then $\mathcal{O}_ Y(Y) \to \mathcal{O}_ X(X)$ would be bijective. This is not the case as soon as $X$, $Y$ are affine and the morphism $X \to Y$ is not an isomorphism.