The Stacks project

Lemma 38.34.8. Let $T$ be a scheme.

  1. If $T' \to T$ is an isomorphism then $\{ T' \to T\} $ is an h covering of $T$.

  2. If $\{ T_ i \to T\} _{i\in I}$ is an h covering and for each $i$ we have an h covering $\{ T_{ij} \to T_ i\} _{j\in J_ i}$, then $\{ T_{ij} \to T\} _{i \in I, j\in J_ i}$ is an h covering.

  3. If $\{ T_ i \to T\} _{i\in I}$ is an h covering and $T' \to T$ is a morphism of schemes then $\{ T' \times _ T T_ i \to T'\} _{i\in I}$ is an h covering.

Proof. Follows immediately from the corresponding statement for either ph or V coverings (Topologies, Lemma 34.8.8 or 34.10.9) and the fact that the class of morphisms which are locally of finite presentation is preserved under base change and composition. $\square$


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