The Stacks project

Lemma 73.6.3. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$.

1. If $X' \to X$ is an isomorphism then $\{ X' \to X\}$ is a syntomic covering of $X$.

2. If $\{ X_ i \to X\} _{i\in I}$ is a syntomic covering and for each $i$ we have a syntomic covering $\{ X_{ij} \to X_ i\} _{j\in J_ i}$, then $\{ X_{ij} \to X\} _{i \in I, j\in J_ i}$ is a syntomic covering.

3. If $\{ X_ i \to X\} _{i\in I}$ is a syntomic covering and $X' \to X$ is a morphism of algebraic spaces then $\{ X' \times _ X X_ i \to X'\} _{i\in I}$ is a syntomic covering.