Lemma 24.3.2. Let $\mathcal{C}$ be a site.

A composition of coverings in $\text{SR}(\mathcal{C})$ is a covering.

If $K \to L$ is a covering in $\text{SR}(\mathcal{C})$ and $L' \to L$ is a morphism, then $L' \times _ L K$ exists and $L' \times _ L K \to L'$ is a covering.

If $\mathcal{C}$ has products of pairs, and $A \to B$ and $K \to L$ are coverings in $\text{SR}(\mathcal{C})$, then $A \times K \to B \times L$ is a covering.

Let $X \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$. Then (1) and (2) holds for $\text{SR}(\mathcal{C}, X)$ and (3) holds if $\mathcal{C}$ has fibre products.

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