Lemma 18.30.6. In Situation 18.30.5 assume (1) holds.

Every sheaf of sets is the target of a surjective map whose source is a coproduct $\coprod h_{U_ i}^\# $ with $U_ i$ in $\mathcal{B}$.

If $\mathcal{O}$ is a sheaf of rings, then every $\mathcal{O}$-module is a quotient of a direct sum $\bigoplus \nolimits j_{U_ i!}\mathcal{O}_{U_ i}$ with $U_ i$ in $\mathcal{B}$.

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