Lemma 35.13.3. Let $\{ f_ i : X_ i \to X\} _{i \in I}$ be a family of morphisms of schemes.

If the family is universal effective epimorphism in the category of schemes, then $\coprod f_ i$ is surjective.

If $X$ and $X_ i$ are affine and the family is a universal effective epimorphism in the category of affine schemes, then $\coprod f_ i$ is surjective.

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