Lemma 87.11.3. Let S be a scheme. Let f : X \to Y be a morphism from an algebraic space over S to a formal algebraic space over S. Then f is representable by algebraic spaces.
Proof. Let Z \to Y be a morphism where Z is a scheme over S. We have to show that X \times _ Y Z is an algebraic space. Choose a scheme U and a surjective étale morphism U \to X. Then U \times _ Y Z \to X \times _ Y Z is representable surjective étale (Spaces, Lemma 65.5.5) and U \times _ Y Z is a scheme by Lemma 87.11.2. Hence the result by Bootstrap, Theorem 80.10.1. \square
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