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Rig-surjectivity of locally finite type morphisms is preserved under composition

Lemma 88.21.3. Let $S$ be a scheme. Let $f : X \to Y$ and $g : Y \to Z$ be morphisms of formal algebraic spaces over $S$. Assume $X$, $Y$, $Z$ are locally Noetherian and $f$ and $g$ locally of finite type. Then if $f$ and $g$ are rig-surjective, so is $g \circ f$.

Proof. Follows in a straightforward manner from the definitions (and Formal Spaces, Lemma 87.24.3). $\square$

Comments (1)

Comment #2112 by Matthew Emerton on

Suggested slogan: rig-surjectivity of locally finite type morphisms is preserved under composition

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