Lemma 87.19.3 (0AQ0)—The Stacks project

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Table of contents
Part 5: Topics in Geometry
Chapter 87: Formal Algebraic Spaces
Section 87.19: Morphisms representable by algebraic spaces
Lemma 87.19.3 (cite)

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Lemma 87.19.3. Let $S$ be a scheme. Let $f : X \to Y$ and $g : Y \to Z$ be morphisms of formal algebraic spaces over $S$ . If $g \circ f : X \to Z$ is representable by algebraic spaces, then $f : X \to Y$ is representable by algebraic spaces.

Proof. Note that the diagonal of $Y \to Z$ is representable by Lemma 87.15.5. Thus $X \to Y$ is representable by algebraic spaces by Bootstrap, Lemma 80.3.10. $\square$

Comments (2)

Comment #1948 by Brian Conrad on April 30, 2016 at 23:56

In the proof, replace : $U \rightarrow V$ " with " $X \rightarrow Y$ ".

Comment #2002 by Johan on May 04, 2016 at 12:17

Thanks, fixed here.

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