Lemma 37.66.5 (0F1X)—The Stacks project

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Part 2: Schemes
Chapter 37: More on Morphisms
Section 37.66: Ind-quasi-affine morphisms
Lemma 37.66.5 (cite)

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Lemma 37.66.5. If $f : X \to Y$ and $g : Y \to Z$ are morphisms of schemes such that $g \circ f$ is ind-quasi-affine, then $f$ is ind-quasi-affine.

Proof. By Lemma 37.66.2, we may work Zariski locally on $Z$ and then on $Y$ , so we lose no generality by assuming that $Z$ , and then also $Y$ , is affine. Then any quasi-compact open of $X$ is quasi-affine, so Lemma 37.66.2 gives the claim. $\square$

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