The Stacks project

Lemma 37.63.5. 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 37.63.2, 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 37.63.2 gives the claim. $\square$


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