The Stacks project

Lemma 37.60.7. Let $f : X \to Y$ be a morphism of schemes pseudo-coherent over a base scheme $S$. Then $f$ is pseudo-coherent.

Proof. This translates into the following algebra result: If $R \to A \to B$ are composable ring maps and $R \to A$, $R \to B$ pseudo-coherent, then $R \to B$ is pseudo-coherent. This follows from More on Algebra, Lemma 15.81.15. $\square$

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