Lemma 37.58.4. A composition of pseudo-coherent morphisms of schemes is pseudo-coherent.
Proof. This translates into the following algebra result: If $A \to B \to C$ are composable pseudo-coherent ring maps then $A \to C$ is pseudo-coherent. This follows from either More on Algebra, Lemma 15.81.13 or More on Algebra, Lemma 15.81.15. $\square$
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