Lemma 29.17.4 (0G42)—The Stacks project

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Part 2: Schemes
Chapter 29: Morphisms of Schemes
Section 29.17: Universally catenary schemes
Lemma 29.17.4 (cite)

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Lemma 29.17.4. Let $S$ be a locally Noetherian scheme. Then $S$ is universally catenary if and only if the irreducible components of $S$ are universally catenary.

Proof. Omitted. For the affine case, please see Algebra, Lemma 10.105.8. $\square$

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