The Stacks project

Lemma 29.35.4. The composition of two morphisms which are unramified is unramified. The same holds for G-unramified morphisms.

Proof. The proof of Lemma 29.35.3 shows that being unramified (resp. G-unramified) is a local property of ring maps. Hence the first statement of the lemma follows from Lemma 29.14.5 combined with the fact that being unramified (resp. G-unramified) is a property of ring maps that is stable under composition, see Algebra, Lemma 10.151.3. $\square$

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