The Stacks project

Lemma 29.30.3. The composition of two morphisms which are syntomic is syntomic.

Proof. In the proof of Lemma 29.30.2 we saw that being syntomic 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 syntomic is a property of ring maps that is stable under composition, see Algebra, Lemma 10.136.17. $\square$

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