Lemma 35.14.4. Let
\[ \xymatrix{ X \ar[rr]_ f \ar[rd]_ p & & Y \ar[dl]^ q \\ & S } \]
be a commutative diagram of morphisms of schemes. Assume that
$f$ is surjective, and syntomic (resp. smooth, resp. étale),
$p$ is syntomic (resp. smooth, resp. étale).
Then $q$ is syntomic (resp. smooth, resp. étale).
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