$\xymatrix{ X \ar[rr]_ f \ar[rd]_ p & & Y \ar[dl]^ q \\ & S }$

be a commutative diagram of morphisms of schemes. Assume that

1. $f$ is surjective, and syntomic (resp. smooth, resp. étale),

2. $p$ is syntomic (resp. smooth, resp. étale).

Then $q$ is syntomic (resp. smooth, resp. étale).

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