The Stacks project

Lemma 81.6.4. Let $S$ be a scheme. Let

\[ \xymatrix{ A \ar[r] \ar[d] & C \ar[d] \ar[r] & E \ar[d] \\ B \ar[r] & D \ar[r] & F } \]

be a commutative diagram of algebraic spaces over $S$. Assume that $A, B, C, D$ and $A, B, E, F$ form cartesian squares and that $B \to D$ is surjective étale. Then $C, D, E, F$ is a cartesian square.

Proof. This is formal. $\square$

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