Lemma 81.6.4 (07VZ)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 81: Pushouts of Algebraic Spaces
Section 81.6: Pushouts along thickenings and affine morphisms
Lemma 81.6.4 (cite)

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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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