Lemma 66.16.6. Let $S$ be a scheme. Let

be a commutative diagram of algebraic spaces over $S$. Let $Z_ i \subset Y_ i$, $i = 1, 2$ be the scheme theoretic image of $f_ i$. Then the morphism $Y_1 \to Y_2$ induces a morphism $Z_1 \to Z_2$ and a commutative diagram

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