Lemma 76.19.12. Let $S$ be a scheme. Let $f : X \to Y$, $g : Y \to Z$ be morphisms of algebraic spaces over $S$. Assume $f$ is formally smooth. Then

Lemma 76.7.8 is short exact.

Lemma 76.19.12. Let $S$ be a scheme. Let $f : X \to Y$, $g : Y \to Z$ be morphisms of algebraic spaces over $S$. Assume $f$ is formally smooth. Then

\[ 0 \to f^*\Omega _{Y/Z} \to \Omega _{X/Z} \to \Omega _{X/Y} \to 0 \]

Lemma 76.7.8 is short exact.

**Proof.**
Follows from the case of schemes, see More on Morphisms, Lemma 37.11.11, by étale localization, see Lemmas 76.19.10 and 76.7.3.
$\square$

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## Comments (2)

Comment #5140 by bouthier on

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