Lemma 70.10.7. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Pullbacks of meromorphic sections are defined in each of the following cases

1. weakly associated points of $X$ are mapped to points of codimension $0$ on $Y$,

2. $f$ is flat,

3. add more here as needed.

Proof. Working étale locally, this translates into the case of schemes, see Divisors, Lemma 31.23.5. To do the translation use Lemma 70.7.5 (description of regular sections), Definition 70.2.2 (definition of weakly associated points), and Properties of Spaces, Lemma 65.11.1 (description of codimension $0$ points). $\square$

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