Definition 70.10.6. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. We say that pullbacks of meromorphic functions are defined for $f$ if for every commutative diagram

$\xymatrix{ U \ar[r] \ar[d] & X \ar[d] \\ V \ar[r] & Y }$

with $U \in X_{\acute{e}tale}$ and $V \in Y_{\acute{e}tale}$ and any section $s \in \mathcal{S}_ Y(V)$ the pullback $f^\sharp (s) \in \mathcal{O}_ X(U)$ is an element of $\mathcal{S}_ X(U)$.

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