Definition 31.23.4. Let $f : (X, \mathcal{O}_ X) \to (Y, \mathcal{O}_ Y)$ be a morphism of locally ringed spaces. We say that pullbacks of meromorphic functions are defined for $f$ if for every pair of open $U \subset X$, $V \subset Y$ such that $f(U) \subset V$, and any section $s \in \Gamma (V, \mathcal{S}_ Y)$ the pullback $f^\sharp (s) \in \Gamma (U, \mathcal{O}_ X)$ is an element of $\Gamma (U, \mathcal{S}_ X)$.

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