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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