Lemma 17.16.1. Let (X, \mathcal{O}_ X) be a ringed space. Let \mathcal{F}, \mathcal{G} be \mathcal{O}_ X-modules. Let x \in X. There is a canonical isomorphism of \mathcal{O}_{X, x}-modules
(\mathcal{F} \otimes _{\mathcal{O}_ X} \mathcal{G})_ x = \mathcal{F}_ x \otimes _{\mathcal{O}_{X, x}} \mathcal{G}_ x
functorial in \mathcal{F} and \mathcal{G}.
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