Lemma 25.3.5. Let $f : X \to Y$ be a morphism of locally ringed spaces. Let $U \subset X$, and $V \subset Y$ be open subsets. Suppose that $f(U) \subset V$. There exists a unique morphism of locally ringed spaces $f|_ U : U \to V$ such that the following diagram is a commutative square of locally ringed spaces
Proof. Omitted. $\square$
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