Lemma 26.3.5. 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
\xymatrix{ U \ar[d]_{f|_ U} \ar[r] & X \ar[d]^ f \\ V \ar[r] & Y }
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