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The Stacks project

Lemma 20.32.1. Let X be a ringed space. Let U \subset X be an open subspace. The restriction of a K-injective complex of \mathcal{O}_ X-modules to U is a K-injective complex of \mathcal{O}_ U-modules.

Proof. Follows from Derived Categories, Lemma 13.31.9 and the fact that the restriction functor has the exact left adjoint j_!. For the construction of j_! see Sheaves, Section 6.31 and for exactness see Modules, Lemma 17.3.4. \square


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