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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