Lemma 20.41.6. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $\mathcal{I}^\bullet $ be a K-injective complex of $\mathcal{O}_ X$-modules. Let $\mathcal{L}^\bullet $ be a complex of $\mathcal{O}_ X$-modules. Then
for all $U \subset X$ open.
Lemma 20.41.6. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $\mathcal{I}^\bullet $ be a K-injective complex of $\mathcal{O}_ X$-modules. Let $\mathcal{L}^\bullet $ be a complex of $\mathcal{O}_ X$-modules. Then
for all $U \subset X$ open.
Proof. We have
The first equality is (20.41.0.1). The second equality is true because $\mathcal{I}^\bullet |_ U$ is K-injective by Lemma 20.32.1. $\square$
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Comment #8624 by nkym on