The Stacks project

Lemma 20.21.1. Let $i : Z \to X$ be the inclusion of a closed subset. Let $\mathcal{I}$ be an injective abelian sheaf on $X$. Then $\mathcal{H}_ Z(\mathcal{I})$ is an injective abelian sheaf on $Z$.

Proof. This follows from Homology, Lemma 12.29.1 as $\mathcal{H}_ Z(-)$ is right adjoint to the exact functor $i_*$. See Modules, Lemmas 17.6.1 and 17.6.3. $\square$

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