The Stacks project

Lemma 85.2.6. Let $X$ be a simplicial space. If $\mathcal{I}$ is an injective abelian sheaf on $X_{Zar}$, then $\mathcal{I}_ n$ is an injective abelian sheaf on $X_ n$.

Proof. This follows from Homology, Lemma 12.29.1 and Lemma 85.2.5. $\square$

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