The Stacks project

Definition 111.30.3. Let $\mathcal{A}$ be an abelian category. Let $I$ be a filtered object of $\mathcal{A}$. Assume the filtration on $I$ is finite. We say $I$ is filtered injective if each $\text{gr}^ p(I)$ is an injective object of $\mathcal{A}$.

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