The Stacks project

Definition 111.30.4. Let $\mathcal{A}$ be an abelian category. We denote $\text{Fil}^ f(\mathcal{A})$ the full subcategory of $\text{Fil}(\mathcal{A})$ whose objects consist of those $A \in \mathop{\mathrm{Ob}}\nolimits (\text{Fil}(\mathcal{A}))$ whose filtration is finite.

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