The Stacks project

Definition 12.24.5. Let $\mathcal{A}$ be an abelian category. Let $(K^\bullet , F)$ be a filtered complex of $\mathcal{A}$. The induced filtration on $H^ n(K^\bullet )$ is the filtration defined by $F^ pH^ n(K^\bullet ) = \mathop{\mathrm{Im}}(H^ n(F^ pK^\bullet ) \to H^ n(K^\bullet ))$.