The Stacks project

Definition 12.23.4. Let $\mathcal{A}$ be an abelian category. Let $(K, F, d)$ be a filtered differential object of $\mathcal{A}$. The induced filtration on $H(K, d)$ is the filtration defined by $F^ pH(K, d) = \mathop{\mathrm{Im}}(H(F^ pK, d) \to H(K, d))$.