The Stacks project

Definition 111.30.6. Let $\mathcal{A}$ be an abelian category. Let $\alpha : K^\bullet \to L^\bullet$ be a morphism of complexes of $\text{Fil}(\mathcal{A})$. We say that $\alpha$ is a filtered quasi-isomorphism if for each $p \in \mathbf{Z}$ the morphism $\text{gr}^ p(K^\bullet ) \to \text{gr}^ p(L^\bullet )$ is a quasi-isomorphism.