Lemma 13.20.1. Let $\mathcal{A}$ be an abelian category. Let $I \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{A})$ be an injective object. Let $I^\bullet $ be a bounded below complex of injectives in $\mathcal{A}$.

$I^\bullet $ computes $RF$ relative to $\text{Qis}^{+}(\mathcal{A})$ for any exact functor $F : K^{+}(\mathcal{A}) \to \mathcal{D}$ into any triangulated category $\mathcal{D}$.

$I$ is right acyclic for any additive functor $F : \mathcal{A} \to \mathcal{B}$ into any abelian category $\mathcal{B}$.

## Comments (2)

Comment #2336 by Keenan Kidwell on

Comment #2407 by Johan on