Lemma 13.20.3. Let $\mathcal{A}$ be an abelian category with enough injectives. Let $F : \mathcal{A} \to \mathcal{B}$ be an additive functor.

The functor $RF$ is an exact functor $D^{+}(\mathcal{A}) \to D^{+}(\mathcal{B})$.

The functor $RF$ induces an exact functor $K^{+}(\mathcal{A}) \to D^{+}(\mathcal{B})$.

The functor $RF$ induces a $\delta $-functor $\text{Comp}^{+}(\mathcal{A}) \to D^{+}(\mathcal{B})$.

The functor $RF$ induces a $\delta $-functor $\mathcal{A} \to D^{+}(\mathcal{B})$.

## Comments (0)