Definition 13.17.2. Let $F : \mathcal{A} \to \mathcal{B}$ be an additive functor between abelian categories. Assume $RF : D^{+}(\mathcal{A}) \to D^{+}(\mathcal{B})$ is everywhere defined. Let $i \in \mathbf{Z}$. The $i$th right derived functor $R^ iF$ of $F$ is the functor

$R^ iF = H^ i \circ RF : \mathcal{A} \longrightarrow \mathcal{B}$

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