Definition 13.16.2. 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 ith 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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