right derived functor

Let \(\mathcal{A}, \mathcal{B}\) be abelian categories, \(\mathcal{F}: \mathcal{A} \rightarrow \mathcal{B}\) a left exact functor Then the right derived functor is defined as universal cohomological delta functor \(\{\mathcal{RF}^n\}_{n \geq 0}\) with a natural isomorphism

\begin{align*} \mathcal{RF}^0 \cong \mathcal{F} \end{align*}

existence of a right derived functor