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Remark 56.22.5. Comment on Theorem 56.22.4. Since $S$ is a final object in the category $\mathcal{C}$, the cohomology groups on the right-hand side are merely the right derived functors of the global sections functor. In fact the proof shows that $H^ p(U, f^*\mathcal{F}) = H^ p_\tau (U, \mathcal{F}^ a)$ for any object $f : U \to S$ of the site $\mathcal{C}$.


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