Lemma 21.34.6. Let (\mathcal{C}, \mathcal{O}) be a ringed site. Let L and M be objects of D(\mathcal{O}). Let \mathcal{I}^\bullet be a K-injective complex of \mathcal{O}-modules representing M. Let \mathcal{L}^\bullet be a complex of \mathcal{O}-modules representing L. Then
for all U \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C}). Similarly, H^0(\Gamma (\mathcal{C}, \mathop{\mathcal{H}\! \mathit{om}}\nolimits ^\bullet (\mathcal{L}^\bullet , \mathcal{I}^\bullet ))) = \mathop{\mathrm{Hom}}\nolimits _{D(\mathcal{O})}(L, M).
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