Remark 20.13.2. Here is a down-to-earth explanation of the meaning of Lemma 20.13.1. It says that given $f : X \to Y$ and $\mathcal{F} \in \textit{Mod}(\mathcal{O}_ X)$ and given an injective resolution $\mathcal{F} \to \mathcal{I}^\bullet $ we have

the last fact coming from Leray's acyclicity lemma (Derived Categories, Lemma 13.16.7) and Lemma 20.11.10. Finally, it combines this with the trivial observation that

to arrive at the commutativity of the diagram of the lemma.

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