Lemma 18.35.3. Let $f : \mathop{\mathit{Sh}}\nolimits (\mathcal{C}) \to \mathop{\mathit{Sh}}\nolimits (\mathcal{D})$ be morphism of topoi. Let $\mathcal{A} \to \mathcal{B}$ be a homomorphism of sheaves of rings on $\mathcal{D}$. Then $f^{-1}\mathop{N\! L}\nolimits _{\mathcal{B}/\mathcal{A}} = \mathop{N\! L}\nolimits _{f^{-1}\mathcal{B}/f^{-1}\mathcal{A}}$.

**Proof.**
Omitted. Hint: Use Lemma 18.33.5.
$\square$

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