Lemma 17.31.4. Let $X$ be a topological space. Let $\mathcal{A} \to \mathcal{B}$ be a homomorphism of sheaves of rings on $X$. Let $x \in X$. Then we have $\mathop{N\! L}\nolimits _{\mathcal{B}/\mathcal{A}, x} = \mathop{N\! L}\nolimits _{\mathcal{B}_ x/\mathcal{A}_ x}$.

**Proof.**
This is a special case of Lemma 17.31.3 for the inclusion map $\{ x\} \to X$.
$\square$

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