Lemma 10.134.3. Let $A \to B$ be a polynomial algebra. Then $\mathop{N\! L}\nolimits _{B/A}$ is homotopy equivalent to the chain complex $(0 \to \Omega _{B/A})$ with $\Omega _{B/A}$ in degree $0$.

**Proof.**
Follows from Lemma 10.134.2 and the fact that $\text{id}_ B : B \to B$ is a presentation of $B$ over $A$ with zero kernel.
$\square$

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