The Stacks project

Lemma 92.14.3. Let $A \to B$ be a surjective ring map whose kernel $I$ is Koszul. Then $L_{B/A}$ is quasi-isomorphic to $I/I^2[1]$.

Proof. Locally on $\mathop{\mathrm{Spec}}(A)$ the ideal $I$ is generated by a Koszul regular sequence, see More on Algebra, Definition 15.32.1. Hence this follows from Lemma 92.6.2. $\square$

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