Lemma 91.8.2. Let $A \to B$ be a ring map such that $B = B \otimes _ A^\mathbf {L} B$. Then $L_{B/A} = 0$ in $D(B)$.

Proof. This is true because $L_{B/A} = L_{B/B} = 0$ by Lemmas 91.8.1 and 91.4.7. $\square$

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