Lemma 15.59.5 (06Y2)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 15: More on Algebra
Section 15.59: Derived tensor product
Lemma 15.59.5 (cite)

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Lemma 15.59.5. Let $R$ be a ring. Let $(K_1^\bullet , K_2^\bullet , K_3^\bullet )$ be a distinguished triangle in $K(R)$ . If two out of three of $K_ i^\bullet$ are K-flat, so is the third.

Proof. Follows from Lemma 15.58.4 and the fact that in a distinguished triangle in $K(R)$ if two out of three are acyclic, so is the third. $\square$

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