Lemma 15.64.6 (064V)—The Stacks project

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Part 1: Preliminaries
Chapter 15: More on Algebra
Section 15.64: Pseudo-coherent modules, I
Lemma 15.64.6 (cite)

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Lemma 15.64.6. Let $R$ be a ring. Let $(K^\bullet , L^\bullet , M^\bullet , f, g, h)$ be a distinguished triangle in $D(R)$ . If two out of three of $K^\bullet , L^\bullet , M^\bullet$ are pseudo-coherent then the third is also pseudo-coherent.

Proof. Combine Lemmas 15.64.2 and 15.64.5. $\square$

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