Lemma 15.81.8. Let $R \to A$ be a finite type ring map. Let $m \in \mathbf{Z}$. Let $K^\bullet , L^\bullet \in D(A)$. If $K^\bullet \oplus L^\bullet$ is $m$-pseudo-coherent (resp. pseudo-coherent) relative to $R$ so are $K^\bullet$ and $L^\bullet$.

Proof. Immediate from Lemma 15.64.8 and the definitions. $\square$

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