Lemma 37.56.12. Let $X \to S$ be a morphism of schemes which is locally of finite type. Let $m \in \mathbf{Z}$. Let $E, K$ be objects of $D(\mathcal{O}_ X)$. If $E \oplus K$ is $m$-pseudo-coherent relative to $S$ so are $E$ and $K$.

**Proof.**
Follows from Cohomology, Lemma 20.44.6 and the definitions.
$\square$

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