Lemma 37.57.13. Let $X \to S$ be a morphism of schemes which is locally of finite type. Let $m \in \mathbf{Z}$. Let $\mathcal{F}^\bullet $ be a (locally) bounded above complex of $\mathcal{O}_ X$-modules such that $\mathcal{F}^ i$ is $(m - i)$-pseudo-coherent relative to $S$ for all $i$. Then $\mathcal{F}^\bullet $ is $m$-pseudo-coherent relative to $S$.

**Proof.**
Follows from Cohomology, Lemma 20.45.7 and the definitions.
$\square$

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