Definition 74.45.3. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$ which is locally of finite type. Let $E$ be an object of $D_\mathit{QCoh}(\mathcal{O}_ X)$. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. Fix $m \in \mathbf{Z}$.

We say $E$ is

*$m$-pseudo-coherent relative to $Y$*if the equivalent conditions of Lemma 74.45.2 are satisfied.We say $E$ is

*pseudo-coherent relative to $Y$*if $E$ is $m$-pseudo-coherent relative to $Y$ for all $m \in \mathbf{Z}$.We say $\mathcal{F}$ is

*$m$-pseudo-coherent relative to $Y$*if $\mathcal{F}$ viewed as an object of $D_\mathit{QCoh}(\mathcal{O}_ X)$ is $m$-pseudo-coherent relative to $Y$.We say $\mathcal{F}$ is

*pseudo-coherent relative to $Y$*if $\mathcal{F}$ viewed as an object of $D_\mathit{QCoh}(\mathcal{O}_ X)$ is pseudo-coherent relative to $Y$.

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