Definition 76.11.1. Let $S$ be a scheme. Let $X \to Y$ be a morphism of algebraic spaces over $S$. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. We say that the *universal flattening of $\mathcal{F}$ exists* if the functor $F_{flat}$ defined in Situation 76.7.8 is an algebraic space. We say that the *universal flattening of $X$ exists* if the universal flattening of $\mathcal{O}_ X$ exists.

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