The Stacks project

Definition 111.36.1. Let $X$ be a scheme. A sheaf $\mathcal{F}$ of $\mathcal{O}_ X$-modules is quasi-coherent if for every affine open $\mathop{\mathrm{Spec}}(R) = U \subset X$ the restriction $\mathcal{F}|_ U$ is of the form $\widetilde M$ for some $R$-module $M$.