Definition:Quasi-Coherent Sheaf of Modules

Definition
Let $\struct {X, \OO_X}$ be a ringed space.

Let $\FF$ be a sheaf of modules $\FF$ over $\OO_X$.

Let $\FF$ be such that:
 * there exists a cover ${\family {U_i} }_{i \mathop \in I}$ of $X$ such that:
 * $\FF {\restriction U}$ is a sheaf of modules over $\OO_X {\restriction U}$ presented by global sections.

Then $\FF$ is quasi-coherent.