\begin{definition}[Definition:Quasi-Coherent Sheaf of Modules]
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'''.
Category:Definitions/Algebraic Geometry
\end{definition}