Definition:Sheaf of Modules Generated By Global Sections

Definition

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

A sheaf of modules $\FF$ over $\OO_X$ is generated by global sections, if there is a set $I$ and an epimorphism

$\begin{xy}\xymatrix@L+2mu@+1em{

\bigoplus_I \OO_X \ar[r] & \FF }\end{xy}$

in the category of $\OO_X$-modules.