Definition:Sheaf of Modules Presented By Global Sections

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

A sheaf of modules $\FF$ over $\OO_X$ is presented by global sections, if there are sets $I$ and $J$ and a short exact sequence
 * $\begin{xy}\xymatrix@L+2mu@+1em{

\bigoplus_I \OO_X \ar[r] & \bigoplus_J \OO_X \ar[r] & \FF \ar[r] & 0 }\end{xy}$

in the category of $\OO_X$-modules.

Also see

 * Definition:Sheaf of Modules Generated By Global Sections
 * Presented by Global Sections implies Generated By Global Sections