\begin{definition}[Definition:Category of Quasi-Coherent Sheaves of Modules]
Let $X$ be a topological space. 
Let $\OO_X$ be a sheaf of commutative rings.
The '''category of quasi-coherent $\OO_X$-modules''' $\map {\mathbf {QCoh} } {X, \OO_X}$ is the category with:
{{DefineCategory
|ob = quasi-coherent $\OO_X$-modules
|mor = morphisms $\OO_X$-modules
|id = identity morphisms on presheaves
|comp = composition of morphisms of presheaves
}}
\end{definition}