Sheaf of modules
= Sheaf of modules
{wiki=Sheaf_(mathematics)#Sheaves_of_modules}
For a <ringed space> $(X,\mathcal O_X)$, a sheaf of $\mathcal O_X$-modules is a sheaf $\mathcal F$ such that every $\mathcal F(U)$ is an $\mathcal O_X(U)$-module and restriction maps preserve scalar multiplication.