sheaf of modules

《Algebraic Geometry》 · 第 109 页 · Chapter II，Section 5，Definitions

Let $(X,\mathcal O_X)$ be a ringed space. A sheaf of $\mathcal O_X$-modules is a sheaf $\mathcal F$ on $X$ such that for each open set $U\subseteq X$, $\mathcal F(U)$ is an $\mathcal O_X(U)$-module and the restriction maps are compatible with the module structures.