In Wikipedia, I was looking for the definition of quasi-coherent sheaf. However I got confused.
It seems to me that quasi-coherent sheaf is a sheaf of sheaves.
Though, indeed, it says quasi-coherent sheaves are subcategory of $\mathcal{O}_X$-modules, where $\mathcal{O}_X$-modules are defined as follows:
Let $X$ be a topological space and consider a locally ringed space $(X, \mathcal{O}_X)$. Then the wikipedia defines $\mathcal{O}_X$-modules to be a sheaf $F$ such that $F(U)$ is a module over the ring $\mathcal{O}_X(U)$ for every open set $U$ in $X$. Thats each $\mathcal{O}_X$-module is a sheaf $F$.
Next, the last para of wikipedia says, a sheaf of $\mathcal{O}_X$-modules (which itself a sheaf $F$) is quasi-coherent if it is, locally, isomorphic to the cokernel of the map between free $\mathcal{O}_X$-modules. Thus it seems to me that quasi-coherent sheaf is a sheaf of sheaves.
Can someone explain it please ?
Thanks