  Let $\mathcal C$ be closed symmetric monoidal Grothendieck category. We
define the pure derived category with respect to the monoidal structure via a
relative injective model category structure on the category
$\mathbf{C}(\mathcal C)$ of unbounded chain complexes in $\mathcal C$. We use
$\lambda$-Purity techniques to get this. As application we define the stalkwise
pure derived category of the category of quasi--coherent sheaves on a
quasi-separated scheme. We also give a different approach by using the category
of flat quasi--coherent sheaves.
