On the tensor product of well generated dg categories

We endow the homotopy category of well generated (pretriangulated) dg categories with a tensor product satisfying universal property. The resulting monoidal structure is symmetric and closed respect to cocontinuous RHom (in sense To\"en [26]). give construction in terms localisations derived categories, making use enhanced Gabriel-Popescu theorem [21]. Given regular cardinal alpha, we define construct homotopically alpha-cocomplete prove that alpha-continuous [21]) product. In particular, this shows preserves alpha-compactness.