Moreover, the category of (mixed) Hodge structures admits a good notion of tensor product, corresponding to the product of varieties, as well as related concepts of "inner Hom" and "dual object", making it into a Tannakian category. By Tannaka–Krein philosophy, this category is equivalent to the category of finite-dimensional representations of a certain group, which Deligne, Milne and et el. has explicitly described, see and . The description of this group was recast in more geometrical terms by . The corresponding (much more involved) analysis for rational pure polarizable Hodge structures was done by .