A generalization of Deligne's construction may be found here: http://arxiv.org/abs/0911.4979. To recoved Deligne's construction one simply takes the perspective that any abelian category is a module category over . Here we define , for any finite dimensional vector space and object to be the unique object representing the functor (really internal hom).
In general let be right, left -module categories for any tensor category. Then the is defined as the unique (up to a unique equivalence) universal object for right exact in each variable -balanced bifunctors from the cartesian product . As such it follows that where denotes the product of abelian categories defined in ``Categories Tannakiennes".
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