A category with finite products and finite coproducts is said to be distributive if the canonical map AxB+AxC-->Ax(B+C) is invertible for all objects A, B, and C. Given a distributive category D, we describe a universal functor D-->Dex preserving finite products and finite coproudcts, for which Dex is extensive; that is, for all objects A and B the functor Dex/A x Dex/B--> Dex/(A+B) is an equivalence of categories.
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