In an additive category, why is finite products the same as finite coproducts?
This is relatively easy to prove when the category is R-mod, but my intuition/creativity fails to see how the method can be extended to arbritrary additive categories
Specifically, a category (in Weibel, "An introduction to homological algebra") is called additive if the Hom-sets are abelian groups, composition of morphisms distribute over addition, and such that it has a distinguished zero object (that is, an object that is both initial and terminal).
After giving this definition, Weibel claims, without further explanation, that "this structure is enough to make finite products the same as finite coproducts".
How is this?