I need to prove this:
Let F be a functor between abelian categories. F is aditive iff is right exact or left exact.
I think that for <-- I'll need to use the characterization:
F between aditive categories is an aditive functor iff F preserves products (or coproducts).
So I'll need to prove that if F is right exact, then it preserves coproducts and if F is left exact, it preserves products, and then I could use this result, but I'm not sure about it.
Any help or idea to both sides of the proof is welcome, thanks in advance!