Implication Details
Claim: Given a functor whose domain has finite coproducts, if it preserves preserves coequalizers and preserves preserves finite coproducts, then it is right exact.
Proof: This follows from the dual implication.
Claim: Given a functor whose domain has finite coproducts, if it preserves preserves coequalizers and preserves preserves finite coproducts, then it is right exact.
Proof: This follows from the dual implication.