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