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