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