Implication Details
Claim: Given a symmetric monoidal category whose underlying category is infinitary codistributive, if it is cocartesian, then it is infinitary codistributive.
Proof: This follows from the dual implication.
Claim: Given a symmetric monoidal category whose underlying category is infinitary codistributive, if it is cocartesian, then it is infinitary codistributive.
Proof: This follows from the dual implication.