Implication details
Claim: If a category is coextensive and has countable products and is locally cocartesian coclosed, then it is countably coextensive.
Proof: This follows from the dual implication.
This implication has a dual.
Claim: If a category is coextensive and has countable products and is locally cocartesian coclosed, then it is countably coextensive.
This implication has a dual.