Implication details
Claim: If a category is essentially countable and is thin and is ℵ₁-cofiltered, then it has an initial object.
Proof: This follows from the dual implication.
This implication has a dual.
Claim: If a category is essentially countable and is thin and is ℵ₁-cofiltered, then it has an initial object.
This implication has a dual.