Implication details
Claim: If a category is an elementary cotopos and has ℵ₂-small copowers, then it has ℵ₂-small powers.
Proof: This follows from the dual implication.
This implication has a dual.
Claim: If a category is an elementary cotopos and has ℵ₂-small copowers, then it has ℵ₂-small powers.
This implication has a dual.