Implication Details
Claim: If a category is complete and is essentially small and is thin, then it is cocomplete.
Proof: The supremum of a subset in a (small) preordered set is the infimum of the set of upper bounds.
Claim: If a category is complete and is essentially small and is thin, then it is cocomplete.
Proof: The supremum of a subset in a (small) preordered set is the infimum of the set of upper bounds.