Implication Details
Claim: If a category has cartesian filtered colimits and is thin, then it has exact filtered colimits.
Proof: In a thin category, every (finite) limit can be reduced to a (finite) product.
Claim: If a category has cartesian filtered colimits and is thin, then it has exact filtered colimits.
Proof: In a thin category, every (finite) limit can be reduced to a (finite) product.