Implication Details
Assumptions: cartesian filtered colimits, countable coproducts, distributive
Conclusions: countably distributive
Proof: Each functor preserves finite coproducts and filtered colimits, hence all countable coproducts.
Assumptions: cartesian filtered colimits, countable coproducts, distributive
Conclusions: countably distributive
Proof: Each functor preserves finite coproducts and filtered colimits, hence all countable coproducts.