Implication details
Claim: If a category has countable coproducts and has ℵ₁-filtered colimits, then it has coproducts.
Proof: This follows from the dual implication.
This implication has a dual.
Show 7 categories using this implication
- category of finitely generated abelian groups
- delooping of a group
- delooping of an infinite uncountable group
- category of finite abelian groups
- category of finite-dimensional vector spaces
- category of finite-dimensional vector spaces [uncountable field]
- category of finitely generated projective modules over the ring of dual numbers