Implication details
Claim: If a category has countable products and has ℵ₁-cofiltered limits, then it has products.
Proof: The product is the -cofiltered limit of the countable partial products where ranges over the countable subsets of .
This implication has a dual.
Show 10 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 groups
- category of finite-dimensional vector spaces
- category of finite-dimensional vector spaces [uncountable field]
- partially ordered set of natural numbers
- category of finitely generated projective modules over the ring of dual numbers
- category of combinatorial species