Implication details
Claim: If a category has finite powers and has sequential limits, then it has countable powers.
Proof: We can write as the limit of the sequence with transition morphisms , , i.e., for .
This implication has a dual.
Show 25 categories using this implication
- category of coproducts of Euclidean spaces
- category of finite abelian groups
- category of finite sets
- category of finite-dimensional vector spaces
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of finite-dimensional vector spaces [uncountable field]
- category of free abelian groups
- category of finitely generated free abelian groups
- category of countable groups
- category of finitely generated groups
- category of smooth manifolds
- category of metric spaces with non-expansive maps
- category of pseudo-metric spaces with non-expansive maps
- category of finitely generated projective modules over the ring of dual numbers
- category of quivers with finite components
- category of schemes
- category of connected sequences of sets
- category of countable sets
- category of empty-or-finite pairs of sets
- category of combinatorial species
- category of countable-dimensional vector spaces
- category of large vector spaces over a large field with a small basis
- category of finite Z-sets
- category of ω-sets