Implication details
Claim: If a category is countably coextensive, then it has countable products.
Proof: This follows from the dual implication.
This implication has a dual.
Show 36 categories using this implication
- empty category
- discrete category on two objects
- category of finitely generated abelian groups
- delooping of the bicyclic monoid
- delooping of the double bicyclic monoid
- delooping of the additive monoid of natural numbers
- category of coproducts of Euclidean spaces
- category of finite sets and injections
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets of even cardinality
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of free abelian groups
- category of finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of countable groups
- category of finitely generated groups
- category of smooth manifolds
- category of metric spaces with non-expansive maps
- partially ordered collection of ordinal numbers
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets without isolated points
- category of quivers with finite components
- category of schemes
- category of connected sequences of sets
- category of countable sets
- category of countably infinite sets
- discrete category of sets
- category of sets with finite-to-one maps
- category of empty-or-finite pairs of sets
- category of countable-dimensional vector spaces
- category of large vector spaces over a large field with a small basis
- category of ω-sets
- walking idempotent