Implication details
Claim: If a category has countable copowers and is essentially countable, then it is thin.
Proof: This follows from the dual implication.
This implication has a dual.
Show 19 categories using this implication
- category of finitely generated abelian groups
- delooping of an infinite countable group
- delooping of the additive monoid of natural numbers
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of coproducts of Euclidean spaces
- category of finite-dimensional vector spaces [countable 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 smooth manifolds
- category of partially ordered sets without isolated points
- category of quivers with finite components
- category of schemes
- category of countable sets
- category of large families of sets which are mostly empty
- category of countable-dimensional vector spaces
- category of large vector spaces over a large field with a small basis