Implication Details
Claim: If a category has countable copowers and is locally finite, then it is thin.
Proof: This follows from the dual implication.
Show 22 categories using this implication
- category of finite sets and bijections
- delooping of a non-trivial finite group
- category of coproducts of Euclidean spaces
- category of finite sets and injections
- category of finite abelian groups
- category of finite sets of even cardinality
- category of finite-dimensional vector spaces [finite field]
- category of free abelian groups
- category of countable groups
- category of smooth manifolds
- category of partially ordered sets without isolated points
- 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
- cocompletion of a discrete–pair join
- forked commutative square
- walking fork
- walking idempotent
- walking parallel pair
- walking splitting