Implication Details
Claim: If a category has copowers and is essentially small, then it is thin.
Proof: This follows from the dual implication.
This implication has a dual.
Show 40 categories using this implication
- category of finitely generated abelian groups
- category of finite sets and bijections
- delooping of a group
- delooping of an infinite countable group
- delooping of a non-trivial finite group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- simplex category
- category of coproducts of Euclidean spaces
- category of finite sets and injections
- category of finite sets and surjections
- category of finite abelian groups
- category of finite groups
- category of finite sets of even cardinality
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- 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 finitely generated free modules over Z x Z
- category of metric spaces with continuous maps
- partially ordered set of extended natural numbers
- category of partially ordered sets without isolated points
- category of finitely generated projective modules over the ring of dual numbers
- category of combinatorial species
- category of large vector spaces over a large field with a small basis
- category of finite Z-sets
- forked commutative square
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking coreflexive pair
- walking fork
- walking idempotent
- walking morphism
- walking parallel pair
- walking splitting