Implication details
Claim: If a category has copowers, then it has ℵ₂-small copowers.
Proof: This follows from the dual implication.
This implication has a dual.
Show 25 categories using this implication
- empty category
- discrete category on two objects
- delooping of the additive monoid of ordinal numbers
- category of finite ordered sets
- category of finite sets
- category of fields
- category of fields of characteristic zero
- category of countable groups
- category of finitely generated groups
- category of smooth manifolds
- category of metric spaces with non-expansive maps
- partially ordered set of natural numbers
- category of pseudo-metric spaces with non-expansive maps
- category of connected sequences of sets
- category of sets and bijections
- category of countable sets
- discrete category of sets
- category of large families of sets and bijections
- category of large families of sets which are mostly singletons
- category of sets with finite-to-one maps
- category of non-empty sets
- category of empty-or-finite pairs of sets
- category of countable-dimensional vector spaces
- category of ω-sets
- walking span