Implication Details
Claim: If a category has a parametrized natural numbers object, then it has a natural numbers object.
Proof: Every parametrized natural numbers object is also a natural numbers object; it suffices to apply the universal property with .
Show 28 categories using this implication
- trivial category
- category of small categories
- simplex category
- category of coproducts of Euclidean spaces
- category of F(I)-sets
- category of finite ordered sets
- category of finite sets
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- partially ordered set of extended natural numbers
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of preordered sets
- category of quivers with finite components
- category of connected sequences of sets
- category of large families of sets
- category of large families of sets which are mostly singletons
- indiscrete category of sets
- category of non-empty sets
- category of empty-or-finite pairs of sets
- category of combinatorial species
- category of finite Z-sets
- preordered set of integers w.r.t. divisibility
- walking coreflexive pair
- walking isomorphism