Implication details
Claim: If a category is cocartesian coclosed and has a conatural numbers object, then it has a coparametrized conatural numbers object.
Proof: This follows from the dual implication.
This implication has a dual.
Show 39 categories using this implication
- category of abelian groups
- category of large families of abelian groups
- category of finitely generated abelian groups
- category of algebras
- category of Banach spaces with linear contractions
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of cochain complexes of abelian groups
- category of coproducts of Euclidean spaces
- category of filtered vector spaces
- category of finite abelian groups
- 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 finitely generated groups
- category of measurable spaces
- category of partially ordered sets without isolated points
- category of finitely generated projective modules over the ring of dual numbers
- category of left modules over a ring
- category of left modules over a division ring
- category of left modules over a non-semisimple ring
- category of sets and relations
- category of rings
- category of sequences of abelian groups
- category of pointed sets
- category of abelian sheaves
- category of pointed topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of long transfinite sequences of abelian groups
- category of uniform spaces
- category of vector spaces
- category of countable-dimensional vector spaces
- category of large vector spaces over a large field with a small basis
- category of graded abelian groups
- category of graded modules over a graded ring
- walking splitting