Implication details
Claim: If a category has countable powers and has an initial object, then it has a conatural numbers object.
Proof: This follows from the dual implication.
This implication has a dual.
Show 22 categories using this implication
- category of large families of abelian groups
- category of algebras
- category of commutative algebras
- category of commutative rings
- category of cochain complexes of abelian groups
- category of F(I)-sets
- category of filtered vector spaces
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of M-sets
- category of rings
- category of sequences of abelian groups
- category of sets
- category of large families of sets
- category of sheaves
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of long transfinite sequences of abelian groups
- category of large families of vector spaces which are mostly zero
- category of Z-sets
- category of graded abelian groups
- category of graded modules over a graded ring