Implication Details
Claim: If a category is pointed, then it has a natural numbers object.
Proof: If is a zero object, then is readily seen to be a natural numbers object; alternatively, this follows from Lemma 3 here.
Show 38 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- category of Banach spaces with linear contractions
- category of commutative monoids
- simplex category
- category of finite abelian groups
- category of finite groups
- 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 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 finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of groups
- category of countable groups
- category of metric spaces with non-expansive maps
- category of monoids
- category of pseudo-metric spaces with non-expansive maps
- 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 rngs
- category of connected sequences of sets
- category of pointed sets
- category of large families of sets which are mostly singletons
- category of empty-or-finite pairs of sets
- category of combinatorial species
- category of pointed topological spaces
- category of vector spaces
- category of finite Z-sets
- walking coreflexive pair
- walking splitting