Implication details
Claim: If a category has equalizers and has zero morphisms, then it has kernels.
Proof: This is trivial.
This implication has a dual.
Show 19 categories using this implication
- empty category
- category of large families of abelian groups
- category of Banach spaces with linear contractions
- category of commutative monoids
- category of finite groups
- category of finitely generated free abelian groups
- category of groups
- category of countable groups
- category of finitely generated groups
- category of monoids
- partially ordered collection of ordinal numbers
- category of finitely generated projective modules over the ring of dual numbers
- category of rngs
- category of pointed sets
- category of pointed topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of long transfinite sequences of abelian groups
- walking splitting