Implication Details
Assumptions: abelian
Conclusions: regular
Reason: In an abelian category, every epimorphism is regular, and epimorphisms are pullback-stable, see Mac Lane, Ch. VIII.
Show 18 categories using this implication
- trivial category
- category of abelian groups
- category of finitely generated abelian groups
- category of small categories
- simplex category
- category of finite abelian groups
- category of posets
- category of prosets
- category of left modules over a ring
- category of left modules over a division ring
- category of non-empty sets
- category of abelian sheaves
- category of topological spaces
- category of pointed topological spaces
- category of torsion abelian groups
- category of vector spaces
- walking coreflexive pair
- walking isomorphism