Implication Details
Assumptions: abelian
Conclusions: regular
Proof: In an abelian category, every epimorphism is regular, and epimorphisms are pullback-stable, see Mac Lane, Ch. VIII.
Show 27 categories using this implication
- category of abelian groups
- category of abelian sheaves
- category of finite abelian groups
- 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 abelian groups
- category of Hausdorff spaces
- category of left modules over a division ring
- category of left modules over a ring
- category of locally ringed spaces
- category of measurable spaces
- category of metric spaces with non-expansive maps
- category of metric spaces with ∞ allowed
- category of non-empty sets
- category of pointed topological spaces
- category of posets
- category of prosets
- category of pseudo-metric spaces with non-expansive maps
- category of small categories
- category of topological spaces
- category of torsion abelian groups
- category of vector spaces
- simplex category
- trivial category
- walking coreflexive pair
- walking isomorphism