Every abelian category is regular
= Every abelian category is regular
An abelian category has finite limits, and every morphism factors through its image as an epimorphism followed by a monomorphism. Every epimorphism is the cokernel of its kernel, hence a <regular epimorphism>, and epimorphisms in an abelian category are stable under pullback. Therefore every abelian category is a <regular category>.