Special Cases
- A pre-abelian category is an additive category in which every morphism has a kernel and a cokernel.
- An abelian category is a pre-abelian category such that every monomorphism and epimorphism is normal.
The additive categories most commonly studied are in fact abelian categories; for example, Ab is an abelian category.
Read more about this topic: Additive Category
Famous quotes containing the words special and/or cases:
“... [the] special relation of women to children, in which the heart of the world has always felt there was something sacred, serves to impress upon women certain tendencies, to endow them with certain virtues ... which will render them of special value in public affairs.”
—Mary Putnam Jacobi (18421906)
“Only by being guilty of Folly does mortal man in many cases arrive at the perception of Sense. A thought which should forever free us from hasty imprecations upon our ever-recurring intervals of Folly; since though Folly be our teacher, Sense is the lesson she teaches; since, if Folly wholly depart from us, Further Sense will be her companion in the flight, and we will be left standing midway in wisdom.”
—Herman Melville (18191891)