Additive Categories - Special Cases

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 Categories

Famous quotes containing the words special and/or cases:

    “Navarette, a Chinese missionary, agrees with Leibniz and says that “It is the special providence of God that the Chinese did not know what was done in Christendom; for if they did, there would be never a man among them, but would spit in our faces.””
    —Matthew Tindal (1653–1733)

    “There are few cases in which mere popularity should be considered a proper test of merit; but the case of song-writing is, I think, one of the few.”
    —Edgar Allan Poe (1809–1845)