Special Cases
Most of these special cases of preadditive categories have all been mentioned above, but they're gathered here for reference.
- A ring is a preadditive category with exactly one object.
- An additive category is a preadditive category with all finite biproducts.
- A pre-Abelian category is an additive category with all kernels and cokernels.
- An Abelian category is a pre-Abelian category such that every monomorphism and epimorphism is normal.
The preadditive categories most commonly studied are in fact Abelian categories; for example, Ab is an Abelian category.
Read more about this topic: Preadditive Category
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)
“In cases of defense ‘tis best to weigh
The enemy more mighty than he seems.”
—William Shakespeare (1564–1616)