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:
“The gap between ideals and actualities, between dreams and achievements, the gap that can spur strong men to increased exertions, but can break the spirit of others—this gap is the most conspicuous, continuous land mark in American history. It is conspicuous and continuous not because Americans achieve little, but because they dream grandly. The gap is a standing reproach to Americans; but it marks them off as a special and singularly admirable community among the world’s peoples.”
—George F. Will (b. 1941)
“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)