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:
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—William James (1842–1910)
“For the most part, we are not where we are, but in a false position. Through an infirmity of our natures, we suppose a case, and put ourselves into it, and hence are in two cases at the same time, and it is doubly difficult to get out.”
—Henry David Thoreau (1817–1862)