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:
“When a mother quarrels with a daughter, she has a double dose of unhappiness—hers from the conflict, and empathy with her daughter’s from the conflict with her. Throughout her life a mother retains this special need to maintain a good relationship with her daughter.”
—Terri Apter (20th century)
“Medication alone is not to be relied on. In one half the cases medicine is not needed, or is worse than useless. Obedience to spiritual and physical laws—hygeine [sic] of the body, and hygeine of the spirit—is the surest warrant for health and happiness.”
—Harriot K. Hunt (1805–1875)