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:
“Research shows clearly that parents who have modeled nurturant, reassuring responses to infants’ fears and distress by soothing words and stroking gentleness have toddlers who already can stroke a crying child’s hair. Toddlers whose special adults model kindliness will even pick up a cookie dropped from a peer’s high chair and return it to the crying peer rather than eat it themselves!”
—Alice Sterling Honig (20th century)
“In cases of defense ‘tis best to weigh
The enemy more mighty than he seems.”
—William Shakespeare (1564–1616)