Examples
The original example of an additive category is the category of abelian groups Ab. The zero object is the trivial group, the addition of morphisms is given point-wise, and biproducts are given by direct sums.
More generally, every module category over a ring R is additive, and so in particular, the category of vector spaces over a field K is additive.
The algebra of matrices over a ring, thought of as a category as described below, is also additive.
Read more about this topic: Additive Category
Famous quotes containing the word examples:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)