History
Abelian categories were introduced by Buchsbaum (1955) (under the name of "exact category") and Grothendieck (1957) in order to unify various cohomology theories. At the time, there was a cohomology theory for sheaves, and a cohomology theory for groups. The two were defined differently, but they had similar properties. In fact, much of category theory was developed as a language to study these similarities. Grothendieck unified the two theories: they both arise as derived functors on abelian categories; the abelian category of sheaves of abelian groups on a topological space, and the abelian category of G-modules for a given group G.
Read more about this topic: Abelian Category
Famous quotes containing the word history:
“Spain is an overflow of sombreness ... a strong and threatening tide of history meets you at the frontier.”
—Wyndham Lewis (1882–1957)
“Modern Western thought will pass into history and be incorporated in it, will have its influence and its place, just as our body will pass into the composition of grass, of sheep, of cutlets, and of men. We do not like that kind of immortality, but what is to be done about it?”
—Alexander Herzen (1812–1870)
“They are a sort of post-house,where the Fates
Change horses, making history change its tune,
Then spur away o’er empires and o’er states,
Leaving at last not much besides chronology,
Excepting the post-obits of theology.”
—George Gordon Noel Byron (1788–1824)