History
The ideas were developed in the period 1955-1965 (which was roughly the time at which the requirements of algebraic topology were met but those of algebraic geometry were not). From the point of view of abstract category theory the work of comonads of Beck was a summation of those ideas; see Beck's monadicity theorem.
The difficulties of algebraic geometry with passage to the quotient are acute. The urgency (to put it that way) of the problem for the geometers accounts for the title of the 1959 Grothendieck seminar TDTE on theorems of descent and techniques of existence (see FGA) connecting the descent question with the representable functor question in algebraic geometry in general, and the moduli problem in particular.
Read more about this topic: Descent (category Theory)
Famous quotes containing the word history:
“I assure you that in our next class we will concern ourselves solely with the history of Egypt, and not with the more lurid and non-curricular subject of living mummies.”
—Griffin Jay, and Reginald LeBorg. Prof. Norman (Frank Reicher)
“Certainly there is not the fight recorded in Concord history, at least, if in the history of America, that will bear a moment’s comparison with this, whether for the numbers engaged in it, or for the patriotism and heroism displayed.”
—Henry David Thoreau (1817–1862)
“History is more or less bunk. It’s tradition. We don’t want tradition. We want to live in the present and the only history that is worth a tinker’s damn is the history we make today.”
—Henry Ford (1863–1947)