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:
“The history of mankind interests us only as it exhibits a steady gain of truth and right, in the incessant conflict which it records between the material and the moral nature.”
—Ralph Waldo Emerson (1803–1882)
“A man will not need to study history to find out what is best for his own culture.”
—Henry David Thoreau (1817–1862)