Descent along torsors

In mathematics, given a "G"-torsor "X" → "Y" and a stack "F", the descent along torsors says there is a canonical equivalence between "F"("Y"), the category of "Y"-points and "F"("X")"G", the category of "G"-equivariant "X"-points. It is a basic example of descent, since it says the "equivariant data" (which is an additional data) allows one to "descend" from "X" to "Y".
When "G" is the Galois group of a finite Galois extension "L"/"K", for the "G"-torsor formula_1, this generalizes classical Galois descent (cf. field of definition).
For example, one can take "F" to be the stack of quasi-coherent sheaves (in an appropriate topology). Then "F"("X")"G" consists of equivariant sheaves on "X"; thus, the descent in this case says that to give an equivariant sheaf on "X" is to give a sheaf on the quotient "X"/"G".