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Results tagged with descent
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user 290
10
votes
What is descent data (of higher categories), conceptually?
Before given the explicit construction, I would like to know what SHOULD the descent data be. Or more precisely what are the properties that descent data must satisfy? … Descent is the higher version of this story where the kernel pair is replaced by the Cech complex and $F$ takes values in a higher category. …
- 118k
31
votes
Why are monadicity and descent related?
$f$ should be descent iff it is surjective, and descent should intuitively say that a sheaf on $X$ descends to a sheaf on $Y$ iff for all $y \in Y$, all of the sets $A_x, f(x) = y$ are canonically identified … This is a geometric form of Galois descent. …
- 118k
6
votes
Accepted
Geometric intuition for the condition of Galois descent
Let $G \to E \to B$ be a principal bundle. It's classified by a map $f : B \to BG$ in the sense that $E$ is the homotopy fiber of this map. This means that $E$ has a certain universal property: namely …
- 118k