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Results tagged with descent
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user 11640
10
votes
What is descent data (of higher categories), conceptually?
The category of descent data is indeed the homotopy limit of your cosimplicial diagram. … So, morally, the category of descent data generalises the set of matching elements of a presheaf with respect to a cover. …
- 15.9k
4
votes
0
answers
157
views
What is the equivalent of Artin gluing for quasicoherent sheaves?
Then, by flat descent, or just computing by hand, we have the following bipullback square:
$$\require{AMScd}
\begin{CD}
\textbf{Mod} (\mathbb{Z}) @>>> \textbf{Mod} (\mathbb{Z} [p^{-1}]) \\
@VVV \cong @ …
- 15.9k
1
vote
Accepted
Pullback as a local property
Yes, this is a question of descent. More precisely you are asking whether the base change functor $F : \mathbf{Mfd}_{/ C} \to \prod_i \mathbf{Mfd}_{/ U_i}$ reflects pullbacks. … In short, $F$ is conservative because jointly surjective families of open embeddings satisfy the descent condition in $\mathbf{Mfd}$.
By the way, I would not call $\mathbf{Mfd}$ a nice category. …
- 15.9k