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Results tagged with grothendieck-topology
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user 118688
2
votes
0
answers
227
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Significance of some expected results when defining Grothendieck topology
Let $\mathcal{C}$ be a category. Fixing an object $U$ of $\mathcal{C}$, there are some obvious functors we can associate to it, for example:
$h_U:\mathcal{C}^{op}\rightarrow \text{Set}$ given by $V\ …
- 6,023
0
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Grothendieck topology for a non-small category
Over a large site there is in general no sheafification functor
https://ncatlab.org/nlab/show/sheafification. For how to get around
this, the keyword is dense subsite
https://ncatlab.org/nlab …
2
votes
1
answer
663
views
Why care about Grothendieck topology? [closed]
Noah Schweber said here the following:
Why would you want a notion of sheaf theory for objects more general
than topological spaces? Well, the original motivation (to my
understanding) was to …
- 6,023
2
votes
1
answer
540
views
Stack associated to Groupoid object in category $\text{Sch}/S$
Consider the category of manifolds $\text{Man}$.
A groupoid object in the category of manifolds is called a Lie groupoid, denoted by $\mathcal{G}$. There is a way to associate a stack (over the cate …
- 6,023
0
votes
What is the geometric description of the set of isomorphism class of $G$-torsors over a site...
This is not a complete answer, too long for a comment.
If we start with an arbitrary site $\mathcal{C}$ and if we want to define the notion of a $G$-torsor over $\mathcal{C}$, then $G$ is not expecte …
- 6,023