All Questions
Tagged with differentiable-stacks lie-groupoids
10 questions
3
votes
1
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182
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Morita equivalence of Lie groupoids and isomorphism of differentiable stacks
It's a well known fact two Lie groupoids are Morita-equivalent iff they induce isomorphic differentiable stacks (I'll call this statement "(1)").
It's also well known that there is a ...
- 105
3
votes
0
answers
131
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Bibundle induced by a morphism of stacks
[This is a repost, because I've written the wrong page number in the previous version of this question. I'm sorry]
I'm currently reading "Orbifolds as stacks" by Eugene Lerman and I'm stuck ...
- 105
3
votes
0
answers
99
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Cohomology of differentiable stacks: should the sheaf be fine?
I'm reading these Behrend's notes on cohomology of stacks, and I can't get over a detail in the fifth page.
Let $X_\bullet=(X_1\rightrightarrows X_0)$ be a Lie groupoid and let $\mathcal{N}$ be its ...
- 105
4
votes
0
answers
194
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Cohomology of a differentiable stack: evaluation at a point
I'm reading these Behrend's notes on cohomology of stacks, and I can't get over a detail in the fourth page.
Let $X_\bullet=(X_1\rightrightarrows X_0)$ be a Lie groupoid and let $\mathcal{N}$ be its ...
- 105
5
votes
1
answer
291
views
What does it mean for a space to be a differentiable stack?
(I'd like to premise that I'm not an expert about these topics (just a student), so many of my doubts and perplexities are probably symptoms of my mathematical immaturity)
I'm currently studying ...
- 105
6
votes
1
answer
402
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Anafunctors vs the plus construction
Given a Lie groupoid $G$, we can view it as representing a prestack on $\text{Mfld}$ by sending and manfold $M$ to the groupoid of smooth functors and smooth natural transformations
$$G(M) := \text{...
- 160
1
vote
0
answers
67
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Is there an inverse image functor for sheaves on stacks?
I'm interested specifically in an inverse image functor between differentiable stacks, ie. stacks coming from Lie groupoids. Specifically, if I have a morphism of Lie groupoids $H\to G$ and I have a ...
- 1,198
2
votes
1
answer
159
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Necessary and sufficient conditions for a Lie groupoid to present a stack
Let $\mathcal{G} = G_1 \rightrightarrows G_0$ be a Lie Groupoid (although I am also interested in groupoids internal to other sites), the stack associated to $\mathcal{G}$, which is sometimes denoted $...
3
votes
0
answers
184
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Lie group (topological group) action on differentiable stack (topological stack)
Let $G$ be a Lie group and $\mathcal{D}$ be a differentiable stack (I am also ok to start with a topological group and topological stack).
I have seen someone mentioning somewhere that the notion of ...
- 6,023
2
votes
2
answers
530
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Fibered product of stacks comes from a Lie groupoid
I am adding some context here. I am reading Introduction to Differentiable Stacks by Gregory Ginot.
In page no $7$, just before the remark $2.2$ he says the following.
One shall be careful that ...
- 6,023