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Results tagged with lie-groupoids
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user 3473
2
votes
Accepted
Necessary and sufficient conditions for a Lie groupoid to present a stack
Note that $\hat r\mathcal{G}$ is always a prestack. This is basically equivalent to the fact that $C^\infty(-,G_1)$ is a sheaf, and it means that your functor
$$
\hat r\mathcal{G}(U) \to \mathrm{holi …
- 4,519
3
votes
What is the 2-category whose 0-objects are Lie algebroids?
I'm ashamed to give the following abstract nonsense answer to this excellent question. Also, this is just an expansion of Santiago's first comment above.
We'll have to talk about morphisms between L …
- 4,519
15
votes
0
answers
194
views
Are Lie groupoids just groupoids internal to smooth manifolds?
It seems to be common to say "no" - but is this true?
Two weeks ago I asked for a counterexample, but received no replies.
To give some background, let's recall that the difference between Lie groupoi …
- 4,519
7
votes
0
answers
117
views
Example of a groupoid internal to the category of smooth manifolds that is not a Lie groupoid
This questions is about the distinction between:
Lie groupoids: we require source and target maps to be submersions. This implies that the domain of the composition map, $G_1 \;{}_s\!\times_t G_1$, i …
- 4,519
14
votes
Applications of topological and diferentiable stacks
I would like to point out that stacks are "just" higher analogues of sheaves - a very basic tool to arrange structure. The same is true for topological or differentiable stacks. So I think everybody w …
- 4,519