1
vote
1answer
292 views

When are $k$-sectors of a Lie groupoid a manifold?

Let ${\mathcal{G} = \lbrace s,t:G_1 \to G_0 \rbrace}$ be a Lie groupoid. Define $$(\mathcal{G}^k)_0:=\lbrace (a_1,\dots,a_k) \in G_1^k\mid s(a_1)=t(a_1)=\dots=s(a_k)=t(a_k) \rbrace$$ (This is the ...
4
votes
2answers
454 views

Is there a “geometric” language that describes the equivalence groupoid of a foliated manifold?

Sitting on the couch in my office is a certain groupoid. It's waiting for me to say something to it. My problem is that I don't know its language. My question here is for some suggestions. Here, ...
14
votes
3answers
535 views

What is the 2-category whose 0-objects are Lie algebroids?

Recall the notion of Lie algebroid (n Lab, Wikipedia). One motivation for studying Lie algebroids is that they are infinitesimal versions of Lie groupoids, and Lie groupoids present stacks. In ...