# Tagged Questions

**8**

votes

**1**answer

559 views

### Learning higher differential geometry

I have read parts of the motivation on nlab and all the posts on MO I could find on the subject, and by now there are a few questions on my mind. If they trivial for someone who understands the ...

**20**

votes

**4**answers

1k views

### What is an $(\infty,1)$-topos, and why is this a good setting for doing differential geometry?

In this post on the n-Category CafĂ©, Urs Schreiber says that, "The theory of G-principal bundles makes sense in any $(\infty,1)$-topos." I followed the link to the nLab and tried to chase definitions, ...

**1**

vote

**1**answer

170 views

### gluing bundles as a 2-colimit

Is the gluing of bundles from not-necessarily trivial bundles just some kind of 2-colimit?

**2**

votes

**4**answers

4k views

### Cotangent bundle of a differentiable stack

If you ever wanted to construct the tangent bundle of a differentiable stack, it's relatively simple:
First, if $\mathbf{X}$ is a stack coming from a Lie groupoid $\mathcal{G}$, you could just say ...

**5**

votes

**1**answer

348 views

### Connections on principal bundles via stacks?

Let G be a Lie group and M a smooth manifold. Suppose that P is a principal G-bundle over M. Then by Yoneda, this corresponds to a smooth map $p:M \to \left\[G\right]$, where $\left\[G\right]$ is the ...