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(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 ...

I'm learning about Lie groupoids and was inspired (by Mackenzie's book) to consider the following problem. Consider first a principal bundle $P\xrightarrow G M$; we can construct the quotient manifold ...

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 ...

I am trying to understand about Lie groupoids but not able to get feeling for what it actually is. So, question here is, What are Lie groupoids? How similar are they to Lie groups, Groupoids and ...

When constructing the Lie algebra $L(G)$ of a Lie group $G$, one usually uses the identification of the tangent space $T_1 G$ with left invariant vector fields $\mathcal{V}^l(G)$ to construct the Lie ...