# Questions tagged [lie-groupoids]

A Lie groupoid can thus be thought of as a "many-object generalization" of a Lie group, just as a groupoid is a many-object generalization of a group.

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### Reference request: Integration of A-paths.

Recall that an A-path for a Lie Algebroid is an an algebroid morphism from the tangent bundle over the unit interval $[0,1]= I$ to a general Lie algebroid $A$. Now, whenever A is the algebroid of some ...
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### Why are gerbes so scarce in recent research?

I have recently been exposed to gerbes for an undergraduate research project and I feel like this structure has very little mention anywhere really. Most papers that deal with anything relating to it ...
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### Is the product of two Lie groupoids always a Lie groupoid?

Let $\mathcal{G}=[G_1 \rightrightarrows G_0]$ and $\mathcal{H}=[H_1 \rightrightarrows H_0]$ be two Lie groupoids. Consider the product category $\mathcal{G} \times \mathcal{H}$. My question: Is the ...
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### How units of a Lie groupoid act on a manifold?

The definition of a Lie groupoid action given in Sébastien Racanière's notes (up to notation) says that the action of a Lie groupoid $\mathcal{G} \rightrightarrows M$ on a smooth manifold $Q$ consists ...
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### Lie groupoid associated to an incomplete vector field

Let $M$ be a smooth manifold and $X \in \mathfrak{X}(M)$ be a vector field. If $X$ is complete, its flow defines a group action $\Bbb R \circlearrowright M$ via $t \cdot x \doteq \Phi_X(t,x)$. This ...
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### Cancellation law in a Lie groupoid

I'm playing around with the definition of a Lie groupoid following Eckhard Meinrenken's notes. I read the thing for the first time in my life like an hour ago, so assume that I don't know anything ...
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