问了一个我自己也不懂的问题,这是真把它当老师了
What is Lie groupoid?
A Lie groupoid is a mathematical object that generalizes the notion of a Lie group. Whereas a Lie group is a group that is also a smooth manifold, a Lie groupoid is a category that is also a smooth manifold, in which the morphisms are invertible with respect to some operation, and the composition and inversion operations are smooth.
More formally, a Lie groupoid is a category equipped with a smooth structure such that the set of morphisms between any two objects is a smooth manifold, and the composition and inversion operations are smooth maps.
Lie groupoids play an important role in geometry and topology, and they have applications in fields such as differential geometry, algebraic geometry, and physics. One important example of a Lie groupoid is the tangent groupoid of a smooth manifold, which is the category whose objects are points on the manifold and whose morphisms are tangent vectors at those points. Another important example is the fundamental groupoid of a space, which is the category whose objects are points on the space and whose morphisms are homotopy classes of paths connecting those points.
感觉有点把我讲懂的感觉了,然而我完全无法判断这个回答的好坏。。。
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