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In mathematics, a Lie groupoid is a groupoid where the set of objects and the set of morphisms are both manifolds, all the category operations (source and target, composition, identity-assigning map and inversion) are smooth, and the source and target operations are submersions. Lie groupoids were introduced by Charles Ehresmann under the name differentiable groupoids.

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  • Grupoide de Lie (es)
  • Lie groupoid (en)
  • 리 준군 (ko)
  • 李群胚 (zh)
rdfs:comment
  • Un grupoide de Lie es un grupoide donde ambos, el grupoide y el espacio base son variedades y las funciones origen y final son funciones diferenciables cuya diferencial es suryectiva, es decir son sumersiones suryectivas. Esta definición generaliza la de grupo de Lie: los grupos de Lie son los grupoides de Lie donde el espacio base es trivial. (es)
  • 미분기하학에서, 리 준군(Lie準群, 영어: Lie groupoid)는 대상과 사상의 공간이 각각 매끄러운 다양체를 이루는 준군이다. (이산) 준군과 리 군의 공통적인 일반화이다. (ko)
  • 在数学中,李群胚(Lie groupoid)是满足如下条件的:对象集合 与态射集合 都是流形,源与靶运算 是,以及所有范畴运算(源与靶,复合,单位映射)都是光滑的。 就像群胚是有许多对象的群,一个李群胚可以想象为“有许多对象的李群推广”。恰如每个李群有一个李代数,每个李群胚有一个李代数胚。 (zh)
  • In mathematics, a Lie groupoid is a groupoid where the set of objects and the set of morphisms are both manifolds, all the category operations (source and target, composition, identity-assigning map and inversion) are smooth, and the source and target operations are submersions. Lie groupoids were introduced by Charles Ehresmann under the name differentiable groupoids. (en)
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