| dbo:abstract
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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. 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. Accordingly, while Lie groups provide a natural model for (classical) continuous symmetries, Lie groupoids are often used as model for (and arise from) generalised, point-dependent symmetries. Extending the correspondence between Lie groups and Lie algebras, Lie groupoids are the global counterparts of Lie algebroids. Lie groupoids were introduced by Charles Ehresmann under the name differentiable groupoids. (en)
- 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)
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| rdfs:comment
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- 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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