In mathematics, a Lie groupoid is a groupoid where the set Ob {\displaystyle \operatorname {Ob} } of objects and the set Mor {\displaystyle \operatorname {Mor} } of morphisms are both manifolds, all the category operations are smooth, and the source and target operations s, t : Mor → Ob {\displaystyle s,t:\operatorname {Mor} \to \operatorname {Ob} } are submersions. Wikipedia