A Lie groupoid morphism between two Lie groupoids G ⇉ ⇉ M and H ⇉ ⇉ N is a groupoid morphism F : G → → H , f : M → → N (i.e. a functor between the categories G and H ), where both F and f are smooth. The kernel ker ⁡ ⁡ ( F ) := { g ∈ ∈ G ∣ ∣ F ( g ) = 1 s ( g ) } of a morphism between Lie groupoids over the same base manifold is automatically a normal Lie subgroupoid.