A Lie subgroupoid of a Lie groupoid G ⇉ ⇉ M is a subgroupoid H ⇉ ⇉ N (i.e. a subcategory of the category G ) with the extra requirement that H ⊆ ⊆ G is an immersed submanifold. As for a subcategory, a (Lie) subgroupoid is called wide if N = M . Any Lie groupoid G ⇉ ⇉ M has two canonical wide subgroupoids: