Definition 6

Let G be a groupoid. A subgroupoid of G is a subcategory H of G such that the inverse of every arrow of G belonging to H is an arrow of H.

Let G be a groupoid. Every subgroupoid of G is a groupoid. Every full subquiver of G is a subgroupoid of G. The intersection of a family of subgroupoids of G is a subgroupoid of G.

Let H be a subquiver of G. The intersection of the subgroupoids of G of which H is a subquiver is called the subgroupoid of G generated by H. The set of its vertices is equal to that of H and its orbits are the connected components of H.