Groupoid

Summary

A groupoid is a category in which every morphism is invertible. A group is the same as a groupoid with one object, so groupoids generalize groups to symmetries between several objects. The fundamental groupoid of a space, the action groupoid of a group action and the groupoid of an equivalence relation are standard examples. Groupoids model homotopy 1-types, and they appear in topology, geometry and the theory of stacks.