Groupoid

Definition

A groupoid generalizes the notion of a group to a category in which every morphism is an isomorphism. That is, there is an operation ${\_}^{-1}:\mathcal{C}[A,B]\to \mathcal{C}[B,A]$ which provides an inverse of each arrows in such a way that $f\circ f^{-1}=id$, $f^{-1}\circ f=id$.

Remarks

• A groupoid with 1 element is a group.