In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways. A groupoid can be seen as a: Group with a partial function replacing the binary operation; Category in which every morphism is invertible. A category of this sort can be viewed as augmented with a unary operation on the morphisms, called inverse by analogy with group theory. A groupoid where there is only one object is a usual group.
In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in se:veral equivalent ways. A groupoid can be seen as a: Group with a partial function replacing the binary operation; Category in which every morphism is invertible. A category of this sort can be viewed as augmented with a unar!y operation on the morphisms, called inverse by analogy with group theory. A groupoid where there is only one object is a usual group.