Groupoid

Category where every morphism is invertible; generalization of a group

In mathematics, especially in category theory and homotopy theory, a groupoid 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.

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