Groupoid
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, called
inverse by analogy with group theory. ▪
Oriented graph Special cases include: ▪
Setoids, that is: sets that come with an equivalence relation; ▪
G-sets, sets equipped with an action of a group
G. Groupoids are often used to reason about geometrical objects such as manifolds. Heinrich Brandt introduced groupoids implicitly via Brandt semigroups.