groupoid

American  

[groo-poid] / ˈgru pɔɪd /

noun

Mathematics.

1. an algebraic system closed under a binary operation.

---

Etymology

Origin of groupoid

First recorded in 1940–45; group + -oid

Example Sentences

We can use the points and paths of a space to translate problems of topology into problems of algebra: each topological space X has an associated category π1X called the “fundamental groupoid” of X. The objects of this category are the points of the space, and the transformations are paths.

From Scientific American

A key advantage of the fundamental groupoid construction is that it is “functorial,” meaning that a continuous function f: X → Y between topological spaces gives rise to a corresponding transformation π1f: π1X → π1Y between the fundamental groupoids.

From Scientific American

The fundamental groupoid is not a complete invariant, however.

From Scientific American

In the fundamental groupoid of the circle, the different wiggling versions of a path between two points can be labeled by integers that record the number of times the trajectory winds around the circle and a + or sign indicating, respectively, a clockwise or counterclockwise direction of transit.

From Scientific American

In contrast, in the fundamental groupoid of the disk, there is only one path up to homotopy between any pair of points.

From Scientific American