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groupoid

A groupoid $G$ is a set together with a binary operation $\cdot : G \times G \longrightarrow G$ . The groupoid (or ``magma'') is closed under the operation.

There is also a separate, category-theoretic definition of ``groupoid.''

groupoid is owned by Aaron Krowne.

How to Cite This Entry

Aaron Krowne. "groupoid" (version 7). PlanetMath.org. Freely available at http://planetmath.org/Groupoid.html.

Classification

AMS MSC:

20N02 (Group theory and generalizations :: Other generalizations of groups :: Sets with a single binary operation (groupoids))

Pending Errata and Addenda

None. [ View all 2 ]

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Discussion

Closed binary operation by ratboy on 2004-06-04 12:13:46

The remark about closure seems redundant. How could a set G fail to be closed under a binary operation on G? If, on the other hand, the intent is to define the relevant notion of closure, there ought to be some mention of the situation where it matters: a subset C of G is a subgroupoid of G if the restriction of the operation to CxC is a binary operation on C.

[ reply | up ]

disambiguation? by Axel Boldt on 2002-11-06 15:54:19

Since some groupoids of the first kind are also groupoids of the second kind, and vice versa, I think it would be beneficial to have two articles, one about groupoid (binary operation) and one about groupoid (category). That way, people could link to the article they want. Right now, the word "groupoid" cannot be used in any article without immediately giving the intended definition.