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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.”

Related:

Semigroup, Group, LoopAndQuasigroup

Synonym:

magma

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

20N02*no label found*

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## Comments

## disambiguation?

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.

## Re: disambiguation?

Yeah, I'll split them up now.

apk

## Closed binary operation

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.