# Definitions for groupoidgroupoid

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1. groupoidnoun

A magma: a set with a total binary operation.

2. groupoidnoun

A set with a partial binary operation that is associative and has inverses and identities.

A groupoid is a category in which every morphism is an isomorphism.

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1. 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.

### Numerology

1. Chaldean Numerology

The numerical value of groupoid in Chaldean Numerology is: 2

2. Pythagorean Numerology

The numerical value of groupoid in Pythagorean Numerology is: 6

### Popularity rank by frequency of use

groupoid#100000#160176#333333

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"groupoid." Definitions.net. STANDS4 LLC, 2023. Web. 23 Mar. 2023. <https://www.definitions.net/definition/groupoid>.

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