[Home]Groupoids

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Abbreviation: BinOp

Definition

A groupoid is a structure A = (A,·) where · is any binary operation on A.

Morphisms

Let A and B be groupoids. A morphism from A to B is a function h : AB that is a homomorphism: h(x·y) = h(xh(y).

Some results

Examples

Properties

Classtype variety
Equational theory decidable
Quasiequational theory
First-order theory undecidable
Locally finite no
Residual size unbounded
Congruence distributive no
Congruence modular no
Congruence n-permutable no
Congruence regular no
Congruence uniform no
Congruence extension property no
Definable principal congruences no
Equationally definable principal congruences no
Amalgamation property yes
Strong amalgamation property yes
Epimorphisms are surjective yes

Finite members

Size 1:  1
Size 2:  10
Size 3:  3330
[Size 4]?:  178981952
[Size 5]?:  2483527537094825
[Size 6]?:  14325590003318891522275680
[Size 7]?:  50976900301814584087291487087214170039
[Size 8]?:  155682086691137947272042502251643461917498835481022016
[Michael A. Harrison, The number of isomorphism types of finite algebras, Proc. Amer. Math. Soc. 17 (1966) 731--737 MRreview]

Subclasses

Commutative groupoids
[Idempotent groupoids]?
Semigroups
[Left-distributive groupoids]?

Superclasses


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Last edited March 24, 2003 11:16 pm (diff)
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