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Groupoids

Abbreviation: BinOp

Definition

A groupoid is a structure $\mathbf{A}=\langle A,\cdot\rangle$ where $\cdot$ is any binary operation on $A$.

Morphisms

Let $\mathbf{A}$ and $\mathbf{B}$ be groupoids. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism:

$h(x\cdot y)=h(x)\cdot h(y)$

Examples

Example 1:

Basic results

Properties

Finite members

n # of algebras
1 1
2 10
3 3330
4 178981952
5 2483527537094825
6 14325590003318891522275680
7 50976900301814584087291487087214170039
8 155682086691137947272042502251643461917498835481022016

Michael A. Harrison, The number of isomorphism types of finite algebras, Proc. Amer. Math. Soc., 17 1966, 731–737 MRreview

Subclasses

Superclasses

References