## Commutative Groupoids

Abbreviation: CBinOp

### Definition

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

##### Morphisms

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

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

Example 1:

### Properties

Classtype variety decidable undecidable no unbounded no no no no no no no no yes yes yes

### Finite members

$\begin{array}{lr} f(1)= &1\\ f(2)= &\\ f(3)= &\\ f(4)= &\\ f(5)= &\\ f(6)= &\\ \end{array}$

### Subclasses

[[Commutative semigroups]]
[[Idempotent commutative groupoids]]
[[Commutative left-distributive groupoids]]

[[Groupoids]]