Abbreviation: CBinOp

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

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:

$\begin{array}{lr}

f(1)= &1\\
f(2)= &\\
f(3)= &\\
f(4)= &\\
f(5)= &\\
f(6)= &\\

\end{array}$

[[Commutative semigroups]] 

[[Idempotent commutative groupoids]] 

[[Commutative left-distributive groupoids]] 

[[Groupoids]]