Abbreviation: ConBin

A \emph{conjugative binar} is a binar $\mathbf{A}=\langle A,\cdot\rangle$ such that

$\cdot$ is conjugative: $\exists w, \ x\cdot w=y \iff \exists w, \ w\cdot x=y$.

Let $\mathbf{A}$ and $\mathbf{B}$ be commutative binars. 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:

Commutative binars

Conjugative semigroups

Binars