Conjugative binars

Abbreviation: ConBin

Definition

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

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

Morphisms

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:

Properties

Classtype first-order no no no no no no

n # of algebras
1 1
2 4
3 215