Abbreviation: RBand
A \emph{rectangular band} is a bands $\mathbf{B}=\langle B,\cdot \rangle $ such that
$\cdot $ is rectangular: $x\cdot y\cdot x=x$.
A \emph{rectangular band} is a bands $\mathbf{B}=\langle B,\cdot \rangle $ such that
$x\cdot y\cdot z=x\cdot z$.
Let $\mathbf{B}$ and $\mathbf{C}$ be rectangular bands. A morphism from $\mathbf{B}$ to $\mathbf{C}$ is a function $h:B\rightarrow C$ that is a homomorphism:
$h(xy)=h(x)h(y)$
$\begin{array}{lr}
f(1)= &1
f(2)= &
f(3)= &
f(4)= &
f(5)= &
f(6)= &
f(7)= &
\end{array}$