Abbreviation: RLat$_b$

A \emph{bounded residuated lattice} is a residuated lattice that is bounded:

$\bot$ is the least element: $\bot\vee x=x$

$\top$ is the greatest element: $\top\vee x=\top$

Let $\mathbf{A}$ and $\mathbf{B}$ be bounded residuated lattices. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a residuated lattice homomorphism $h:A\rightarrow B$ that preserves the bounds: $h(\bot)=\bot$ and $h(\top)=\top$.

Example 1:

$\begin{array}{lr}

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

\end{array}$ $\begin{array}{lr}

f(6)= &\\
f(7)= &\\
f(8)= &\\
f(9)= &\\
f(10)= &\\

\end{array}$

[[...]] subvariety

[[...]] expansion

[[...]] supervariety

[[...]] subreduct