\begin{definition}[Definition:Semilattice Homomorphism]
Let $\struct {S, \circ}$ and $\struct {T, *}$ be semilattices.
Let $\phi: S \to T$ be a mapping such that $\circ$ has the morphism property under $\phi$.
That is, $\forall a, b \in S$:
:$\map \phi {a \circ b} = \map \phi a * \map \phi b$
Then $\phi: \struct {S, \circ} \to \struct {T, *}$ is a semilattice homomorphism.
\end{definition}