Definition:Semilattice Homomorphism

Definition

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.

Also see

• Results about semilattice homomorphisms can be found here.

Sources

• 1982: Peter T. Johnstone: Stone Spaces ... (previous) ... (next): Chapter $\text I$: Preliminaries, Definition $1.3$