An algebraic lattice is a complete lattice A = (A,∨,∧) such that every element is a join of compact elements.
An element c ∈ A is compact if for every subset S ⊆ A such that c ≤ ∨S, there exists a finite subset S0 of S such that c ≤ ∨S0.
Let A and B be algebraic lattices. A morphism from A to B is a function h : A→B that is a complete homomorphism: h(∨S) = ∨h[S] and h(∧S) = ∧h[S].
|Strong amalgamation property||yes|
|Epimorphisms are surjective||yes|