An algebraic poset is a directed complete partial order P = (P, ≤ )
the set of compact elements below any element is directed and
every element is the join of all compact elements below it.
An element c ∈ P is compact if for every subset S ⊆ P such that c ≤ ∨S, there exists a finite subset S0 of S such that c ≤ ∨S0.
The set of compact elements of P is denoted by K(P).
Let P and Q be algebraic posets. A morphism from P to Q is a function f : P→Q that is Scott-continuous, which means that f preserves all directed joins: z = ∨D ⇒ f(z) = ∨f[D] for all directed sets D ⊆ P.
|Strong amalgamation property|
|Epimorphisms are surjective|