An amalgam can be formally defined as a 5-tuple (A,f,B,g,C) such that A,B,C are structures having the same signature, and f: A → B, g: A → C are injective morphisms that are referred to as embeddings.
A class K of structures has the amalgamation property if for every amalgam with A,B,C ∈ K and A ≠ Ø, there exist both a structure D ∈ K and embeddings f': B → D, g': C → D such that .