Theory of 2-Structures, Part II: Representation Through Labeled Tree Families

Abstract This paper (which is the second part of a whole consisting of two parts) continues the investigation of the theory of 2-structures initiated in Part I. In particular we investigate hierarchical representations of 2-structures through trees where the “local” relationship between direct descendants of an inner node of a tree is given through a 2-structure. The main result of the paper is that (for such hierarchical definition) it suffices to consider trees where these local relationships are given by either a primitive 2-structure or a complete 2-structure or a linear 2-structure. Hence, each 2-structure can be constructed from (decomposed into) primitive, complete and linear 2-structures.