[1][2] Perhaps the most well-developed example of this general notion is the subfield of abstract algebra called representation theory, which studies the representing of elements of algebraic structures by linear transformations of vector spaces.
A key class of such problems stems from the fact that, like adjacency in undirected graphs, intersection of sets (or, more precisely, non-disjointness) is a symmetric relation.
[3] One foundational result here, due to Paul Erdős and his colleagues, is that every n-vertex graph may be represented in terms of intersection among subsets of a set of size no more than n2/4.
[5] Dual to the observation above that every graph is an intersection graph is the fact that every partially ordered set (also known as poset) is isomorphic to a collection of sets ordered by the inclusion (or containment) relation ⊆.
Since each of those structures may be thought of, intuitively, as a meaning of the image Y (one of the things that Y is trying to tell us), this phenomenon is called polysemy—a term borrowed from linguistics.