Description:
<jats:p>We call classification the operation consisting of distributing objects in classes or groups which are, in general, less numerous than them. The relations between these classes may be (or not) partially or totally ordered. So there exist many kinds of classification schemes. Formally speaking, a classification may be a lattice, a semilattice, a chain, a hypergraph, a matroid, a tree, etc. Our purpose is to find the underlying mathematical structure of all these classifications. We explain how we can represent them in a unique way, constituting what has been called before a ”metaclassification” and which is, in fact, a Chu space. Thus, category theory can describe in terms of morphisms different operations on classifications that, according to Barwise and Seligman, we report in the following. Finally, we show that such a ”metaclassification” is the fundamental brick from which we can get some information about the mathematical continuum.</jats:p>