Multigraph of multigraphs

An n-category is a n-graph (a multigraph) with an algebraic structure. We introduce a graph of graphs and, for a k-tuple of natural numbers n(i) ∈ N, an (n(1),...,n(k))-graph: a (n(1),...,n(i))-graph of (n(i+1),...,n(k))-graphs for 1 ≤ i < k. A multigraph of multigraphs include, among others, the concepts of a prefunctor and a prenatural transformation as more fundamental concepts than functor and natural transformation.
The presented formalism gives the appropriate mathematical foundations for multi-scale analysis of hierarchical systems, among other applications. Several examples are considered.