A MetaStructure is a higher-level framework that treats entire collections of structures as single objects, equipped with natural operations that preserve isomorphisms across different domains. The term “Structure” here refers broadly to mathematical systems as well as real-world models. An Iterated MetaStructure generalizes this idea recursively, generating successive layers in which structures of structures form deeper hierarchical meta-levels. In this work, we extend and investigate the properties of Algebra, Topology, Lattices, Queues, Markov Chains, and Intervals through the lens of MetaStructures and Iterated MetaStructures.
Takaaki Fujita (Mon,) studied this question.