On the mathematics of higher structures

Abstract

In a series of papers, we have discussed higher structures in science in general, and developed a framework called hyperstructures for describing and working with higher structures. We discussed the philosophy behind higher structures and formulated a principle in six stages – the Hyperstructure Principle – for forming higher structures. In this paper, we will relate hyperstructures and the general principle to known mathematical structures. We also discuss how they may give rise to new mathematical structures and prepare a framework for a mathematical theory.