Mixtures and the hierarchical groupoid structure of <i>n</i> -fold groupoids

The theory of n -fold groupoids is contextualized by applications to solid composites. The concept of defects of misalignment between the various constituents of a multi-composite is introduced and a definition of a representative n -fold material groupoid is proposed. The hierarchical structure of the various ranks of participant groupoids is shown to be equivalent to the graph of a hypercube. Examples of possible applications are presented.