• Corpus ID: 1659905

N-tuple groups and matched n-tuples of groups

@article{Majard2011NtupleGA,
  title={N-tuple groups and matched n-tuples of groups},
  author={D. Majard},
  journal={arXiv: Category Theory},
  year={2011}
}
  • D. Majard
  • Published 30 December 2011
  • Mathematics, Physics
  • arXiv: Category Theory
This paper proves that the category of vacant n-tuple groupoids is equivalent to the category of factorizations of groupoids by n subgroupoids. Moreover it extends this equivalence to the category of maximally exclusive n-tuple groupoids, that we define, and (n+1)-factorizations of groupoids with a normal abelian subgroupoid. Finally it shows that in the smooth case, such a factorization gives a presentation of the Poincar\'e group as a triple groupoid. 
1 Citations
On Double Groups and the Poincaré group
In [22], Crane and Sheppard considered the structure of the Poincare group as a 2-Group, and derived important information about its representations in a 2-Category suited for representations of

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