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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}
}

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.

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