N-tuple groups and matched n-tuples of groups

Abstract

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 Poincaré group as a triple groupoid.

15 pages, 8 figures

References in corpus (2)

• Double groupoids, matched pairs and then matched triples
• On Double Groups and the Poincaré group

Cited by in corpus (1)

• On Double Groups and the Poincaré group