#
n-tuple groupoids and optimally coupled factorizations

##
Dany Majard

In this paper, we prove that the category of vacant $n$-tuple
groupoids is equivalent to the category of factorizations of
groupoids by $n$ factors that satisfy some Yang-Baxter type
equation. Moreover we extend this equivalence to the category of
maximally exclusive $n$-tuple groupoids, which we define, by
dropping one assumption. The paper concludes by a note on how
these results could tell us more about some Lie groups of
interest.

Keywords:
factorization, groupoid, cubical categories

2010 MSC:
18D05,18A32,18B40

*Theory and Applications of Categories,*
Vol. 28, 2013,
No. 12, pp 304-331.

Published 2013-05-30.

http://www.tac.mta.ca/tac/volumes/28/12/28-12.pdf

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