Geodesic
n-tuple groupoids and optimally coupled factorizations
Theory and applications of categories, Tome 28 (2013), pp. 304-331 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

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Classification : 18D05, 18A32, 18B40
Keywords: factorization, groupoid, cubical categories 
@article{TAC_2013_28_a11,
     author = {Dany Majard},
     title = {n-tuple groupoids and optimally coupled factorizations},
     journal = {Theory and applications of categories},
     pages = {304--331},
     year = {2013},
     volume = {28},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2013_28_a11/}
}
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Dany Majard. n-tuple groupoids and optimally coupled factorizations. Theory and applications of categories, Tome 28 (2013), pp. 304-331. http://geodesic.mathdoc.fr/item/TAC_2013_28_a11/