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arXiv · 0812.4685

Three Crossed Modules

Z. Arvasİ·T. S. Kuzpinari·E. Ö. Uslu
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Abstract

We introduce the notion of 3-crossed module, which extends the notions of 1-crossed module (Whitehead) and 2-crossed module (Conduché). We show that the category of 3-crossed modules is equivalent to the category of simplicial groups having a Moore complex of length 3. We make explicit the relationship with the cat$^{3}$-groups (Loday) and the 3-hyper-complexes (Cegarra-Carrasco), which also model algebraically homotopy 4-types.

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Z. Arvasİ, T. S. Kuzpinari, E. Ö. Uslu. 2009-07-21. Three Crossed Modules. https://arxiv.org/abs/0812.4685

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