Three Crossed Modules

Details Three Crossed Modules Three Crossed Modules

2008-12-26

arxiv.org/abs/0812.4685v2

Mathematics

Category Theory

Crossed module, 2-crossed module, Simplicial group, Moore complex

Scientific paper

We introduce the notion of 3-crossed module, which extends the notions of 1-crossed module (Whitehead) and 2-crossed module (Conduch\'e). 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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