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arxiv: 0812.4685 · v2 · submitted 2008-12-26 · 🧮 math.CT · math.AT

Three Crossed Modules

Z. Arvas\.I , T. S. Kuzpinari , E. \"O. Uslu This is my paper
classification 🧮 math.CT math.AT
keywords crossedmodulecategorygroupsmodulesalgebraicallycegarra-carrascocomplex
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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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  1. 3-Crossed Module Structure in the Five-Dimensional Topological Axion Electrodynamics

    hep-th 2026-02 unverdicted novelty 6.0

    The five-dimensional topological axion electrodynamics is shown to possess a 3-crossed module structure through modified Stueckelberg couplings required for background gauge invariance.