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math.CT2026
An Equivalence of Categories between 3-Crossed Modules and Gray 4-Groups
Masaki Fukuda, Tommy Shu
In this paper, we investigate the relation between the category of 3-crossed modules and the category of Gray-type 4-groups. The notion of a 3-crossed module was first introduced b…
math.CT2025
3-Crossed modules, Quasi-categories, and the Moore complex
Masaki Fukuda, Tommy Shu
The established equivalence between 2-crossed modules and Gray 3-groups [M. Sarikaya and E. Ulualan, 2024] serves as a benchmark for higher-dimensional algebraic models. However, t…