4 papers
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…
3-Crossed Module Structure in the Five-Dimensional Topological Axion Electrodynamics
Masaki Fukuda, Tommy Shu, Ryo Yokokura
In this paper, we investigate the higher-group symmetry structure of a five-dimensional topological theory, which is described by a 3-crossed module. The model is obtained by a fiv…
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…
Topological invariants of 3-dimensional manifold with boundary by using crossed module
Tommy Shu
J.H.C. Whitehead introduced the concept of crossed modules in the early 20th century. These crossed modules are crucial for algebraic models of 2-type homotopy, which involve conne…