In this paper, we have constructed the close relationship between 2-crossed modules and Gray 3-groupoids with a single object (Gray 3-groups). Using both the equivalence between 2-crossed modules and Gray 3-groups, and the Gray category structure over the category of chain complexes of vector spaces; we describe linear representations as certain 3-functors.
Keywords: 2-Groupoid, Gray 3-groupoids, 2-crossed modules, homotopy, linear representation
2020 MSC: 18B40, 18G45, 20C99, 55U15, 55U35, 20L05.
Theory and Applications of Categories, Vol. 41, 2024, No. 45, pp 1557-1595.
Published 2024-10-16.
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