Geodesic
Comparing 2-crossed modules with Gray 3-groups
Theory and applications of categories, Tome 41 (2024), pp. 1557-1595.

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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.
Publié le :
Classification : 18B40, 18G45, 20C99, 55U15, 55U35, 20L05.
Keywords: 2-Groupoid, Gray 3-groupoids, 2-crossed modules, homotopy, linear representation 
@article{TAC_2024_41_a44,
     author = {Murat Sarikaya and Erdal Ulualan},
     title = {Comparing 2-crossed modules with {Gray} 3-groups},
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     pages = {1557--1595},
     publisher = {mathdoc},
     volume = {41},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a44/}
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Murat Sarikaya; Erdal Ulualan. Comparing 2-crossed modules with Gray 3-groups. Theory and applications of categories, Tome 41 (2024), pp. 1557-1595. http://geodesic.mathdoc.fr/item/TAC_2024_41_a44/