Geodesic
On the representations of 2-groups in Baez-Crans 2-vector spaces
Theory and applications of categories, Tome 31 (2016), pp. 907-927

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We study the theory of representations of a 2-group G in Baez-Crans 2-vector spaces over a field k of arbitrary characteristic, and the corresponding 2-vector spaces of intertwiners. We also characterize the irreducible and indecomposable representations. Finally, it is shown that when the 2-group is finite and the base field k is of characteristic zero or coprime to the orders of the homotopy groups of G, the theory essentially reduces to the theory of k-linear representations of the first homotopy group of G, the remaining homotopy invariants of G playing no role.

Publié le :
Classification : 18D05, 18D10, 20L05
Keywords: 2-groups (categorical groups), 2-vector spaces, Representations, 2-categories 
@article{TAC_2016_31_a31,
     author = {Benjamin A. Heredia and Josep Elgueta},
     title = {On the representations of 2-groups in {Baez-Crans} 2-vector spaces},
     journal = {Theory and applications of categories},
     pages = {907--927},
     publisher = {mathdoc},
     volume = {31},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2016_31_a31/}
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Benjamin A. Heredia; Josep Elgueta. On the representations of 2-groups in Baez-Crans 2-vector spaces. Theory and applications of categories, Tome 31 (2016), pp. 907-927. http://geodesic.mathdoc.fr/item/TAC_2016_31_a31/