Geodesic
On the 3-representations of groups and the 2-categorical traces
Theory and applications of categories, Tome 30 (2015), pp. 1999-2047.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

To 2-categorify the theory of group representations, we introduce the notions of the 3-representation of a group in a strict 3-category and the strict 2-categorical action of a group on a strict 2-category. We also 2-categorify the concept of the trace by introducing the 2-categorical trace of a 1-endomorphism in a strict 3-category. For a 3-representation $\rho$ of a group G and an element f of G, the 2-categorical trace $Tr_2\rho_f$ is a category. Moreover, the centralizer of f in G acts categorically on this 2-categorical trace. We construct the induced strict 2-categorical action of a finite group, and show that the 2-categorical trace $Tr_2$ takes an induced strict 2-categorical action into an induced categorical action of the initia groupoid. As a corollary, we get the 3-character formula of the induced strict 2-categorical action.
Publié le :
Classification : 18D05, 18D99, 20J99, 20C99
Keywords: the 3-representation of a group in a 3-category, the 2-categorical trace, the 3-cocycle condition, the induced strict 2-categorical actions, the 3-character, 2-categorification 
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     author = {Wei Wang},
     title = {On the 3-representations of groups and the 2-categorical traces},
     journal = {Theory and applications of categories},
     pages = {1999--2047},
     publisher = {mathdoc},
     volume = {30},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a55/}
}
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Wei Wang. On the 3-representations of groups and the 2-categorical traces. Theory and applications of categories, Tome 30 (2015), pp. 1999-2047. http://geodesic.mathdoc.fr/item/TAC_2015_30_a55/