nLab 2-representation

Idea

A 2-representation of a 2-group $G$ is an infinity-action of $G$ on a 2-vector space $V$. The higher analog of the representation of a group.

Related concepts

• representation, infinity-representation

References

• Nora Ganter, Mikhail Kapranov: Representation and character theory in 2-categories, Adv. Math. 217 5 (2008) 2268-2300 [math.AT/0602510, doi:10.1016/j.aim.2007.10.004]

• Nora Ganter, Mikhail Kapranov: Symmetric and exterior powers of categories, Journal of Transformation Groups 19 1 (2014) 57-103 [arxiv/1110.4753, doi:10.1007/s00031-014-9255-z]

• Nora Ganter: Inner products of 2-representations, Advances in Mathematics 285 (2015) 301-351 [arXiv:1110.1711 doi:10.1016/j.aim.2015.05.015]

• Zhen Huan, 2-Representations of Lie 2-groups and 2-Vector Bundles (arXiv:2208.10042)

On 2-representations of the string 2-group on 2-vector spaces and the construction of the stringor bundle:

• Peter Kristel, Matthias Ludewig, Konrad Waldorf, A representation of the string 2-group, [arXiv:2206.09797]

Reviewed in:

• Konrad Waldorf, The stringor bundle, talk at QFT and Cobordism, CQTS (Mar 2023) [web]

On categorification of the notion of characters of linear representations:

• Kate Ponto, Travis Wheeler: Character theory for 2-representations [arXiv:2609.21052]