On the representations of 2-groups in baez-crans 2-vector spaces

Benjamín A. Heredia, Josep Elgueta

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)907-927
Number of pages21
JournalTheory and Applications of Categories
Volume31
Publication statusPublished - 6 Oct 2016

Keywords

  • 2-categories
  • 2-groups (categorical groups)
  • 2-vector spaces
  • Representations

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