publication . Preprint . 2004

Representation theory of 2-groups on finite dimensional 2-vector spaces

Elgueta, Josep;
Open Access English
  • Published: 09 Aug 2004
Abstract
In this paper, the 2-category $\mathfrak{Rep}_{{\bf 2Mat}_{\mathbb{C}}}(\mathbb{G})$ of (weak) representations of an arbitrary (weak) 2-group $\mathbb{G}$ on (some version of) Kapranov and Voevodsky's 2-category of (complex) 2-vector spaces is studied. In particular, the set of equivalence classes of representations is computed in terms of the invariants $\pi_0(\mathbb{G})$, $\pi_1(\mathbb{G})$ and $[\alpha]\in H^3(\pi_0(\mathbb{G}),\pi_1(\mathbb{G}))$ classifying $\mathbb{G}$. Also the categories of morphisms (up to equivalence) and the composition functors are determined explicitly. As a consequence, we obtain the the {\it monoidal} category of linear represen...
Subjects
arXiv: Mathematics::Category TheoryMathematics::Algebraic TopologyMathematics::K-Theory and Homology
free text keywords: Mathematics - Category Theory, Mathematics - Representation Theory
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