Categorical representations of categorical groups

Abstract

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A simple example is computed in explicit detail.

35 pages. v2: improved presentation with additional proofs

References in corpus (5)

• Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
• Geometrical measurements in three-dimensional quantum gravity
• 2-categorical Poincare Representations and State Sum Applications
• A More Sensitive Lorentzian State Sum
• Homologically Twisted Invariants Related to (2+1)- and (3+1)-Dimensional State-Sum Topological Quantum Field Theories

Cited by in corpus (24)

• An Invitation to Higher Gauge Theory
• Higher gauge theory and a non-Abelian generalization of 2-form electrodynamics
• Higher categorical symmetries and gauging in two-dimensional spin systems
• On unitary 2-representations of finite groups and topological quantum field theory
• Infinite-Dimensional Representations of 2-Groups
• A 2-categorical state sum model
• Categorifying the Knizhnik-Zamolodchikov Connection
• Crossed modules of Hopf algebras and of associative algebras and two-dimensional holonomy
• 2-Groups, trialgebras and their Hopf categories of representations
• A Cubical Set Approach to 2-Bundles with Connection and Wilson Surfaces
• 2-Group Representations for Spin Foams
• Representation theory of 2-groups on finite dimensional 2-vector spaces
• Strict quantum 2-groups
• A More Sensitive Lorentzian State Sum
• Categorifying the $sl(2,C)$ Knizhnik-Zamolodchikov Connection via an Infinitesimal 2-Yang-Baxter Operator in the String Lie-2-Algebra
• Twisted actions of categorical groups
• On Double Groups and the Poincaré group
• The geometry of unitary 2-representations of finite groups and their 2-characters
• Categorifying measure theory: a roadmap
• On the regular representation of an (essentially) finite 2-group
• Link invariants from finite categorical groups and braided crossed modules
• Path space connections and categorical geometry
• Higher Dimensional Homology Algebra III:Projective Resolutions and Derived 2-Functors in (2-SGp)
• Link invariants from finite categorical groups