Vol. 290, No. 2, 2017

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ISSN: 0030-8730
On the classification of pointed fusion categories up to weak Morita equivalence

Bernardo Uribe

Vol. 290 (2017), No. 2, 437–466
Abstract

A pointed fusion category is a rigid tensor category with finitely many isomorphism classes of simple objects which moreover are invertible. Two tensor categories C and D are weakly Morita equivalent if there exists an indecomposable right module category over C such that FunC(,) and D are tensor equivalent. We use the Lyndon–Hochschild–Serre spectral sequence associated to abelian group extensions to give necessary and sufficient conditions in terms of cohomology classes for two pointed fusion categories to be weakly Morita equivalent. This result allows one to classify the equivalence classes of pointed fusion categories of any given global dimension.

Keywords
tensor category, pointed tensor category, weak Morita equivalence, fusion category
Mathematical Subject Classification 2010
Primary: 18D10
Secondary: 20J06
Milestones
Received: 20 July 2016
Revised: 7 February 2017
Accepted: 10 March 2017
Published: 25 July 2017
Authors
Bernardo Uribe
Departamento de Matemáticas y Estadística
Universidad del Norte
Barranquilla
Colombia