Tensor categories: A selective guided tour

Abstract

These are the lecture notes for a short course on tensor categories. The coverage in these notes is relatively non-technical, focussing on the essential ideas. They are meant to be accessible for beginners, but it is hoped that also some of the experts will find something interesting in them. Once the basic definitions are given, the focus is mainly on k-linear categories with finite dimensional hom-spaces. Connections with quantum groups and low dimensional topology are pointed out, but these notes have no pretension to cover the latter subjects at any depth. Essentially, these notes should be considered as annotations to the extensive bibliography.

57 pages. Notes for a three-hour lecture course. Extensively revised, updated and extended. To appear in Revista de la Unión Matemática Argentina

References in corpus (11)

• A 2-categories companion
• Congruence Subgroups and Generalized Frobenius-Schur Indicators
• On blocks of Deligne's category Rep(S_t)
• Group-theoretical properties of nilpotent modular categories
• Morita classes of algebras in modular tensor categories
• Les variétés sur le corps à un élément
• Algebraic Quantum Field Theory
• Hopf Algebras and Congruence Subgroups
• On classification of modular tensor categories
• The monoidal centre as a limit
• The double of a Hopf monad

Cited by in corpus (6)

• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers
• Poisson boundaries of monoidal categories
• A rigidity result for extensions of braided tensor C*-categories derived from compact matrix quantum groups
• On the Killing form of Lie Algebras in Symmetric Ribbon Categories
• Categorical Generalization and Physical Structuralism