Bundles of C*-categories and duality

Details Bundles of C*-categories and duality Bundles of C*-categories and duality

2005-10-27

arxiv.org/abs/math/0510594v3

Journal of Functional Analysis 247 (2007) 351-377

Mathematics

Category Theory

25 pages; contains the first part of the previous version, published on Journal of Functional Analysis

Scientific paper

We introduce the notions of multiplier C*-category and continuous bundle of C*-categories, as the categorical analogues of the corresponding C*-algebraic notions. Every symmetric tensor C*-category with conjugates is a continuous bundle of C*-categories, with base space the spectrum of the C*-algebra associated with the identity object. We classify tensor C*-categories with fibre the dual of a compact Lie group in terms of suitable principal bundles. This also provides a classification for certain C*-algebra bundles, with fibres fixed-point algebras of O_d.

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