Finitely semisimple spherical categories and modular categories are self-dual |
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Authors: | Hendryk Pfeiffer |
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Affiliation: | Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V2T 1Z2, Canada |
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Abstract: | We show that every essentially small finitely semisimple k-linear additive spherical category for which k=End(1) is a field, is equivalent to its dual over the long canonical forgetful functor. This includes the special case of modular categories. In order to prove this result, we show that the universal coend of the spherical category, with respect to the long forgetful functor, is self-dual as a Weak Hopf Algebra. |
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Keywords: | 16W30 18D10 |
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