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On normal tensor functors and coset decompositions for fusion categories. (English) Zbl 1333.18008

Fusion categories arise in many areas of mathematics and physics, most notably in the theory of semisimple (quasi-)Hopf algebras and conformal field theory. In some aspects, a fusion category looks like a group from categorical level. This paper makes progresses along this line and introduced the notion a double cosets relative to two fusion subcategories of a fusion category. Based on this notion, the authors studied several equivalence relations associated with a tensor functor. Moreover, the authors researched the composition of tensor functors and radical of a fusion category. This is a paper with fruitful results.
A minor misprint: Page 592, line -16, “facts facts” should be “facts”.

MSC:

18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
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References:

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