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      Deformations of some biset-theoretic categories

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      Author(s)
      Öğüt, İsmail Alperen
      Advisor
      Barker, Laurence John
      Date
      2020-09
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      We define the subgroup category, a category on the class of finite groups where the morphisms are given by the subgroups of the direct products and the composition is the star product. We also introduce some of its deformations and provide a criteria for their semisimplicity. We show that biset category can be realized as an invariant subcategory of the subgroup category, where the composition is much simpler. With this correspondence, we obtain some of the deformations of the biset category. We further our methods to the fibred biset category by introducing the subcharacter partial category. Similarly, we also realize the fibred biset category and some of its deformations in a category where the composition is more easily described.
      Keywords
      Biset functor
      Fibred biset functor
      Subgroup category
      Partial category
      Semisimplicity
      Semisimple deformation
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      http://hdl.handle.net/11693/54044
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      • Dept. of Mathematics - Ph.D. / Sc.D. 48
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