G - functors arising from categorical group actions on abelian categories
Burciu, S.
Original · EN
A Mackey type decomposition for group actions on abelian categories is described. This allows us to define new Mackey functors which associates to any subgroup the K-theory of the corresponding equivariantized abelian category. In the case of an action by tensor autoequivalences the Mackey functor at the level of Grothendieck rings has a Green functor structure. As an application we give a description of the Grothendieck rings of equivariantized fusion categories under group actions by tensor autoequivalences on graded fusion categories.
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