G - functors arising from categorical group actions on abelian categories

S. Burciu

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arXiv · 1305.3432

G - functors arising from categorical group actions on abelian categories

S. Burciu

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Abstract

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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S. Burciu. 2013-05-15. G - functors arising from categorical group actions on abelian categories. https://arxiv.org/abs/1305.3432

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