Abstract
In this paper we introduce the notion of a categorical Mackey functor. This categorical notion allows us to obtain new Mackey functors by passing to Quillen’s K-theory of the corresponding abelian categories. In the case of an action by monoidal autoequivalences on a monoidal category the Mackey functor obtained at the level of Grothendieck rings has in fact a Green functor structure.
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Communicated by A. Constantin.
The research was done in part during a stay at the Erwin Schrödinger Institute, Vienna, in the frame of the Programme Modern Trends in Topological Quantum Field Theory in February 2014. The author thanks the ESI and the organizers of the Programme for the support and kind hospitality.
This research was supported by a grant of Ministry of Research and Innovation CNCS-UEFISCDI, Project No. PN-III-P4-ID-PCE-2016-0157, within PNCDI III.
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Burciu, S. On monoidal group actions on tensor categories and their Green functors. Monatsh Math 188, 431–459 (2019). https://doi.org/10.1007/s00605-018-1156-0
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DOI: https://doi.org/10.1007/s00605-018-1156-0