Green 2-functors

Dell’Ambrogio, Ivo

doi:10.1090/tran/8681

Green 2-functors
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Trans. Amer. Math. Soc. 375 (2022), 7783-7829 Request permission

Abstract:

We extend the theory of Mackey 2-functors provided by Balmer and Dell’Ambrogio [Mackey 2-functors and Mackey 2-motives, European Mathematical Society (EMS), Zürich, 2020] by defining the appropriate notion of rings, namely Green 2-functors. After providing the first results of our theory and abundant examples, we show how all classical Green functors familiar from representation theory and topology arise by decategorification, in various ways, of some Green 2-functor occurring in Nature.

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Green 2-functors
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