Green 2-functors

Abstract

We extend the theory of Mackey 2-functors introduced in arXiv:1808.04902 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.

arXiv comment46 pages. A few remaining typos corrected in journal proofs. Final version, to appear in Trans. AMS