Green equivalences in equivariant mathematics

  title={Green equivalences in equivariant mathematics},
  author={Paul Balmer and Ivo Dell'Ambrogio},
  journal={Mathematische Annalen},
We establish Green equivalences for all Mackey 2-functors, without assuming Krull-Schmidt. By running through the examples of Mackey 2-functors, we recover all variants of the Green equivalence and Green correspondence known in representation theory and obtain new ones in several other contexts. Such applications include equivariant stable homotopy theory in topology and equivariant sheaves in geometry. 
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