nLab
Green functor

Under construction

Content

Idea

In the GG-equivariant context for a finite group GG, the role of abelian groups in non-equivariant algebra is now taken by Mackey functors. The category of Mackey functors is a closed symmetric monoidal category with symmetric monoidal product, the box product. Green functors are commutative monoids for this box product.

A Green functor is a Mackey functor R̲\underline{R} such that for all finite GG-sets TT, R̲(T)\underline{R}(T) is commutative ring, such that all restriction maps are maps of commutative rings, and such that if f:TTf: T\to T' is a map of finite GG-sets, then we have the Frobenius reciprocity relation

aT f(b)=T f(R f(a)b) a \cdot T_f(b) = T_f(R_f(a) \cdot b)

for all aR̲(T)a \in \underline{R}(T') and bR̲(T)b \in \underline{R}(T).

Last revised on August 8, 2017 at 03:40:22. See the history of this page for a list of all contributions to it.