Biset transformations of Tambara functors

Details Biset transformations of Tambara functors Biset transformations of Tambara functors

2011-05-04

arxiv.org/abs/1105.0714v1

Mathematics

Category Theory

19 pages

Scientific paper

If we are given an $H$-$G$-biset $U$ for finite groups $G$ and $H$, then any Mackey functor on $G$ can be transformed by $U$ into a Mackey functor on $H$. In this article, we show that the biset transformation is also applicable to Tambara functors, and in fact forms a functor between the category of Tambara functors on $G$ and $H$. This biset transformation functor is compatible with some algebraic operations on Tambara functors, such as ideal quotients or fractions. In the latter part, we also construct the left adjoint of the biset transformation.

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