Norms of Generalized Mackey and Tambara Functors

TL;DR

This paper generalizes the concept of Tambara functors by replacing the underlying category of finite G-sets, extending existing results to a broader context including motivic Tambara functors.

Contribution

It extends Hoyer's results on G-Tambara functors to a more general setting where the base category is replaced, encompassing motivic Tambara functors.

Findings

Generalized the notion of Tambara functors

Extended Hoyer's results to new contexts

Unified various types of Tambara functors

Abstract

Let $G$ be a finite group. A $G$-Tambara functor can be defined as a product-preserving functor $\mathcal{P}_G \to \mathsf{Set}$ (satisfying one additional condition), where $\mathcal{P}_G$ is a category that is constructed in a straightforward way from the category of finite $G$-sets. By replacing the category of finite $G$-sets with other categories, we obtain a more general notion of "Tambara functor". This more general notion subsumes the notion of motivic Tambara functors introduced by Bachmann. In this article, we extend a result of Hoyer about $G$-Tambara functors to this more general context.