Graded Tambara Functors

TL;DR

This paper introduces the concept of $ o(G)$-graded Tambara functors and demonstrates their connection to $G$-spectra with norm multiplication, expanding the algebraic framework in equivariant stable homotopy theory.

Contribution

It defines $ o(G)$-graded Tambara functors and establishes their relation to $G$-spectra with norm multiplication, providing a new algebraic perspective.

Findings

$ o(G)$-graded Tambara functors are well-defined.

Any $G$-spectrum with norm multiplication induces an $ o(G)$-graded Tambara functor.

The work bridges equivariant spectra and algebraic structures in a novel way.

Abstract

We define the notion of an $\mathcal{RO}(G)$-graded Tambara functor and prove that any $G$-spectrum with norm multiplication gives rise to such an $\mathcal{RO}(G)$-graded Tambara functor.