Multiplicativity in Mandell's Inverse K-theory

TL;DR

This paper demonstrates that Mandell's inverse K-theory functor preserves multiplicative structures, advancing the understanding of its algebraic properties and paving the way for future equivariant generalizations.

Contribution

It proves that Mandell's inverse K-theory functor preserves multiplicative structures, a key step towards an equivariant extension.

Findings

Mandell's inverse K-theory functor preserves multiplicative structure

Establishes groundwork for equivariant generalization

Connects Gamma-categories with permutative categories

Abstract

We show that Mandell's inverse $K$-theory functor from $\Gamma$-categories to permutative categories preserves multiplicative structure. This is a first step towards an equivariant generalization that would be inverse to the construction of Bohmann and Osorno.