# nLab spectrum with G-action

Contents

### Context

#### Stable Homotopy theory

stable homotopy theory

Introduction

# Contents

#### Representation theory

representation theory

geometric representation theory

# Contents

## Idea

For $G$ a topological group, a spectrum with $G$-action is a spectrum equipped with an action of $G$. In other words, it is a functor from $BG$ to the (infinity,1)-category of spectra. The stable homotopy theory of spectra with $G$-action is part of the subject of equivariant stable homotopy theory.

Spectra with $G$-action are sometimes called “doubly naive” $G$-spectra. They are even more naive than naive G-spectra, and can be identified with the full subcategory of G-spectra consisting of “Borel-complete” $G$-spectra (see Prop. 6.17 in MNN or Thm. II.2.7 in NS).