## Abstract

In [12], we reworked and generalized equivariant infinite loop space theory, which shows how to construct G-spectra from G-spaces with suitable structure. In this paper, we construct a new variant of the equivariant Segal machine that starts from the category [Figure presented] of finite sets rather than from the category [Figure presented] of finite G-sets and which is equivalent to the machine studied in [19,12]. In contrast to the machine in [19,12], the new machine gives a lax symmetric monoidal functor from the symmetric monoidal category of [Figure presented]–G-spaces to the symmetric monoidal category of orthogonal G-spectra. We relate it multiplicatively to suspension G-spectra and to Eilenberg–Mac Lane G-spectra via lax symmetric monoidal functors from based G-spaces and from abelian groups to [Figure presented]–G-spaces. Even non-equivariantly, this gives an appealing new variant of the Segal machine. This new variant makes the equivariant generalization of the theory essentially formal, hence likely to be applicable in other contexts.

Original language | English |
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Pages (from-to) | 2425-2454 |

Number of pages | 30 |

Journal | Journal of Pure and Applied Algebra |

Volume | 223 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2019 |

### Bibliographical note

Publisher Copyright:© 2018 Elsevier B.V.

### Funding

B. Guillou was supported by Simons Foundation Grant No. 282316 and NSF grant DMS-1710379. M. Merling was supported by NSF grant DMS-1709461. A.M. Osorno was supported by Simons Foundation Grant No. 359449, the Woodrow Wilson Career Enhancement Fellowship, and NSF grant DMS-1709302. NSF RTG grantDMS-1344997 supported several collaborator visits to Chicago. B. Guillou was supported by Simons Foundation Grant No. 282316 and NSF grant DMS-1710379 . M. Merling was supported by NSF grant DMS-1709461 . A.M. Osorno was supported by Simons Foundation Grant No. 359449 , the Woodrow Wilson Career Enhancement Fellowship , and NSF grant DMS-1709302 . NSF RTG grant DMS-1344997 supported several collaborator visits to Chicago.

Funders | Funder number |
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Woodrow Wilson Career Enhancement Fellowship | DMS-1709302, DMS-1344997 |

National Science Foundation Arctic Social Science Program | DMS-1709461, DMS-1710379, 359449 |

Directorate for Mathematical and Physical Sciences | 1710379, 1344997, 1709461, 1709302 |

Simons Foundation | 282316 |

Woodrow Wilson National Fellowship Foundation | |

National Stroke Foundation |

## Keywords

- Equivariant stable homotopy theory
- Infinite loop space machine

## ASJC Scopus subject areas

- Algebra and Number Theory