## Algebraic & Geometric Topology

### Constructing equivariant spectra via categorical Mackey functors

#### Abstract

We give a functorial construction of equivariant spectra from a generalized version of Mackey functors in categories. This construction relies on the recent description of the category of equivariant spectra due to Guillou and May. The key element of our construction is a spectrally enriched functor from a spectrally enriched version of permutative categories to the category of spectra that is built using an appropriate version of $K$–theory. As applications of our general construction, we produce a new functorial construction of equivariant Eilenberg–Mac Lane spectra for Mackey functors and for suspension spectra for finite $G$–sets.

#### Article information

Source
Algebr. Geom. Topol., Volume 15, Number 1 (2015), 537-563.

Dates
Received: 16 June 2014
Revised: 4 August 2014
Accepted: 9 August 2014
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510840922

Digital Object Identifier
doi:10.2140/agt.2015.15.537

Mathematical Reviews number (MathSciNet)
MR3325747

Zentralblatt MATH identifier
1314.55005

#### Citation

Bohmann, Anna Marie; Osorno, Angélica. Constructing equivariant spectra via categorical Mackey functors. Algebr. Geom. Topol. 15 (2015), no. 1, 537--563. doi:10.2140/agt.2015.15.537. https://projecteuclid.org/euclid.agt/1510840922

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