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ISSN (electronic): 1472-2739
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Constructing equivariant spectra via categorical Mackey functors

Anna Marie Bohmann and Angélica Osorno

Algebraic & Geometric Topology 15 (2015) 537–563

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.

equivariant stable homotopy theory, equivariant spectra, Mackey functors, permutative categories
Mathematical Subject Classification 2010
Primary: 55P42, 55P91
Secondary: 18D20
Received: 16 June 2014
Revised: 4 August 2014
Accepted: 9 August 2014
Published: 23 March 2015
Anna Marie Bohmann
Department of Mathematics
Northwestern University
Evanston, IL 60208
Angélica Osorno
Department of Mathematics
Reed College
Portland, OR 97202