Models of G-spectra as presheaves of spectra

Abstract

Let G be a finite group. We give Quillen equivalent models for the category of G-spectra as categories of spectrally enriched functors from explicitly described domain categories to nonequivariant spectra. Our preferred model is based on equivariant infinite loop space theory applied to elementary categorical data. It recasts equivariant stable homotopy theory in terms of point-set level categories of G-spans and nonequivariant spectra. We also give a more topologically grounded model based on equivariant Atiyah duality.

Final version. To appear in Algebraic & Geometric Topology. Section 3.1, which gives models for several important constructions on G-spectra, is new in this version. 46 pages

References in corpus (11)

• Higher Topos Theory
• Algebras and modules in monoidal model categories
• Diagram spaces and symmetric spectra
• Permutative categories, multicategories, and algebraic K-theory
• Diagram spaces, diagram spectra, and spectra of units
• Spectral Mackey functors and equivariant algebraic K-theory (II)
• Equivariant iterated loop space theory and permutative G-categories
• Strictification of categories weakly enriched in symmetric monoidal categories
• Categorical models for equivariant classifying spaces
• Constructing equivariant spectra via categorical Mackey functors
• Tensor product for symmetric monoidal categories

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• A Grothendieck-Witt space for stable infinity categories with duality
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• A slice refinement of Bökstedt periodicity
• On the parametrized Tate construction
• Derived Mackey functors and $C_{p^n}$-equivariant cohomology
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• Higher Lawvere theories
• A genuine $G$-spectrum for the cut-and-paste $K$-theory of $G$-manifolds