Constructing Equivariant Spectra via Categorical Mackey Functors
نویسنده
چکیده
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–MacLane spectra for Mackey functors and for suspension spectra for finite G-sets.
منابع مشابه
Research Narrative
Introduction – Categorifying Parshin’s conjecture 1 1. Higher categories and unicity 2 1.1. Iterated complete Segal spaces 3 1.2. Relative categories and higher relative categories 3 1.3. The Unicity Theorem 3 2. Algebraic K-theory 3 2.1. The new fundamental theorems of K-theory 4 2.2. TheTheorem of the Heart 4 2.3. New localization sequences 4 2.4. Deligne Conjecture for K-theory 4 2.5. A high...
متن کاملSome Remarks on the Structure of Mackey Functors
All Mackey functors over a finite group G are built up by short exact sequences from Mackey functors arising from modules over the integral group rings of appropriate subquotients W H of G. The equivariant cohomology theories with coefficients in Mackey functors arising from W H-modules admit particularly simple descriptions. Let G be a finite group. The notion of a Mackey functor plays a funda...
متن کاملSpectral Mackey Functors and Equivariant Algebraic K - Theory ( Ii )
We study the “higher algebra” of spectral Mackey functors, which the first named author introduced in Part I of this paper. In particular, armed with our new theory of symmetric promonoidal ∞-categories and a suitable generalization of the second named author’s Day convolution, we endow the∞-category of Mackey functors with a wellbehaved symmetric monoidal structure. This makes it possible to s...
متن کاملar X iv : 0 80 4 . 02 64 v 1 [ m at h . A T ] 1 A pr 2 00 8 A MODEL FOR EQUIVARIANT EILENBERG - MAC LANE SPECTRA
Let G be a finite group. For a based G-space X and a Mackey functor M , a topological Mackey functor X e ⊗M is constructed. When X is a based G-CW complex, X e ⊗M is shown to be an infinite loop space in the sense of G-spaces. This gives a version of the RO(G)-graded equivariant Dold-Thom theorem. Applying a variant of Elmendorf’s construction, we get a model for the Eilenberg-Mac Lane spectrum...
متن کاملar X iv : m at h / 04 10 16 2 v 1 [ m at h . A T ] 6 O ct 2 00 4 EQUIVARIANT UNIVERSAL COEFFICIENT AND KÜNNETH SPECTRAL SEQUENCES
We construct hyper-homology spectral sequences of Z-graded and RO(G)-graded Mackey functors for Ext and Tor over G-equivariant S-algebras (A∞ ring spectra) for finite groups G. These specialize to universal coefficient and Künneth spectral sequences.
متن کامل