nLab
infinity-permutation representation

Context

Higher algebra

Algebraic theories

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Algebras and modules

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Higher algebras

  • symmetric monoidal (∞,1)-category of spectra

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Model category presentations

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Geometry on formal duals of algebras

Theorems

(,1)(\infty,1)-Category theory

Background

Basic concepts

  • / (,1)(\infty,1)-categories

Universal constructions

Local presentation

Theorems

Extra stuff, structure, properties

Models

Contents

Idea

An ∞-representation on objects of ∞Grpd.

The analog on (∞,1)-category theory of a permutation representation.

Properties

Tannaka duality

See at Tannaka duality the section For ∞-permutation representations.

Grothendieck construction

By the (∞,1)-Grothendieck construction \infty-permutation representations

BGGrpd \mathbf{B}G \to \infty \mathrm{Grpd}

correspond to ∞-functors

V//GBG V//G \to \mathbf{B}G

sitting in fiber sequences

VV//GBG, V \to V//G \to \mathbf{B}G \,,

where V//GV//G is the corresponding action ∞-groupoid?.

Created on December 12, 2011 at 22:59:32. See the history of this page for a list of all contributions to it.