nLab
Quillen adjunction between equivariant simplicial sets and equivariant connective dgc-algebras

Contents

Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (,1)(\infty,1)-categories

Model structures

for \infty-groupoids

for ∞-groupoids

for rational \infty-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general

specific

for stable/spectrum objects

for (,1)(\infty,1)-categories

for stable (,1)(\infty,1)-categories

for (,1)(\infty,1)-operads

for (n,r)(n,r)-categories

for (,1)(\infty,1)-sheaves / \infty-stacks

Rational homotopy theory

Representation theory

Contents

Statement

Proposition

(Quillen adjunction between equivariant simplicial sets and equivariant connective dgc-algebras)

Let GG be a finite group.

The GG-equivariant PL de Rham complex-construction is the left adjoint in a Quillen adjunction between

(GdgcAlgebras k 0) proj op QuexpΩ PLdR GSimplicialSets Qu \big( G dgcAlgebras^{\geq 0}_{k} \big)^{op}_{proj} \underoverset { \underset {\;\;\; exp \;\;\;} {\longrightarrow} } { \overset {\;\;\;\Omega^\bullet_{PLdR}\;\;\;} {\longleftarrow} } {\bot_{\mathrlap{Qu}}} G SimplicialSets_{Qu}

(Scull 08, Prop. 5.1)

References

Created on September 25, 2020 at 13:16:12. See the history of this page for a list of all contributions to it.