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

Contents

model category

## Model structures

for ∞-groupoids

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

#### Rational homotopy theory

differential graded objects

and

## Sullivan models

#### Representation theory

representation theory

geometric representation theory

# Contents

## Statement

###### Proposition

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

Let $G$ be a finite group.

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

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

## References

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