# nLab linear model category

Contents

model category

## Model structures

for ∞-groupoids

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

#### Stable homotopy theory

stable homotopy theory

Introduction

# Contents

## Definition

A model category is called linear if it has a zero object (is a “pointed category”) and for all of its objects $X$, the unit

$X \stackrel{\simeq}{\longrightarrow} \Omega \Sigma X$

(of the (reduced suspension $\dashv$ loop space object)-adjunction) is a weak equivalence.

## References

• Stefan Schwede, Spectra in model categories and applications to the algebraic cotangent complex, Journal of Pure and Applied Algebra 120 (1997) 77-104 (pdf)

Created on February 10, 2016 at 07:48:40. See the history of this page for a list of all contributions to it.