# 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 hence a pointed model 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

Last revised on January 31, 2021 at 03:08:23. See the history of this page for a list of all contributions to it.