# nLab spectral sequence of a simplicial stable homotopy type

Contents

### Context

#### Stable Homotopy theory

stable homotopy theory

Introduction

# Contents

#### Homological algebra

homological algebra

Introduction

diagram chasing

# Contents

## Idea

For $\mathcal{C}$ a stable (∞,1)-category and $X_\bullet$ a simplicial object in an (∞,1)-category in $\mathcal{C}$, then the simplicial skeleta of $X$ give it the structure of a filtered object in an (∞,1)-category. The corresponding spectral sequence of a filtered stable homotopy type has as its first page the Moore complexes of the corresponding simplicial objects of homotopy groups.

## References

The general theory is developed in

Quick review is in

Last revised on February 1, 2016 at 16:42:24. See the history of this page for a list of all contributions to it.