(also nonabelian homological algebra)

**Context**

**Basic definitions**

**Stable homotopy theory notions**

**Constructions**

**Lemmas**

**Homology theories**

**Theorems**

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.

- for the Cech nerve of an E-∞ algebra $E$ this yields the $E$-Adams spectral sequence.

The general theory is developed in

- Jacob Lurie, section 1.2.4 of
*Higher Algebra*

Quick review is in

- Dylan Wilson section 1.2 of
*Spectral Sequences from Sequences of Spectra: Towards the Spectrum of the Category of Spectra*lecture at*2013 Pre-Talbot Seminar*(pdf)

Last revised on February 1, 2016 at 21:42:24. See the history of this page for a list of all contributions to it.