Holmstrom Spectral sequences frameworks

http://mathoverflow.net/questions/68899/how-does-one-view-the-de-rham-spectral-sequence-as-a-grothendieck-spectral-sequen

A book by Grandis: http://www.worldscibooks.com/mathematics/8483.html

http://mathoverflow.net/questions/110812/what-kind-of-spectral-sequences-come-from-double-complexes

Spectral sequences on one blackboard: http://chromotopy.org/?p=721

Some things are in Freitag and Kiehl (short notation???)

arXiv:1007.0632 Homotopy spectral sequences from arXiv Front: math.CT by Marco Grandis In homotopy theory, exact sequences and spectral sequences consist of groups and pointed sets, linked by actions. We prove that the theory of such exact and spectral sequences can be established in a categorical setting which is based on the existence of kernels and cokernels with respect to an assigned ideal of null morphisms, a generalisation of abelian categories and Puppe-exact categories.

arXiv:1001.1556 A general framework for homotopic descent and codescent from arXiv Front: math.KT by Kathryn Hess In this paper we elaborate a general homotopy-theoretic framework in which to study problems of descent and completion and of their duals, codescent and cocompletion. Our approach to homotopic (co)descent and to derived (co)completion can be viewed as $\infty$-category-theoretic, as our framework is constructed in the universe of simplicially enriched categories, which are a model for $(\infty, 1)$-categories

We provide general criteria, reminiscent of Mandell’s theorem on $E_{\infty}$-algebra models of $p$-complete spaces, under which homotopic (co)descent is satisfied. Furthermore, we construct general descent and codescent spectral sequences, which we interpret in terms of derived (co)completion and homotopic (co)descent

We show that a number of very well-known spectral sequences, such as the unstable and stable Adams spectral sequences, the Adams-Novikov spectral sequence and the descent spectral sequence of a map, are examples of general (co)descent spectral sequences. There is also a close relationship between the Lichtenbaum-Quillen conjecture and homotopic descent along the Dwyer-Friedlander map from algebraic K-theory to étale K-theory. Moreover, there are intriguing analogies between derived cocompletion (respectively, completion) and homotopy left (respectively, right) Kan extensions and their associated assembly (respectively, coassembly) maps.

nLab page on Spectral sequences frameworks