Spectral/README.md

# Spectral Sequences

Formalization project of the CMU HoTT group towards formalizing the Serre spectral sequence. 

Currently in the project: Jeremy Avigad, Steve Awodey, Ulrik Buchholtz, Floris van Doorn, Egbert Rijke, Mike Shulman.

## Resources
- [Mike's blog post](http://homotopytypetheory.org/2013/08/08/spectral-sequences/)
- We learned about the Serre spectral sequence from [Hatcher's chapter about spectral sequences](https://www.math.cornell.edu/~hatcher/SSAT/SSATpage.html).
- Lang's algebra (revised 3rd edition) contains a chapter on general homology theory, with a section on spectral sequences. Thus, we can use this book at least as an outline for the algebraic part of the project.

## Things to do for Lean spectral sequences project

###To Do:
- R-modules, vector spaces,
- some basic theory: product, tensor, hom, projective,
- categories of algebras, abelian categories,
- snake lemma (Jeremy) 

###Already Done:
- definition of algebraic structures such as groups, rings, fields, 
- some algebra: quotient, product, free.