Merge branch 'master' of https://github.com/cmu-phil/Spectral

README.md

@@ -9,36 +9,36 @@ Jeremy Avigad, Steve Awodey, Ulrik Buchholtz, Floris van Doorn, Clive Newstead,
 - [Mike's blog post](http://homotopytypetheory.org/2013/08/08/spectral-sequences/) at the HoTT blog.
 - [Mike's blog post](https://golem.ph.utexas.edu/category/2013/08/what_is_a_spectral_sequence.html) at the n-category café.
 - The [Licata-Finster article](http://dlicata.web.wesleyan.edu/pubs/lf14em/lf14em.pdf) about Eilenberg-Mac Lane spaces.
-- There is an [entry about spectrification](http://ncatlab.org/nlab/show/higher+inductive+type#spectrification) on the nlab.
 - 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.
+- Mac Lane's Homology contains a lot of homological algebra and a chapter on spectral sequences, including exact couples.
 
 ## Things to do for Lean spectral sequences project
 
 ### Algebra To Do:
-- R-modules, vector spaces,
+- [R-modules](http://ncatlab.org/nlab/show/module), [vector spaces](http://ncatlab.org/nlab/show/vector+space),
 - some basic theory: product, tensor, hom, projective,
-- categories of algebras, abelian categories,
+- categories of algebras, [abelian categories](http://ncatlab.org/nlab/show/abelian+category),
 - exact sequences, short and long
-- snake lemma (Jeremy) 
-- 5-lemma
-- chain complexes and homology
-- exact couples, probably just of Z-graded objects
-- derived exact couples
+- [snake lemma](http://ncatlab.org/nlab/show/snake+lemma) 
+- [5-lemma](http://ncatlab.org/nlab/show/five+lemma)
+- [chain complexes](http://ncatlab.org/nlab/show/chain+complex) and [homology](http://ncatlab.org/nlab/show/homology)
+- [exact couples](http://ncatlab.org/nlab/show/exact+couple), probably just of Z-graded objects, and derived exact couples
 - spectral sequence of an exact couple
-- convergence of spectral sequences
+- [convergence of spectral sequences](http://ncatlab.org/nlab/show/spectral+sequence#ConvergenceOfSpectralSequences)
 
 ### Topology To Do:
-- pointed types, fiber and cofiber sequences (is this in the library already?)
-- prespectra and spectra, suspension
-- spectrification
-- parametrized smash and hom between types and spectra
+- fiber and cofiber sequences (is this in the library already?)
+- [prespectra](http://ncatlab.org/nlab/show/spectrum+object) and [spectra](http://ncatlab.org/nlab/show/spectrum), suspension
+- [spectrification](http://ncatlab.org/nlab/show/higher+inductive+type#spectrification)
+- [parametrized spectra](http://ncatlab.org/nlab/show/parametrized+spectrum), parametrized smash and hom between types and spectra
 - fiber and cofiber sequences of spectra, stability
 - long exact sequences from (co)fiber sequences of spectra
-- Eilenberg-MacLane spaces and spectra
+- [Eilenberg-MacLane spaces](http://ncatlab.org/nlab/show/Eilenberg-Mac+Lane+space) and spectra
 - Postnikov towers of spectra
 - exact couple of a tower of spectra
 
 ### Already Done:
+- pointed types
 - definition of algebraic structures such as groups, rings, fields, 
 - some algebra: quotient, product, free.