Update README.md with roadmap based on Mike's blog post
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@ -11,12 +11,30 @@ Currently in the project: Jeremy Avigad, Steve Awodey, Ulrik Buchholtz, Floris v
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## Things to do for Lean spectral sequences project
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###To Do:
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### Algebra To Do:
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- R-modules, vector spaces,
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- some basic theory: product, tensor, hom, projective,
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- categories of algebras, abelian categories,
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- exact sequences, short and long
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- snake lemma (Jeremy)
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- 5-lemma
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- chain complexes and homology
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- exact couples, probably just of Z-graded objects
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- derived exact couples
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- spectral sequence of an exact couple
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- convergence of spectral sequences
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###Already Done:
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### Topology To Do:
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- pointed types, fiber and cofiber sequences (is this in the library already?)
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- prespectra and spectra, suspension
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- spectrification
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- parametrized smash and hom between types and spectra
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- fiber and cofiber sequences of spectra, stability
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- long exact sequences from (co)fiber sequences of spectra
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- Eilenberg-MacLane spaces and spectra
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- Postnikov towers of spectra
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- exact couple of a tower of spectra
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### Already Done:
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- definition of algebraic structures such as groups, rings, fields,
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- some algebra: quotient, product, free.
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