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Author SHA1 Message Date
Floris van Doorn
a716ef2108 applications: prove almost completely that S^3 and S^2 have the same high enough homotopy groups 
There is one missing fact, which is that the equivalence between S^1 and the fiber of the hopf fibration respects the basepoint
 2016-04-11 23:17:10 -04:00
Floris van Doorn
9a476fecfe sec86: finish proof of stability of spheres as groups 2016-04-11 15:55:28 -04:00
Floris van Doorn
0f9433c921 Rename some files, use the new LES file for the application file. 2016-04-07 17:28:33 -04:00
Floris van Doorn
37fbe56b8c Finish construction of the LES of homotopy groups without signs 
The maps on every level are just the functorial action of the homotopy groups (possibly composed by a cast), but there are no compositions with path inversion.
There are also some updates in various files after changes in the HoTT library.
 2016-04-07 17:28:19 -04:00
Mike Shulman
a6bf82618f feat(homotopy/spectrum): sections of parametrized spectra 2016-03-25 09:33:36 -07:00
Mike Shulman
af5a3091bb Merge branch 'master' of github.com:cmu-phil/Spectral 2016-03-24 16:30:22 -07:00
Mike Shulman
f8f7f69bcd Finish proof of pfiber_equiv_of_square 2016-03-24 16:30:10 -07:00
Ulrik Buchholtz
288e0d71b2 make everything compile on lean post 6f74f6522... 2016-03-24 16:14:44 -04:00
Ulrik Buchholtz
5a23744094 update README to reflect recent discussion 2016-03-24 13:27:21 -04:00
Egbert Rijke
652ca1da84 working on the join theorem 2016-03-24 13:27:21 -04:00
Ulrik Buchholtz
9ca4a3fbb1 start spherical fibrations (NB post #1021 lean) 2016-03-24 13:27:21 -04:00
Floris van Doorn
97d7d0c108 updates after changes in the HoTT library 2016-03-24 13:27:21 -04:00
Floris van Doorn
0483966328 prove the Freudenthal Suspension Theorem 2016-03-24 13:27:21 -04:00
Floris van Doorn
a76e4fce08 prove that the join of two spheres is a sphere 2016-03-24 13:27:21 -04:00
Mike Shulman
22e75da53e chain complexes of spectra 2016-03-23 11:32:25 -07:00
Mike Shulman
559777e45c index spectra by a general succ_str, +Z, or +N, as appropriate 2016-03-23 11:31:38 -07:00
Mike Shulman
5379c2e253 feat(homotopy/spectrum): fibers of spectra 2016-03-23 11:31:06 -07:00
Mike Shulman
104378f2c3 feat(homotopy/spectrum): use namespaces and better typeclasses 2016-03-21 15:53:25 -07:00
Mike Shulman
2bb5176b97 feat(homotopy/spectrum): basic definitions and cotensors by types 2016-03-20 20:16:36 -07:00
Floris van Doorn
6d11d025dd remove namespace equiv.ops 2016-03-03 11:56:56 -05:00
Floris van Doorn
b7c4f3b6a7 use have instead of assert 2016-03-03 11:05:44 -05:00
Floris van Doorn
1213001a6a feat(LES_applications): give most of the proof of 8.4.8 2016-03-02 22:14:32 -05:00
Floris van Doorn
a578b1c42e Add computing version of the LES of homotopy groups. 
Start on applications of the LES.
Also finish proofs in sec83 (I've also included them in the latest pull request for the Lean-HoTT library).
 2016-03-02 19:10:12 -05:00
Floris van Doorn
b7f2b9d689 update after renamings in the HoTT library 2016-02-22 20:53:48 -05:00
Floris van Doorn
5c9355c4c1 feat(chain_complex): give the construction of the LES of homotopy groups 
This commit defines "type_chain_complex" which is a typal variant of a chain complex, where the exactness condition is formulated without a propositional truncation in it. The fiber sequence of a pointed map is an instance of this structure.
It also defines "chain_complex" which is the usual notion of a chain complex: a sequence of pointed sets with pointed maps between them, such that the kernel and image of consecutive maps coincide.
The biggest part of this commit is the definition of the long exact sequence of homotopy groups of a pointed map. The definition uses the fiber sequence of a pointed map.
 2016-02-22 20:53:48 -05:00
Clive Newstead
efd5d25039 Merge branch 'master' of https://github.com/cmu-phil/Spectral 2016-02-18 16:18:02 -05:00
Clive Newstead
ae01bcba86 Created sec83.hlean 2016-02-18 16:16:55 -05:00
cnewstead
5342e41863 Delete clive.hlean 2016-02-18 14:04:05 -05:00
Floris van Doorn
52f59f8592 rename long_exact_sequence to chain_complex 2016-02-09 18:27:38 -05:00
Floris van Doorn
d1619c1b53 feat(homotopy/long_exact_sequence): change to chain complexes as basic structure 
Also prove that the equivalences are pointed equivalences
 2016-02-09 18:25:59 -05:00
Floris van Doorn
8f9ef03ad2 feat(homotopy/LES): continue working on the LES of homotopy groups 2016-02-05 00:51:00 -05:00
Floris van Doorn
c926955c8b begin LESs 2016-02-04 19:02:15 -05:00
Clive Newstead
2f150dce1f Playing with groups 2016-02-04 15:31:41 -05:00
Clive Newstead
103e4f72fe Learning how to Git... 2016-02-04 14:02:39 -05:00
Clive Newstead
3a09986692 Created clive.hlean 2016-02-04 14:00:48 -05:00
Floris van Doorn
895050d155 fix(*): fix broken files 2016-02-04 13:38:33 -05:00
Steve Awodey
6889eba5ea added homotopy subdirectory and sample file 
to formalize Chapter 8 of the book
 2016-01-21 14:33:54 -05:00