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
Floris van Doorn
cb40d9b8fc
add some copyright notices and LICENSE file
2016-04-06 12:35:30 -04:00
Floris van Doorn
c1038a3f96
give the definition of the I-ary direct sum
2016-03-31 13:22:45 -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
Egbert Rijke
960e7075bd
initiating graded.hlean
2016-03-24 14:24:47 -04:00
Egbert Rijke
0b1fbbe3e1
initiating algebra folder
2016-03-24 14:19:06 -04:00
Floris van Doorn
6807883830
port module from the standard library
2016-03-24 13:41:51 -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
00978587e5
update README
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
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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
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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
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to formalize Chapter 8 of the book
2016-01-21 14:33:54 -05:00
Steve Awodey
2c97f5cef7
Merge remote-tracking branch 'origin/master'
...
# Conflicts:
# group_theory/basic.hlean
2016-01-21 14:27:14 -05:00
Steve Awodey
392ee8555a
added HoTT Book Chapter 8 to do
2016-01-21 14:25:17 -05:00
Ulrik Buchholtz
5f11c03d60
add rough sketch of dependency graph
2016-01-21 14:18:00 -05:00
Floris van Doorn
01e0d1897b
some cleanup
2015-12-10 21:17:29 -05:00
Floris van Doorn
3c9ca4b51c
working on tensor group
2015-12-10 20:25:32 -05:00
Floris van Doorn
492b433cc6
show that groups form a precategory (category todo)
2015-12-10 20:24:36 -05:00
Egbert Rijke
304bcc472a
homework accomplished
2015-12-10 18:37:30 -05:00
