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155 commits

Author SHA1 Message Date
Floris van Doorn
6e6fad5cb2 fix error 2017-06-05 17:09:48 -04:00
Floris van Doorn
ed7de51d02 move basic lemmas from the spectral repository to the main repository 2017-06-02 12:15:31 -04:00
Floris van Doorn
c7fb842124 checkpoint EM 2017-06-01 10:57:15 -04:00
Floris van Doorn
9a3eed11bb move some stuff to more appropriate places (before big move to HoTT library) 2017-05-26 17:32:42 -04:00
Floris van Doorn
9ad673682d add stuff about Postnikov towers, EM-spaces and components 2017-05-26 05:17:02 -04:00
Floris van Doorn
6fbbc051e2 postnikov tower WIP 2017-05-25 22:51:11 -04:00
Floris van Doorn
a7b746c813 define parametrized cohomology 2017-05-24 08:27:06 -04:00
Floris van Doorn
73a34e9edf finish construction of exact couple from a sequence of spectrum maps 2017-05-21 00:39:53 -04:00
Floris van Doorn
cea1250ca6 Work on the construction of exact couples 2017-05-21 00:39:53 -04:00
Ulrik Buchholtz
a7ec040f57 work on degrees 2017-04-29 14:05:39 +02:00
Ulrik Buchholtz
cb45181a13 remove unused definition from realprojective 2017-04-28 11:26:21 +02:00
Floris van Doorn
91931ca338 generalize is_exact 2017-03-30 17:05:32 -04:00
Floris van Doorn
3cd846a757 checkpoint, smash susp 2017-03-30 17:05:32 -04:00
Floris van Doorn
773e9f9a2e susp and other things 2017-03-30 17:00:15 -04:00
Floris van Doorn
b781de8473 simplify smash proof 2017-03-30 17:00:15 -04:00
Floris van Doorn
9cf51e98cd start on notes 2017-03-30 17:00:15 -04:00
Floris van Doorn
b9ed007161 Remove some old files 2017-03-07 22:55:51 -05:00
Floris van Doorn
47532e4315 Prove the naturality of the smash-pmap adjunction, and hence of the associativity of the smash product 2017-03-07 22:40:24 -05:00
Floris van Doorn
f013c631d0 Finish the naturality of the smash-pmap adjunction 2017-03-03 17:43:03 -05:00
Floris van Doorn
013ca8d5f2 make progress on naturality of smash-pmap adjunction 
The only fact left to be proven is a property (which is an equality of phomotopies) of the functorial action of the smash product
 2017-03-03 17:43:03 -05:00
Floris van Doorn
ad43cd56f0 Work on the cofiber sequence and basic properties of cohomology theories 2017-03-03 17:42:38 -05:00
Floris van Doorn
78512444e8 prove that the cohomology of an Eilenberg-MacLane spectrum satisfies the dimension axiom 2017-02-18 19:01:24 -05:00
Floris van Doorn
81fe7df61f fix definition of spectrum cohomology, and prove that spectrum cohomology forms a cohomology theory 2017-02-18 16:56:50 -05:00
Floris van Doorn
c0b7740f13 order of arguments in group.mk has changed 2017-02-02 17:16:14 -05:00
Floris van Doorn
d6de922d1f give last step of associativity of smash 
there are still unproven lemma's
 2017-02-02 17:16:01 -05:00
Floris van Doorn
216a25af4f fix typo 2017-02-02 17:15:46 -05:00
Floris van Doorn
00e01fd2a6 feat(homotopy): prove adjunction between smash product and pointed maps 
also develop library for equality reasoning on pointed homotopies.
Also do the renamings like homomorphism -> is_mul_hom
 2017-01-18 23:19:06 +01:00
Floris van Doorn
b2bfc978bf continue on associativity of smash, and add some properties about the wedge sum 2017-01-14 21:08:00 +01:00
Floris van Doorn
802eec812f Prove some basic properties about the smash product, and start on its associativity 2017-01-14 21:07:36 +01:00
Floris van Doorn
b7f53b90d7 more on pushouts, interaction with sums, and induction principle for certain cofibers 
latter part ported from Agda
 2017-01-14 21:07:36 +01:00
Floris van Doorn
cb3fac2fb3 start on torus = S^1 x S^1 2017-01-14 21:07:36 +01:00
Floris van Doorn
db72ff0a66 more pushout lemmas, continue with smash of the circle 2017-01-14 21:07:36 +01:00
Floris van Doorn
372ca7297c finish proof that smash is the cofiber of the map from the wedge to the product 2017-01-14 21:07:36 +01:00
Floris van Doorn
6594be4292 prove some lemmas about pushouts, and start on the formulation of the 3x3 lemma 2017-01-14 21:06:17 +01:00
Floris van Doorn
7f6752e14f Show that the Eilenberg-MacLane-space-functor induces an equivalence of categories 2017-01-14 21:05:34 +01:00
Ulrik Buchholtz
43f5112c86 move realprojective over from K-Theory repo 2017-01-10 10:50:24 +01:00
Floris van Doorn
b08457c77f move things to the Lean library, and update after changes in the Lean library 2016-11-24 00:11:55 -05:00
Floris van Doorn
4f1db25e16 Work on the uniqueness of Eilenberg-Maclane spaces 2016-11-23 23:54:32 -05:00
Floris van Doorn
c96f3d18f2 Work on the smash product 2016-11-23 23:53:26 -05:00
Floris van Doorn
9df0b25ae5 some additions to the smash product and direct sums 2016-11-14 14:44:29 -05:00
Floris van Doorn
704717e9ae minor changes 2016-11-03 15:34:06 -04:00
Floris van Doorn
79dea677e8 colimit, start on encode-decode proof 2016-10-13 16:01:59 -04:00
Floris van Doorn
a31c15e384 continue on spectrification 2016-10-13 16:01:54 -04:00
Floris van Doorn
946506af5c define smash without any 2-paths and work on smashing with the circle 2016-10-13 15:49:47 -04:00
Floris van Doorn
b3765932d9 work on spectrification 2016-10-13 15:49:47 -04:00
Floris van Doorn
0a15d184b2 cohomology: define cohomology as abelian groups and define the functorial action 2016-10-13 15:49:17 -04:00
Floris van Doorn
258671578d EM: add functorial action and equivalence of 1-Type*[0] and Group 
n-Type*[k] is new notation for n-truncated k-connected pointed types. All 'subnotations' are also defined
 2016-09-23 17:16:48 -04:00
Floris van Doorn
d8c694e113 update after changes in the HoTT library. Mostly some naming and notation changes 2016-09-23 17:16:25 -04:00
Floris van Doorn
a34606c64f small changes, remove old file 2016-09-23 17:12:46 -04:00
Floris van Doorn
5fbcbfe6e8 prove that the degree of composites is the product of the degrees 2016-09-17 00:02:22 -04:00
Floris van Doorn
fb55292c34 add move_to_lib: a file where we can put theorems which should be moved to files in the HoTT library 2016-09-16 20:23:05 -04:00
Floris van Doorn
d4508eee2f start on mapping spectra 2016-09-16 16:13:55 -04:00
Floris van Doorn
6fca83a2ed finish the construction of the LES for spectrum maps 2016-09-15 19:19:03 -04:00
Floris van Doorn
e7c3144dbd fill in sorry in spherical_fibrations 2016-09-15 18:05:58 -04:00
Floris van Doorn
683a515178 progress on LES of spectrum maps 2016-09-15 17:57:33 -04:00
Floris van Doorn
6cec5dcdaa fix definition of homotopy group of spectrum, continue of LES of spectra 2016-09-14 18:46:53 -04:00
Floris van Doorn
9d00ea2f6f feat(spectrum): start on the LES of homotopy groups for spectra 2016-09-09 16:45:44 -04:00
Floris van Doorn
c9af080cc2 feat(splice): prove a lemma on how to splice chain complexes together 2016-09-09 16:43:39 -04:00
Floris van Doorn
b45e20d0cc feat(cohomology): start on cohomology file 2016-09-09 16:43:09 -04:00
Floris van Doorn
78492bbe09 feat(EM): Work on uniqueness of K(G,n)'s 2016-09-01 14:08:42 -04:00
Floris van Doorn
dc2a26745e move results to HoTT library, and start on uniqueness of K(G, n) for n>1 2016-06-26 09:26:13 +01:00
Floris van Doorn
21c6e8f7e5 small changes after changes in HoTT library 2016-06-26 09:26:13 +01:00
Floris van Doorn
9f5d7bda9f more stuff 2016-04-26 17:33:17 -04:00
Floris van Doorn
62c134df4e whitehead corollaries 2016-04-26 16:07:15 -04:00
Floris van Doorn
ba7b25d00f move files to the HoTT library and update after changes in the HoTT library 2016-04-25 19:51:17 -04:00
Floris van Doorn
0af9c0ecc7 prove is_equiv_π_of_is_connected for functions where the domain and codomain live in different universes 2016-04-14 17:15:03 -04:00
Floris van Doorn
7d7ddaff9f give the LES of a fibration sequence 2016-04-13 12:20:22 -04:00
Floris van Doorn
2de92db5b6 some cleanup 2016-04-12 17:59:15 -04:00
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