Egbert Rijke
55b831d713
Merge branch 'master' of https://github.com/cmu-phil/Spectral
2017-06-28 17:53:22 +01:00
Egbert Rijke
d3f42e5a3c
starting to think about equivalences of prespectra
2017-06-28 17:53:09 +01:00
Ulrik Buchholtz
9934c9c73d
trivial homotopy groups of truncated spectra
2017-06-28 17:19:23 +01:00
Egbert Rijke
2092e4a83b
resolve merge conflict
2017-06-28 15:53:27 +01:00
Egbert Rijke
f4e74687f9
conjecture about prespectrification
2017-06-28 15:49:46 +01:00
Ulrik Buchholtz
1c07806726
work on strunc
2017-06-28 15:22:45 +01:00
Floris van Doorn
d814c472ab
add strunc file for truncatedness/truncations of spectra
2017-06-28 13:15:49 +01:00
Floris van Doorn
635b10821f
temporarily disable proof, which caused error after redefinition of phomotopy
2017-06-28 11:08:41 +01:00
Floris van Doorn
cfdfa0f22a
Work on the fact that pointed dependent products preserve fibration sequences
...
We now define pointed homotopies as dependent pointed maps, and have some properties about pointed sigmas
2017-06-19 02:03:54 -04:00
Floris van Doorn
a2c4e0858d
clean up computation of fiber of postnikov tower
2017-06-15 17:49:48 -04:00
Floris van Doorn
0885a7ef4a
renamed pequiv.MK2 to pequiv.MK
2017-06-14 22:56:03 -04:00
Floris van Doorn
b6fa4e8716
compute fibers of postnikov tower
2017-06-14 22:56:03 -04:00
Floris van Doorn
b8de7ffd80
work on functorial action of prespectrum homotopy groups
2017-06-09 17:42:10 -04:00
d057ddec51
Add Hpwedge.
2017-06-09 15:01:21 -06:00
Robert Rose
9cfc13d4cf
naturality for wedge elimination
2017-06-09 16:51:13 -04:00
Yuri Sulyma
c8043a6f9f
Merge branch 'master' of github.com:fpvandoorn/Spectral
2017-06-09 12:24:58 -06:00
Yuri Sulyma
39883fd3ee
A bit of code for incoherent homotopies between maps of spectra
2017-06-09 12:24:33 -06:00
0acc5c786d
Add fwedge_down_left.
2017-06-09 11:55:59 -06:00
spiceghello
2e55a4a4ef
fwedge_prespectrum
2017-06-09 11:51:04 -06:00
88dc53d113
Add the missing 'p'.
2017-06-09 11:22:52 -06:00
Floris van Doorn
61e3a9ce0e
redefine homology to use smash with prespectra
2017-06-09 12:25:21 -04:00
f098063d96
More lemmas about fwedge.
2017-06-09 06:35:56 -06:00
Yuri Sulyma
5826288a48
composition/inverse for homotopies of pointed spaces and spectra
2017-06-08 20:07:46 -06:00
Yuri Sulyma
cf3dec8fb9
Merge branch 'master' of github.com:fpvandoorn/Spectral
2017-06-08 20:01:47 -06:00
Yuri Sulyma
aa54adf770
Use psquare/phsquare in spectrum
2017-06-08 20:01:41 -06:00
spiceghello
b2ab29c3c3
on colim.elim o pinclusion, and corollary on spectra
2017-06-08 18:28:25 -06:00
Floris van Doorn
e4168439c0
work on homotopy group of prespectrum
2017-06-08 20:09:48 -04:00
4165f9a613
Add pwedge_pequiv and plift_pwedge.
2017-06-08 16:44:02 -06:00
spiceghello
a06ecd4523
part of spectrify_elim
2017-06-08 15:08:22 -06:00
Yuri Sulyma
3fd6e8e852
Merge branch 'master' of github.com:fpvandoorn/Spectral
2017-06-08 14:04:58 -06:00
Yuri Sulyma
7f637206a0
Add a few spectrification things
2017-06-08 14:03:10 -06:00
Yuri Sulyma
ec852ca73f
Merge branch 'master' of github.com:fpvandoorn/Spectral
2017-06-07 09:39:46 -06:00
Yuri Sulyma
abe46fd211
Functoriality of smashing a pointed space with a prespectrum
2017-06-07 09:39:26 -06:00
Floris van Doorn
3881982774
small changes to spectrum
2017-06-07 00:54:52 -04:00
Floris van Doorn
5e4c536d27
progress on spectrify
2017-06-06 17:07:22 -04:00
Yuri Sulyma
7125413a9a
Renamed homology file + fixed a superfluous hypothesis in spectrify_map
2017-06-06 12:08:37 -06:00
76a0f5a683
Add plift_psusp.
2017-06-06 11:55:21 -06:00
Floris van Doorn
aef91cd344
fix error when compiling
2017-06-06 13:26:30 -04:00
Yuri Sulyma
3f62c7b500
Define a homology theory in hlean
2017-06-06 10:26:35 -06:00
Floris van Doorn
dc2c697885
fix error
2017-06-06 12:00:08 -04:00
spiceghello
56f7ea093e
smash_prespectrum
2017-06-06 09:41:51 -06:00
Floris van Doorn
6ded2b94d7
give type to (pre)spectrum.mk
2017-06-06 00:43:11 -04:00
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
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
