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109 commits

Author SHA1 Message Date
Floris van Doorn
bcb78b4575 minor additions 2018-03-24 16:57:24 -04:00
Floris van Doorn
2f957b7828 higher groups: finalize file 2018-01-31 21:39:01 -05:00
Floris van Doorn
9914352e10 higher groups: prove equivalence of categories for 0-Grp 2018-01-31 12:32:20 -05:00
Floris van Doorn
85b04639cb higher groups: prove naturality of all adjunctions 2018-01-30 20:28:15 -05:00
Floris van Doorn
98092df59c various things about higher groups 2018-01-30 16:11:13 -05:00
Floris van Doorn
e0365d2c65 higher_groups: finish adjunction between loop and deloop 2018-01-29 15:30:10 -05:00
Floris van Doorn
0949070096 Prove stabilization and work on equivalence of categories 2018-01-28 18:30:21 -05:00
Ulrik Buchholtz
f51dac9045 rename pequiv.sigma_char_equiv' to pequiv.sigma_char_pmap 2018-01-26 18:15:32 +01:00
Floris van Doorn
6de6e72a03 simplify proof of is_trunc_Grp 2018-01-23 12:44:05 -05:00
Ulrik Buchholtz
d7b8530718 prove that [n;k]Grp is an (n+1)-type 2018-01-21 12:28:43 +01:00
Floris van Doorn
d5a0080355 prove various properties about pointed truncated and/or connected types 2018-01-19 17:25:34 -05:00
Floris van Doorn
a22ac8af28 work on connectification of a type 2018-01-19 10:07:46 -05:00
Floris van Doorn
44cf88a2a5 fix connectivity levels, they were off by one 2018-01-17 19:18:20 -05:00
Floris van Doorn
9cf33dd3a7 continue working on higher groups 2018-01-17 19:18:17 -05:00
Floris van Doorn
aa191493e9 give alternative definition of free group on a set with decidable equality 2018-01-17 19:18:13 -05:00
Floris van Doorn
743985e3d8 Work on pointed naturality of smash-C 2018-01-17 19:17:05 -05:00
Floris van Doorn
d4ab6e15ef small changes in colimit 2017-11-30 18:06:02 +01:00
Floris van Doorn
899e3cf2e4 prove that iota is n-truncated/n-connected if the maps in the sequence are 2017-11-24 19:37:49 -05:00
Floris van Doorn
03cacd2dc1 move colimit project here 2017-11-22 16:15:35 -05:00
Floris van Doorn
12a9345df1 Restructure spectral sequences, compute cohomology of projective space 
This is still work in progress. Spectral sequences should be more usable, and probably the degrees of graded maps should be group homomorphisms so that we can reindex spectral sequences.
 2017-11-22 16:14:07 -05:00
Jonas Frey
f89edc5403 * cleaned up univalent_subcategory.hlean 
* removed duplicates from move_to_lib.hlean
 2017-09-14 16:22:12 -04:00
Floris van Doorn
b9c2145fab add naturality of sigma's commuting with pushouts 2017-08-22 22:34:22 +01:00
Floris van Doorn
a001491183 various properties of pushout: commutation with sums and sigma's 2017-08-02 23:06:16 +01:00
Floris van Doorn
9a693f1ee3 define pmap in terms of ppi. Also move many facts about ppi to the standard library 2017-07-21 15:55:27 +01:00
Floris van Doorn
3367c20f9d make pointed suspension and spheres the default 
There is one proof in realprojective which I couldn't quite fix, so for now I left a sorry
 2017-07-20 18:03:13 +01:00
Floris van Doorn
a5c80f79c6 work a bit on Eilenberg-MacLane spaces 2017-07-20 18:02:58 +01:00
Floris van Doorn
6bbe5ef450 reorganize some files in the library. In particular, split up spectrum 2017-07-17 15:39:49 +01:00
Floris van Doorn
c98c9bb1e6 proof naturality of pointed funext. This finishes the proof of the Serre Spectral Sequence. 
We use a different proof strategy for the naturality than pursued the last week.
We proof the unpointed version of the naturality by generalizing it from loops to paths so that we can apply path induction.
For the pointed version, we do some ugly calculations to cancel noncomputable applications of funext
 2017-07-16 01:11:55 +01:00
Floris van Doorn
df54ac858e finish functoriality of ppi_compose_left 2017-07-13 16:19:44 +01:00
Floris van Doorn
969906d480 complete psigma_gen_functor_psquare 2017-07-11 15:19:08 +01:00
Floris van Doorn
83f7761d31 work on naturality squares 2017-07-11 14:21:05 +01:00
Ulrik Buchholtz
bb3995c573 isomorphism of truncations of h-groups 2017-07-08 12:22:54 +01:00
Floris van Doorn
90f4acb3f6 fix definition of atiyah-hirzebruch spectral sequence, define serre spectral sequence 
The construction of the Serre spectral sequence is done up to 11 sorry's, all which are marked with 'TODO FOR SSS'. 8 of them are equivalences related to cohomology (6 of which are corollaries of the other 2), 2 of them are calculations on int, and the last is in the definition of a spectrum map.
 2017-07-07 22:35:30 +01:00
Steve Awodey
f6978927b2 working toward associativity of the wedge 2017-07-07 20:36:01 +01:00
Floris van Doorn
e24865d48b compute fiber of postnikov_smap 2017-07-05 20:59:38 +01:00
Floris van Doorn
36cce7acda work on translation from reduced cohomology to unreduced cohomology 2017-07-04 12:57:46 +01:00
Floris van Doorn
63ec1b8d37 progress on atiyah-hirzebruch and serre spectral sequences 
Note: the Serre spectral sequence only works for unreduced cohomology, so we need some results for that
For reduced homology we might get a similar result if we replace the sigma in the RHS by a dependent version of the smash product
 2017-07-02 01:14:18 +01:00
Floris van Doorn
f54011335d define atiyah-hirzebruch exact couple 
this commit also defines str and strunc_elim
proving that the exact couple is bounded, and that it converges to the right this is still todo
 2017-07-01 20:02:31 +01:00
Ulrik Buchholtz
3cf424ef27 add is_strunc_spi 2017-07-01 13:02:23 +01:00
Floris van Doorn
f8f0157df5 define ==> notation for convergence of spectral sequences 2017-06-30 13:55:39 +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
b8de7ffd80 work on functorial action of prespectrum homotopy groups 2017-06-09 17:42:10 -04:00
Yuri Sulyma
5826288a48 composition/inverse for homotopies of pointed spaces and spectra 2017-06-08 20:07:46 -06:00
favonia
bc69a96faa Rename homomorphism_comp_compute. 2017-06-08 16:49:47 -06:00
Robert Rose
85c0ae53a6 Merge branch 'master' of https://github.com/fpvandoorn/Spectral 2017-06-08 18:22:41 -04:00
Robert Rose
8b97339ffa seq_colim universal property 2017-06-08 18:17:23 -04:00
Yuri Sulyma
3fd6e8e852 Merge branch 'master' of github.com:fpvandoorn/Spectral 2017-06-08 14:04:58 -06:00
Yuri Sulyma
a3146d0d2a Fix bug 2017-06-08 14:03:29 -06:00