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
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
610aa351b8
Add interchange.
2017-06-07 12:03:13 -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
a292dba89f
Merge two group namespaces.
2017-06-06 17:18:10 -06:00
