Frederik Hanghøj Iversen
ac01b786a7
Cleanup
2018-03-22 14:27:16 +01:00
Frederik Hanghøj Iversen
ebcab2528e
Prove second inverse law for from/to-isomorphism
2018-03-22 13:49:53 +01:00
Frederik Hanghøj Iversen
d816ba657b
QED! Show that the category of homotopic sets are univalent.
2018-03-22 12:11:27 +01:00
Frederik Hanghøj Iversen
52ca0b6732
Merge remote-tracking branch 'Saizan/dev' into dev
2018-03-22 11:54:22 +01:00
Frederik Hanghøj Iversen
d12122ce60
Add another approach for univalence in Set
2018-03-22 11:50:07 +01:00
Andrea Vezzosi
66ab7138a6
generalized lem3 and made progress for Sets univalence
2018-03-22 10:41:38 +00:00
Frederik Hanghøj Iversen
807a0f3dcd
Slight readability improvement
2018-03-21 18:05:25 +01:00
Frederik Hanghøj Iversen
181edc0cd5
Prove step 3 in proof of unvivalence for hSet without ua
2018-03-21 17:52:32 +01:00
Frederik Hanghøj Iversen
8f67ff9f36
Use explicit parameter for hSet
2018-03-21 15:01:31 +01:00
Frederik Hanghøj Iversen
ae0ff092f8
Use prelude everywhere
2018-03-21 14:56:43 +01:00
Frederik Hanghøj Iversen
29f45d1426
Delete equality module
2018-03-21 14:47:01 +01:00
Frederik Hanghøj Iversen
183906dc8c
Define and use custom prelude
2018-03-21 14:39:56 +01:00
Frederik Hanghøj Iversen
084befbbc6
Merge remote-tracking branch 'Saizan/dev' into dev
...
From Andrea:
The problem with "h" there is that ve-re is building a square, "(qq0 j
, h)" is a fine element of the sigma type, but it does not really
connect "(g ∘ f) e" to "e" across dimension "i", in particular it does
not reduce to "e" when "i" is "i1".
2018-03-21 13:31:28 +01:00
Frederik Hanghøj Iversen
cd3514c8cf
Formatting
2018-03-21 13:25:24 +01:00
Andrea Vezzosi
ed3b3047e6
Progress on univalence for sets.
2018-03-21 12:00:47 +00:00
Frederik Hanghøj Iversen
890154a81d
Simplify qualified imports, change make-target: clean
2018-03-21 12:28:26 +01:00
Frederik Hanghøj Iversen
4beb48e066
Use correct order for left- and right identity
...
Define and use helpers left- and right identity
2018-03-21 11:58:50 +01:00
Frederik Hanghøj Iversen
31257a4d97
Do not export helpers in Fun
2018-03-21 11:58:50 +01:00
Frederik Hanghøj Iversen
811a6bf58e
Make univalence a submodule of RawCategory
2018-03-21 11:58:23 +01:00
Frederik Hanghøj Iversen
b03bfb0c77
Restructure in free monad
2018-03-20 14:58:27 +01:00
Frederik Hanghøj Iversen
66cb5b363d
[WIP] Finnish all intermediate steps for univalence of hSets
2018-03-20 13:26:40 +01:00
Frederik Hanghøj Iversen
2188e690a0
Prove identity law for coercions.
2018-03-20 12:12:09 +01:00
Frederik Hanghøj Iversen
30725d71b6
[WIP] Scary goal
2018-03-20 11:58:54 +01:00
Frederik Hanghøj Iversen
32d1833d51
[WIP] A long way towards proving univalence in the category of hSets
2018-03-20 11:27:04 +01:00
Frederik Hanghøj Iversen
43563d1ad9
[WIP] Univalence for category of homotopy sets
2018-03-19 16:27:03 +01:00
Frederik Hanghøj Iversen
2058154c65
Helpers to work with isomorphisms and equivalences
2018-03-19 15:15:03 +01:00
Frederik Hanghøj Iversen
f69ab0ee62
[WIP] Univalence for the category of hSets
2018-03-19 14:08:59 +01:00
Frederik Hanghøj Iversen
438978973d
Construct isomorphism from equivalence
...
Using this somewhat round-about way of constructing an isomorphism from
an equivalence has made typechecking slower in some situations.
E.g. if you're constructing an equivalence from gradLemma and later use
that constructed equivalence to recover the isomorphism, then you
might as well have kept using those functions.
2018-03-15 12:33:00 +01:00
Frederik Hanghøj Iversen
091e77b583
Rename IsProduct.isProduct to IsProduct.ump
...
[WIP]: Also some stuff about propositionality for products.
2018-03-14 10:23:23 +01:00
Frederik Hanghøj Iversen
896e0d3d37
Stuff about univalence for the category of functors
2018-03-13 10:24:50 +01:00
Frederik Hanghøj Iversen
35390c02d3
Stuff about univalence in the category of sets
2018-03-12 13:38:48 +01:00
Frederik Hanghøj Iversen
acb5ff4f2b
Closer to showing univalence for the category of sets
2018-03-08 14:44:23 +01:00
Frederik Hanghøj Iversen
52297d9073
Clean-up in the category of categories
2018-03-08 11:54:13 +01:00
Frederik Hanghøj Iversen
d01514cbdb
Do not use ugly ':'-syntax to disambiguate fields
2018-03-08 11:29:16 +01:00
Frederik Hanghøj Iversen
48672b01bd
Use dotted expression in Cat
2018-03-08 11:20:51 +01:00
Frederik Hanghøj Iversen
5ad506a09f
Rename func* and func-> to omap and fmap respectively
2018-03-08 11:03:56 +01:00
Frederik Hanghøj Iversen
63b5f5c68d
Use long name for product object
2018-03-08 10:46:28 +01:00
Frederik Hanghøj Iversen
4e7b350188
Factor out objects
2018-03-08 10:28:05 +01:00
Frederik Hanghøj Iversen
faf4c54188
Make parameters explicit
2018-03-08 10:22:21 +01:00
Frederik Hanghøj Iversen
fae492a1e3
Restructure products
2018-03-08 10:20:29 +01:00
Frederik Hanghøj Iversen
b61749bb91
Fixup some todo-notes
2018-03-08 01:10:52 +01:00
Frederik Hanghøj Iversen
fa9a470875
Update backlog
2018-03-08 00:54:42 +01:00
Frederik Hanghøj Iversen
9ec6ce9eba
Use other equality principle
2018-03-05 17:10:41 +01:00
Frederik Hanghøj Iversen
ddd5f17c05
Move propositionality stuff about natural transformations to that module
2018-03-05 15:02:36 +01:00
Frederik Hanghøj Iversen
2b92cee254
Prettier names in Fun
2018-03-05 14:55:45 +01:00
Frederik Hanghøj Iversen
bb379fa196
Implement category of presheaves
2018-03-05 14:50:53 +01:00
Frederik Hanghøj Iversen
1bf565b87a
Have yoneda without having a category of categories
...
I did break some things in Cat.Categories.Cat but since this is
unprovable anyways it's not that big a deal.
2018-03-05 13:52:59 +01:00
Frederik Hanghøj Iversen
5c3616bca5
Make argument to presheaf explicit
2018-03-05 11:17:31 +01:00
Frederik Hanghøj Iversen
a4890a42cf
Define Monoidal categories without depending on category of categories
2018-03-05 11:13:58 +01:00
Frederik Hanghøj Iversen
5902c6121b
Further reduce dependency on impossible facts.
...
Provide the data for the product in the category of categories without
requiring such a category to actually exist
2018-03-05 11:07:42 +01:00
