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
Frederik Hanghøj Iversen
77006011d3
Minimize dependency on category of categories
2018-03-05 10:35:33 +01:00
Frederik Hanghøj Iversen
8f8800cb67
More stuff about kleisli \equiv monoidal
2018-03-05 10:28:16 +01:00
Frederik Hanghøj Iversen
44526b85eb
Move CwF
2018-02-25 15:24:44 +01:00
Frederik Hanghøj Iversen
f0beec1530
Rename Opposite to opposite
2018-02-25 15:23:33 +01:00
Frederik Hanghøj Iversen
caddf83a09
Let IsCategory reexport RawCategory
2018-02-25 14:37:28 +01:00
Frederik Hanghøj Iversen
0ca11874bc
Remove old name for functor composition
2018-02-24 12:55:08 +01:00
Frederik Hanghøj Iversen
cb8533b84a
Rename natural transformation composition
2018-02-23 17:43:38 +01:00
Frederik Hanghøj Iversen
689a6467c6
Move stuff about natural transformations to own module
2018-02-23 17:33:09 +01:00
Frederik Hanghøj Iversen
5796b791b8
Almost prove that arrows are sets in the cateogry of families
2018-02-23 13:59:35 +01:00
Frederik Hanghøj Iversen
a321a9c8b2
Use hLevels in Fam
2018-02-23 13:39:59 +01:00
Frederik Hanghøj Iversen
3d0916f448
Use correct name for hSets
2018-02-23 13:20:30 +01:00
Frederik Hanghøj Iversen
4874ed0795
Rename distrib to isDistributive
2018-02-23 12:53:35 +01:00
Frederik Hanghøj Iversen
48423cc816
Rename arrowIsSet to arrowsAreSets
2018-02-23 12:51:44 +01:00
Frederik Hanghøj Iversen
6446435a49
Rename ident to isIdentity
2018-02-23 12:49:41 +01:00
Frederik Hanghøj Iversen
5cbc409770
Rename assoc to isAssociative
2018-02-23 12:43:49 +01:00
Frederik Hanghøj Iversen
852056cc44
Add type-synonyms in functor
2018-02-23 12:41:15 +01:00
