Frederik Hanghøj Iversen
629115661b
Formatting in yoneda
2018-03-21 11:58:50 +01:00
Frederik Hanghøj Iversen
b6a9befd9c
Naming and formatting
2018-03-21 11:58:50 +01:00
Frederik Hanghøj Iversen
63a51fbfdc
Include modules in "everything"-module
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
Andrea Vezzosi
f7f8953a42
Voe: Use the isomorphism directly for better computation
2018-03-15 13:39:42 +00:00
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
360e2b95dd
Make parameter to monad equivalence explicit
2018-03-14 11:20:07 +01:00
Frederik Hanghøj Iversen
7aec22b30a
Expose both monad formulations qualified from Cat.Category.Monad
2018-03-14 11:00:52 +01:00
Frederik Hanghøj Iversen
6229decfb2
Merge branch 'master' into dev
2018-03-14 10:50:57 +01:00
Frederik Hanghøj Iversen
41e2d02c8d
[WIP] Prove voe §2.3
...
By Andrea
The reason you cannot use cong in [1] is that §2-fromMonad result type
depends on the input, you need a dependent version of cong:
cong-d : ∀ {ℓ} {A : Set ℓ} {ℓ'} {B : A → Set ℓ'} {x y : A}
→ (f : (x : A) → B x)
→ (eq : x ≡ y)
→ PathP (\ i → B (eq i)) (f x) (f y)
cong-d f p = λ i → f (p i)
I attach a modified Voevodsky.agda.
Notice that the definition of "t" is still highlighted in yellow,
that's because it being a homogeneous path depends on the exact
definition of lem, see the comment with the two definitional equality
constraints.
2018-03-14 10:30:42 +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
7065455712
More readable goal for voevodsky's construction
2018-03-13 11:29:13 +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
fe453a6d3a
Trying to prove cummulativity of homotopy levels
2018-03-12 16:00:27 +01:00
Frederik Hanghøj Iversen
c52384b012
Change name of fromMonad
2018-03-12 14:43:43 +01:00
Frederik Hanghøj Iversen
5e092964c8
Change naming and fuse some modules
2018-03-12 14:38:52 +01:00
Frederik Hanghøj Iversen
ccf753d438
Move monoidal and kleisli representation to own modules
2018-03-12 14:23:23 +01:00
Frederik Hanghøj Iversen
8dadfa22a0
Add documentation header to monad module
2018-03-12 14:11:31 +01:00
Frederik Hanghøj Iversen
aa645fb11e
Move voevodsky's construction to own module
2018-03-12 14:04:10 +01:00
Frederik Hanghøj Iversen
c0cf6789cd
Use propositions straight from the horses mouth
2018-03-12 13:56:49 +01:00
Frederik Hanghøj Iversen
a7214fcc66
Finish equality principle for categories
2018-03-12 13:51:29 +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
2fcc583646
Add note
2018-03-08 10:50:18 +01:00
Frederik Hanghøj Iversen
63b5f5c68d
Use long name for product object
2018-03-08 10:46:28 +01:00
Frederik Hanghøj Iversen
486238e114
Add goals for propositionality of products
2018-03-08 10:38:46 +01:00
Frederik Hanghøj Iversen
1ef57a19f4
Cosmetics
2018-03-08 10:30:35 +01:00
Frederik Hanghøj Iversen
4e7b350188
Factor out objects
2018-03-08 10:28:05 +01:00
Frederik Hanghøj Iversen
181bd1af53
Factor out category
2018-03-08 10:24:17 +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
e43bee6d9f
Feels really close
2018-03-08 00:36:38 +01:00
Frederik Hanghøj Iversen
c8fef1d2b5
Use different name for function composition
2018-03-08 00:22:55 +01:00
Frederik Hanghøj Iversen
36cbe711fb
Sort of half of the proof of an inverse
2018-03-08 00:09:49 +01:00
Frederik Hanghøj Iversen
459718da23
Finish proof of equivalence of klesili/monoidal categories!!
2018-03-07 17:30:09 +01:00
Frederik Hanghøj Iversen
19103e1678
Update cubical
2018-03-07 16:24:43 +01:00
Frederik Hanghøj Iversen
93d075a6d3
Attempt at proving pureNTEq
2018-03-07 15:23:07 +01:00
Frederik Hanghøj Iversen
00e6e1aa66
State problem with approach
2018-03-07 11:45:11 +01:00
Frederik Hanghøj Iversen
aa64e01084
Remove some cruft
2018-03-07 11:33:08 +01:00
Frederik Hanghøj Iversen
125123846e
Lay out a strategy for showing the equivalence
2018-03-07 11:29:58 +01:00
Frederik Hanghøj Iversen
085e6eb3d7
Stuff about voe-2-3
2018-03-06 23:18:33 +01:00
Frederik Hanghøj Iversen
110e3510c5
Use postulates
2018-03-06 15:55:03 +01:00
Frederik Hanghøj Iversen
5ae68df582
Prove that fmap is mapped correctly
2018-03-06 15:53:11 +01:00
Frederik Hanghøj Iversen
4d528a7077
Clean-up
2018-03-06 11:25:29 +01:00
Frederik Hanghøj Iversen
485703c85e
Tidy up
2018-03-06 10:16:42 +01:00
Frederik Hanghøj Iversen
0cebe1e866
Make private
2018-03-06 10:06:45 +01:00
Frederik Hanghøj Iversen
4de27aa06c
Naming
2018-03-06 10:05:35 +01:00
Frederik Hanghøj Iversen
9173468b03
Use omap/fmap
2018-03-06 09:56:44 +01:00
Frederik Hanghøj Iversen
bdd67aee53
Rename RR to Romap
2018-03-06 09:55:18 +01:00
Frederik Hanghøj Iversen
c57cd5c991
Define stuff in monoidal record
2018-03-06 09:52:37 +01:00
Frederik Hanghøj Iversen
cfb7925cb5
Renaming
2018-03-06 09:45:04 +01:00
Frederik Hanghøj Iversen
b6457a0b14
Add comment
2018-03-06 09:41:29 +01:00
Frederik Hanghøj Iversen
7647a452cd
Tidy up proof a bit
2018-03-06 09:39:48 +01:00
Frederik Hanghøj Iversen
35419ad86e
Rename eta and mu
2018-03-06 09:35:50 +01:00
Frederik Hanghøj Iversen
f8e08288a0
Cosmetics
2018-03-05 17:31:13 +01:00
Frederik Hanghøj Iversen
9ec6ce9eba
Use other equality principle
2018-03-05 17:10:41 +01:00
Frederik Hanghøj Iversen
3151fb3e46
Prove propositionality for naturality
2018-03-05 16:35:47 +01:00
Frederik Hanghøj Iversen
7f4a8a65b8
More stuff about opposite being an involution
2018-03-05 16:10:27 +01:00
Frederik Hanghøj Iversen
b26ea18257
Cleanup in nattrans
2018-03-05 15:04:16 +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
ce4dd83969
Prove that the yoneda embedding is distributive
2018-03-05 14:42:12 +01:00
Frederik Hanghøj Iversen
7fbca1aeeb
Clean-up yoneda embedding
2018-03-05 14:04:04 +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
059c74b687
Use already defined category
2018-03-05 11:15:45 +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
b079f5e426
Prove propositionality for IsMonad
2018-03-02 13:31:46 +01:00
Frederik Hanghøj Iversen
c4e3625746
Finish proof of distributivity
2018-03-01 20:47:36 +01:00
Frederik Hanghøj Iversen
2ceb027f7a
Prove monad-equality principle for kleisly monads
2018-03-01 20:23:34 +01:00
Frederik Hanghøj Iversen
f2164a6717
Prove equality principle for monads
2018-03-01 20:12:49 +01:00
Frederik Hanghøj Iversen
a7f31bb3e2
Prove "foreign naturality condition"
2018-03-01 18:00:51 +01:00
Frederik Hanghøj Iversen
f526fd6010
Prove inverse law
2018-03-01 17:50:06 +01:00
Frederik Hanghøj Iversen
ff2952e9ad
Make postulate
2018-03-01 14:59:19 +01:00
Frederik Hanghøj Iversen
ae46a48861
Define goals in Kleisli
2018-03-01 14:58:01 +01:00
Frederik Hanghøj Iversen
64a0292755
Cosmetics
2018-03-01 14:19:46 +01:00
Frederik Hanghøj Iversen
e8b29e1f7f
\mu is join and it's a natural transformation!
2018-02-28 23:41:59 +01:00
Frederik Hanghøj Iversen
9d3b17245f
Provide \zeta
2018-02-28 19:32:07 +01:00
Frederik Hanghøj Iversen
f2b1a36a75
Define and use Endofunctor
2018-02-28 19:03:11 +01:00
Frederik Hanghøj Iversen
3c77c69cf6
Move functor definition to Kleisli.Monad
2018-02-28 19:00:21 +01:00
Frederik Hanghøj Iversen
70221377d3
Move proof of equivalence to IsMonad making them lemmas
2018-02-28 18:55:32 +01:00
Frederik Hanghøj Iversen
1aaf81552c
Move another proof to category definition
2018-02-26 20:42:00 +01:00
Frederik Hanghøj Iversen
101b2639e1
Move proof to category definition
2018-02-26 20:31:47 +01:00
Frederik Hanghøj Iversen
5b5d21f777
Formatting
2018-02-26 20:23:31 +01:00
Frederik Hanghøj Iversen
a0944d69b1
Documentation in Monad
2018-02-26 20:08:48 +01:00
Frederik Hanghøj Iversen
67993be27b
Add reverse function composition to category
2018-02-26 20:00:24 +01:00
Frederik Hanghøj Iversen
47882b1110
Rename zeta to pure
2018-02-26 19:58:27 +01:00
Frederik Hanghøj Iversen
043641462d
Prove distributive law for monads!
2018-02-26 19:57:05 +01:00
Frederik Hanghøj Iversen
7cddba97a8
Shorten definition
2018-02-25 19:03:48 +01:00
Frederik Hanghøj Iversen
2c6132768e
Remove Pathy and Bij
2018-02-25 15:29:52 +01:00
Frederik Hanghøj Iversen
5caecf9796
Rename properties to yoneda
2018-02-25 15:28:42 +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
cd98736d02
Add documentation in Category-module
2018-02-25 15:21:38 +01:00
Frederik Hanghøj Iversen
2e7220567a
Move lemma into IsCategory
2018-02-25 14:44:03 +01:00
Frederik Hanghøj Iversen
d63ecc3a65
Use abbreviation
2018-02-25 14:39:11 +01:00
Frederik Hanghøj Iversen
caddf83a09
Let IsCategory reexport RawCategory
2018-02-25 14:37:28 +01:00
Frederik Hanghøj Iversen
5deabb7546
Forgot to add monoid-module
2018-02-25 14:28:01 +01:00
Frederik Hanghøj Iversen
ce46e0ae7a
Module-ify
2018-02-25 14:27:37 +01:00
Frederik Hanghøj Iversen
12dddc2067
Use a module
2018-02-25 03:12:51 +01:00
Frederik Hanghøj Iversen
4c298855e0
[WIP] Proving other fusion law
...
Also set up framework for equality principle for monads
2018-02-25 03:09:25 +01:00
Frederik Hanghøj Iversen
a6b01929f0
Prove distributive law
2018-02-25 01:27:20 +01:00
Frederik Hanghøj Iversen
a447cd9c7c
Syntax
2018-02-24 20:41:47 +01:00
Frederik Hanghøj Iversen
9d09363f78
Expand definition of isDistributive somewhat
...
Also contains some side-tracks
2018-02-24 20:37:21 +01:00
Frederik Hanghøj Iversen
e7abab0e4c
Add pure and >=> to kleisli category
2018-02-24 19:08:20 +01:00
Frederik Hanghøj Iversen
be505cdfbe
Prove IsAssociative
2018-02-24 19:07:58 +01:00
Frederik Hanghøj Iversen
5d9c820fa2
Add note about haskell
2018-02-24 15:25:07 +01:00
Frederik Hanghøj Iversen
e4e327d1d2
[WIP] equivalence of kleisli- resp. monoidal- representation of monad
2018-02-24 15:13:25 +01:00
Frederik Hanghøj Iversen
3e12331294
Monoidal monads addendum
2018-02-24 14:01:57 +01:00
Frederik Hanghøj Iversen
4ec13fe509
Implement monads in the kleisli form
2018-02-24 14:00:52 +01:00
Frederik Hanghøj Iversen
0ca11874bc
Remove old name for functor composition
2018-02-24 12:55:08 +01:00
Frederik Hanghøj Iversen
8527fe0df4
Rename functor composition - implement monads...
...
In their monoidal form.
2018-02-24 12:52:16 +01:00
Frederik Hanghøj Iversen
cb8533b84a
Rename natural transformation composition
2018-02-23 17:43:38 +01:00
Frederik Hanghøj Iversen
dd11b69c71
Documentation for natural transformations
2018-02-23 17:37:27 +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
f5dded9561
Do not use IsCategory directly
2018-02-23 16:41:17 +01:00
Frederik Hanghøj Iversen
39284b8d99
Changes in CwF
2018-02-23 14:13:55 +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
7787a8f0be
Indentation
2018-02-23 12:52:14 +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
Frederik Hanghøj Iversen
a57f45d93f
Remove yet another postulate
2018-02-23 12:33:20 +01:00
Frederik Hanghøj Iversen
34dec9406d
Do not mention IsFunctor outside the module that defines it
2018-02-23 12:29:10 +01:00
Frederik Hanghøj Iversen
e46edf1f68
Chain reexport things in Functor
2018-02-23 12:21:16 +01:00
Frederik Hanghøj Iversen
885fd8fa69
Drastically simplify proofs
2018-02-23 12:15:39 +01:00
Frederik Hanghøj Iversen
3f3247c870
Remove commented code
2018-02-23 12:05:38 +01:00
Frederik Hanghøj Iversen
de1d19c442
Readd stuff about the yoneda embedding
2018-02-23 11:24:22 +01:00
