 Frederik Hanghøj Iversen
|
c8fef1d2b5
|
Use different name for function composition
|
2018-03-08 00:22:55 +01:00 |
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Frederik Hanghøj Iversen
|
36cbe711fb
|
Sort of half of the proof of an inverse
|
2018-03-08 00:09:49 +01:00 |
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Frederik Hanghøj Iversen
|
459718da23
|
Finish proof of equivalence of klesili/monoidal categories!!
|
2018-03-07 17:30:09 +01:00 |
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|
Frederik Hanghøj Iversen
|
19103e1678
|
Update cubical
|
2018-03-07 16:24:43 +01:00 |
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|
Frederik Hanghøj Iversen
|
93d075a6d3
|
Attempt at proving pureNTEq
|
2018-03-07 15:23:07 +01:00 |
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Frederik Hanghøj Iversen
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00e6e1aa66
|
State problem with approach
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2018-03-07 11:45:11 +01:00 |
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Frederik Hanghøj Iversen
|
aa64e01084
|
Remove some cruft
|
2018-03-07 11:33:08 +01:00 |
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|
Frederik Hanghøj Iversen
|
125123846e
|
Lay out a strategy for showing the equivalence
|
2018-03-07 11:29:58 +01:00 |
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Frederik Hanghøj Iversen
|
085e6eb3d7
|
Stuff about voe-2-3
|
2018-03-06 23:18:33 +01:00 |
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Frederik Hanghøj Iversen
|
110e3510c5
|
Use postulates
|
2018-03-06 15:55:03 +01:00 |
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Frederik Hanghøj Iversen
|
5ae68df582
|
Prove that fmap is mapped correctly
|
2018-03-06 15:53:11 +01:00 |
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Frederik Hanghøj Iversen
|
4d528a7077
|
Clean-up
|
2018-03-06 11:25:29 +01:00 |
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|
Frederik Hanghøj Iversen
|
485703c85e
|
Tidy up
|
2018-03-06 10:16:42 +01:00 |
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|
Frederik Hanghøj Iversen
|
0cebe1e866
|
Make private
|
2018-03-06 10:06:45 +01:00 |
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|
Frederik Hanghøj Iversen
|
4de27aa06c
|
Naming
|
2018-03-06 10:05:35 +01:00 |
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Frederik Hanghøj Iversen
|
9173468b03
|
Use omap/fmap
|
2018-03-06 09:56:44 +01:00 |
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Frederik Hanghøj Iversen
|
bdd67aee53
|
Rename RR to Romap
|
2018-03-06 09:55:18 +01:00 |
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|
Frederik Hanghøj Iversen
|
c57cd5c991
|
Define stuff in monoidal record
|
2018-03-06 09:52:37 +01:00 |
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|
Frederik Hanghøj Iversen
|
cfb7925cb5
|
Renaming
|
2018-03-06 09:45:04 +01:00 |
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Frederik Hanghøj Iversen
|
b6457a0b14
|
Add comment
|
2018-03-06 09:41:29 +01:00 |
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Frederik Hanghøj Iversen
|
7647a452cd
|
Tidy up proof a bit
|
2018-03-06 09:39:48 +01:00 |
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|
Frederik Hanghøj Iversen
|
35419ad86e
|
Rename eta and mu
|
2018-03-06 09:35:50 +01:00 |
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|
Frederik Hanghøj Iversen
|
f8e08288a0
|
Cosmetics
|
2018-03-05 17:31:13 +01:00 |
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Frederik Hanghøj Iversen
|
9ec6ce9eba
|
Use other equality principle
|
2018-03-05 17:10:41 +01:00 |
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Frederik Hanghøj Iversen
|
3151fb3e46
|
Prove propositionality for naturality
|
2018-03-05 16:35:47 +01:00 |
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|
Frederik Hanghøj Iversen
|
7f4a8a65b8
|
More stuff about opposite being an involution
|
2018-03-05 16:10:27 +01:00 |
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|
Frederik Hanghøj Iversen
|
b26ea18257
|
Cleanup in nattrans
|
2018-03-05 15:04:16 +01:00 |
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Frederik Hanghøj Iversen
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ddd5f17c05
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Move propositionality stuff about natural transformations to that module
|
2018-03-05 15:02:36 +01:00 |
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Frederik Hanghøj Iversen
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2b92cee254
|
Prettier names in Fun
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2018-03-05 14:55:45 +01:00 |
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Frederik Hanghøj Iversen
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bb379fa196
|
Implement category of presheaves
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2018-03-05 14:50:53 +01:00 |
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Frederik Hanghøj Iversen
|
ce4dd83969
|
Prove that the yoneda embedding is distributive
|
2018-03-05 14:42:12 +01:00 |
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|
Frederik Hanghøj Iversen
|
7fbca1aeeb
|
Clean-up yoneda embedding
|
2018-03-05 14:04:04 +01:00 |
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Frederik Hanghøj Iversen
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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 |
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Frederik Hanghøj Iversen
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5c3616bca5
|
Make argument to presheaf explicit
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2018-03-05 11:17:31 +01:00 |
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Frederik Hanghøj Iversen
|
059c74b687
|
Use already defined category
|
2018-03-05 11:15:45 +01:00 |
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Frederik Hanghøj Iversen
|
a4890a42cf
|
Define Monoidal categories without depending on category of categories
|
2018-03-05 11:13:58 +01:00 |
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|
Frederik Hanghøj Iversen
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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 |
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|
Frederik Hanghøj Iversen
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77006011d3
|
Minimize dependency on category of categories
|
2018-03-05 10:35:33 +01:00 |
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Frederik Hanghøj Iversen
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8f8800cb67
|
More stuff about kleisli \equiv monoidal
|
2018-03-05 10:28:16 +01:00 |
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Frederik Hanghøj Iversen
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b079f5e426
|
Prove propositionality for IsMonad
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2018-03-02 13:31:46 +01:00 |
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Frederik Hanghøj Iversen
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c4e3625746
|
Finish proof of distributivity
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2018-03-01 20:47:36 +01:00 |
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Frederik Hanghøj Iversen
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2ceb027f7a
|
Prove monad-equality principle for kleisly monads
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2018-03-01 20:23:34 +01:00 |
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Frederik Hanghøj Iversen
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f2164a6717
|
Prove equality principle for monads
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2018-03-01 20:12:49 +01:00 |
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Frederik Hanghøj Iversen
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a7f31bb3e2
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Prove "foreign naturality condition"
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2018-03-01 18:00:51 +01:00 |
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Frederik Hanghøj Iversen
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f526fd6010
|
Prove inverse law
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2018-03-01 17:50:06 +01:00 |
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Frederik Hanghøj Iversen
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ff2952e9ad
|
Make postulate
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2018-03-01 14:59:19 +01:00 |
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Frederik Hanghøj Iversen
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ae46a48861
|
Define goals in Kleisli
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2018-03-01 14:58:01 +01:00 |
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Frederik Hanghøj Iversen
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64a0292755
|
Cosmetics
|
2018-03-01 14:19:46 +01:00 |
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Frederik Hanghøj Iversen
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e8b29e1f7f
|
\mu is join and it's a natural transformation!
|
2018-02-28 23:41:59 +01:00 |
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Frederik Hanghøj Iversen
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9d3b17245f
|
Provide \zeta
|
2018-02-28 19:32:07 +01:00 |
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Frederik Hanghøj Iversen
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f2b1a36a75
|
Define and use Endofunctor
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2018-02-28 19:03:11 +01:00 |
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Frederik Hanghøj Iversen
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3c77c69cf6
|
Move functor definition to Kleisli.Monad
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2018-02-28 19:00:21 +01:00 |
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Frederik Hanghøj Iversen
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70221377d3
|
Move proof of equivalence to IsMonad making them lemmas
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2018-02-28 18:55:32 +01:00 |
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Frederik Hanghøj Iversen
|
1aaf81552c
|
Move another proof to category definition
|
2018-02-26 20:42:00 +01:00 |
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Frederik Hanghøj Iversen
|
101b2639e1
|
Move proof to category definition
|
2018-02-26 20:31:47 +01:00 |
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Frederik Hanghøj Iversen
|
5b5d21f777
|
Formatting
|
2018-02-26 20:23:31 +01:00 |
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Frederik Hanghøj Iversen
|
a0944d69b1
|
Documentation in Monad
|
2018-02-26 20:08:48 +01:00 |
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Frederik Hanghøj Iversen
|
67993be27b
|
Add reverse function composition to category
|
2018-02-26 20:00:24 +01:00 |
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Frederik Hanghøj Iversen
|
47882b1110
|
Rename zeta to pure
|
2018-02-26 19:58:27 +01:00 |
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Frederik Hanghøj Iversen
|
043641462d
|
Prove distributive law for monads!
|
2018-02-26 19:57:05 +01:00 |
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Frederik Hanghøj Iversen
|
7cddba97a8
|
Shorten definition
|
2018-02-25 19:03:48 +01:00 |
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Frederik Hanghøj Iversen
|
2c6132768e
|
Remove Pathy and Bij
|
2018-02-25 15:29:52 +01:00 |
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Frederik Hanghøj Iversen
|
5caecf9796
|
Rename properties to yoneda
|
2018-02-25 15:28:42 +01:00 |
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Frederik Hanghøj Iversen
|
44526b85eb
|
Move CwF
|
2018-02-25 15:24:44 +01:00 |
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Frederik Hanghøj Iversen
|
f0beec1530
|
Rename Opposite to opposite
|
2018-02-25 15:23:33 +01:00 |
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Frederik Hanghøj Iversen
|
cd98736d02
|
Add documentation in Category-module
|
2018-02-25 15:21:38 +01:00 |
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Frederik Hanghøj Iversen
|
2e7220567a
|
Move lemma into IsCategory
|
2018-02-25 14:44:03 +01:00 |
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Frederik Hanghøj Iversen
|
d63ecc3a65
|
Use abbreviation
|
2018-02-25 14:39:11 +01:00 |
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Frederik Hanghøj Iversen
|
caddf83a09
|
Let IsCategory reexport RawCategory
|
2018-02-25 14:37:28 +01:00 |
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Frederik Hanghøj Iversen
|
5deabb7546
|
Forgot to add monoid-module
|
2018-02-25 14:28:01 +01:00 |
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Frederik Hanghøj Iversen
|
ce46e0ae7a
|
Module-ify
|
2018-02-25 14:27:37 +01:00 |
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Frederik Hanghøj Iversen
|
12dddc2067
|
Use a module
|
2018-02-25 03:12:51 +01:00 |
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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 |
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Frederik Hanghøj Iversen
|
a6b01929f0
|
Prove distributive law
|
2018-02-25 01:27:20 +01:00 |
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|
Frederik Hanghøj Iversen
|
a447cd9c7c
|
Syntax
|
2018-02-24 20:41:47 +01:00 |
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Frederik Hanghøj Iversen
|
9d09363f78
|
Expand definition of isDistributive somewhat
Also contains some side-tracks
|
2018-02-24 20:37:21 +01:00 |
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Frederik Hanghøj Iversen
|
e7abab0e4c
|
Add pure and >=> to kleisli category
|
2018-02-24 19:08:20 +01:00 |
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Frederik Hanghøj Iversen
|
be505cdfbe
|
Prove IsAssociative
|
2018-02-24 19:07:58 +01:00 |
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Frederik Hanghøj Iversen
|
5d9c820fa2
|
Add note about haskell
|
2018-02-24 15:25:07 +01:00 |
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Frederik Hanghøj Iversen
|
e4e327d1d2
|
[WIP] equivalence of kleisli- resp. monoidal- representation of monad
|
2018-02-24 15:13:25 +01:00 |
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|
Frederik Hanghøj Iversen
|
3e12331294
|
Monoidal monads addendum
|
2018-02-24 14:01:57 +01:00 |
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Frederik Hanghøj Iversen
|
4ec13fe509
|
Implement monads in the kleisli form
|
2018-02-24 14:00:52 +01:00 |
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Frederik Hanghøj Iversen
|
0ca11874bc
|
Remove old name for functor composition
|
2018-02-24 12:55:08 +01:00 |
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|
Frederik Hanghøj Iversen
|
8527fe0df4
|
Rename functor composition - implement monads...
In their monoidal form.
|
2018-02-24 12:52:16 +01:00 |
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|
Frederik Hanghøj Iversen
|
cb8533b84a
|
Rename natural transformation composition
|
2018-02-23 17:43:38 +01:00 |
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|
Frederik Hanghøj Iversen
|
dd11b69c71
|
Documentation for natural transformations
|
2018-02-23 17:37:27 +01:00 |
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|
Frederik Hanghøj Iversen
|
689a6467c6
|
Move stuff about natural transformations to own module
|
2018-02-23 17:33:09 +01:00 |
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|
Frederik Hanghøj Iversen
|
f5dded9561
|
Do not use IsCategory directly
|
2018-02-23 16:41:17 +01:00 |
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Frederik Hanghøj Iversen
|
39284b8d99
|
Changes in CwF
|
2018-02-23 14:13:55 +01:00 |
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Frederik Hanghøj Iversen
|
5796b791b8
|
Almost prove that arrows are sets in the cateogry of families
|
2018-02-23 13:59:35 +01:00 |
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Frederik Hanghøj Iversen
|
a321a9c8b2
|
Use hLevels in Fam
|
2018-02-23 13:39:59 +01:00 |
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|
Frederik Hanghøj Iversen
|
3d0916f448
|
Use correct name for hSets
|
2018-02-23 13:20:30 +01:00 |
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|
Frederik Hanghøj Iversen
|
4874ed0795
|
Rename distrib to isDistributive
|
2018-02-23 12:53:35 +01:00 |
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|
Frederik Hanghøj Iversen
|
7787a8f0be
|
Indentation
|
2018-02-23 12:52:14 +01:00 |
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|
Frederik Hanghøj Iversen
|
48423cc816
|
Rename arrowIsSet to arrowsAreSets
|
2018-02-23 12:51:44 +01:00 |
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|
Frederik Hanghøj Iversen
|
6446435a49
|
Rename ident to isIdentity
|
2018-02-23 12:49:41 +01:00 |
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|
Frederik Hanghøj Iversen
|
5cbc409770
|
Rename assoc to isAssociative
|
2018-02-23 12:43:49 +01:00 |
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|
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 |
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|
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 |
|
|
Frederik Hanghøj Iversen
|
954a89f8d1
|
Expose naturalIsProp
|
2018-02-23 11:12:27 +01:00 |
|
|
Frederik Hanghøj Iversen
|
bc2129b8fc
|
Readd yoneda embedding
|
2018-02-23 10:55:43 +01:00 |
|
|
Frederik Hanghøj Iversen
|
9a4d79fa4e
|
Readd commented code
|
2018-02-23 10:44:23 +01:00 |
|
|
Frederik Hanghøj Iversen
|
3032dc6130
|
Make explicit argument
|
2018-02-23 10:36:59 +01:00 |
|
|
Frederik Hanghøj Iversen
|
cc1ddaac9f
|
Add new type-synonym
|
2018-02-23 10:35:42 +01:00 |
|
|
Frederik Hanghøj Iversen
|
a87d404aad
|
Refactor category of categories
No longer actually define the category. Just define the raw category and
a few results about it.
|
2018-02-23 10:34:37 +01:00 |
|
|
Frederik Hanghøj Iversen
|
32b9ce2ea8
|
Use new syntax in cat
|
2018-02-22 15:31:54 +01:00 |
|
|
Frederik Hanghøj Iversen
|
a82095604d
|
Remove unused function
|
2018-02-21 14:05:10 +01:00 |
|
|
Frederik Hanghøj Iversen
|
9e96e704e8
|
Update Fun according to new naming policy
|
2018-02-21 13:40:24 +01:00 |
|
|
Frederik Hanghøj Iversen
|
57d7eab4cb
|
Make sets a category according to HoTT
|
2018-02-21 13:37:07 +01:00 |
|
|
Frederik Hanghøj Iversen
|
ed40824edc
|
Cosmetics
|
2018-02-21 12:59:31 +01:00 |
|
|
Frederik Hanghøj Iversen
|
edf552cb86
|
Do not define synonym for contractible
|
2018-02-20 18:15:30 +01:00 |
|
|
Frederik Hanghøj Iversen
|
d2da84269f
|
Move some more things into RawCategory
|
2018-02-20 18:14:42 +01:00 |
|
|
Frederik Hanghøj Iversen
|
0c861c4bde
|
Factor univalence out to a seperate module
|
2018-02-20 18:13:06 +01:00 |
|
|
Frederik Hanghøj Iversen
|
a4f8a37e36
|
Proove that IsCategory is a mere proposition!
|
2018-02-20 18:01:26 +01:00 |
|
|
Frederik Hanghøj Iversen
|
159bffa6ae
|
Factor out more from IsCategory
|
2018-02-20 17:59:48 +01:00 |
|
|
Frederik Hanghøj Iversen
|
a016c67b88
|
Succesfully apply path-induction.
Now all that's left to do is prove the original proposition in a
heterogenous equality
|
2018-02-20 17:46:32 +01:00 |
|
|
Frederik Hanghøj Iversen
|
ff496aae09
|
Factor out a useful type-family
|
2018-02-20 17:33:02 +01:00 |
|
|
Frederik Hanghøj Iversen
|
860c91f913
|
Trim mess
|
2018-02-20 16:43:53 +01:00 |
|
|
Frederik Hanghøj Iversen
|
8ef61d9db0
|
Simplify Category
|
2018-02-20 16:26:40 +01:00 |
|
|
Frederik Hanghøj Iversen
|
10df9511a4
|
Move various type-synonyms to RawCategory
|
2018-02-20 16:24:14 +01:00 |
|
|
Frederik Hanghøj Iversen
|
38ec53d5c2
|
Cosmetics
|
2018-02-20 14:08:47 +01:00 |
|
|
Frederik Hanghøj Iversen
|
44eda0ced0
|
Stuff about propositionality of fields of IsCategory
|
2018-02-19 15:46:19 +01:00 |
|
|
Frederik Hanghøj Iversen
|
bec5acdc59
|
Move proposition to wishlist
|
2018-02-19 11:25:16 +01:00 |
|
|
Frederik Hanghøj Iversen
|
89ad60ffef
|
Stuff about the free category
|
2018-02-19 11:09:49 +01:00 |
|
|
Frederik Hanghøj Iversen
|
73ab4d1836
|
Proove identity laws for natural transformations
|
2018-02-16 12:46:25 +01:00 |
|
|
Frederik Hanghøj Iversen
|
a64e2484e3
|
Prove associativity for natural transformations
|
2018-02-16 12:24:58 +01:00 |
|
|
Frederik Hanghøj Iversen
|
7dc7a5aee3
|
Prove that naturalTransformations are sets
Also adds a new module `Cat.Wishlist` of things I hope to put get from
upstream `cubical`.
|
2018-02-16 12:03:02 +01:00 |
|
|
Frederik Hanghøj Iversen
|
23c458983c
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Rely on global cubical again
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2018-02-16 11:37:22 +01:00 |
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Frederik Hanghøj Iversen
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ad84b15da5
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[WIP] natural transformations are sets
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2018-02-16 10:22:46 +01:00 |
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Frederik Hanghøj Iversen
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7d4aae4f49
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Try to show that natural transformations are sets
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2018-02-09 12:09:59 +01:00 |
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Frederik Hanghøj Iversen
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56d689fb4b
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Use arrowIsSet to simplify equality constructor for functors
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2018-02-07 20:19:17 +01:00 |
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Frederik Hanghøj Iversen
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9349b37550
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Refactor Functor - only in module Functor
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2018-02-06 14:31:18 +01:00 |
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Frederik Hanghøj Iversen
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a27292dd53
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Stuff about the free category
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2018-02-06 11:27:22 +01:00 |
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Frederik Hanghøj Iversen
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9f1e82168f
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Move the free category
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2018-02-06 10:35:52 +01:00 |
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Frederik Hanghøj Iversen
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0688f5c372
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Rename arrowIsSet
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2018-02-06 10:34:43 +01:00 |
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Frederik Hanghøj Iversen
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e8ac6786ff
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Changes to the category of categories
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2018-02-05 16:35:33 +01:00 |
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Frederik Hanghøj Iversen
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e8215b2c05
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Move product, exponential, ...
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2018-02-05 14:59:53 +01:00 |
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Frederik Hanghøj Iversen
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83ccde62e9
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Use co-patterns
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2018-02-05 14:47:15 +01:00 |
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Frederik Hanghøj Iversen
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20dc9d26ac
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Move product, exponential and cart closed to own file
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2018-02-05 14:08:30 +01:00 |
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Frederik Hanghøj Iversen
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8022ed349d
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"re-delegate" projections in new module Category
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2018-02-05 12:21:39 +01:00 |
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Frederik Hanghøj Iversen
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22a9a71870
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Split Category into RawCategory and IsCategory
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2018-02-05 11:43:38 +01:00 |
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Frederik Hanghøj Iversen
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fecb4dc1ce
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Towards IsCategory-is-prop
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2018-02-05 10:24:57 +01:00 |
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Frederik Hanghøj Iversen
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e5f1fa018a
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Merge branch 'Saizan-master' into dev
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2018-02-02 15:34:30 +01:00 |
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Frederik Hanghøj Iversen
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19987dd917
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Add some stuff about the category of cubes
Also some feedback from Thierry
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2018-02-02 14:47:51 +01:00 |
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Andrea Vezzosi
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8d5e992e48
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changed IsCategory to follow the HoTT book definition.
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2018-02-01 14:37:55 +00:00 |
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