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
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
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
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
f0beec1530
Rename Opposite to opposite
2018-02-25 15:23:33 +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
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
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
Frederik Hanghøj Iversen
e46edf1f68
Chain reexport things in Functor
2018-02-23 12:21:16 +01:00
Frederik Hanghøj Iversen
de1d19c442
Readd stuff about the yoneda embedding
2018-02-23 11:24:22 +01:00
Frederik Hanghøj Iversen
bc2129b8fc
Readd yoneda embedding
2018-02-23 10:55:43 +01:00
Frederik Hanghøj Iversen
3032dc6130
Make explicit argument
2018-02-23 10:36:59 +01:00
Frederik Hanghøj Iversen
9e96e704e8
Update Fun according to new naming policy
2018-02-21 13:40:24 +01:00
Frederik Hanghøj Iversen
38ec53d5c2
Cosmetics
2018-02-20 14:08:47 +01:00
Frederik Hanghøj Iversen
23c458983c
Rely on global cubical again
2018-02-16 11:37:22 +01:00
Frederik Hanghøj Iversen
7d4aae4f49
Try to show that natural transformations are sets
2018-02-09 12:09:59 +01:00
Frederik Hanghøj Iversen
56d689fb4b
Use arrowIsSet to simplify equality constructor for functors
2018-02-07 20:19:17 +01:00
Frederik Hanghøj Iversen
9349b37550
Refactor Functor - only in module Functor
2018-02-06 14:31:18 +01:00
Frederik Hanghøj Iversen
9f1e82168f
Move the free category
2018-02-06 10:35:52 +01:00
Frederik Hanghøj Iversen
0688f5c372
Rename arrowIsSet
2018-02-06 10:34:43 +01:00
Frederik Hanghøj Iversen
e8ac6786ff
Changes to the category of categories
2018-02-05 16:35:33 +01:00
Frederik Hanghøj Iversen
e8215b2c05
Move product, exponential, ...
2018-02-05 14:59:53 +01:00
Frederik Hanghøj Iversen
8022ed349d
"re-delegate" projections in new module Category
2018-02-05 12:21:39 +01:00
Frederik Hanghøj Iversen
22a9a71870
Split Category into RawCategory and IsCategory
2018-02-05 11:43:38 +01:00
Frederik Hanghøj Iversen
e5f1fa018a
Merge branch 'Saizan-master' into dev
2018-02-02 15:34:30 +01:00
Frederik Hanghøj Iversen
19987dd917
Add some stuff about the category of cubes
...
Also some feedback from Thierry
2018-02-02 14:47:51 +01:00
Frederik Hanghøj Iversen
86d3d7368e
Use equality construction principle
...
Also update submodules
2018-01-30 22:41:18 +01:00
Frederik Hanghøj Iversen
255b0236f9
Use alternative syntax for arrow composition
2018-01-30 19:19:16 +01:00
Frederik Hanghøj Iversen
c87a6fb469
Make IsFunctor a seperate record
2018-01-30 16:24:16 +01:00
Frederik Hanghøj Iversen
4db19b6420
Do not use PathPrelude directly
2018-01-30 11:19:48 +01:00
Frederik Hanghøj Iversen
53816aeb74
One step closer to yoneda
2018-01-30 10:57:24 +01:00
Andrea Vezzosi
2295022619
used presheaf as first component of yoneda
2018-01-25 17:04:00 +00:00
Frederik Hanghøj Iversen
ee2e84edfe
Remove unused bindings
2018-01-25 14:11:28 +01:00
Frederik Hanghøj Iversen
6e25083a47
Comments in yoneda
2018-01-25 13:58:56 +01:00
Frederik Hanghøj Iversen
a480fca956
Clean up some stuff
2018-01-25 12:01:37 +01:00
Frederik Hanghøj Iversen
c5a3673d9b
Prove that Cat is cartesian closed
...
WIP
2018-01-24 16:38:28 +01:00
Frederik Hanghøj Iversen
3fcdf828d8
Implement exponentials
2018-01-21 21:29:15 +01:00
Frederik Hanghøj Iversen
ea3e14af96
Re-add eqpair
2018-01-21 15:03:00 +01:00
Frederik Hanghøj Iversen
793fc30534
Move properties of categories to Cat.Category.Properties
2018-01-21 15:01:01 +01:00
Frederik Hanghøj Iversen
4c13334277
Make properties of a category an instance argument
2018-01-21 14:31:37 +01:00
Frederik Hanghøj Iversen
07e4269399
Make level-parameters to Category explicit
2018-01-21 01:11:08 +01:00
Frederik Hanghøj Iversen
5fd7dcae9d
Notes from Andrea and some stuff about products
2018-01-21 00:21:25 +01:00
Frederik Hanghøj Iversen
da10e63cc8
Fix import-statements. Make file that checks everything
2018-01-17 23:00:27 +01:00
Frederik Hanghøj Iversen
26d449771a
Unfinished stuff about HOM-sets and exponentials
2018-01-15 16:13:23 +01:00
Frederik Hanghøj Iversen
7d6db415a1
Move modules around again.
...
Henceforth all modules shall be placed under the top-level module-name
`Cat` (at least until I've come up with a better name)
Also fixes an issue caused by https://github.com/Saizan/cubical-demo/ redefining Sigma.
2018-01-08 22:48:59 +01:00
