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
Rely on global cubical again
2018-02-16 11:37:22 +01:00
Frederik Hanghøj Iversen
ad84b15da5
[WIP] natural transformations are sets
2018-02-16 10:22:46 +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
a27292dd53
Stuff about the free category
2018-02-06 11:27:22 +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
83ccde62e9
Use co-patterns
2018-02-05 14:47:15 +01:00
Frederik Hanghøj Iversen
20dc9d26ac
Move product, exponential and cart closed to own file
2018-02-05 14:08:30 +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
fecb4dc1ce
Towards IsCategory-is-prop
2018-02-05 10:24:57 +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
Andrea Vezzosi
8d5e992e48
changed IsCategory to follow the HoTT book definition.
2018-02-01 14:37:55 +00:00
Frederik Hanghøj Iversen
6bb8ba3927
Move the category of families
2018-01-31 15:15:00 +01:00
Frederik Hanghøj Iversen
92f0f8e0f0
Rename stuff
2018-01-31 14:39:54 +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
e33911ad9e
Use alternate syntax for arrow-composition
2018-01-30 18:26:11 +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
812662bda3
Rename some variables
2018-01-25 12:47:32 +01:00
Frederik Hanghøj Iversen
7a77ba230c
Move functor-equality to functor module
2018-01-25 12:11:50 +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
6a25a4c3ff
Fix typo, rename implicit variables, implement presheaf
2018-01-22 15:03:04 +01:00
Frederik Hanghøj Iversen
dd3415a69d
Some stuff about CwF's
2018-01-22 14:44:50 +01:00
Frederik Hanghøj Iversen
fd03049c92
Move the category of functors
2018-01-22 14:44:25 +01:00
Frederik Hanghøj Iversen
9fdf6b589b
Use TDNR in Functor
2018-01-22 11:35:37 +01:00
Frederik Hanghøj Iversen
bf1d1566af
Naturality; category of functors and natural transformations
...
WIP
2018-01-22 00:07:44 +01:00
Frederik Hanghøj Iversen
3fcdf828d8
Implement exponentials
2018-01-21 21:29:15 +01:00
Frederik Hanghøj Iversen
922570a5bd
Make some names more explicit
2018-01-21 19:23:24 +01:00
Frederik Hanghøj Iversen
26d210dcc3
Rename the category of categories
2018-01-21 15:23:40 +01:00
Frederik Hanghøj Iversen
b21c9b7a89
Choose new name for functor composition
2018-01-21 15:21:50 +01:00
Frederik Hanghøj Iversen
b158b1d420
Use TDNR
2018-01-21 15:19:15 +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
316de7e4f9
Remove undefined
2018-01-21 14:32:27 +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
0990a3778f
Use EqReasoning and clean up some stuff
2018-01-21 01:03:40 +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
acacfac31c
Type-synonyms for Representable functors and Presheafs
2018-01-17 12:16:07 +01:00
Frederik Hanghøj Iversen
902b953ad0
Implement representable functors
2018-01-17 12:10:18 +01:00
Frederik Hanghøj Iversen
26d449771a
Unfinished stuff about HOM-sets and exponentials
2018-01-15 16:13:23 +01:00
Frederik Hanghøj Iversen
0cd75e6e31
Move functor-stuff to own module
2018-01-08 22:54:53 +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
