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
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
35390c02d3
Stuff about univalence in the category of sets
2018-03-12 13:38:48 +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
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
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
