Frederik Hanghøj Iversen
b7a80d0b86
Proof: Being an initial- terminal- object is a mere proposition
...
Also tries to use this to prove that being a product is a mere
proposition
2018-03-27 12:20:24 +02:00
Frederik Hanghøj Iversen
d3864dbae5
Move properties about natural transformations to that module
2018-03-23 15:20:26 +01:00
Frederik Hanghøj Iversen
ef688202a2
Move identity functor laws to functor module...
...
and make progress on univalence in the functor category
2018-03-23 13:55:03 +01:00
Frederik Hanghøj Iversen
96fb1d3a3b
Formatting
2018-03-23 10:08:28 +01:00
Frederik Hanghøj Iversen
181edc0cd5
Prove step 3 in proof of unvivalence for hSet without ua
2018-03-21 17:52:32 +01:00
Frederik Hanghøj Iversen
ae0ff092f8
Use prelude everywhere
2018-03-21 14:56:43 +01:00
Frederik Hanghøj Iversen
29f45d1426
Delete equality module
2018-03-21 14:47:01 +01:00
Frederik Hanghøj Iversen
183906dc8c
Define and use custom prelude
2018-03-21 14:39:56 +01:00
Frederik Hanghøj Iversen
e98ed89db5
Make propositionality a submodule of the actual proposition
2018-03-21 12:21:47 +01:00
Frederik Hanghøj Iversen
4beb48e066
Use correct order for left- and right identity
...
Define and use helpers left- and right identity
2018-03-21 11:58:50 +01:00
Frederik Hanghøj Iversen
31257a4d97
Do not export helpers in Fun
2018-03-21 11:58:50 +01:00
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
b03bfb0c77
Restructure in free monad
2018-03-20 14:58:27 +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
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
