Frederik Hanghøj Iversen
5bbb40b664
Make progress with univalence in product-category
2018-04-12 13:16:25 +02:00
Frederik Hanghøj Iversen
7fcd8e631a
Modified verion of 9.1.9
2018-04-12 11:21:05 +02:00
Frederik Hanghøj Iversen
1c963db7e6
Make AreInveres an alias for \Sigma
2018-04-11 13:53:33 +02:00
Frederik Hanghøj Iversen
e6a2e3a0f0
Reduce applications of symmetry
2018-04-11 13:18:34 +02:00
Frederik Hanghøj Iversen
c23c2716a5
Move lemma to equivalence-module
2018-04-11 12:27:33 +02:00
Frederik Hanghøj Iversen
db5fb3603a
Banish qualified import of Function - use \o for fun-comp!
2018-04-11 11:12:09 +02:00
Frederik Hanghøj Iversen
c90b064bb0
Rename \o to <<<
2018-04-11 10:58:50 +02:00
Frederik Hanghøj Iversen
772e6778f3
[WIP] Univalence in ad-hoc category in product
2018-04-10 17:17:04 +02:00
Frederik Hanghøj Iversen
fd18985e53
Export TypeIsomorphism as an alias for Equivalence.Isomorphism
2018-04-09 18:10:39 +02:00
Frederik Hanghøj Iversen
69689e7b2a
Use a single version of \simeq
2018-04-06 18:27:24 +02:00
Frederik Hanghøj Iversen
23b562a873
Provide preorder instance for some things - more work on product cat
2018-04-06 16:54:00 +02:00
Frederik Hanghøj Iversen
be56027c37
Remove bad lemma for showing univalence
2018-04-05 15:23:50 +02:00
Frederik Hanghøj Iversen
e69ace21a0
Rename id-to-iso to idToIso
2018-04-05 15:21:54 +02:00
Frederik Hanghøj Iversen
6c5b68a8ac
Add notion of pre-category
2018-04-05 14:39:54 +02:00
Frederik Hanghøj Iversen
8276deb4aa
Rename proj. to fst and snd
2018-04-05 10:41:56 +02:00
Frederik Hanghøj Iversen
d78965d73f
Try to use lemma for proving univalence of product-category thing
2018-04-04 17:45:36 +02:00
Frederik Hanghøj Iversen
f66d180ec3
[WIP] Stronger lemma for univalence
2018-04-04 11:27:03 +02:00
Frederik Hanghøj Iversen
172287f0a7
[QED] The ad-hoc product category has hom-sets that are h-sets
2018-04-03 15:23:11 +02:00
Frederik Hanghøj Iversen
1e5fb7d50a
[WIP] Arrows are sets in special product category
2018-04-03 14:46:36 +02:00
Frederik Hanghøj Iversen
467c5d9c0c
[WIP] Propositionality of products
2018-04-03 12:40:20 +02:00
Frederik Hanghøj Iversen
1c6d9ad2b5
Rename identity in category to ascii-name
2018-04-03 11:36:09 +02:00
Frederik Hanghøj Iversen
41b442c0d8
Merge remote-tracking branch 'Saizan/dev' into dev
2018-03-30 12:23:29 +02:00
Andrea Vezzosi
34e633902f
Category.Product: Factor out use of arrowAreSets to shorten proofs
2018-03-30 11:06:45 +02:00
Frederik Hanghøj Iversen
ba80fe96dc
[WIP] Propositionality for products
2018-03-30 00:12:01 +02:00
Frederik Hanghøj Iversen
432cc78821
Prove assoc and ident for funky category
2018-03-29 15:47:43 +02:00
Andrea Vezzosi
8ac6b97213
isProp (Product C A B) setup
2018-03-29 00:07:49 +02:00
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
