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
04144db606
Simplifications and renaming
2018-04-09 18:02:39 +02:00
Frederik Hanghøj Iversen
735b25de23
Simplify proof and move propUnivalent to a more general setting
2018-04-09 16:03:43 +02:00
Frederik Hanghøj Iversen
69689e7b2a
Use a single version of \simeq
2018-04-06 18:27:24 +02:00
Frederik Hanghøj Iversen
36d92c7ceb
Make the category an index of PreCategory
2018-04-06 17:09:15 +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
bbe9460647
Provide composition of isEquiv's
2018-04-05 20:41:14 +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
b5f89322ac
Add notion of strict category
2018-04-05 15:13:59 +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
84f88ac2ae
Change what is needed
2018-04-04 12:01:29 +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
Frederik Hanghøj Iversen
ffedb83210
Initial objects are also propositional
2018-03-29 14:31:58 +02:00
Frederik Hanghøj Iversen
52ac9b4b78
Terminal objects are propositional
2018-03-29 14:26:47 +02:00
Andrea Vezzosi
8ac6b97213
isProp (Product C A B) setup
2018-03-29 00:07:49 +02:00
Frederik Hanghøj Iversen
facd1167e0
Fix unique existential
2018-03-27 14:18:13 +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
9898685491
Prove that the opposite category is a category
2018-03-26 14:11:15 +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
c8c61a8d03
Half-time report
2018-03-23 11:11:44 +01:00
Frederik Hanghøj Iversen
96fb1d3a3b
Formatting
2018-03-23 10:08:28 +01:00
Frederik Hanghøj Iversen
ac01b786a7
Cleanup
2018-03-22 14:27:16 +01:00
Frederik Hanghøj Iversen
ebcab2528e
Prove second inverse law for from/to-isomorphism
2018-03-22 13:49:53 +01:00
Frederik Hanghøj Iversen
0246c1b5ab
Readability
2018-03-22 12:25:12 +01:00
Frederik Hanghøj Iversen
d816ba657b
QED! Show that the category of homotopic sets are univalent.
2018-03-22 12:11:27 +01:00
Frederik Hanghøj Iversen
52ca0b6732
Merge remote-tracking branch 'Saizan/dev' into dev
2018-03-22 11:54:22 +01:00
Frederik Hanghøj Iversen
d12122ce60
Add another approach for univalence in Set
2018-03-22 11:50:07 +01:00
Andrea Vezzosi
66ab7138a6
generalized lem3 and made progress for Sets univalence
2018-03-22 10:41:38 +00:00
Frederik Hanghøj Iversen
807a0f3dcd
Slight readability improvement
2018-03-21 18:05:25 +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
8f67ff9f36
Use explicit parameter for hSet
2018-03-21 15:01:31 +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
084befbbc6
Merge remote-tracking branch 'Saizan/dev' into dev
...
From Andrea:
The problem with "h" there is that ve-re is building a square, "(qq0 j
, h)" is a fine element of the sigma type, but it does not really
connect "(g ∘ f) e" to "e" across dimension "i", in particular it does
not reduce to "e" when "i" is "i1".
2018-03-21 13:31:28 +01:00
Frederik Hanghøj Iversen
cd3514c8cf
Formatting
2018-03-21 13:25:24 +01:00
Andrea Vezzosi
ed3b3047e6
Progress on univalence for sets.
2018-03-21 12:00:47 +00:00
