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
1c6d9ad2b5
Rename identity in category to ascii-name
2018-04-03 11:36:09 +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
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
c8c61a8d03
Half-time report
2018-03-23 11:11:44 +01:00
Frederik Hanghøj Iversen
ac01b786a7
Cleanup
2018-03-22 14:27:16 +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
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
811a6bf58e
Make univalence a submodule of RawCategory
2018-03-21 11:58:23 +01:00
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
a7214fcc66
Finish equality principle for categories
2018-03-12 13:51:29 +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
b61749bb91
Fixup some todo-notes
2018-03-08 01:10:52 +01:00
Frederik Hanghøj Iversen
5ae68df582
Prove that fmap is mapped correctly
2018-03-06 15:53:11 +01:00
Frederik Hanghøj Iversen
7f4a8a65b8
More stuff about opposite being an involution
2018-03-05 16:10:27 +01:00
Frederik Hanghøj Iversen
b079f5e426
Prove propositionality for IsMonad
2018-03-02 13:31:46 +01:00
Frederik Hanghøj Iversen
67993be27b
Add reverse function composition to category
2018-02-26 20:00:24 +01:00
Frederik Hanghøj Iversen
f0beec1530
Rename Opposite to opposite
2018-02-25 15:23:33 +01:00
Frederik Hanghøj Iversen
cd98736d02
Add documentation in Category-module
2018-02-25 15:21:38 +01:00
Frederik Hanghøj Iversen
2e7220567a
Move lemma into IsCategory
2018-02-25 14:44:03 +01:00
Frederik Hanghøj Iversen
caddf83a09
Let IsCategory reexport RawCategory
2018-02-25 14:37:28 +01:00
Frederik Hanghøj Iversen
9d09363f78
Expand definition of isDistributive somewhat
...
Also contains some side-tracks
2018-02-24 20:37:21 +01:00
Frederik Hanghøj Iversen
7787a8f0be
Indentation
2018-02-23 12:52:14 +01:00
Frederik Hanghøj Iversen
48423cc816
Rename arrowIsSet to arrowsAreSets
2018-02-23 12:51:44 +01:00
Frederik Hanghøj Iversen
6446435a49
Rename ident to isIdentity
2018-02-23 12:49:41 +01:00
Frederik Hanghøj Iversen
5cbc409770
Rename assoc to isAssociative
2018-02-23 12:43:49 +01:00
Frederik Hanghøj Iversen
cc1ddaac9f
Add new type-synonym
2018-02-23 10:35:42 +01:00
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
