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
Frederik Hanghøj Iversen
a4f8a37e36
Proove that IsCategory is a mere proposition!
2018-02-20 18:01:26 +01:00
Frederik Hanghøj Iversen
159bffa6ae
Factor out more from IsCategory
2018-02-20 17:59:48 +01:00
Frederik Hanghøj Iversen
a016c67b88
Succesfully apply path-induction.
...
Now all that's left to do is prove the original proposition in a
heterogenous equality
2018-02-20 17:46:32 +01:00
Frederik Hanghøj Iversen
ff496aae09
Factor out a useful type-family
2018-02-20 17:33:02 +01:00
Frederik Hanghøj Iversen
860c91f913
Trim mess
2018-02-20 16:43:53 +01:00
Frederik Hanghøj Iversen
8ef61d9db0
Simplify Category
2018-02-20 16:26:40 +01:00
Frederik Hanghøj Iversen
10df9511a4
Move various type-synonyms to RawCategory
2018-02-20 16:24:14 +01:00
Frederik Hanghøj Iversen
38ec53d5c2
Cosmetics
2018-02-20 14:08:47 +01:00
Frederik Hanghøj Iversen
44eda0ced0
Stuff about propositionality of fields of IsCategory
2018-02-19 15:46:19 +01:00
Frederik Hanghøj Iversen
bec5acdc59
Move proposition to wishlist
2018-02-19 11:25:16 +01:00
Frederik Hanghøj Iversen
23c458983c
Rely on global cubical again
2018-02-16 11:37:22 +01:00
Frederik Hanghøj Iversen
7d4aae4f49
Try to show that natural transformations are sets
2018-02-09 12:09:59 +01:00
Frederik Hanghøj Iversen
56d689fb4b
Use arrowIsSet to simplify equality constructor for functors
2018-02-07 20:19:17 +01:00
Frederik Hanghøj Iversen
9349b37550
Refactor Functor - only in module Functor
2018-02-06 14:31:18 +01:00
Frederik Hanghøj Iversen
0688f5c372
Rename arrowIsSet
2018-02-06 10:34:43 +01:00
Frederik Hanghøj Iversen
e8ac6786ff
Changes to the category of categories
2018-02-05 16:35:33 +01:00
Frederik Hanghøj Iversen
83ccde62e9
Use co-patterns
2018-02-05 14:47:15 +01:00
Frederik Hanghøj Iversen
20dc9d26ac
Move product, exponential and cart closed to own file
2018-02-05 14:08:30 +01:00
Frederik Hanghøj Iversen
8022ed349d
"re-delegate" projections in new module Category
2018-02-05 12:21:39 +01:00
Frederik Hanghøj Iversen
22a9a71870
Split Category into RawCategory and IsCategory
2018-02-05 11:43:38 +01:00
Frederik Hanghøj Iversen
fecb4dc1ce
Towards IsCategory-is-prop
2018-02-05 10:24:57 +01:00
Frederik Hanghøj Iversen
e5f1fa018a
Merge branch 'Saizan-master' into dev
2018-02-02 15:34:30 +01:00
Frederik Hanghøj Iversen
19987dd917
Add some stuff about the category of cubes
...
Also some feedback from Thierry
2018-02-02 14:47:51 +01:00
Andrea Vezzosi
8d5e992e48
changed IsCategory to follow the HoTT book definition.
2018-02-01 14:37:55 +00:00
Frederik Hanghøj Iversen
255b0236f9
Use alternative syntax for arrow composition
2018-01-30 19:19:16 +01:00
Frederik Hanghøj Iversen
e33911ad9e
Use alternate syntax for arrow-composition
2018-01-30 18:26:11 +01:00
Frederik Hanghøj Iversen
a480fca956
Clean up some stuff
2018-01-25 12:01:37 +01:00
Frederik Hanghøj Iversen
c5a3673d9b
Prove that Cat is cartesian closed
...
WIP
2018-01-24 16:38:28 +01:00
Frederik Hanghøj Iversen
3fcdf828d8
Implement exponentials
2018-01-21 21:29:15 +01:00
Frederik Hanghøj Iversen
793fc30534
Move properties of categories to Cat.Category.Properties
2018-01-21 15:01:01 +01:00
Frederik Hanghøj Iversen
316de7e4f9
Remove undefined
2018-01-21 14:32:27 +01:00
Frederik Hanghøj Iversen
4c13334277
Make properties of a category an instance argument
2018-01-21 14:31:37 +01:00
Frederik Hanghøj Iversen
07e4269399
Make level-parameters to Category explicit
2018-01-21 01:11:08 +01:00
Frederik Hanghøj Iversen
0990a3778f
Use EqReasoning and clean up some stuff
2018-01-21 01:03:40 +01:00
Frederik Hanghøj Iversen
5fd7dcae9d
Notes from Andrea and some stuff about products
2018-01-21 00:21:25 +01:00
Frederik Hanghøj Iversen
902b953ad0
Implement representable functors
2018-01-17 12:10:18 +01:00
Frederik Hanghøj Iversen
0cd75e6e31
Move functor-stuff to own module
2018-01-08 22:54:53 +01:00
Frederik Hanghøj Iversen
7d6db415a1
Move modules around again.
...
Henceforth all modules shall be placed under the top-level module-name
`Cat` (at least until I've come up with a better name)
Also fixes an issue caused by https://github.com/Saizan/cubical-demo/ redefining Sigma.
2018-01-08 22:48:59 +01:00
