Commit graph

352 commits

Author SHA1 Message Date
Frederik Hanghøj Iversen 101b2639e1 Move proof to category definition 2018-02-26 20:31:47 +01:00
Frederik Hanghøj Iversen 5b5d21f777 Formatting 2018-02-26 20:23:31 +01:00
Frederik Hanghøj Iversen a0944d69b1 Documentation in Monad 2018-02-26 20:08:48 +01:00
Frederik Hanghøj Iversen 67993be27b Add reverse function composition to category 2018-02-26 20:00:24 +01:00
Frederik Hanghøj Iversen 47882b1110 Rename zeta to pure 2018-02-26 19:58:27 +01:00
Frederik Hanghøj Iversen 043641462d Prove distributive law for monads! 2018-02-26 19:57:05 +01:00
Frederik Hanghøj Iversen 7cddba97a8 Shorten definition 2018-02-25 19:03:48 +01:00
Frederik Hanghøj Iversen 2c6132768e Remove Pathy and Bij 2018-02-25 15:29:52 +01:00
Frederik Hanghøj Iversen 5caecf9796 Rename properties to yoneda 2018-02-25 15:28:42 +01:00
Frederik Hanghøj Iversen 44526b85eb Move CwF 2018-02-25 15:24:44 +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 d63ecc3a65 Use abbreviation 2018-02-25 14:39:11 +01:00
Frederik Hanghøj Iversen caddf83a09 Let IsCategory reexport RawCategory 2018-02-25 14:37:28 +01:00
Frederik Hanghøj Iversen 5deabb7546 Forgot to add monoid-module 2018-02-25 14:28:01 +01:00
Frederik Hanghøj Iversen ce46e0ae7a Module-ify 2018-02-25 14:27:37 +01:00
Frederik Hanghøj Iversen 12dddc2067 Use a module 2018-02-25 03:12:51 +01:00
Frederik Hanghøj Iversen 4c298855e0 [WIP] Proving other fusion law
Also set up framework for equality principle for monads
2018-02-25 03:09:25 +01:00
Frederik Hanghøj Iversen a6b01929f0 Prove distributive law 2018-02-25 01:27:20 +01:00
Frederik Hanghøj Iversen a447cd9c7c Syntax 2018-02-24 20:41:47 +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 e7abab0e4c Add pure and >=> to kleisli category 2018-02-24 19:08:20 +01:00
Frederik Hanghøj Iversen be505cdfbe Prove IsAssociative 2018-02-24 19:07:58 +01:00
Frederik Hanghøj Iversen 5d9c820fa2 Add note about haskell 2018-02-24 15:25:07 +01:00
Frederik Hanghøj Iversen e4e327d1d2 [WIP] equivalence of kleisli- resp. monoidal- representation of monad 2018-02-24 15:13:25 +01:00
Frederik Hanghøj Iversen 3e12331294 Monoidal monads addendum 2018-02-24 14:01:57 +01:00
Frederik Hanghøj Iversen 4ec13fe509 Implement monads in the kleisli form 2018-02-24 14:00:52 +01:00
Frederik Hanghøj Iversen 0ca11874bc Remove old name for functor composition 2018-02-24 12:55:08 +01:00
Frederik Hanghøj Iversen 8527fe0df4 Rename functor composition - implement monads...
In their monoidal form.
2018-02-24 12:52:16 +01:00
Frederik Hanghøj Iversen cb8533b84a Rename natural transformation composition 2018-02-23 17:43:38 +01:00
Frederik Hanghøj Iversen dd11b69c71 Documentation for natural transformations 2018-02-23 17:37:27 +01:00
Frederik Hanghøj Iversen 689a6467c6 Move stuff about natural transformations to own module 2018-02-23 17:33:09 +01:00
Frederik Hanghøj Iversen f5dded9561 Do not use IsCategory directly 2018-02-23 16:41:17 +01:00
Frederik Hanghøj Iversen 39284b8d99 Changes in CwF 2018-02-23 14:13:55 +01:00
Frederik Hanghøj Iversen 5796b791b8 Almost prove that arrows are sets in the cateogry of families 2018-02-23 13:59:35 +01:00
Frederik Hanghøj Iversen a321a9c8b2 Use hLevels in Fam 2018-02-23 13:39:59 +01:00
Frederik Hanghøj Iversen 3d0916f448 Use correct name for hSets 2018-02-23 13:20:30 +01:00
Frederik Hanghøj Iversen 4874ed0795 Rename distrib to isDistributive 2018-02-23 12:53:35 +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 852056cc44 Add type-synonyms in functor 2018-02-23 12:41:15 +01:00
Frederik Hanghøj Iversen a57f45d93f Remove yet another postulate 2018-02-23 12:33:20 +01:00
Frederik Hanghøj Iversen 34dec9406d Do not mention IsFunctor outside the module that defines it 2018-02-23 12:29:10 +01:00
Frederik Hanghøj Iversen e46edf1f68 Chain reexport things in Functor 2018-02-23 12:21:16 +01:00
Frederik Hanghøj Iversen 885fd8fa69 Drastically simplify proofs 2018-02-23 12:15:39 +01:00
Frederik Hanghøj Iversen 3f3247c870 Remove commented code 2018-02-23 12:05:38 +01:00
Frederik Hanghøj Iversen de1d19c442 Readd stuff about the yoneda embedding 2018-02-23 11:24:22 +01:00
Frederik Hanghøj Iversen 954a89f8d1 Expose naturalIsProp 2018-02-23 11:12:27 +01:00
Frederik Hanghøj Iversen bc2129b8fc Readd yoneda embedding 2018-02-23 10:55:43 +01:00
Frederik Hanghøj Iversen 9a4d79fa4e Readd commented code 2018-02-23 10:44:23 +01:00
Frederik Hanghøj Iversen 3032dc6130 Make explicit argument 2018-02-23 10:36:59 +01:00
Frederik Hanghøj Iversen cc1ddaac9f Add new type-synonym 2018-02-23 10:35:42 +01:00
Frederik Hanghøj Iversen a87d404aad Refactor category of categories
No longer actually define the category. Just define the raw category and
a few results about it.
2018-02-23 10:34:37 +01:00
Frederik Hanghøj Iversen 32b9ce2ea8 Use new syntax in cat 2018-02-22 15:31:54 +01:00
Frederik Hanghøj Iversen a82095604d Remove unused function 2018-02-21 14:05:10 +01:00
Frederik Hanghøj Iversen 9e96e704e8 Update Fun according to new naming policy 2018-02-21 13:40:24 +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 89ad60ffef Stuff about the free category 2018-02-19 11:09:49 +01:00
Frederik Hanghøj Iversen 73ab4d1836 Proove identity laws for natural transformations 2018-02-16 12:46:25 +01:00
Frederik Hanghøj Iversen a64e2484e3 Prove associativity for natural transformations 2018-02-16 12:24:58 +01:00
Frederik Hanghøj Iversen 7dc7a5aee3 Prove that naturalTransformations are sets
Also adds a new module `Cat.Wishlist` of things I hope to put get from
upstream `cubical`.
2018-02-16 12:03:02 +01:00
Frederik Hanghøj Iversen 23c458983c Rely on global cubical again 2018-02-16 11:37:22 +01:00
Frederik Hanghøj Iversen ad84b15da5 [WIP] natural transformations are sets 2018-02-16 10:22:46 +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 a27292dd53 Stuff about the free category 2018-02-06 11:27:22 +01:00
Frederik Hanghøj Iversen 9f1e82168f Move the free category 2018-02-06 10:35:52 +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 e8215b2c05 Move product, exponential, ... 2018-02-05 14:59:53 +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 6bb8ba3927 Move the category of families 2018-01-31 15:15:00 +01:00
Frederik Hanghøj Iversen 92f0f8e0f0 Rename stuff 2018-01-31 14:39:54 +01:00
Frederik Hanghøj Iversen 86d3d7368e Use equality construction principle
Also update submodules
2018-01-30 22:41:18 +01:00
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 c87a6fb469 Make IsFunctor a seperate record 2018-01-30 16:24:16 +01:00
Frederik Hanghøj Iversen 4db19b6420 Do not use PathPrelude directly 2018-01-30 11:19:48 +01:00
Frederik Hanghøj Iversen 53816aeb74 One step closer to yoneda 2018-01-30 10:57:24 +01:00
Andrea Vezzosi 2295022619 used presheaf as first component of yoneda 2018-01-25 17:04:00 +00:00
Frederik Hanghøj Iversen ee2e84edfe Remove unused bindings 2018-01-25 14:11:28 +01:00
Frederik Hanghøj Iversen 6e25083a47 Comments in yoneda 2018-01-25 13:58:56 +01:00
Frederik Hanghøj Iversen 812662bda3 Rename some variables 2018-01-25 12:47:32 +01:00
Frederik Hanghøj Iversen 7a77ba230c Move functor-equality to functor module 2018-01-25 12:11:50 +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 6a25a4c3ff Fix typo, rename implicit variables, implement presheaf 2018-01-22 15:03:04 +01:00
Frederik Hanghøj Iversen dd3415a69d Some stuff about CwF's 2018-01-22 14:44:50 +01:00
Frederik Hanghøj Iversen fd03049c92 Move the category of functors 2018-01-22 14:44:25 +01:00
Frederik Hanghøj Iversen 9fdf6b589b Use TDNR in Functor 2018-01-22 11:35:37 +01:00
Frederik Hanghøj Iversen bf1d1566af Naturality; category of functors and natural transformations
WIP
2018-01-22 00:07:44 +01:00
Frederik Hanghøj Iversen 3fcdf828d8 Implement exponentials 2018-01-21 21:29:15 +01:00
Frederik Hanghøj Iversen 922570a5bd Make some names more explicit 2018-01-21 19:23:24 +01:00
Frederik Hanghøj Iversen 26d210dcc3 Rename the category of categories 2018-01-21 15:23:40 +01:00
Frederik Hanghøj Iversen b21c9b7a89 Choose new name for functor composition 2018-01-21 15:21:50 +01:00
Frederik Hanghøj Iversen b158b1d420 Use TDNR 2018-01-21 15:19:15 +01:00
Frederik Hanghøj Iversen ea3e14af96 Re-add eqpair 2018-01-21 15:03:00 +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 40816eb17a Dummy file to compile everything 2018-01-21 00:21:51 +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 da10e63cc8 Fix import-statements. Make file that checks everything 2018-01-17 23:00:27 +01:00
Frederik Hanghøj Iversen acacfac31c Type-synonyms for Representable functors and Presheafs 2018-01-17 12:16:07 +01:00
Frederik Hanghøj Iversen 902b953ad0 Implement representable functors 2018-01-17 12:10:18 +01:00
Frederik Hanghøj Iversen 26d449771a Unfinished stuff about HOM-sets and exponentials 2018-01-15 16:13:23 +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
Frederik Hanghøj Iversen e3d2c0d39e Move category of Categories to own module 2018-01-08 22:31:12 +01:00
Frederik Hanghøj Iversen 4a98b2aa3d Leftovers... 2017-12-12 12:39:58 +01:00
Frederik Hanghøj Iversen 3e717d4b1f Prove that functor composition gives rise to a functor 2017-12-02 01:36:16 +01:00
Frederik Hanghøj Iversen f0412fa091 Add stub for implementing the cubical type system 2017-11-26 14:57:19 +01:00
Frederik Hanghøj Iversen 1d040e5391 Use bot from stdlib 2017-11-15 22:56:04 +01:00
Frederik Hanghøj Iversen 11f5b89b10 Rename some variables 2017-11-15 21:59:00 +01:00
Frederik Hanghøj Iversen 43cc73c6a8 Rename the category of relations 2017-11-15 21:51:41 +01:00
Frederik Hanghøj Iversen 6ca9368891 Add the category of sets 2017-11-15 21:51:10 +01:00
Frederik Hanghøj Iversen fa5d380ee2 Finnish the proof of the category of relations 2017-11-15 21:49:50 +01:00
Frederik Hanghøj Iversen f524f99481 Finish proof of left and right identity 2017-11-15 20:55:57 +01:00
Frederik Hanghøj Iversen 32244c912a Organize modules 2017-11-10 16:00:00 +01:00
Frederik Hanghøj Iversen 37cb8e0541 Add Primitives 2017-06-07 22:31:49 +02:00
Frederik Hanghøj Iversen 8b6ee46128 Ignore *.agdai 2017-06-07 22:31:39 +02:00
Frederik Hanghøj Iversen f27492217d Add PathPrelude 2017-06-07 22:31:17 +02:00
Frederik Hanghøj Iversen 0f114b1029 Mark questions 2017-06-07 22:24:35 +02:00
Frederik Hanghøj Iversen 38fd690839 Add more instances 2017-06-07 22:03:56 +02:00
Frederik Hanghøj Iversen 8485b55152 Add cubical as a submodule 2017-06-07 15:52:40 +02:00