Commit graph

337 commits

Author SHA1 Message Date
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 896e0d3d37 Stuff about univalence for the category of functors 2018-03-13 10:24:50 +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
Frederik Hanghøj Iversen 5e092964c8 Change naming and fuse some modules 2018-03-12 14:38:52 +01:00
Frederik Hanghøj Iversen ccf753d438 Move monoidal and kleisli representation to own modules 2018-03-12 14:23:23 +01:00
Frederik Hanghøj Iversen 8dadfa22a0 Add documentation header to monad module 2018-03-12 14:11:31 +01:00
Frederik Hanghøj Iversen aa645fb11e Move voevodsky's construction to own module 2018-03-12 14:04:10 +01:00
Frederik Hanghøj Iversen c0cf6789cd Use propositions straight from the horses mouth 2018-03-12 13:56:49 +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 acb5ff4f2b Closer to showing univalence for the category of sets 2018-03-08 14:44:23 +01:00
Frederik Hanghøj Iversen 52297d9073 Clean-up in the category of categories 2018-03-08 11:54:13 +01:00
Frederik Hanghøj Iversen d01514cbdb Do not use ugly ':'-syntax to disambiguate fields 2018-03-08 11:29:16 +01:00
Frederik Hanghøj Iversen 48672b01bd Use dotted expression in Cat 2018-03-08 11:20:51 +01:00
Frederik Hanghøj Iversen 5ad506a09f Rename func* and func-> to omap and fmap respectively 2018-03-08 11:03:56 +01:00
Frederik Hanghøj Iversen 2fcc583646 Add note 2018-03-08 10:50:18 +01:00
Frederik Hanghøj Iversen 63b5f5c68d Use long name for product object 2018-03-08 10:46:28 +01:00
Frederik Hanghøj Iversen 486238e114 Add goals for propositionality of products 2018-03-08 10:38:46 +01:00
Frederik Hanghøj Iversen 1ef57a19f4 Cosmetics 2018-03-08 10:30:35 +01:00
Frederik Hanghøj Iversen 4e7b350188 Factor out objects 2018-03-08 10:28:05 +01:00
Frederik Hanghøj Iversen 181bd1af53 Factor out category 2018-03-08 10:24:17 +01:00
Frederik Hanghøj Iversen faf4c54188 Make parameters explicit 2018-03-08 10:22:21 +01:00
Frederik Hanghøj Iversen fae492a1e3 Restructure products 2018-03-08 10:20:29 +01:00
Frederik Hanghøj Iversen b61749bb91 Fixup some todo-notes 2018-03-08 01:10:52 +01:00
Frederik Hanghøj Iversen fa9a470875 Update backlog 2018-03-08 00:54:42 +01:00
Frederik Hanghøj Iversen e43bee6d9f Feels really close 2018-03-08 00:36:38 +01:00
Frederik Hanghøj Iversen c8fef1d2b5 Use different name for function composition 2018-03-08 00:22:55 +01:00
Frederik Hanghøj Iversen 36cbe711fb Sort of half of the proof of an inverse 2018-03-08 00:09:49 +01:00
Frederik Hanghøj Iversen 459718da23 Finish proof of equivalence of klesili/monoidal categories!! 2018-03-07 17:30:09 +01:00
Frederik Hanghøj Iversen 19103e1678 Update cubical 2018-03-07 16:24:43 +01:00
Frederik Hanghøj Iversen 93d075a6d3 Attempt at proving pureNTEq 2018-03-07 15:23:07 +01:00
Frederik Hanghøj Iversen 00e6e1aa66 State problem with approach 2018-03-07 11:45:11 +01:00
Frederik Hanghøj Iversen aa64e01084 Remove some cruft 2018-03-07 11:33:08 +01:00
Frederik Hanghøj Iversen 125123846e Lay out a strategy for showing the equivalence 2018-03-07 11:29:58 +01:00
Frederik Hanghøj Iversen 085e6eb3d7 Stuff about voe-2-3 2018-03-06 23:18:33 +01:00
Frederik Hanghøj Iversen 110e3510c5 Use postulates 2018-03-06 15:55:03 +01:00
Frederik Hanghøj Iversen 5ae68df582 Prove that fmap is mapped correctly 2018-03-06 15:53:11 +01:00
Frederik Hanghøj Iversen 4d528a7077 Clean-up 2018-03-06 11:25:29 +01:00
Frederik Hanghøj Iversen 485703c85e Tidy up 2018-03-06 10:16:42 +01:00
Frederik Hanghøj Iversen 0cebe1e866 Make private 2018-03-06 10:06:45 +01:00
Frederik Hanghøj Iversen 4de27aa06c Naming 2018-03-06 10:05:35 +01:00
Frederik Hanghøj Iversen 9173468b03 Use omap/fmap 2018-03-06 09:56:44 +01:00
Frederik Hanghøj Iversen bdd67aee53 Rename RR to Romap 2018-03-06 09:55:18 +01:00
Frederik Hanghøj Iversen c57cd5c991 Define stuff in monoidal record 2018-03-06 09:52:37 +01:00
Frederik Hanghøj Iversen cfb7925cb5 Renaming 2018-03-06 09:45:04 +01:00
Frederik Hanghøj Iversen b6457a0b14 Add comment 2018-03-06 09:41:29 +01:00
Frederik Hanghøj Iversen 7647a452cd Tidy up proof a bit 2018-03-06 09:39:48 +01:00
Frederik Hanghøj Iversen 35419ad86e Rename eta and mu 2018-03-06 09:35:50 +01:00
Frederik Hanghøj Iversen f8e08288a0 Cosmetics 2018-03-05 17:31:13 +01:00
Frederik Hanghøj Iversen 9ec6ce9eba Use other equality principle 2018-03-05 17:10:41 +01:00
Frederik Hanghøj Iversen 3151fb3e46 Prove propositionality for naturality 2018-03-05 16:35:47 +01:00
Frederik Hanghøj Iversen 7f4a8a65b8 More stuff about opposite being an involution 2018-03-05 16:10:27 +01:00
Frederik Hanghøj Iversen b26ea18257 Cleanup in nattrans 2018-03-05 15:04:16 +01:00
Frederik Hanghøj Iversen ddd5f17c05 Move propositionality stuff about natural transformations to that module 2018-03-05 15:02:36 +01:00
Frederik Hanghøj Iversen 2b92cee254 Prettier names in Fun 2018-03-05 14:55:45 +01:00
Frederik Hanghøj Iversen bb379fa196 Implement category of presheaves 2018-03-05 14:50:53 +01:00
Frederik Hanghøj Iversen ce4dd83969 Prove that the yoneda embedding is distributive 2018-03-05 14:42:12 +01:00
Frederik Hanghøj Iversen 7fbca1aeeb Clean-up yoneda embedding 2018-03-05 14:04:04 +01:00
Frederik Hanghøj Iversen 1bf565b87a Have yoneda without having a category of categories
I did break some things in Cat.Categories.Cat but since this is
unprovable anyways it's not that big a deal.
2018-03-05 13:52:59 +01:00
Frederik Hanghøj Iversen 5c3616bca5 Make argument to presheaf explicit 2018-03-05 11:17:31 +01:00
Frederik Hanghøj Iversen 059c74b687 Use already defined category 2018-03-05 11:15:45 +01:00
Frederik Hanghøj Iversen a4890a42cf Define Monoidal categories without depending on category of categories 2018-03-05 11:13:58 +01:00
Frederik Hanghøj Iversen 5902c6121b Further reduce dependency on impossible facts.
Provide the data for the product in the category of categories without
requiring such a category to actually exist
2018-03-05 11:07:42 +01:00
Frederik Hanghøj Iversen 77006011d3 Minimize dependency on category of categories 2018-03-05 10:35:33 +01:00
Frederik Hanghøj Iversen 8f8800cb67 More stuff about kleisli \equiv monoidal 2018-03-05 10:28:16 +01:00
Frederik Hanghøj Iversen b079f5e426 Prove propositionality for IsMonad 2018-03-02 13:31:46 +01:00
Frederik Hanghøj Iversen c4e3625746 Finish proof of distributivity 2018-03-01 20:47:36 +01:00
Frederik Hanghøj Iversen 2ceb027f7a Prove monad-equality principle for kleisly monads 2018-03-01 20:23:34 +01:00
Frederik Hanghøj Iversen f2164a6717 Prove equality principle for monads 2018-03-01 20:12:49 +01:00
Frederik Hanghøj Iversen a7f31bb3e2 Prove "foreign naturality condition" 2018-03-01 18:00:51 +01:00
Frederik Hanghøj Iversen f526fd6010 Prove inverse law 2018-03-01 17:50:06 +01:00
Frederik Hanghøj Iversen ff2952e9ad Make postulate 2018-03-01 14:59:19 +01:00
Frederik Hanghøj Iversen ae46a48861 Define goals in Kleisli 2018-03-01 14:58:01 +01:00
Frederik Hanghøj Iversen 64a0292755 Cosmetics 2018-03-01 14:19:46 +01:00
Frederik Hanghøj Iversen e8b29e1f7f \mu is join and it's a natural transformation! 2018-02-28 23:41:59 +01:00
Frederik Hanghøj Iversen 9d3b17245f Provide \zeta 2018-02-28 19:32:07 +01:00
Frederik Hanghøj Iversen f2b1a36a75 Define and use Endofunctor 2018-02-28 19:03:11 +01:00
Frederik Hanghøj Iversen 3c77c69cf6 Move functor definition to Kleisli.Monad 2018-02-28 19:00:21 +01:00
Frederik Hanghøj Iversen 70221377d3 Move proof of equivalence to IsMonad making them lemmas 2018-02-28 18:55:32 +01:00
Frederik Hanghøj Iversen 1aaf81552c Move another proof to category definition 2018-02-26 20:42:00 +01:00
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