 Frederik Hanghøj Iversen
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e8b29e1f7f
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\mu is join and it's a natural transformation!
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2018-02-28 23:41:59 +01:00 |
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Frederik Hanghøj Iversen
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9d3b17245f
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Provide \zeta
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2018-02-28 19:32:07 +01:00 |
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Frederik Hanghøj Iversen
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f2b1a36a75
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Define and use Endofunctor
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2018-02-28 19:03:11 +01:00 |
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Frederik Hanghøj Iversen
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3c77c69cf6
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Move functor definition to Kleisli.Monad
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2018-02-28 19:00:21 +01:00 |
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Frederik Hanghøj Iversen
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70221377d3
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Move proof of equivalence to IsMonad making them lemmas
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2018-02-28 18:55:32 +01:00 |
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Frederik Hanghøj Iversen
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1aaf81552c
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Move another proof to category definition
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2018-02-26 20:42:00 +01:00 |
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Frederik Hanghøj Iversen
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101b2639e1
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Move proof to category definition
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2018-02-26 20:31:47 +01:00 |
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Frederik Hanghøj Iversen
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5b5d21f777
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Formatting
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2018-02-26 20:23:31 +01:00 |
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Frederik Hanghøj Iversen
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a0944d69b1
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Documentation in Monad
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2018-02-26 20:08:48 +01:00 |
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Frederik Hanghøj Iversen
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67993be27b
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Add reverse function composition to category
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2018-02-26 20:00:24 +01:00 |
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Frederik Hanghøj Iversen
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47882b1110
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Rename zeta to pure
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2018-02-26 19:58:27 +01:00 |
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Frederik Hanghøj Iversen
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043641462d
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Prove distributive law for monads!
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2018-02-26 19:57:05 +01:00 |
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Frederik Hanghøj Iversen
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7cddba97a8
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Shorten definition
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2018-02-25 19:03:48 +01:00 |
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Frederik Hanghøj Iversen
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2c6132768e
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Remove Pathy and Bij
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2018-02-25 15:29:52 +01:00 |
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Frederik Hanghøj Iversen
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5caecf9796
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Rename properties to yoneda
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2018-02-25 15:28:42 +01:00 |
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Frederik Hanghøj Iversen
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44526b85eb
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Move CwF
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2018-02-25 15:24:44 +01:00 |
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Frederik Hanghøj Iversen
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f0beec1530
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Rename Opposite to opposite
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2018-02-25 15:23:33 +01:00 |
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Frederik Hanghøj Iversen
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cd98736d02
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Add documentation in Category-module
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2018-02-25 15:21:38 +01:00 |
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Frederik Hanghøj Iversen
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2e7220567a
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Move lemma into IsCategory
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2018-02-25 14:44:03 +01:00 |
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Frederik Hanghøj Iversen
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d63ecc3a65
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Use abbreviation
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2018-02-25 14:39:11 +01:00 |
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Frederik Hanghøj Iversen
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caddf83a09
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Let IsCategory reexport RawCategory
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2018-02-25 14:37:28 +01:00 |
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Frederik Hanghøj Iversen
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5deabb7546
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Forgot to add monoid-module
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2018-02-25 14:28:01 +01:00 |
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Frederik Hanghøj Iversen
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ce46e0ae7a
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Module-ify
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2018-02-25 14:27:37 +01:00 |
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Frederik Hanghøj Iversen
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12dddc2067
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Use a module
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2018-02-25 03:12:51 +01:00 |
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Frederik Hanghøj Iversen
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4c298855e0
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[WIP] Proving other fusion law
Also set up framework for equality principle for monads
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2018-02-25 03:09:25 +01:00 |
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Frederik Hanghøj Iversen
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a6b01929f0
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Prove distributive law
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2018-02-25 01:27:20 +01:00 |
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Frederik Hanghøj Iversen
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a447cd9c7c
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Syntax
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2018-02-24 20:41:47 +01:00 |
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Frederik Hanghøj Iversen
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9d09363f78
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Expand definition of isDistributive somewhat
Also contains some side-tracks
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2018-02-24 20:37:21 +01:00 |
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Frederik Hanghøj Iversen
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e7abab0e4c
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Add pure and >=> to kleisli category
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2018-02-24 19:08:20 +01:00 |
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Frederik Hanghøj Iversen
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be505cdfbe
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Prove IsAssociative
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2018-02-24 19:07:58 +01:00 |
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Frederik Hanghøj Iversen
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5d9c820fa2
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Add note about haskell
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2018-02-24 15:25:07 +01:00 |
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Frederik Hanghøj Iversen
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e4e327d1d2
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[WIP] equivalence of kleisli- resp. monoidal- representation of monad
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2018-02-24 15:13:25 +01:00 |
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Frederik Hanghøj Iversen
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3e12331294
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Monoidal monads addendum
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2018-02-24 14:01:57 +01:00 |
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Frederik Hanghøj Iversen
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4ec13fe509
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Implement monads in the kleisli form
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2018-02-24 14:00:52 +01:00 |
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Frederik Hanghøj Iversen
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0ca11874bc
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Remove old name for functor composition
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2018-02-24 12:55:08 +01:00 |
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Frederik Hanghøj Iversen
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8527fe0df4
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Rename functor composition - implement monads...
In their monoidal form.
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2018-02-24 12:52:16 +01:00 |
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Frederik Hanghøj Iversen
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cb8533b84a
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Rename natural transformation composition
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2018-02-23 17:43:38 +01:00 |
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Frederik Hanghøj Iversen
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dd11b69c71
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Documentation for natural transformations
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2018-02-23 17:37:27 +01:00 |
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Frederik Hanghøj Iversen
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689a6467c6
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Move stuff about natural transformations to own module
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2018-02-23 17:33:09 +01:00 |
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Frederik Hanghøj Iversen
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f5dded9561
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Do not use IsCategory directly
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2018-02-23 16:41:17 +01:00 |
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Frederik Hanghøj Iversen
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39284b8d99
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Changes in CwF
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2018-02-23 14:13:55 +01:00 |
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Frederik Hanghøj Iversen
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5796b791b8
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Almost prove that arrows are sets in the cateogry of families
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2018-02-23 13:59:35 +01:00 |
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Frederik Hanghøj Iversen
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a321a9c8b2
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Use hLevels in Fam
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2018-02-23 13:39:59 +01:00 |
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Frederik Hanghøj Iversen
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3d0916f448
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Use correct name for hSets
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2018-02-23 13:20:30 +01:00 |
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Frederik Hanghøj Iversen
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4874ed0795
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Rename distrib to isDistributive
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2018-02-23 12:53:35 +01:00 |
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Frederik Hanghøj Iversen
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7787a8f0be
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Indentation
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2018-02-23 12:52:14 +01:00 |
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Frederik Hanghøj Iversen
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48423cc816
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Rename arrowIsSet to arrowsAreSets
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2018-02-23 12:51:44 +01:00 |
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Frederik Hanghøj Iversen
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6446435a49
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Rename ident to isIdentity
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2018-02-23 12:49:41 +01:00 |
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Frederik Hanghøj Iversen
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5cbc409770
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Rename assoc to isAssociative
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2018-02-23 12:43:49 +01:00 |
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Frederik Hanghøj Iversen
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852056cc44
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Add type-synonyms in functor
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2018-02-23 12:41:15 +01:00 |
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Frederik Hanghøj Iversen
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a57f45d93f
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Remove yet another postulate
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2018-02-23 12:33:20 +01:00 |
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Frederik Hanghøj Iversen
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34dec9406d
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Do not mention IsFunctor outside the module that defines it
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2018-02-23 12:29:10 +01:00 |
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Frederik Hanghøj Iversen
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e46edf1f68
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Chain reexport things in Functor
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2018-02-23 12:21:16 +01:00 |
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Frederik Hanghøj Iversen
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885fd8fa69
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Drastically simplify proofs
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2018-02-23 12:15:39 +01:00 |
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Frederik Hanghøj Iversen
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3f3247c870
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Remove commented code
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2018-02-23 12:05:38 +01:00 |
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Frederik Hanghøj Iversen
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de1d19c442
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Readd stuff about the yoneda embedding
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2018-02-23 11:24:22 +01:00 |
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Frederik Hanghøj Iversen
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954a89f8d1
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Expose naturalIsProp
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2018-02-23 11:12:27 +01:00 |
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Frederik Hanghøj Iversen
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bc2129b8fc
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Readd yoneda embedding
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2018-02-23 10:55:43 +01:00 |
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Frederik Hanghøj Iversen
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9a4d79fa4e
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Readd commented code
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2018-02-23 10:44:23 +01:00 |
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Frederik Hanghøj Iversen
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3032dc6130
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Make explicit argument
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2018-02-23 10:36:59 +01:00 |
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Frederik Hanghøj Iversen
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cc1ddaac9f
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Add new type-synonym
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2018-02-23 10:35:42 +01:00 |
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Frederik Hanghøj Iversen
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a87d404aad
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Refactor category of categories
No longer actually define the category. Just define the raw category and
a few results about it.
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2018-02-23 10:34:37 +01:00 |
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Frederik Hanghøj Iversen
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32b9ce2ea8
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Use new syntax in cat
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2018-02-22 15:31:54 +01:00 |
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Frederik Hanghøj Iversen
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a82095604d
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Remove unused function
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2018-02-21 14:05:10 +01:00 |
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Frederik Hanghøj Iversen
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9e96e704e8
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Update Fun according to new naming policy
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2018-02-21 13:40:24 +01:00 |
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Frederik Hanghøj Iversen
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57d7eab4cb
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Make sets a category according to HoTT
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2018-02-21 13:37:07 +01:00 |
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Frederik Hanghøj Iversen
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ed40824edc
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Cosmetics
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2018-02-21 12:59:31 +01:00 |
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Frederik Hanghøj Iversen
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edf552cb86
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Do not define synonym for contractible
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2018-02-20 18:15:30 +01:00 |
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Frederik Hanghøj Iversen
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d2da84269f
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Move some more things into RawCategory
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2018-02-20 18:14:42 +01:00 |
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Frederik Hanghøj Iversen
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0c861c4bde
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Factor univalence out to a seperate module
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2018-02-20 18:13:06 +01:00 |
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Frederik Hanghøj Iversen
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a4f8a37e36
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Proove that IsCategory is a mere proposition!
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2018-02-20 18:01:26 +01:00 |
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Frederik Hanghøj Iversen
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159bffa6ae
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Factor out more from IsCategory
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2018-02-20 17:59:48 +01:00 |
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Frederik Hanghøj Iversen
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a016c67b88
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Succesfully apply path-induction.
Now all that's left to do is prove the original proposition in a
heterogenous equality
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2018-02-20 17:46:32 +01:00 |
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Frederik Hanghøj Iversen
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ff496aae09
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Factor out a useful type-family
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2018-02-20 17:33:02 +01:00 |
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Frederik Hanghøj Iversen
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860c91f913
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Trim mess
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2018-02-20 16:43:53 +01:00 |
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Frederik Hanghøj Iversen
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8ef61d9db0
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Simplify Category
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2018-02-20 16:26:40 +01:00 |
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Frederik Hanghøj Iversen
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10df9511a4
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Move various type-synonyms to RawCategory
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2018-02-20 16:24:14 +01:00 |
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Frederik Hanghøj Iversen
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38ec53d5c2
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Cosmetics
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2018-02-20 14:08:47 +01:00 |
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Frederik Hanghøj Iversen
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44eda0ced0
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Stuff about propositionality of fields of IsCategory
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2018-02-19 15:46:19 +01:00 |
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Frederik Hanghøj Iversen
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bec5acdc59
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Move proposition to wishlist
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2018-02-19 11:25:16 +01:00 |
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Frederik Hanghøj Iversen
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89ad60ffef
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Stuff about the free category
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2018-02-19 11:09:49 +01:00 |
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Frederik Hanghøj Iversen
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73ab4d1836
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Proove identity laws for natural transformations
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2018-02-16 12:46:25 +01:00 |
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Frederik Hanghøj Iversen
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a64e2484e3
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Prove associativity for natural transformations
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2018-02-16 12:24:58 +01:00 |
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Frederik Hanghøj Iversen
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7dc7a5aee3
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Prove that naturalTransformations are sets
Also adds a new module `Cat.Wishlist` of things I hope to put get from
upstream `cubical`.
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2018-02-16 12:03:02 +01:00 |
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Frederik Hanghøj Iversen
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23c458983c
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Rely on global cubical again
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2018-02-16 11:37:22 +01:00 |
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Frederik Hanghøj Iversen
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ad84b15da5
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[WIP] natural transformations are sets
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2018-02-16 10:22:46 +01:00 |
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Frederik Hanghøj Iversen
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7d4aae4f49
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Try to show that natural transformations are sets
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2018-02-09 12:09:59 +01:00 |
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Frederik Hanghøj Iversen
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56d689fb4b
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Use arrowIsSet to simplify equality constructor for functors
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2018-02-07 20:19:17 +01:00 |
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Frederik Hanghøj Iversen
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9349b37550
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Refactor Functor - only in module Functor
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2018-02-06 14:31:18 +01:00 |
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Frederik Hanghøj Iversen
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a27292dd53
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Stuff about the free category
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2018-02-06 11:27:22 +01:00 |
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Frederik Hanghøj Iversen
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9f1e82168f
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Move the free category
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2018-02-06 10:35:52 +01:00 |
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Frederik Hanghøj Iversen
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0688f5c372
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Rename arrowIsSet
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2018-02-06 10:34:43 +01:00 |
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Frederik Hanghøj Iversen
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e8ac6786ff
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Changes to the category of categories
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2018-02-05 16:35:33 +01:00 |
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Frederik Hanghøj Iversen
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e8215b2c05
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Move product, exponential, ...
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2018-02-05 14:59:53 +01:00 |
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Frederik Hanghøj Iversen
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83ccde62e9
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Use co-patterns
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2018-02-05 14:47:15 +01:00 |
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Frederik Hanghøj Iversen
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20dc9d26ac
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Move product, exponential and cart closed to own file
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2018-02-05 14:08:30 +01:00 |
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Frederik Hanghøj Iversen
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8022ed349d
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"re-delegate" projections in new module Category
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2018-02-05 12:21:39 +01:00 |
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Frederik Hanghøj Iversen
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22a9a71870
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Split Category into RawCategory and IsCategory
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2018-02-05 11:43:38 +01:00 |
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Frederik Hanghøj Iversen
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fecb4dc1ce
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Towards IsCategory-is-prop
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2018-02-05 10:24:57 +01:00 |
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Frederik Hanghøj Iversen
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e5f1fa018a
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Merge branch 'Saizan-master' into dev
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2018-02-02 15:34:30 +01:00 |
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