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