 Frederik Hanghøj Iversen
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fe453a6d3a
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Trying to prove cummulativity of homotopy levels
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2018-03-12 16:00:27 +01:00 |
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Frederik Hanghøj Iversen
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c52384b012
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Change name of fromMonad
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2018-03-12 14:43:43 +01:00 |
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Frederik Hanghøj Iversen
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5e092964c8
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Change naming and fuse some modules
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2018-03-12 14:38:52 +01:00 |
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Frederik Hanghøj Iversen
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ccf753d438
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Move monoidal and kleisli representation to own modules
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2018-03-12 14:23:23 +01:00 |
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Frederik Hanghøj Iversen
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8dadfa22a0
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Add documentation header to monad module
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2018-03-12 14:11:31 +01:00 |
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Frederik Hanghøj Iversen
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aa645fb11e
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Move voevodsky's construction to own module
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2018-03-12 14:04:10 +01:00 |
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Frederik Hanghøj Iversen
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c0cf6789cd
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Use propositions straight from the horses mouth
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2018-03-12 13:56:49 +01:00 |
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Frederik Hanghøj Iversen
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a7214fcc66
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Finish equality principle for categories
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2018-03-12 13:51:29 +01:00 |
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Frederik Hanghøj Iversen
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35390c02d3
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Stuff about univalence in the category of sets
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2018-03-12 13:38:48 +01:00 |
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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
|
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
|
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
|
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
|
cd98736d02
|
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
|
Use abbreviation
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2018-02-25 14:39:11 +01:00 |
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Frederik Hanghøj Iversen
|
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
|
5deabb7546
|
Forgot to add monoid-module
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2018-02-25 14:28:01 +01:00 |
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Frederik Hanghøj Iversen
|
ce46e0ae7a
|
Module-ify
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2018-02-25 14:27:37 +01:00 |
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Frederik Hanghøj Iversen
|
12dddc2067
|
Use a module
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2018-02-25 03:12:51 +01:00 |
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Frederik Hanghøj Iversen
|
4c298855e0
|
[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
|
a6b01929f0
|
Prove distributive law
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2018-02-25 01:27:20 +01:00 |
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Frederik Hanghøj Iversen
|
a447cd9c7c
|
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
|
Expand definition of isDistributive somewhat
Also contains some side-tracks
|
2018-02-24 20:37:21 +01:00 |
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Frederik Hanghøj Iversen
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e7abab0e4c
|
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
|
be505cdfbe
|
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
|
Add note about haskell
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2018-02-24 15:25:07 +01:00 |
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Frederik Hanghøj Iversen
|
e4e327d1d2
|
[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
|
3e12331294
|
Monoidal monads addendum
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2018-02-24 14:01:57 +01:00 |
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Frederik Hanghøj Iversen
|
4ec13fe509
|
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
|
0ca11874bc
|
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
|
8527fe0df4
|
Rename functor composition - implement monads...
In their monoidal form.
|
2018-02-24 12:52:16 +01:00 |
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Frederik Hanghøj Iversen
|
cb8533b84a
|
Rename natural transformation composition
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2018-02-23 17:43:38 +01:00 |
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Frederik Hanghøj Iversen
|
dd11b69c71
|
Documentation for natural transformations
|
2018-02-23 17:37:27 +01:00 |
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Frederik Hanghøj Iversen
|
689a6467c6
|
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
|
f5dded9561
|
Do not use IsCategory directly
|
2018-02-23 16:41:17 +01:00 |
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Frederik Hanghøj Iversen
|
39284b8d99
|
Changes in CwF
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2018-02-23 14:13:55 +01:00 |
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Frederik Hanghøj Iversen
|
5796b791b8
|
Almost prove that arrows are sets in the cateogry of families
|
2018-02-23 13:59:35 +01:00 |
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Frederik Hanghøj Iversen
|
a321a9c8b2
|
Use hLevels in Fam
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2018-02-23 13:39:59 +01:00 |
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Frederik Hanghøj Iversen
|
3d0916f448
|
Use correct name for hSets
|
2018-02-23 13:20:30 +01:00 |
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Frederik Hanghøj Iversen
|
4874ed0795
|
Rename distrib to isDistributive
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2018-02-23 12:53:35 +01:00 |
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Frederik Hanghøj Iversen
|
7787a8f0be
|
Indentation
|
2018-02-23 12:52:14 +01:00 |
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Frederik Hanghøj Iversen
|
48423cc816
|
Rename arrowIsSet to arrowsAreSets
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2018-02-23 12:51:44 +01:00 |
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Frederik Hanghøj Iversen
|
6446435a49
|
Rename ident to isIdentity
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2018-02-23 12:49:41 +01:00 |
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Frederik Hanghøj Iversen
|
5cbc409770
|
Rename assoc to isAssociative
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2018-02-23 12:43:49 +01:00 |
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Frederik Hanghøj Iversen
|
852056cc44
|
Add type-synonyms in functor
|
2018-02-23 12:41:15 +01:00 |
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Frederik Hanghøj Iversen
|
a57f45d93f
|
Remove yet another postulate
|
2018-02-23 12:33:20 +01:00 |
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Frederik Hanghøj Iversen
|
34dec9406d
|
Do not mention IsFunctor outside the module that defines it
|
2018-02-23 12:29:10 +01:00 |
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Frederik Hanghøj Iversen
|
e46edf1f68
|
Chain reexport things in Functor
|
2018-02-23 12:21:16 +01:00 |
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Frederik Hanghøj Iversen
|
885fd8fa69
|
Drastically simplify proofs
|
2018-02-23 12:15:39 +01:00 |
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Frederik Hanghøj Iversen
|
3f3247c870
|
Remove commented code
|
2018-02-23 12:05:38 +01:00 |
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Frederik Hanghøj Iversen
|
de1d19c442
|
Readd stuff about the yoneda embedding
|
2018-02-23 11:24:22 +01:00 |
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Frederik Hanghøj Iversen
|
954a89f8d1
|
Expose naturalIsProp
|
2018-02-23 11:12:27 +01:00 |
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Frederik Hanghøj Iversen
|
bc2129b8fc
|
Readd yoneda embedding
|
2018-02-23 10:55:43 +01:00 |
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Frederik Hanghøj Iversen
|
9a4d79fa4e
|
Readd commented code
|
2018-02-23 10:44:23 +01:00 |
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Frederik Hanghøj Iversen
|
3032dc6130
|
Make explicit argument
|
2018-02-23 10:36:59 +01:00 |
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Frederik Hanghøj Iversen
|
cc1ddaac9f
|
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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