Commit graph

492 commits

Author SHA1 Message Date
Frederik Hanghøj Iversen 360e2b95dd Make parameter to monad equivalence explicit 2018-03-14 11:20:07 +01:00
Frederik Hanghøj Iversen 7aec22b30a Expose both monad formulations qualified from Cat.Category.Monad 2018-03-14 11:00:52 +01:00
Frederik Hanghøj Iversen 6229decfb2 Merge branch 'master' into dev 2018-03-14 10:50:57 +01:00
Frederik Hanghøj Iversen 41e2d02c8d [WIP] Prove voe §2.3
By Andrea

The reason you cannot use cong in [1] is that §2-fromMonad result type
depends on the input, you need a dependent version of cong:

cong-d : ∀ {ℓ} {A : Set ℓ} {ℓ'} {B : A → Set ℓ'} {x y : A}
               → (f : (x : A) → B x)
               → (eq : x ≡ y)
               → PathP (\ i → B (eq i)) (f x) (f y)
cong-d f p = λ i → f (p i)

I attach a modified Voevodsky.agda.

Notice that the definition of "t" is still highlighted in yellow,
that's because it being a homogeneous path depends on the exact
definition of lem, see the comment with the two definitional equality
constraints.
2018-03-14 10:30:42 +01:00
Frederik Hanghøj Iversen 091e77b583 Rename IsProduct.isProduct to IsProduct.ump
[WIP]: Also some stuff about propositionality for products.
2018-03-14 10:23:23 +01:00
Frederik Hanghøj Iversen 7065455712 More readable goal for voevodsky's construction 2018-03-13 11:29:13 +01:00
Frederik Hanghøj Iversen 3ab88395dc Merge branch 'dev' 2018-03-13 10:41:54 +01:00
Frederik Hanghøj Iversen 6db2a3e5d4 Update changelog and backlog 2018-03-13 10:41:37 +01:00
Frederik Hanghøj Iversen 896e0d3d37 Stuff about univalence for the category of functors 2018-03-13 10:24:50 +01:00
Frederik Hanghøj Iversen fe453a6d3a Trying to prove cummulativity of homotopy levels 2018-03-12 16:00:27 +01:00
Frederik Hanghøj Iversen c52384b012 Change name of fromMonad 2018-03-12 14:43:43 +01:00
Frederik Hanghøj Iversen 5e092964c8 Change naming and fuse some modules 2018-03-12 14:38:52 +01:00
Frederik Hanghøj Iversen ccf753d438 Move monoidal and kleisli representation to own modules 2018-03-12 14:23:23 +01:00
Frederik Hanghøj Iversen 8dadfa22a0 Add documentation header to monad module 2018-03-12 14:11:31 +01:00
Frederik Hanghøj Iversen aa645fb11e Move voevodsky's construction to own module 2018-03-12 14:04:10 +01:00
Frederik Hanghøj Iversen c0cf6789cd Use propositions straight from the horses mouth 2018-03-12 13:56:49 +01:00
Frederik Hanghøj Iversen a7214fcc66 Finish equality principle for categories 2018-03-12 13:51:29 +01:00
Frederik Hanghøj Iversen 35390c02d3 Stuff about univalence in the category of sets 2018-03-12 13:38:48 +01:00
Frederik Hanghøj Iversen acb5ff4f2b Closer to showing univalence for the category of sets 2018-03-08 14:44:23 +01:00
Frederik Hanghøj Iversen 52297d9073 Clean-up in the category of categories 2018-03-08 11:54:13 +01:00
Frederik Hanghøj Iversen d01514cbdb Do not use ugly ':'-syntax to disambiguate fields 2018-03-08 11:29:16 +01:00
Frederik Hanghøj Iversen 48672b01bd Use dotted expression in Cat 2018-03-08 11:20:51 +01:00
Frederik Hanghøj Iversen 5ad506a09f Rename func* and func-> to omap and fmap respectively 2018-03-08 11:03:56 +01:00
Frederik Hanghøj Iversen 2fcc583646 Add note 2018-03-08 10:50:18 +01:00
Frederik Hanghøj Iversen 63b5f5c68d Use long name for product object 2018-03-08 10:46:28 +01:00
Frederik Hanghøj Iversen 486238e114 Add goals for propositionality of products 2018-03-08 10:38:46 +01:00
Frederik Hanghøj Iversen 1ef57a19f4 Cosmetics 2018-03-08 10:30:35 +01:00
Frederik Hanghøj Iversen 4e7b350188 Factor out objects 2018-03-08 10:28:05 +01:00
Frederik Hanghøj Iversen 181bd1af53 Factor out category 2018-03-08 10:24:17 +01:00
Frederik Hanghøj Iversen faf4c54188 Make parameters explicit 2018-03-08 10:22:21 +01:00
Frederik Hanghøj Iversen fae492a1e3 Restructure products 2018-03-08 10:20:29 +01:00
Frederik Hanghøj Iversen b61749bb91 Fixup some todo-notes 2018-03-08 01:10:52 +01:00
Frederik Hanghøj Iversen fa9a470875 Update backlog 2018-03-08 00:54:42 +01:00
Frederik Hanghøj Iversen e43bee6d9f Feels really close 2018-03-08 00:36:38 +01:00
Frederik Hanghøj Iversen c8fef1d2b5 Use different name for function composition 2018-03-08 00:22:55 +01:00
Frederik Hanghøj Iversen 36cbe711fb Sort of half of the proof of an inverse 2018-03-08 00:09:49 +01:00
Frederik Hanghøj Iversen 459718da23 Finish proof of equivalence of klesili/monoidal categories!! 2018-03-07 17:30:09 +01:00
Frederik Hanghøj Iversen 19103e1678 Update cubical 2018-03-07 16:24:43 +01:00
Frederik Hanghøj Iversen 50f51db4fc Update readme 2018-03-07 15:40:52 +01:00
Frederik Hanghøj Iversen 3749124d09 Switch to experimental branch of stdlib 2018-03-07 15:38:37 +01:00
Frederik Hanghøj Iversen 93d075a6d3 Attempt at proving pureNTEq 2018-03-07 15:23:07 +01:00
Frederik Hanghøj Iversen bf605e09fe Update commit refs 2018-03-07 15:10:36 +01:00
Frederik Hanghøj Iversen 00e6e1aa66 State problem with approach 2018-03-07 11:45:11 +01:00
Frederik Hanghøj Iversen aa64e01084 Remove some cruft 2018-03-07 11:33:08 +01:00
Frederik Hanghøj Iversen 125123846e Lay out a strategy for showing the equivalence 2018-03-07 11:29:58 +01:00
Frederik Hanghøj Iversen 085e6eb3d7 Stuff about voe-2-3 2018-03-06 23:18:33 +01:00
Frederik Hanghøj Iversen 110e3510c5 Use postulates 2018-03-06 15:55:03 +01:00
Frederik Hanghøj Iversen 5ae68df582 Prove that fmap is mapped correctly 2018-03-06 15:53:11 +01:00
Frederik Hanghøj Iversen 4d528a7077 Clean-up 2018-03-06 11:25:29 +01:00
Frederik Hanghøj Iversen 485703c85e Tidy up 2018-03-06 10:16:42 +01:00