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293 commits

Author SHA1 Message Date
Frederik Hanghøj Iversen 438978973d Construct isomorphism from equivalence
Using this somewhat round-about way of constructing an isomorphism from
an equivalence has made typechecking slower in some situations.

E.g. if you're constructing an equivalence from gradLemma and later use
that constructed equivalence to recover the isomorphism, then you
might as well have kept using those functions.
2018-03-15 12:33:00 +01:00
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