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Author SHA1 Message Date
Frederik Hanghøj Iversen 69689e7b2a Use a single version of \simeq 2018-04-06 18:27:24 +02:00
Frederik Hanghøj Iversen 36d92c7ceb Make the category an index of PreCategory 2018-04-06 17:09:15 +02:00
Frederik Hanghøj Iversen 23b562a873 Provide preorder instance for some things - more work on product cat 2018-04-06 16:54:00 +02:00
Frederik Hanghøj Iversen bbe9460647 Provide composition of isEquiv's 2018-04-05 20:41:14 +02:00
Frederik Hanghøj Iversen be56027c37 Remove bad lemma for showing univalence 2018-04-05 15:23:50 +02:00
Frederik Hanghøj Iversen e69ace21a0 Rename id-to-iso to idToIso 2018-04-05 15:21:54 +02:00
Frederik Hanghøj Iversen b5f89322ac Add notion of strict category 2018-04-05 15:13:59 +02:00
Frederik Hanghøj Iversen 6c5b68a8ac Add notion of pre-category 2018-04-05 14:39:54 +02:00
Frederik Hanghøj Iversen 8276deb4aa Rename proj. to fst and snd 2018-04-05 10:41:56 +02:00
Frederik Hanghøj Iversen d78965d73f Try to use lemma for proving univalence of product-category thing 2018-04-04 17:45:36 +02:00
Frederik Hanghøj Iversen 84f88ac2ae Change what is needed 2018-04-04 12:01:29 +02:00
Frederik Hanghøj Iversen f66d180ec3 [WIP] Stronger lemma for univalence 2018-04-04 11:27:03 +02:00
Frederik Hanghøj Iversen 172287f0a7 [QED] The ad-hoc product category has hom-sets that are h-sets 2018-04-03 15:23:11 +02:00
Frederik Hanghøj Iversen 1e5fb7d50a [WIP] Arrows are sets in special product category 2018-04-03 14:46:36 +02:00
Frederik Hanghøj Iversen 467c5d9c0c [WIP] Propositionality of products 2018-04-03 12:40:20 +02:00
Frederik Hanghøj Iversen 1c6d9ad2b5 Rename identity in category to ascii-name 2018-04-03 11:36:09 +02:00
Frederik Hanghøj Iversen 41b442c0d8 Merge remote-tracking branch 'Saizan/dev' into dev 2018-03-30 12:23:29 +02:00
Andrea Vezzosi 34e633902f Category.Product: Factor out use of arrowAreSets to shorten proofs 2018-03-30 11:06:45 +02:00
Frederik Hanghøj Iversen ba80fe96dc [WIP] Propositionality for products 2018-03-30 00:12:01 +02:00
Frederik Hanghøj Iversen 432cc78821 Prove assoc and ident for funky category 2018-03-29 15:47:43 +02:00
Frederik Hanghøj Iversen ffedb83210 Initial objects are also propositional 2018-03-29 14:31:58 +02:00
Frederik Hanghøj Iversen 52ac9b4b78 Terminal objects are propositional 2018-03-29 14:26:47 +02:00
Andrea Vezzosi 8ac6b97213 isProp (Product C A B) setup 2018-03-29 00:07:49 +02:00
Frederik Hanghøj Iversen facd1167e0 Fix unique existential 2018-03-27 14:18:13 +02:00
Frederik Hanghøj Iversen b7a80d0b86 Proof: Being an initial- terminal- object is a mere proposition 
Also tries to use this to prove that being a product is a mere
proposition
 2018-03-27 12:20:24 +02:00
Frederik Hanghøj Iversen 9898685491 Prove that the opposite category is a category 2018-03-26 14:11:15 +02:00
Frederik Hanghøj Iversen d3864dbae5 Move properties about natural transformations to that module 2018-03-23 15:20:26 +01:00
Frederik Hanghøj Iversen ef688202a2 Move identity functor laws to functor module... 
and make progress on univalence in the functor category
 2018-03-23 13:55:03 +01:00
Frederik Hanghøj Iversen c8c61a8d03 Half-time report 2018-03-23 11:11:44 +01:00
Frederik Hanghøj Iversen 96fb1d3a3b Formatting 2018-03-23 10:08:28 +01:00
Frederik Hanghøj Iversen ac01b786a7 Cleanup 2018-03-22 14:27:16 +01:00
Frederik Hanghøj Iversen ebcab2528e Prove second inverse law for from/to-isomorphism 2018-03-22 13:49:53 +01:00
Frederik Hanghøj Iversen 0246c1b5ab Readability 2018-03-22 12:25:12 +01:00
Frederik Hanghøj Iversen d816ba657b QED! Show that the category of homotopic sets are univalent. 2018-03-22 12:11:27 +01:00
Frederik Hanghøj Iversen 52ca0b6732 Merge remote-tracking branch 'Saizan/dev' into dev 2018-03-22 11:54:22 +01:00
Frederik Hanghøj Iversen d12122ce60 Add another approach for univalence in Set 2018-03-22 11:50:07 +01:00
Andrea Vezzosi 66ab7138a6 generalized lem3 and made progress for Sets univalence 2018-03-22 10:41:38 +00:00
Frederik Hanghøj Iversen 807a0f3dcd Slight readability improvement 2018-03-21 18:05:25 +01:00
Frederik Hanghøj Iversen 181edc0cd5 Prove step 3 in proof of unvivalence for hSet without ua 2018-03-21 17:52:32 +01:00
Frederik Hanghøj Iversen 8f67ff9f36 Use explicit parameter for hSet 2018-03-21 15:01:31 +01:00
Frederik Hanghøj Iversen ae0ff092f8 Use prelude everywhere 2018-03-21 14:56:43 +01:00
Frederik Hanghøj Iversen 29f45d1426 Delete equality module 2018-03-21 14:47:01 +01:00
Frederik Hanghøj Iversen 183906dc8c Define and use custom prelude 2018-03-21 14:39:56 +01:00
Frederik Hanghøj Iversen 084befbbc6 Merge remote-tracking branch 'Saizan/dev' into dev 
From Andrea:

The problem with "h" there is that ve-re is building a square, "(qq0 j
, h)" is a fine element of the sigma type, but it does not really
connect "(g ∘ f) e" to "e" across dimension "i", in particular it does
not reduce to "e" when "i" is "i1".
 2018-03-21 13:31:28 +01:00
Frederik Hanghøj Iversen cd3514c8cf Formatting 2018-03-21 13:25:24 +01:00
Andrea Vezzosi ed3b3047e6 Progress on univalence for sets. 2018-03-21 12:00:47 +00:00
Frederik Hanghøj Iversen 890154a81d Simplify qualified imports, change make-target: clean 2018-03-21 12:28:26 +01:00
Frederik Hanghøj Iversen e98ed89db5 Make propositionality a submodule of the actual proposition 2018-03-21 12:21:47 +01:00
Frederik Hanghøj Iversen 4beb48e066 Use correct order for left- and right identity 
Define and use helpers left- and right identity
 2018-03-21 11:58:50 +01:00
Frederik Hanghøj Iversen 31257a4d97 Do not export helpers in Fun 2018-03-21 11:58:50 +01:00
Frederik Hanghøj Iversen 629115661b Formatting in yoneda 2018-03-21 11:58:50 +01:00
Frederik Hanghøj Iversen b6a9befd9c Naming and formatting 2018-03-21 11:58:50 +01:00
Frederik Hanghøj Iversen 63a51fbfdc Include modules in "everything"-module 2018-03-21 11:58:50 +01:00
Frederik Hanghøj Iversen 811a6bf58e Make univalence a submodule of RawCategory 2018-03-21 11:58:23 +01:00
Frederik Hanghøj Iversen b03bfb0c77 Restructure in free monad 2018-03-20 14:58:27 +01:00
Frederik Hanghøj Iversen 66cb5b363d [WIP] Finnish all intermediate steps for univalence of hSets 2018-03-20 13:26:40 +01:00
Frederik Hanghøj Iversen 2188e690a0 Prove identity law for coercions. 2018-03-20 12:12:09 +01:00
Frederik Hanghøj Iversen 30725d71b6 [WIP] Scary goal 2018-03-20 11:58:54 +01:00
Frederik Hanghøj Iversen 32d1833d51 [WIP] A long way towards proving univalence in the category of hSets 2018-03-20 11:27:04 +01:00
Frederik Hanghøj Iversen 43563d1ad9 [WIP] Univalence for category of homotopy sets 2018-03-19 16:27:03 +01:00
Frederik Hanghøj Iversen 2058154c65 Helpers to work with isomorphisms and equivalences 2018-03-19 15:15:03 +01:00
Frederik Hanghøj Iversen f69ab0ee62 [WIP] Univalence for the category of hSets 2018-03-19 14:08:59 +01:00
Andrea Vezzosi f7f8953a42 Voe: Use the isomorphism directly for better computation 2018-03-15 13:39:42 +00:00
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 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