Commit graph

294 commits

Author SHA1 Message Date
Frederik Hanghøj Iversen e6a2e3a0f0 Reduce applications of symmetry 2018-04-11 13:18:34 +02:00
Frederik Hanghøj Iversen 770bce52a2 Use 3rd formulation of univalence 2018-04-11 12:54:22 +02:00
Frederik Hanghøj Iversen 4ff8f155ab [QED] Get equivalence from 3rd formulation 2018-04-11 12:46:22 +02:00
Frederik Hanghøj Iversen c23c2716a5 Move lemma to equivalence-module 2018-04-11 12:27:33 +02:00
Frederik Hanghøj Iversen db5fb3603a Banish qualified import of Function - use \o for fun-comp! 2018-04-11 11:12:09 +02:00
Frederik Hanghøj Iversen c90b064bb0 Rename \o to <<< 2018-04-11 10:58:50 +02:00
Frederik Hanghøj Iversen 6d59a8f79e Add note about proving 9.1.9 2018-04-10 17:33:22 +02:00
Frederik Hanghøj Iversen 772e6778f3 [WIP] Univalence in ad-hoc category in product 2018-04-10 17:17:04 +02:00
Frederik Hanghøj Iversen fd18985e53 Export TypeIsomorphism as an alias for Equivalence.Isomorphism 2018-04-09 18:10:39 +02:00
Frederik Hanghøj Iversen 04144db606 Simplifications and renaming 2018-04-09 18:02:39 +02:00
Frederik Hanghøj Iversen 735b25de23 Simplify proof and move propUnivalent to a more general setting 2018-04-09 16:03:43 +02:00
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