Commit graph

458 commits

Author SHA1 Message Date
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
Frederik Hanghøj Iversen af25db7e31 Merge remote-tracking branch 'Saizan/dev' into dev 2018-03-29 13:36:09 +02:00
Frederik Hanghøj Iversen 2f6b129ed6 Move proposal to report, use xelatex 2018-03-29 13:32:48 +02:00
Frederik Hanghøj Iversen 8752b1435d Update report 2018-03-29 13:32:06 +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 a713d560d5 Preview target 2018-03-23 11:33:55 +01:00
Frederik Hanghøj Iversen 1dde3f8e74 Restructure latex-stuff 2018-03-23 11:22:17 +01:00
Frederik Hanghøj Iversen 8ff93e04ec Move proposal to doc/ 2018-03-23 11:13:52 +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 73c3b35631 Merge branch 'dev' 2018-03-22 14:52:01 +01:00
Frederik Hanghøj Iversen 4ae898dfe0 Update backlog and changelog 2018-03-22 14:51:43 +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