From: Matt Oliveri <atm...@gmail.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Impredicative set + function extensionality + proof irrelevance consistent?
Date: Fri, 22 Dec 2017 16:25:24 -0800 (PST) [thread overview]
Message-ID: <ae361df7-8227-4a6c-b74b-b3f1a02eb39d@googlegroups.com> (raw)
In-Reply-To: <84edd3f3-4d2b-4864-a7bd-808cebcef72f@googlegroups.com>
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On Friday, December 22, 2017 at 4:20:21 PM UTC-5, Martín Hötzel Escardó
wrote:
>
> There may be some confusion about univalence and equality of subsets
> of a type.
>
> [...]
>
> Now, from a subset A : ℙ X, we get a type A' and an embedding A' → X.
> (The construction works like this: we have A : X → Prop, and a
> projection Prop → U. Then the type A' is the sum (Σ) of composite
> function. The embedding is the first projection.)
>
> It is definitely not the case that if A'=B' for A,B : ℙ X then A=B.
>
> [...]
>
> All the misunderstandings in the previous messages are caused by
> looking at the particular type X=1 without enough care.
>
> And I think this is what Thomas is pointing out.
>
Huh? Your isEven/isOdd example is fine, but there, X ≠ 1. Is it not the
case that if A'=B' for A,B : ℙ 1 then A=B? (Note the specialization to 1.)
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next prev parent reply other threads:[~2017-12-23 0:25 UTC|newest]
Thread overview: 54+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-12-11 4:22 Kristina Sojakova
2017-12-11 11:42 ` [HoTT] " Jon Sterling
2017-12-11 12:15 ` Kristina Sojakova
2017-12-11 12:43 ` Jon Sterling
2017-12-11 14:28 ` Thomas Streicher
2017-12-11 14:32 ` Kristina Sojakova
2017-12-11 14:23 ` Thorsten Altenkirch
2017-12-12 10:15 ` Andrea Vezzosi
2017-12-12 11:03 ` Thorsten Altenkirch
2017-12-12 12:02 ` Thomas Streicher
2017-12-12 12:21 ` Thorsten Altenkirch
2017-12-12 13:17 ` Jon Sterling
2017-12-12 19:29 ` Thomas Streicher
2017-12-12 19:52 ` Martin Escardo
2017-12-12 23:14 ` Michael Shulman
2017-12-14 12:32 ` Thorsten Altenkirch
2017-12-14 18:52 ` Michael Shulman
2017-12-16 15:21 ` Thorsten Altenkirch
2017-12-17 12:55 ` Michael Shulman
2017-12-17 17:08 ` Ben Sherman
2017-12-17 17:16 ` Thorsten Altenkirch
2017-12-17 22:43 ` Floris van Doorn
2017-12-15 17:00 ` Thomas Streicher
2017-12-17 8:47 ` Thorsten Altenkirch
2017-12-17 10:21 ` Thomas Streicher
2017-12-17 11:39 ` Thorsten Altenkirch
2017-12-18 7:41 ` Matt Oliveri
2017-12-18 10:00 ` Michael Shulman
2017-12-18 11:55 ` Matt Oliveri
2017-12-18 16:24 ` Michael Shulman
2017-12-18 20:08 ` Matt Oliveri
2017-12-18 10:10 ` Thorsten Altenkirch
2017-12-18 11:17 ` Matt Oliveri
2017-12-18 12:09 ` Matt Oliveri
2017-12-18 11:52 ` Thomas Streicher
2017-12-19 11:26 ` Thorsten Altenkirch
2017-12-19 13:52 ` Andrej Bauer
2017-12-19 14:44 ` Thorsten Altenkirch
2017-12-19 15:31 ` Thomas Streicher
2017-12-19 16:10 ` Thorsten Altenkirch
2017-12-19 16:31 ` Thomas Streicher
2017-12-19 16:37 ` Thorsten Altenkirch
2017-12-20 11:00 ` Thomas Streicher
2017-12-20 11:16 ` Thorsten Altenkirch
2017-12-20 11:41 ` Thomas Streicher
2017-12-21 0:42 ` Matt Oliveri
2017-12-22 11:18 ` Thorsten Altenkirch
2017-12-22 21:20 ` Martín Hötzel Escardó
2017-12-22 21:36 ` Martín Hötzel Escardó
2017-12-23 0:25 ` Matt Oliveri [this message]
2017-12-19 16:41 ` Steve Awodey
2017-12-20 0:14 ` Andrej Bauer
2017-12-20 3:55 ` Steve Awodey
[not found] ` <fa8c0c3c-4870-4c06-fd4d-70be992d3ac0@skyskimmer.net>
2017-12-14 13:28 ` Thorsten Altenkirch
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