From: Matt Oliveri <atm...@gmail.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] A puzzle about "univalent equality"
Date: Wed, 7 Sep 2016 16:18:33 -0700 (PDT) [thread overview]
Message-ID: <a88b7834-5ce8-47d6-803a-d2a98ed27084@googlegroups.com> (raw)
In-Reply-To: <143ade6b-1b68-36fe-a765-c54d9f6fac8c@googlemail.com>
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On Tuesday, September 6, 2016 at 6:14:24 PM UTC-4, Martin Hotzel Escardo
wrote:
>
> Some people like the K-axiom for U because ... (let them fill the answer).
>
It allows you to interpret (within type theory) the types of ITT + K as
types of U, and their elements as the corresponding elements. (Conjecture?)
Whereas without K, we don't know how to interpret ITT types as types of U.
In other words, K is a simple way to give ITT reflection.
Can we stare at the type (Id U X Y) objectively, mathematically, say
> within intensional MLTT, where it was introduced, and, internally in
> MLTT, ponder what it can be, and identify the only "compelling" thing it
> can be as the type of equivalences X~Y, where "compelling" is a notion
> remote from univalence?
>
How does Zermelo-style set-theoretic equality get ruled out as a potential
"compelling" meaning for identity? Of course, there's a potential argument
about what "compelling" ought to be getting at. You seem to not consider
set-theoretic equality compelling, which I can play along with.
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next prev parent reply other threads:[~2016-09-07 23:18 UTC|newest]
Thread overview: 18+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-09-05 16:54 Andrew Polonsky
2016-09-05 21:40 ` [HoTT] " Michael Shulman
2016-09-05 21:51 ` Dan Licata
2016-09-06 7:30 ` Andrew Polonsky
2016-09-06 12:32 ` Michael Shulman
2016-09-06 12:56 ` Dan Licata
2016-09-06 12:57 ` Peter LeFanu Lumsdaine
2016-09-06 13:44 ` Andrew Polonsky
2016-09-06 22:14 ` Martin Escardo
2016-09-07 23:18 ` Matt Oliveri [this message]
2016-09-08 4:14 ` Michael Shulman
2016-09-08 6:06 ` Jason Gross
2016-09-08 9:11 ` Martin Escardo
2016-09-08 6:34 ` Matt Oliveri
2016-09-08 6:45 ` Michael Shulman
2016-09-08 9:07 ` Martin Escardo
2016-09-08 9:51 ` Thomas Streicher
2016-09-19 12:40 ` Robin Adams
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