Discussion of Homotopy Type Theory and Univalent Foundations
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From: Andrew Polonsky <andrew....@gmail.com>
To: Dan Licata <d...@cs.cmu.edu>
Cc: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] A puzzle about "univalent equality"
Date: Tue, 6 Sep 2016 09:30:33 +0200	[thread overview]
Message-ID: <CABcT7WBZo8bt6dtfDowd2nOYrtLPwsCC4Yxara1sZ5_oHeUQFw@mail.gmail.com> (raw)
In-Reply-To: <9064B371-C3B0-45F5-8720-90E6D10E211C@cs.cmu.edu>

Thanks, Mike and Dan.  And congratulations on giving essentially
identical solutions at essentially identical times, in two different
languages!

> I would be very surprised if there was something like this that was not provable in "book HoTT”.

I believe there can't be, either.  But maybe this "belief" is really a
matter of definition, in that the equalities which are "supposed to"
hold, are precisely those which can be derived in book HoTT.

What I find subtle in the above example is that it apparently cannot
be done with the "pre-HoTT" FunExt axiom; you need to use the stronger
formulation, that the canonical map (f=g -> f==g) is an equivalence,
to make the transports compute.

Cheers,
Andrew

  reply	other threads:[~2016-09-06  7:30 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 [this message]
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
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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