From: Martin Escardo <escardo...@googlemail.com>
To: "HomotopyT...@googlegroups.com" <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Re: Joyal's version of the notion of equivalence
Date: Sat, 8 Oct 2016 01:21:37 +0100 [thread overview]
Message-ID: <cb48b96b-1dc6-fc80-51c9-c6293d4fd4dc@googlemail.com> (raw)
In-Reply-To: <25c7daf7-8c0f-97de-7d3d-34851bf50a98@googlemail.com>
On 08/10/16 00:51, 'Martin Escardo' via Homotopy Type Theory wrote:
> This shouldn't have happened (it seems like a bug):
Oh, well. Let me retype everything again from memory, in a shorter
way, and then this time send it to everybody.
The main insight of univalent type theory is the formulation of
equivalence (as e.g. the contractibility of all fibers) so that it is
a proposition.
An equivalent formulation, attributed to Joyal, and discussed in the
Book, is that the function has a given left inverse and that the
function also has a given right inverse, where both "given" are
expressed with Sigma. One can prove that this notion of
Joyal-equivalence is a proposition, in MLTT, assuming funext, which is
nice and slightly surprising at first sight.
But where does this formulation of the notion of equiavelence come from?
Best,
Martin
next prev parent reply other threads:[~2016-10-08 0:21 UTC|newest]
Thread overview: 14+ messages / expand[flat|nested] mbox.gz Atom feed top
[not found] <963893a3-bfdf-d9bd-8961-19bab69e0f7c@googlemail.com>
2016-10-07 23:51 ` Martin Escardo
2016-10-08 0:21 ` Martin Escardo [this message]
2016-10-08 17:34 ` [HoTT] " Joyal, André
2016-10-09 18:31 ` Martin Escardo
2016-10-09 18:56 ` Joyal, André
2016-10-11 22:54 ` Martin Escardo
2016-10-12 9:45 ` Peter LeFanu Lumsdaine
2016-10-12 13:21 ` Dan Christensen
2016-10-12 22:45 ` [HoTT] " Martin Escardo
2016-10-12 22:17 ` Vladimir Voevodsky
2016-10-12 23:55 ` Martin Escardo
2016-10-13 10:14 ` Thomas Streicher
2016-10-13 7:14 ` Joyal, André
2016-10-13 12:48 ` Egbert Rijke
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