Discussion of Homotopy Type Theory and Univalent Foundations
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From: Steve Awodey <awo...@cmu.edu>
To: Thorsten Altenkirch <Thorsten....@nottingham.ac.uk>
Cc: Michael Shulman <shu...@sandiego.edu>,
	Stefan Monnier <mon...@iro.umontreal.ca>,
	"homotopyt...@googlegroups.com" <homotopyt...@googlegroups.com>
Subject: Re: [HoTT] "Identifications" ?
Date: Mon, 4 May 2020 12:53:59 -0400	[thread overview]
Message-ID: <14AEC162-00A7-41E5-88EF-11501EF7C2AB@gmail.com> (raw)
In-Reply-To: <D83C2B3E-AF61-409B-BE3A-A98839A00CF6@nottingham.ac.uk>



> On May 4, 2020, at 12:17 PM, Thorsten Altenkirch <Thorsten....@nottingham.ac.uk> wrote:
> 
> 
>    I’m afraid that someone may have hacked Thorsten’s email account. The real Thorsten went through all this with us many years ago. 
>    : - )
> 
> One of our dogs gained access to my laptop - sorry. These animals can be very awkward.
> 
> However, even the real Thorsten had a friendly argument with Andre Joyal when we were writing the book about whether to use = for the equality type. 

I remember that conversation. 
I think we decided to put the question “what does x=y mean?” aside, 
until we had taken care of more important things.

So is it time now?

Steve

> 
> Thorsten
> 
> On 04/05/2020, 17:08, "Steve Awodey" <steve...@gmail.com> wrote:
> 
>    I’m afraid that someone may have hacked Thorsten’s email account. The real Thorsten went through all this with us many years ago. 
>    : - )
> 
> 
>> On May 4, 2020, at 12:00, Michael Shulman <shu...@sandiego.edu> wrote:
>> 
>> The word "path" is closely tied to the homotopy interpretation, and to
>> the classical perspective of oo-groupoids presented via topological
>> spaces, which has various problems.  This is particularly an issue in
>> cohesive type theory, where there is a separate "point-set level"
>> notion of path that it is important to distinguish from
>> identifications.
>> 
>>> On Mon, May 4, 2020 at 7:48 AM Stefan Monnier <mon...@iro.umontreal.ca> wrote:
>>> 
>>>> I don't think using "identification" necessarily implies any
>>>> difference between "identification" and "equality".  I don't think of
>>>> it that way.  For me the point is just to have a word that refers to
>>>> an *element* of an identity type.  Calling it "an equality" can have
>>>> the wrong connotation because classically, an equality is just a
>>>> proposition (or a true proposition), whereas an element of an identity
>>>> type carries information.  Calling it "an identification" suggests
>>>> exactly the information that it carries: a way of identifying two
>>>> things.
>>> 
>>> I thought that's what "path" was for?
>>> 
>>> 
>>>       Stefan "who really doesn't know what he's talking about"
>>> 
>> 
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> 
> 
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  reply	other threads:[~2020-05-04 16:54 UTC|newest]

Thread overview: 26+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2020-05-04  9:35 Thorsten Altenkirch
2020-05-04 10:59 ` [HoTT] " stre...
2020-05-04 11:04   ` Steve Awodey
2020-05-04 11:17   ` Thorsten Altenkirch
2020-05-04 11:42     ` Nicolai Kraus
2020-05-04 12:04       ` Thorsten Altenkirch
2020-05-04 12:06     ` Thomas Streicher
2020-05-04 12:12       ` Thorsten Altenkirch
2020-05-04 12:39         ` Thomas Streicher
2020-05-04 13:16 ` Michael Shulman
2020-05-04 14:17   ` Thorsten Altenkirch
2020-05-04 14:48   ` Stefan Monnier
2020-05-04 15:46     ` Nicolai Kraus
2020-05-04 15:57       ` Thorsten Altenkirch
2020-05-04 15:59     ` Michael Shulman
2020-05-04 16:07       ` Steve Awodey
2020-05-04 16:17         ` Thorsten Altenkirch
2020-05-04 16:53           ` Steve Awodey [this message]
2020-05-04 17:25             ` Thorsten Altenkirch
2020-05-04 17:43               ` Michael Shulman
2020-05-04 17:55               ` Steve Awodey
2020-05-04 16:21         ` Peter LeFanu Lumsdaine
2020-05-04 16:16       ` Joyal, André
2020-05-04 20:38         ` Joyal, André
2020-05-07 19:43 ` Martín Hötzel Escardó
2020-05-08 10:41   ` [HoTT] " Thorsten Altenkirch

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