Re: [HoTT] "Identifications" ?

[Steve Awodey <awo...@cmu.edu>]

> 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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