Discussion of Homotopy Type Theory and Univalent Foundations
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From: "Joyal, André" <"joyal..."@uqam.ca>
To: Michael Shulman <shu...@sandiego.edu>,
	Stefan Monnier <mon...@iro.umontreal.ca>
Cc: Thorsten Altenkirch <Thorsten....@nottingham.ac.uk>,
	"homotopyt...@googlegroups.com" <homotopyt...@googlegroups.com>
Subject: RE: [HoTT] "Identifications" ?
Date: Mon, 4 May 2020 16:16:27 +0000	[thread overview]
Message-ID: <8C57894C7413F04A98DDF5629FEC90B1652F3F0F@Pli.gst.uqam.ca> (raw)
In-Reply-To: <CAOvivQx_2TinRHBrmOAZFnmFp8VVQ-yMcPvtKFtX-d9wGsD+2Q@mail.gmail.com>

Dear all,

I am tempted to add my grain of salt to this discussion.
I like the word "identification". 
But what about "iso" ?
It means "equal". As in "iso-morphism", "iso-tope", etc.

https://wordinfo.info/unit/2795/page:9

Best,
André

________________________________________
From: homotopyt...@googlegroups.com [homotopyt...@googlegroups.com] on behalf of Michael Shulman [shu...@sandiego.edu]
Sent: Monday, May 04, 2020 11:59 AM
To: Stefan Monnier
Cc: Thorsten Altenkirch; homotopyt...@googlegroups.com
Subject: Re: [HoTT] "Identifications" ?

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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  parent reply	other threads:[~2020-05-04 16:16 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
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 [this message]
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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