Discussion of Homotopy Type Theory and Univalent Foundations
 help / color / mirror / Atom feed
From: Thorsten Altenkirch <Thorsten....@nottingham.ac.uk>
To: Michael Shulman <shu...@sandiego.edu>
Cc: "homotopyt...@googlegroups.com" <homotopyt...@googlegroups.com>
Subject: Re: [HoTT] "Identifications" ?
Date: Mon, 4 May 2020 14:17:23 +0000	[thread overview]
Message-ID: <7A5CCED7-4FFC-43EE-AD3C-699899C19520@nottingham.ac.uk> (raw)
In-Reply-To: <CAOvivQz1avq5PgK1FHWp1d4-U6UzV=Vdvo9iRp_3WjaXxNUskg@mail.gmail.com>

This seems reasonable. I usually say "equality proofs" but the word proof also has other conotations. Also what is an element of 3 <= 4, if not a proof or evidence? Maybe it is a inidentification? __

Thorsten

On 04/05/2020, 14:17, "Michael Shulman" <shu...@sandiego.edu> 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.

    On Mon, May 4, 2020 at 2:35 AM Thorsten Altenkirch
    <Thorsten....@nottingham.ac.uk> wrote:
    >
    > I am just reading a paper which uses the word “Identification” instead of equality. I think this has been proposed by Bob Harper. Can anybody enlighten me what is the difference between identifications and equality? Maybe there is an identification between them but they are not equal? Are the real numbers 0.999… identified or are they equal?
    >
    >
    >
    > Thorsten
    >
    > This message and any attachment are intended solely for the addressee
    > and may contain confidential information. If you have received this
    > message in error, please contact the sender and delete the email and
    > attachment.
    >
    > Any views or opinions expressed by the author of this email do not
    > necessarily reflect the views of the University of Nottingham. Email
    > communications with the University of Nottingham may be monitored
    > where permitted by law.
    >
    >
    >
    > --
    > You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group.
    > To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyT...@googlegroups.com.
    > To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/BBC0B8F3-AB16-4196-B9B9-B1B3031B2D7D%40nottingham.ac.uk.




This message and any attachment are intended solely for the addressee
and may contain confidential information. If you have received this
message in error, please contact the sender and delete the email and
attachment. 

Any views or opinions expressed by the author of this email do not
necessarily reflect the views of the University of Nottingham. Email
communications with the University of Nottingham may be monitored 
where permitted by law.





  reply	other threads:[~2020-05-04 14:17 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 [this message]
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
2020-05-04 20:38         ` Joyal, André
2020-05-07 19:43 ` Martín Hötzel Escardó
2020-05-08 10:41   ` [HoTT] " Thorsten Altenkirch

Reply instructions:

You may reply publicly to this message via plain-text email
using any one of the following methods:

* Save the following mbox file, import it into your mail client,
  and reply-to-all from there: mbox

  Avoid top-posting and favor interleaved quoting:
  https://en.wikipedia.org/wiki/Posting_style#Interleaved_style

* Reply using the --to, --cc, and --in-reply-to
  switches of git-send-email(1):

  git send-email \
    --in-reply-to=7A5CCED7-4FFC-43EE-AD3C-699899C19520@nottingham.ac.uk \
    --to="thorsten...."@nottingham.ac.uk \
    --cc="homotopyt..."@googlegroups.com \
    --cc="shu..."@sandiego.edu \
    --subject='Re: [HoTT] "Identifications" ?' \
    /path/to/YOUR_REPLY

  https://kernel.org/pub/software/scm/git/docs/git-send-email.html

* If your mail client supports setting the In-Reply-To header
  via mailto: links, try the mailto: link

This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).