Discussion of Homotopy Type Theory and Univalent Foundations
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From: Steve Awodey <steve...@gmail.com>
To: stre...@mathematik.tu-darmstadt.de
Cc: Thorsten Altenkirch <Thorsten....@nottingham.ac.uk>,
	"homotopyt...@googlegroups.com" <homotopyt...@googlegroups.com>
Subject: Re: [HoTT] "Identifications" ?
Date: Mon, 4 May 2020 07:04:09 -0400	[thread overview]
Message-ID: <958244CE-832E-4DF7-8A83-A98D70D59193@gmail.com> (raw)
In-Reply-To: <f23c7b1ada3c6fd99e47a70620c9e278.squirrel@webmail.mathematik.tu-darmstadt.de>

This terminology was first proposed by Dan Grayson in one of our discussions in Simonyi Hall, as a way of understanding the elements of identity types. It’s used occasionally in the book. 

Regards,
Steve 

> On May 4, 2020, at 06:59, stre...@mathematik.tu-darmstadt.de 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?
> 
> You may identify things which are not equal. So ''identify'' seems to mean
> consider as equal.
> In a sense this is very descriptive for what is going on in HoTT where one
> never performs quotients but rather widens equivalence relations.
> This is really different in the respective topos models as eg simplicial
> sets or already the topos of reflexive graphs as exemplified by N. Kraus's
> puzzling counterexample.
> 
> Thomas
> 
> -- 
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  reply	other threads:[~2020-05-04 11:04 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 [this message]
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
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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