From: Thorsten Altenkirch <Thorsten....@nottingham.ac.uk> To: Thomas Streicher <stre...@mathematik.tu-darmstadt.de> Cc: "homotopyt...@googlegroups.com" <homotopyt...@googlegroups.com> Subject: Re: [HoTT] "Identifications" ? Date: Mon, 4 May 2020 12:12:04 +0000 [thread overview] Message-ID: <31C5A7B0-8512-4ABD-8DAA-EF3A1FA0EEFF@nottingham.ac.uk> (raw) In-Reply-To: <20200504120620.GA14623@mathematik.tu-darmstadt.de> Hi Thomas But I am not "interpreting HoTT in SSet". I am just working in HoTT. You are doing Metamathematics, I am just talking about Mathematics. Sure when you consider models of your theory you can say that certain equalities are just metatheoretic equalities and others are non-trivial equalities. Do you think of a model of set theory when you do set theory? Cheers, Thorsten On 04/05/2020, 13:06, "Thomas Streicher" <stre...@mathematik.tu-darmstadt.de> wrote: Hi Thorsten, > 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. > > What puzzling counterexample is this? I learnt it from Nicolai when he gave a little talk at CSL 2017 when given a prize for his thesis. The counterexample or rather my appreciation of it I have made a little note on which I have put for convenience at https://www.mathematik.tu-darmstadt.de/~streicher/kraus.pdf The point is that interpreting HoTT in sSet is very different from the traditional interpretation of logic in sSet. The same happens already the topos of reflexive graphs. Propositions are connected reflexive graphs and thee are very man nonisomorphic such guys but HoTT identifies them all. But this has nothing to do with HoTT per se. For example you can interpret HOL in assemblies in two very different ways once `a la topos (proof irrelevant) and once `a la model of TT (proof relevant). In mathematics equality is a very relative notion. But one may perform quotients to reconcile them... Thomas 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.
next prev parent reply other threads:[~2020-05-04 12:12 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 [this message] 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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