From: Kristina Sojakova <email@example.com> To: "Rafaël Bocquet" <firstname.lastname@example.org>, "Homotopy Type Theory" <HomotopyTypeTheory@googlegroups.com> Subject: Re: [HoTT] HoTT with extensional equality Date: Tue, 7 Jan 2020 17:11:36 -0500 Message-ID: <email@example.com> (raw) In-Reply-To: <firstname.lastname@example.org> Hello Rafael, Thank you for the reference. I browsed the paper; it seems to me that the theory does not appear to support identity reflection. I am looking for a truly extensional form of equality (in addition to the usual one), where equal terms are syntactically identified. Kristina On 1/7/2020 5:03 PM, Rafaël Bocquet wrote: > Hello, > > I think that the paper "Two-Level Type Theory and Applications" > (https://arxiv.org/abs/1705.03307), whose last version has been > submitted on arXiv last month, answers these questions. One of the > intended models of 2LTT is the presheaf category Ĉ over any model C of > HoTT, and this presheaf model is conservative over C, essentially > because the Yoneda embedding is fully faithful. This means that we can > always work in 2LTT instead of HoTT. > > Rafaël > > On 1/7/20 8:59 PM, Kristina Sojakova wrote: >> Dear all, >> >> I have been increasingly running into situations where I wished I had >> an extensional equality type with a reflection rule in HoTT, in >> addition to the intensional one to which univalence pertains. I know >> that type systems with two equalities have been studied in the HoTT >> community (e.g., VV's HTS), but last time I discussed this with >> people it seemed the situation was not yet well-understood. So my >> question is, what exactly goes wrong if we endow HoTT with an >> extensional type? >> >> Thank you, >> >> Kristina >> -- 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 HomotopyTypeTheoryemail@example.com. To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/60639a49-a1c6-0cfd-0bdf-65ad45b14e24%40gmail.com.
next prev parent reply index Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top 2020-01-07 19:59 Kristina Sojakova 2020-01-07 22:03 ` Rafaël Bocquet 2020-01-07 22:11 ` Kristina Sojakova [this message] 2020-01-07 22:18 ` Rafaël Bocquet [not found] ` <CALCpNBoWKXbQgdJ2Pqq_G7J_0D48OVGUeQoBnOfDHzC__GWkHA@mail.gmail.com> 2020-01-07 23:26 ` Kristina Sojakova
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 \ --firstname.lastname@example.org \ --email@example.com \ --cc=HomotopyTypeTheory@googlegroups.com \ --firstname.lastname@example.org \ /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
Discussion of Homotopy Type Theory and Univalent Foundations Archives are clonable: git clone --mirror http://inbox.vuxu.org/hott Example config snippet for mirrors Newsgroup available over NNTP: nntp://inbox.vuxu.org/vuxu.archive.hott AGPL code for this site: git clone https://public-inbox.org/public-inbox.git