From: Anders Mortberg <email@example.com> To: Kristina Sojakova <firstname.lastname@example.org> Cc: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com> Subject: Re: [HoTT] Different definitions of Sn Date: Wed, 18 Sep 2019 10:32:19 +0200 Message-ID: <CAMWCppm0sB2ZDMPM-jUYVpn8qxFJEfep6rsZs=8k=hh6yGQF1w@mail.gmail.com> (raw) In-Reply-To: <email@example.com> Hi Kristina, We have proofs for S^0, S^1, S^2 and S^3 in Cubical Agda: https://github.com/agda/cubical/blob/master/Cubical/HITs/Susp/Base.agda However, I don't think we can even write down the general version of S^n as a type with a point and an n-loop with the schema implemented in Cubical Agda. As far as I know no other schema for HITs support this kind of types either. -- Anders On Tue, Sep 17, 2019 at 9:56 PM Kristina Sojakova <firstname.lastname@example.org> wrote: > > Hello everybody, > > Is it worked out somewhere that the two definitions of Sn as a > suspension on one hand and a HIT with a point and an n-loop on the other > hand are equivalent? This is also an exercise in the book. I know > Favonia has some Agda code on spheres but I couldn't find this result in > there. > > Thanks, > > 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/6c150b9c-fba6-47c1-2a6d-975b90f64638%40gmail.com. -- 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 HomotopyTypeTheoryfirstname.lastname@example.org. To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/CAMWCppm0sB2ZDMPM-jUYVpn8qxFJEfep6rsZs%3D8k%3Dhh6yGQF1w%40mail.gmail.com.
next prev parent reply index Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top 2019-09-17 19:56 Kristina Sojakova 2019-09-18 8:32 ` Anders Mortberg [this message] 2019-09-18 9:00 ` Guillaume Brunerie 2019-09-18 12:00 ` Anders Mörtberg 2019-09-18 16:27 ` Licata, Dan 2019-09-18 19:19 ` Michael Shulman
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