From: Nils Anders Danielsson <firstname.lastname@example.org> To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com> Subject: Re: [HoTT] Injective types Date: Tue, 7 May 2019 14:42:03 +0200 Message-ID: <email@example.com> (raw) In-Reply-To: <firstname.lastname@example.org> On 02/05/2019 22.46, email@example.com wrote: > I can confirm from a 26k line Agda development (with comments and > repeated blank lines removed in this counting of the number of lines) > that not once did I need to embed a universe into a larger universe, > except when I wanted to state the theorem that any universe is a > retract of any larger universe if one assumes the propositional > resizing axiom (any proposition in a universe U has an equivalent copy > in any universe V). So I would say that such situations are *extremely > rare* in practice. I once wrote some code where I made use of univalence at three different levels. Does anyone know if one can prove that univalence at one level implies univalence at lower levels, without making use of cumulativity? -- /NAD -- 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/5fa99a80-56ed-abc5-d64f-876c192bca6a%40cse.gu.se. For more options, visit https://groups.google.com/d/optout.
next prev parent reply index Thread overview: 11+ messages / expand[flat|nested] mbox.gz Atom feed top 2019-04-30 23:05 escardo.martin 2019-05-01 2:50 ` Michael Shulman 2019-05-01 6:25 ` escardo.martin 2019-05-01 16:55 ` Michael Shulman 2019-05-02 20:46 ` escardo.martin 2019-05-03 11:45 ` Michael Shulman 2019-05-03 13:25 ` Kenji Maillard 2019-05-03 18:23 ` Thierry Coquand 2019-05-07 12:42 ` Nils Anders Danielsson [this message] 2019-05-07 13:51 ` Andreas Nuyts 2019-05-07 22:06 ` Martín Hötzel Escardó
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