Discussion of Homotopy Type Theory and Univalent Foundations
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From: Nils Anders Danielsson <nad@cse.gu.se>
To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] Injective types
Date: Tue, 7 May 2019 14:42:03 +0200
Message-ID: <5fa99a80-56ed-abc5-d64f-876c192bca6a@cse.gu.se> (raw)
In-Reply-To: <2b380e43-8623-4900-b529-1e267155562f@googlegroups.com>

On 02/05/2019 22.46, escardo.martin@gmail.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?


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  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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Discussion of Homotopy Type Theory and Univalent Foundations

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