Discussion of Homotopy Type Theory and Univalent Foundations
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From: "Martín Hötzel Escardó" <escardo.martin@gmail.com>
To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] Re: Proof that something is an embedding without assuming excluded middle?
Date: Thu, 15 Nov 2018 11:23:20 -0800 (PST)	[thread overview]
Message-ID: <1c1cd0d1-47d2-4067-a8c8-69104150f528@googlegroups.com> (raw)
In-Reply-To: <246b6c0d-39c6-4279-8149-40d1129047fc@googlegroups.com>


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On Thursday, 15 November 2018 11:05:42 UTC, Martín Hötzel Escardó wrote:
>
>
>   (P → 𝓤) ≃  M
>
> We take M := Σ (X : 𝓤), is-equiv (κ X),
> where the function κ X : X → (P → X) is defined by κ x p = x
>

I think something interesting is happening here. We have the "open" 
modality  
P → (-), and the sub-universe M of modal types coincides with the modal
reflection  P → 𝓤 of the universe 𝓤. In particular, this means that the 
sub-universe of modal types is itself a modal type. Has this kind of thing 
been
observed before, for this modality and possibly the classes of modalities 
already considered in the literature?

Martin

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  reply	other threads:[~2018-11-15 19:23 UTC|newest]

Thread overview: 12+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2018-11-13 20:32 [HoTT] " Martín Hötzel Escardó
2018-11-13 20:36 ` [HoTT] " Martín Hötzel Escardó
2018-11-13 23:47 ` Jean Joseph
2018-11-14 10:23   ` Martín Hötzel Escardó
2018-11-14 11:07     ` Paolo Capriotti
2018-11-14 15:52       ` Michael Shulman
2018-11-15 11:05         ` Martín Hötzel Escardó
2018-11-15 19:23           ` Martín Hötzel Escardó [this message]
2018-11-15 19:29             ` Michael Shulman
2018-11-15 22:26               ` Martín Hötzel Escardó
2018-11-15 23:38                 ` Michael Shulman
2018-11-14 19:00       ` Martín Hötzel Escardó

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