Discussion of Homotopy Type Theory and Univalent Foundations
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From: Alexander Gietelink Oldenziel <a.f.d.a.gietelinkoldenziel@gmail.com>
To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: [HoTT] Kripke-Joyal Semantics and HoTT
Date: Tue, 8 Oct 2019 08:07:15 -0700 (PDT)
Message-ID: <1b613bab-505c-4880-9778-4e3206872294@googlegroups.com> (raw)

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Dear all,

It is my understanding that the interpretation of HoTT inside higher topoi 
is an ongoing field of research. Much of this business involves subtle 
strictness properties and things like contextual and syntactic categories. 
In the 1-topos case there is the Kripke-Joyal/Stack - semantics. These 
semantics are easy to use in practice.  Naively, it seems one could lift 
the Kripke-Joyal semantics by not asking for truth but simply an inhabitant 
of a type. 

Has this been investigated at all? Is it ultimately fruitless?

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Thread overview: 3+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2019-10-08 15:07 Alexander Gietelink Oldenziel [this message]
2019-10-08 16:36 ` Ali Caglayan
2019-10-10 21:20   ` Michael Shulman

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Discussion of Homotopy Type Theory and Univalent Foundations

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