Discussion of Homotopy Type Theory and Univalent Foundations
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From: Kristina Sojakova <sojakova.kristina@gmail.com>
To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: [HoTT] HoTT with extensional equality
Date: Tue, 7 Jan 2020 14:59:10 -0500
Message-ID: <8de08372-b17d-c153-73ad-4cd8b6c49758@gmail.com> (raw)

Dear all,

I have been increasingly running into situations where I wished I had an 
extensional equality type with a  reflection rule in HoTT, in addition 
to the intensional one to which univalence pertains. I know that type 
systems with two equalities have been studied in the HoTT community 
(e.g., VV's HTS), but last time I discussed this with people it seemed 
the situation was not yet well-understood. So my question is, what 
exactly goes wrong if we endow HoTT with an extensional type?

Thank you,

Kristina

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Thread overview: 5+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2020-01-07 19:59 Kristina Sojakova [this message]
2020-01-07 22:03 ` Rafaël Bocquet
2020-01-07 22:11   ` Kristina Sojakova
2020-01-07 22:18     ` Rafaël Bocquet
     [not found]     ` <CALCpNBoWKXbQgdJ2Pqq_G7J_0D48OVGUeQoBnOfDHzC__GWkHA@mail.gmail.com>
2020-01-07 23:26       ` Kristina Sojakova

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Discussion of Homotopy Type Theory and Univalent Foundations

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