From: Thomas Streicher <stre...@mathematik.tu-darmstadt.de>
To: Martin Escardo <escardo...@googlemail.com>
Cc: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] A puzzle about "univalent equality"
Date: Thu, 8 Sep 2016 11:51:07 +0200 [thread overview]
Message-ID: <20160908095107.GA25319@mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <e40b8630-9d14-53c7-b94a-0441e4776b2c@googlemail.com>
Intensional type theory is consistent with extensional type theory
which can be interpreted in any locally cartesian category. Equality
is there interpreted via diagonals (in slice categories). This does
not at all assume quantification over an untyped universe.
Adding K to ITT is an attempt to approach ETT and keeping type
checking decidable.
Most of the known models of type theory are models of extensional type
theory. This collection contains all lcc's and all toposes. I have no
problem to recall these...
Models of ITT but not of ETT and not validating Univalence were
constructed in my Habilitation Thesis and more recently in the Thesis
of Tamara von Glehn.
Thomas
next prev parent reply other threads:[~2016-09-08 9:51 UTC|newest]
Thread overview: 18+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-09-05 16:54 Andrew Polonsky
2016-09-05 21:40 ` [HoTT] " Michael Shulman
2016-09-05 21:51 ` Dan Licata
2016-09-06 7:30 ` Andrew Polonsky
2016-09-06 12:32 ` Michael Shulman
2016-09-06 12:56 ` Dan Licata
2016-09-06 12:57 ` Peter LeFanu Lumsdaine
2016-09-06 13:44 ` Andrew Polonsky
2016-09-06 22:14 ` Martin Escardo
2016-09-07 23:18 ` Matt Oliveri
2016-09-08 4:14 ` Michael Shulman
2016-09-08 6:06 ` Jason Gross
2016-09-08 9:11 ` Martin Escardo
2016-09-08 6:34 ` Matt Oliveri
2016-09-08 6:45 ` Michael Shulman
2016-09-08 9:07 ` Martin Escardo
2016-09-08 9:51 ` Thomas Streicher [this message]
2016-09-19 12:40 ` Robin Adams
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