Discussion of Homotopy Type Theory and Univalent Foundations
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From: Thierry Coquand <Thierry...@cse.gu.se>
To: "univalent-...@googlegroups.com" <univalent-...@googlegroups.com>,
	homotopytypetheory <homotopyt...@googlegroups.com>
Subject: HIT
Date: Fri, 10 Mar 2017 13:35:01 +0000	[thread overview]
Message-ID: <A3B65291-FD1F-4ABF-9CDD-D2DF34451E2C@chalmers.se> (raw)
In-Reply-To: <FAECD168-CDCC-4DC2-8968-3CEB59D26E71@ias.edu>

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  For completness, I wrote here<http://www.cse.chalmers.se/~coquand/fac.pdf> the semantics of some HIT (the circle and the
trivial cofibration-fibration factorisation of a map) in constructive set theory.
Since one has to define inductively at the same time a family of sets and
suitable maps between these sets, this is an example of an indexed
inductive-recursive definition, and one can follow Stuart Allen’s idea
(LICS 1987) of defining by induction instead relations which should represent
the -graphs- of these functions, and prove then by induction that these are functional graphs.
(This replaces the transfinite induction of the small object argument.)
 Thierry

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  parent reply	other threads:[~2017-03-10 13:35 UTC|newest]

Thread overview: 22+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2017-02-23 14:47 about the HTS Vladimir Voevodsky
2017-02-23 14:57 ` [HoTT] " Benedikt Ahrens
2017-02-23 18:08   ` Vladimir Voevodsky
2017-02-23 18:52     ` Benedikt Ahrens
2017-02-23 21:45       ` Vladimir Voevodsky
     [not found]         ` <87k28fek09.fsf@capriotti.io>
2017-02-24 14:36           ` [UniMath] " Vladimir Voevodsky
2017-02-24 15:06             ` Paolo Capriotti
2017-02-24 15:10               ` Vladimir Voevodsky
2017-03-10 13:35             ` Thierry Coquand [this message]
2017-02-24 14:36         ` Paolo Capriotti
2017-02-25 19:19 ` Thierry Coquand
2017-02-27 18:50   ` [UniMath] " Vladimir Voevodsky
2017-02-27 18:53     ` Vladimir Voevodsky
2017-02-27 18:58       ` Thierry Coquand
2017-02-28  2:17         ` Vladimir Voevodsky
2017-03-01 20:23           ` Thierry Coquand
2017-03-20 15:12 ` Matt Oliveri
2017-03-22 16:49   ` [HoTT] " Thierry Coquand
2017-03-22 21:01     ` Vladimir Voevodsky
2017-03-23 11:22       ` Matt Oliveri
2017-03-23 11:33         ` Michael Shulman
2017-03-23 12:16           ` Matt Oliveri

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