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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next prev 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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