From: Matthieu Sozeau <matthie...@inria.fr>
To: homotopytypetheory <homotopyt...@googlegroups.com>
Subject: Is [Equiv Type_i Type_i] contractible?
Date: Thu, 27 Oct 2016 15:15:33 +0000 [thread overview]
Message-ID: <CALgtc7gp1VhjzF4h5GxpPCcsj0VUiGu4vuwQrrODDQU9u0jO+w@mail.gmail.com> (raw)
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Dear all,
we've been stuck with N. Tabareau and his student Théo Winterhalter on
the above question. Is it the case that all equivalences between a universe
and itself are equivalent to the identity? We can't seem to prove (or
disprove) this from univalence alone, and even additional parametricity
assumptions do not seem to help. Did we miss a counterexample? Did anyone
investigate this or can produce a proof as an easy corollary? What is the
situation in, e.g. the simplicial model?
-- Matthieu
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next reply other threads:[~2016-10-27 15:15 UTC|newest]
Thread overview: 14+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-10-27 15:15 Matthieu Sozeau [this message]
2016-10-27 15:19 ` [HoTT] " Martin Escardo
2016-10-27 15:38 ` Martin Escardo
2016-10-27 17:09 ` Nicolai Kraus
2016-10-27 17:08 ` Vladimir Voevodsky
2016-10-27 17:12 ` Ulrik Buchholtz
2016-10-27 19:44 ` [HoTT] " Richard Williamson
2016-10-27 20:38 ` Ulrik Buchholtz
2016-10-30 20:56 ` Richard Williamson
2016-10-31 10:00 ` Eric Finster
2016-10-31 13:07 ` MLTT with proof-relevant judgmental equality? Neel Krishnaswami
2016-10-31 21:43 ` [HoTT] " Andrej Bauer
2016-10-31 22:01 ` Neel Krishnaswami
2016-10-27 20:18 ` Is [Equiv Type_i Type_i] contractible? nicolas tabareau
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