Discussion of Homotopy Type Theory and Univalent Foundations
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From: Bas Spitters <b.a.w.spitters@gmail.com>
To: homotopytypetheory <homotopytypetheory@googlegroups.com>
Subject: [HoTT] Joyal's definition of elementary higher topos
Date: Fri, 21 Feb 2020 14:23:37 +0100
Message-ID: <CAOoPQuQc317E8qUEOWJ2JQD_iXAFyE=Wcttruqd5A8tRpHqttg@mail.gmail.com> (raw)

In 2014, Andra Joyal proposed a definition of an elementary higher topos.

"This lecture contains a proposed definition that is not an
(∞,1)-category but a presentation of one by a model category-like
structure; this is closer to the type theory, but further from the
intended examples. In particular, there are unresolved coherence
questions even as to whether every Grothendieck (∞,1)-topos can be
presented by a model in Joyal’s sense (in particular, how strict can a
universe be made, and can the natural numbers object be made
fibrant)."
https://ncatlab.org/nlab/show/elementary+%28infinity%2C1%29-topos

Has there been any progress on these coherence questions?

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Thread overview: 3+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2020-02-21 13:23 Bas Spitters [this message]
2020-02-21 22:13 ` Michael Shulman
2020-02-23 23:56   ` Michael Shulman

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Discussion of Homotopy Type Theory and Univalent Foundations

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