Discussion of Homotopy Type Theory and Univalent Foundations
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* [HoTT] Joyal's definition of elementary higher topos
@ 2020-02-21 13:23 Bas Spitters
  2020-02-21 22:13 ` Michael Shulman
  0 siblings, 1 reply; 3+ messages in thread
From: Bas Spitters @ 2020-02-21 13:23 UTC (permalink / raw)
  To: homotopytypetheory

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

Has there been any progress on these coherence questions?

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2020-02-21 13:23 [HoTT] Joyal's definition of elementary higher topos Bas Spitters
2020-02-21 22:13 ` Michael Shulman
2020-02-23 23:56   ` Michael Shulman

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