Discussion of Homotopy Type Theory and Univalent Foundations
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From: Ian Orton <ri...@cam.ac.uk>
To: HomotopyTypeTheory@googlegroups.com
Subject: Weaker forms of univalence
Date: Wed, 19 Jul 2017 17:26:49 +0100	[thread overview]
Message-ID: <cc0c916a-7cf6-426e-189e-0a86a7e5bbbc@cam.ac.uk> (raw)

Consider the following three statements, for all types A and B:

   (1)  (A ≃ B) -> (A = B)
   (2)  (A ≃ B) ≃ (A = B)
   (3)  isEquiv idtoeqv

(3) is the full univalence axiom and we have implications (3) -> (2) -> 
(1), but can we say anything about the other directions? Do we have (1) 
-> (2) or (2) -> (3)? Can we construct models separating any/all of 
these three statements?

Thanks,
Ian

             reply	other threads:[~2017-07-19 16:26 UTC|newest]

Thread overview: 11+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2017-07-19 16:26 Ian Orton [this message]
2017-07-19 17:19 ` [HoTT] " Michael Shulman
2017-07-19 18:04   ` Nicolai Kraus
2017-07-20  6:56   ` Bas Spitters
2017-07-20 11:59     ` Steve Awodey
2017-07-20 17:57       ` Michael Shulman
2017-07-21  1:36         ` Matt Oliveri
2017-07-21  7:43           ` Peter LeFanu Lumsdaine
2017-07-19 17:21 ` Jason Gross
2017-07-19 17:28   ` Michael Shulman
2017-07-19 18:02     ` Jason Gross

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