From: "Martín Hötzel Escardó" <"escardo..."@gmail.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Univalence from scratch
Date: Wed, 7 Mar 2018 13:10:53 -0800 (PST) [thread overview]
Message-ID: <7f3c276a-2d81-4235-8f2a-c4d82ea4f827@googlegroups.com> (raw)
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I have often seen competent mathematicians and logicians, outside our
circle, making technically erroneous comments about the univalence axiom,
in conversations, in talks, and even in public material, in journals or the
web.
For some time I was a bit upset about this. But maybe this is our fault, by
often trying to explain univalence only imprecisely, mixing the explanation
of the models with the explanation of the underlying theory (MLTT, identity
types, universe), with none of the two explained sufficiently precisely.
There are long, precise explanations such as the HoTT book, for example,
or, the formalizations in Coq, Agda and Lean.
But perhaps we don't have publicly available material with a
self-contained, brief and complete formulation of univalence, so that
interested mathematicians and logicians can try to contemplate the axiom in
a fully defined form.
Here is an attempt to rectify this:
https://arxiv.org/abs/1803.02294
This also has an ancillary Agda file with univalence defined from scratch
(without the use of any library at all). Perhaps somebody should add a Coq
"version from scratch" of this.
There is also a web version of this
(http://www.cs.bham.ac.uk/~mhe/agda-new/UnivalenceFromScratch.html) to try
to make this as accessible as possible, with the text and the Agda code
together.
M.
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next reply other threads:[~2018-03-07 21:10 UTC|newest]
Thread overview: 11+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-03-07 21:10 Martín Hötzel Escardó [this message]
2018-03-08 1:37 ` [HoTT] " Jason Gross
2018-03-08 10:04 ` Martin Escardo
2018-03-08 3:50 ` Matt Oliveri
2018-03-08 9:25 ` [HoTT] " Andrej Bauer
2018-03-08 9:26 ` Andrej Bauer
2018-03-08 10:04 ` Martin Escardo
2018-03-09 5:00 ` [HoTT] " N. Raghavendra
2018-03-09 7:02 ` Jason Gross
2018-03-09 9:13 ` N. Raghavendra
2018-04-25 2:10 ` Jeff Olson
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