From: Eric Finster <ericf...@gmail.com>
To: Michael Shulman <shu...@sandiego.edu>
Cc: "Martín Hötzel Escardó" <"escardo..."@gmail.com>,
"Homotopy Type Theory" <"HomotopyT..."@googlegroups.com>
Subject: Re: [HoTT] Re: Where is the problem with initiality?
Date: Fri, 1 Jun 2018 23:53:39 +0200 [thread overview]
Message-ID: <CAGYJgta0MpqdZm2nR0ruubRzKWBGDjxL1Zfn5pC9x7_DZUid3Q@mail.gmail.com> (raw)
In-Reply-To: <CAOvivQwJnf-We4a3cKE1X-N4gKfX59XP2-8R9SQ-MRTv9FXdOQ@mail.gmail.com>
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> > I don't think the initial model is a set. Is it?
>
> This is the big conjecture that Thorsten and I actually agree on: that
> the initial infinity-CwF in fact happens to be a 1-CwF. Thorsten
> wants to prove this by explicitly constructing the initial
> infinity-CwF and then proving that it is a 1-CwF; my preference would
> be to construct the initial 1-CwF in a careful way (e.g. with only
> normal forms and hereditary substitution) so that one can prove that
> it is in fact the initial infinity-CwF as well. But in both cases the
> conjectured result is the same, and even the important ingredient in
> the expected proof is roughly the same: the existence of normal forms
> and normalization.
>
>
Right, and I think I'm more or less on board with the conjecture.
Although as you start adding more structure to your CwF, things get a bit
murkier...
Is it still okay with dependent products ... umm ... and what about if I
add a class of HIT's?
To take things really far: if there is such a thing as the free elementary
infty-topos, is it a 1-category?
This somehow seems dubious, no?
So it seems to me at some point, something has to break in our notion of
what syntax for higher algebraic objects *is* in the first place.
Which is why I would not want to make the assumption from the outset that
syntax must necessarily be decidable.
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next prev parent reply other threads:[~2018-06-01 21:55 UTC|newest]
Thread overview: 57+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-05-22 5:46 Michael Shulman
2018-05-22 16:47 ` Ambrus Kaposi
2018-05-23 16:26 ` [HoTT] " Thorsten Altenkirch
2018-05-24 5:52 ` Michael Shulman
2018-05-24 8:11 ` Thorsten Altenkirch
2018-05-24 9:53 ` Ambrus Kaposi
2018-05-24 17:26 ` Michael Shulman
2018-05-26 9:21 ` Thomas Streicher
2018-05-26 11:47 ` Michael Shulman
2018-05-26 16:47 ` stre...
2018-05-27 5:14 ` Bas Spitters
2018-05-28 22:39 ` Michael Shulman
2018-05-29 9:15 ` [HoTT] " Thorsten Altenkirch
2018-05-29 15:15 ` Michael Shulman
2018-05-30 9:33 ` Thomas Streicher
2018-05-30 9:37 ` Thorsten Altenkirch
2018-05-30 10:10 ` Thomas Streicher
2018-05-30 12:08 ` Thorsten Altenkirch
2018-05-30 13:40 ` Thomas Streicher
2018-05-30 14:38 ` Thorsten Altenkirch
2018-05-30 10:53 ` Alexander Kurz
2018-05-30 12:05 ` Thorsten Altenkirch
2018-05-30 19:07 ` Michael Shulman
2018-05-31 10:06 ` Thorsten Altenkirch
2018-05-31 11:05 ` Michael Shulman
2018-05-31 19:02 ` Alexander Kurz
2018-06-01 9:55 ` Martin Escardo
2018-06-01 17:07 ` Martín Hötzel Escardó
2018-06-01 17:43 ` Eric Finster
2018-06-01 19:55 ` Martín Hötzel Escardó
2018-06-01 20:59 ` András Kovács
2018-06-01 21:06 ` Martín Hötzel Escardó
2018-06-01 21:23 ` Michael Shulman
2018-06-01 21:53 ` Eric Finster [this message]
2018-06-01 22:09 ` Michael Shulman
2018-06-02 15:06 ` Eric Finster
2018-06-05 20:04 ` Michael Shulman
2018-06-02 5:13 ` Thomas Streicher
2018-06-01 21:52 ` Jasper Hugunin
2018-06-01 22:00 ` Eric Finster
2018-06-01 21:27 ` Matt Oliveri
2018-06-02 5:21 ` Ambrus Kaposi
2018-06-02 6:01 ` Thomas Streicher
2018-06-02 14:35 ` Thorsten Altenkirch
2018-05-30 13:30 ` Jon Sterling
2018-06-05 7:52 ` Andrej Bauer
2018-06-05 8:37 ` David Roberts
2018-06-05 9:46 ` Gabriel Scherer
2018-06-05 22:19 ` Martín Hötzel Escardó
2018-06-05 22:54 ` Martín Hötzel Escardó
2018-06-05 22:12 ` Richard Williamson
2018-06-06 15:05 ` Thorsten Altenkirch
2018-06-06 19:25 ` Richard Williamson
2018-05-29 14:00 ` Jon Sterling
2018-05-30 22:35 ` Michael Shulman
2018-05-31 10:48 ` Martín Hötzel Escardó
2018-05-31 11:09 ` Michael Shulman
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