From: Matt Oliveri <atm...@gmail.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Re: cubical type theory with UIP
Date: Sat, 29 Jul 2017 00:29:37 -0700 (PDT) [thread overview]
Message-ID: <c439b17a-edb4-4359-8e02-ad34fe24ee72@googlegroups.com> (raw)
In-Reply-To: <1501295143.1889059.1056222744.2C07029A@webmail.messagingengine.com>
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On Friday, July 28, 2017 at 10:25:44 PM UTC-4, Jonathan Sterling wrote:
>
> On Fri, Jul 28, 2017, at 06:47 PM, Matt Oliveri wrote:
> > I'm confused. So you want a cubical type theory with only hsets? In what
> > sense would there be cubes, other than just points? I thoght OTT had
> > propositional extensionality. Though maybe that's only for strict props.
>
> I think 'propositional extensionality' in OTT was for objects which were
> propositions *by definition*, as opposed to h-props in HoTT (which is
> something that you prove about a type, and doesn't merely follow from
> the intension of the type).
>
Right, that's what I meant by strict props. If so, it still seems like it
should work to redefine equality for types such that hprops are quotiented
based on logical equivalence, and equality of other types is left alone.
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next prev parent reply other threads:[~2017-07-29 7:29 UTC|newest]
Thread overview: 20+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-07-23 22:54 Michael Shulman
2017-07-29 1:47 ` Matt Oliveri
2017-07-29 2:25 ` [HoTT] " Jon Sterling
2017-07-29 7:29 ` Matt Oliveri [this message]
2017-07-29 6:19 ` Michael Shulman
2017-07-29 7:23 ` Matt Oliveri
2017-07-29 8:07 ` Michael Shulman
2017-07-29 10:19 ` Matt Oliveri
2017-07-29 11:08 ` Matt Oliveri
2017-07-29 21:19 ` Michael Shulman
[not found] ` <8f052071-09e0-74db-13dc-7f76bc71e374@cs.bham.ac.uk>
2017-07-31 3:49 ` Matt Oliveri
2017-07-31 15:50 ` Michael Shulman
2017-07-31 17:36 ` Matt Oliveri
2017-08-01 9:14 ` Neelakantan Krishnaswami
2017-08-01 9:20 ` Michael Shulman
2017-08-01 9:34 ` James Cheney
2017-08-01 16:26 ` Michael Shulman
2017-08-01 21:27 ` Matt Oliveri
2017-07-31 4:19 ` Matt Oliveri
2017-08-02 9:40 ` [HoTT] " Andrea Vezzosi
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