From: Edmund Robinson <edmund.robinson@eecs.qmul.ac.uk>
To: Andrej Bauer <andrej.bauer@andrej.com>
Cc: categories list <categories@mta.ca>
Subject: Re: A category internal to itself
Date: Thu, 5 Sep 2013 09:27:13 +0100 [thread overview]
Message-ID: <E1VHZ6w-0003XT-Sx@mlist.mta.ca> (raw)
In-Reply-To: <E1VHI4M-0006nv-1u@mlist.mta.ca>
There are some forms of set theory in which there are restrictions on the forms of comprehension allowed, and as a result there is a set of all sets. Quine's New Foundations is one of these. It has a simple restriction on the forms of predicates allowed in comprehensions. Put simply this is that you can assign (integer) levels to the variables in the formula so that x e y only occurs when y is at the level immediately above x. This means that in models of this set theory there is also an internal category of all sets.
best
Edmund
On 4 Sep 2013, at 10:23, Andrej Bauer wrote:
> Chatting at a conference, the question came up why there is no
> (non-trivial) category which is "internal to itself" (interpret this
> in some sensible sense). And over coffee we thought this must be well
> known, but not to us. Can somene shed some light on the matter?
>
> With kind regards,
>
> Andrej
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2013-09-05 8:27 UTC|newest]
Thread overview: 10+ messages / expand[flat|nested] mbox.gz Atom feed top
2013-09-04 9:23 Andrej Bauer
2013-09-04 20:04 ` Eduardo J. Dubuc
2013-09-04 22:11 ` Colin McLarty
2013-09-05 8:27 ` Edmund Robinson [this message]
2013-09-05 11:30 ` Zhen Lin Low
2013-09-05 13:44 ` Alex Simpson
[not found] ` <20130906080410.GA19753@mathematik.tu-darmstadt.de>
2013-09-06 8:20 ` Zhen Lin Low
[not found] ` <CAB0nkh3zxgAV4tU1jr5ZTWw0exgQEcjGVSyRDqy=T0XE6DaG6Q@mail.gmail.com>
2013-09-06 12:33 ` Thomas Streicher
[not found] ` <CAOzx82rUa8KRkngePON8Gh1KttzZ1-3AKNpP5DQNY7RfEj1VTQ@mail.gmail.com>
2013-09-05 11:46 ` Colin McLarty
[not found] ` <CAOOzEh-04Cq7L_k7v6qxWTYRhkWZw862kmPzLaSNZUgr8Zvzdw@mail.gmail.com>
2013-09-06 9:48 ` Andrej Bauer
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