From: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
To: David Leduc <david.leduc6@googlemail.com>
Cc: Richard Garner <rhgg2@hermes.cam.ac.uk>, categories@mta.ca
Subject: Re: equality is beautiful
Date: Mon, 22 Mar 2010 10:17:36 +0100 [thread overview]
Message-ID: <E1NtiqK-0006T4-Jf@mailserv.mta.ca> (raw)
In-Reply-To: <E1Nr7TS-00057n-2e@mailserv.mta.ca>
> What about the characterization of limits in terms of products and
> equalizers? It states that the limit of a functor F:J->C is
> constructed by products indexed by the set(oid) of objects and the
> set(oid) of arrows of J. But if you don't allow equality on objects in
> J, you only have a preset of object, not a set(oid).
I don't see a problem here. Usually one speaks about small limits, i.e. limits
of diagrams whose shape is a small category. But small categories are categories
internal to the base. Now under the quite common assumption that this base has
finite limits one can speak about equality of objects in the shape of the diagram.
Thomas
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2010-03-22 9:17 UTC|newest]
Thread overview: 17+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-03-14 8:51 David Leduc
2010-03-15 11:25 ` Toby Bartels
2010-03-16 1:59 ` Michael Shulman
[not found] ` <4B9EE601.5070801@uchicago.edu>
2010-03-16 8:03 ` Richard Garner
2010-03-20 7:18 ` David Leduc
2010-03-21 2:17 ` Michael Shulman
[not found] ` <c3f821001003201917w4476a777i53fda02cb9bece66@mail.gmail.com>
2010-03-21 17:54 ` Richard Garner
2010-03-21 19:36 ` Toby Bartels
2010-03-22 9:17 ` Thomas Streicher [this message]
2010-03-22 16:15 ` Michael Shulman
-- strict thread matches above, loose matches on Subject: below --
2010-03-21 21:32 Bas Spitters
2010-01-03 7:23 the definition of "evil" Peter Selinger
2010-01-05 20:04 ` dagger not evil Joyal, André
[not found] ` <B3C24EA955FF0C4EA14658997CD3E25E370F5672@CAHIER.gst.uqam.ca>
[not found] ` <B3C24EA955FF0C4EA14658997CD3E25E370F5673@CAHIER.gst.uqam.ca>
2010-01-09 3:29 ` equality is beautiful Joyal, André
2010-01-10 17:17 ` Steve Vickers
2010-01-10 19:54 ` Vaughan Pratt
2010-01-11 2:26 ` Richard Garner
2010-01-13 11:53 ` lamarche
2010-01-13 21:29 ` Michael Shulman
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