From: Richard Garner <rhgg2@hermes.cam.ac.uk>
To: Michael Shulman <shulman@uchicago.edu>
Cc: Toby Bartels <toby+categories@ugcs.caltech.edu>,
categories@mta.ca, David Leduc <david.leduc6@googlemail.com>
Subject: Re: equality is beautiful
Date: Tue, 16 Mar 2010 08:03:19 +0000 (GMT) [thread overview]
Message-ID: <E1NrWKw-0005Zw-Oy@mailserv.mta.ca> (raw)
In-Reply-To: <4B9EE601.5070801@uchicago.edu>
> To rephrase what Toby said: the construction of limits via products and
> equalizers only works for limits over a domain category which has a
> set(oid) of objects (what Toby calls a "strict category"), whether that
> set is large or small.
Is this really the case? Given any type (=preset) A and any
term A --> ob C (for C a non-strict category), one can define
what it means to be a product of this family of objects in C.
Now given a non-strict category J and a functor F:J->C, one
may construct the limit of F as an equaliser of two morphisms
between products in the usual way. I don't see where equality
on objects is necessary, or even useful.
Richard
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2010-03-16 8:03 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 [this message]
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
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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