From: Gaucher Philippe <gaucher@pps.jussieu.fr>
To: Eduardo Dubuc <edubuc@dm.uba.ar>
Cc: Categories <categories@mta.ca>
Subject: Re: size_question
Date: Wed, 29 Jun 2011 09:01:15 +0200 [thread overview]
Message-ID: <E1Qbuja-0002e4-Lv@mlist.mta.ca> (raw)
In-Reply-To: <E1Qbemr-0007r1-Up@mlist.mta.ca>
Le mardi 28 juin 2011 19:39:10, vous avez écrit :
> This is a naive question on non naive foundations.
>
> Consider the inclusion S_f C S of finite sets in sets.
>
> Is the category S_f closed under finite limits and at the same time small ?
>
> For example, there are a proper class of singletons, all finite. Thus a
> proper class of empty limits.
This is the definition of quasi-small, not small: a set of isomorphism classes
? The category of finite sets is quasi-small, not small. And we need the axiom
of choice for that, as for many things in category theory.
pg.
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prev parent reply other threads:[~2011-06-29 7:01 UTC|newest]
Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top
2011-06-28 17:39 size_question Eduardo Dubuc
2011-06-29 2:43 ` size_question James Lipton
2011-07-02 12:24 ` size_question Andrej Bauer
2011-07-02 20:05 ` size_question Thomas Streicher
2011-07-03 15:01 ` size_question F. William Lawvere
2011-06-29 7:01 ` Gaucher Philippe [this message]
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