From: "Dr. P.T. Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
To: categories@mta.ca
Subject: Re: Pro C
Date: Thu, 31 May 2001 13:57:45 +0100 (BST) [thread overview]
Message-ID: <Pine.SUN.3.92.1010531135334.11481B-100000@emu.dpmms.cam.ac.uk> (raw)
In-Reply-To: <200105300438.f4U4chS51110@transbay.net>
On Tue, 29 May 2001, Bill Rowan wrote:
>
> I have read that if C is a category, and the axiom of choice is assumed, then
> Pro C is equivalent to its full subcategory of diagrams where the diagram
> category is an inversely-directed set. Does anyone know where this is proved
> in the literature?
>
> Thanks,
>
> Bill Rowan
>
Choice isn't needed: all you need is the result that, for any filtered
category C, there is a directed poset P and a final functor P --> C.
There is a proof of this somewhere in SGA4 (I don't have the reference
to hand), where it is attributed to Pierre Deligne; but I suspect it
may be older than this.
Peter Johnstone
next prev parent reply other threads:[~2001-05-31 12:57 UTC|newest]
Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top
2001-05-30 4:38 Bill Rowan
2001-05-31 11:42 ` William Boshuck
2001-06-01 8:48 ` Prof. T.Porter
2001-05-31 12:57 ` Dr. P.T. Johnstone [this message]
2001-06-01 13:23 Dan Isaksen
2001-06-08 12:37 Jiri Rosicky
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