From: "Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>
To: Andrej Bauer <andrej.bauer@andrej.com>
Cc: Steve Vickers <s.j.vickers@cs.bham.ac.uk>,
zoran skoda <zskoda@gmail.com>,
categories list <categories@mta.ca>
Subject: Re: A conditon on maps between sheaves
Date: Mon, 28 Mar 2011 10:40:20 +0100 (BST) [thread overview]
Message-ID: <E1Q4YYJ-0001S8-UC@mlist.mta.ca> (raw)
In-Reply-To: <E1Q3wqF-000057-Gr@mlist.mta.ca>
On Sun, 27 Mar 2011, Andrej Bauer wrote:
> Steve Vickers wrote:
>> For example: take B to be the circle and E' its Moebius double cover,
>> which has no global sections. Then for every x in B you can take U = B
>> and your condition holds vacuously for any f whatsoever.
>>
>> If E = E'+E' then the codiagonal f has your property but is not mono.
>
> I apologize for the noise, I got my conditions all wrong when I tried
> to "optimize" them for the categories list. As it turns out my
> condition means that I have a map of etale spaces which is bijective
> on fibers (and the spaces in question are Hausdorff locally compact).
> So is there a name for that other than "bijective on fibers"?
Yes -- it's called an isomorphism. The fibre functors are jointly
conservative.
Peter Johnstone
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
prev parent reply other threads:[~2011-03-28 9:40 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2011-03-12 1:33 Andrej Bauer
2011-03-13 16:25 ` zoran skoda
2011-03-14 14:27 ` Steve Vickers
2011-03-27 18:27 ` Andrej Bauer
2011-03-28 9:40 ` Prof. Peter Johnstone [this message]
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