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From: "Prof. Peter Johnstone"
Newsgroups: gmane.science.mathematics.categories
Subject: Re: A conditon on maps between sheaves
Date: Mon, 28 Mar 2011 10:40:20 +0100 (BST)
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Cc: Steve Vickers , zoran skoda , categories list
To: Andrej Bauer
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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
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