From: Andrej Bauer <andrej.bauer@andrej.com>
To: George Janelidze <George.Janelidze@uct.ac.za>
Cc: categories list <categories@mta.ca>
Subject: Re: Reflection to 0-dimensional locales
Date: Thu, 8 Feb 2018 23:29:39 +0100 [thread overview]
Message-ID: <E1ek9by-0003qg-4N@mlist.mta.ca> (raw)
In-Reply-To: <E1ej35U-00050M-Iw@mlist.mta.ca>
On Tue, Feb 6, 2018 at 12:01 PM, George Janelidze
<George.Janelidze@uct.ac.za> wrote:
> Dear Colleagues,
>
> Let me repeat from my exchange of massages with Steve Vickers:
>
>> As you know, a locale is called 0-dimensional if all its elements are
>> joins
>> of complemented ones. By a morphism L--->L' of locales I shall mean a map
>> L'--->L that preserves all joins and finite meets (as usually). The
>> inclusion functor
>>
>> 0-Dimensional locales--->Locales
>>
>> has a left adjoint F, for which
>>
>> F(L)={x in L | x is a join of complementary elements}.
>>
>> Question: Is F semi-left-exact?
Can Example 1 in
https://dml.cz/bitstream/handle/10338.dmlcz/119250/CommentatMathUnivCarolRetro_42-2001-2_13.pdf
be put to some use to answer the question negatively? It shows that
the zero-dimensional reflection in topological spaces does not
preserve finite products. The example uses fairly nice subspaces of R
and R^2.
With kind regards,
Andrej
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2018-02-08 22:29 UTC|newest]
Thread overview: 12+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-02-04 10:52 Topos theory for spaces of connected components Steve Vickers
2018-02-04 16:48 ` Marta Bunge
2018-02-04 19:11 ` George Janelidze
2018-02-04 20:57 ` John Baez
2018-02-05 16:12 ` Steve Vickers
[not found] ` <CY4PR22MB010230974FC6F0E254C1272FDFFF0@CY4PR22MB0102.namprd22.prod.outlook.com>
2018-02-05 14:03 ` Steve Vickers
2018-02-05 20:46 ` Eduardo J. Dubuc
2018-02-09 1:04 ` Marta Bunge
[not found] ` <5D815D7C26A24888833B8478A002DE64@ACERi3>
[not found] ` <26035BC6-EB7E-4622-A376-DB737CCEF2BB@cs.bham.ac.uk>
[not found] ` <E1eisBq-00027k-Tn@mlist.mta.ca>
2018-02-06 11:01 ` Reflection to 0-dimensional locales George Janelidze
2018-02-08 22:29 ` Andrej Bauer [this message]
2018-02-11 21:38 ` George Janelidze
[not found] ` <51180F2A7C24424DAB19B751068688C5@ACERi3>
2018-02-14 19:06 ` Matias M
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