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From: "Townsend, Christopher" <Christopher.Townsend@rbccm.com>
To: <categories@mta.ca>
Subject: A representation theorem for Geometric Morphism
Date: Tue, 9 Aug 2005 14:29:47 +0100	[thread overview]
Message-ID: <EE7D40281B517A41AF5A90847A61F2790DDC90C0@SEW39051.oak.fg.rbc.com> (raw)

If f:F->E is a geometric morphism between elementary toposes then there
is a, well known, adjunction Sigma_f -! f* between the category of
locales internal to E and the category of locales internal to F. A
property of this adjunction is that f* commutes with the upper (and
lower) power locale functors. I think that this actually characterizes
geometric morphisms: given an adjunction L-!R between locales internal
in E and locales internal in F such that the right adjoint (R) commutes
with the upper and lower power locales then there exists a geometric
morphism, f:F->E such that L=Sigma_f and R=f*. Has anyone looked at this
type of result before? 

 

Thanks, Christopher (Townsend)

 

 



                 reply	other threads:[~2005-08-09 13:29 UTC|newest]

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