* A representation theorem for Geometric Morphism
@ 2005-08-09 13:29 Townsend, Christopher
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From: Townsend, Christopher @ 2005-08-09 13:29 UTC (permalink / raw)
To: categories
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)
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