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I have splitt off open geometric morphism from open map and expanded slightly.
But this is not satisfactory yet…
Is open immersion of schemes, or more generally, open immersion of ringed spaces open in a similar sense within the category of ringed spaces ?
I changed one of the characterizations of open geometric morphisms. Originally it said: $f$ is open if and only if its localic reflection is an open map of locales. With this formulation, it is not clear that “localic reflection” is taken relative over the codomain topos (rather than over the base topos).
Jens Hemelaer
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