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I looked at open map. Does the reference given there cover all cases discussed in the article? Or is there some other reference in which the axiomatization of open and étale maps in toposes is described?
If I understand you correctly, then since the categories of topological spaces, locales, and toposes are not themselves toposes, I think the answer is trivially “no”. One could try to adapt the axioms to more general categories, of course.
Thanks! I will see if it is what I am looking for.
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