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1. • CommentRowNumber1.
   • CommentAuthorStephan A Spahn
   • CommentTimeFeb 1st 2012
   • (edited Feb 1st 2012)
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   Author: Stephan A Spahn
   Format: MarkdownItexI 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?

   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?

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeFeb 1st 2012
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   Author: Mike Shulman
   Format: MarkdownItexIf 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.

   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.

3. • CommentRowNumber3.
   • CommentAuthorStephan A Spahn
   • CommentTimeFeb 2nd 2012
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   Author: Stephan A Spahn
   Format: MarkdownItexThanks! I will see if it is what I am looking for.

   Thanks! I will see if it is what I am looking for.