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A topos is a category that behaves very much like the category of sets and possesses a good notion of localization. Related to topos are: sheaves, presheaves, descent, stacks, localization,...

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Is there a notion of a complex/analytic diffeological space?

Perhaps the general solution to your question can be found in "A theory of plots" by Atsushi Yamaguchi here? Slides from his talk at the last conference on diffeology and differential homotopy are her …
Patrick I-Z's user avatar
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5 votes

Advantages of diffeological spaces over general sheaves

If you are an algebraist: general sheaves. If you are a geometer: diffeology. I will try to explain what I mean. I may however still modify the following. The philosophy of the theory of sheaves is s …
Patrick I-Z's user avatar
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