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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,...

4 votes

Why is the concept of topos a "metamorphosis" of the concept of space?

In sense, a sheaf over a space is 'representation' of the space. Somewhat akin to a module being a representation of a ring. So, a the catergory (topos) of sheaves over a space plays the same role the …
Mukul Patel's user avatar